Jussi Tiitola  

Market Efficiency and Market Timing: Evidence 

from US listed CEFs 

 

 

 

 

 

 

 

 

 

 

Vaasa 2025 

School of finance  

Master9s thesis in Finance 



UNIVERSITY OF VAASA 

School of finance 

Author:    Jussi Tiitola 

Title of the Thesis:  Market Efficiency and Market Timing: Evidence from US listed CEFs 

Degree:    Master of Finance 

Programme:   Finance Master program 

Supervisor:   John Kihn 

Year:    2025 PAGES: 79 

ABSTRACT: 

This study investigates the phenomenon of CEFs mispricing and the objective is to show that the 

CEFs mispricing is continuous and can be exploited. The foundational theory of finance implies 

mispricing within the CEFs is impossible, and any deviation from the CEF NAV is unambiguous 

proof of inefficiency. Furthermore, academic papers researching the topic of CEFs mispricing 

often argue that the mispricing of CEFs is mostly due to overall (economic) factors instead of 

fund specific factors. In short, neither foundational theory or more mainstream empirical work 

allows for the possibility of mispricing with respect to CEFs. 

 

Yet evidence shows that CEFs relative mispricing is a rule rather than an exception. Moreover, 

CEF-specific factors do not seem to have a significant impact on mispricing, and the effect of 

macroeconomic factors seems limited, as well as a large amount of mispricing remains unex-

plained. In fact, the mispricing of a CEF does not seem to depend on the mispricing of other 

funds, and that mispricing tends to be mean reverting. At stark odds to normative theory, the 

results from the trading analysis detailed in this study show that simplified mean reversion-

based trading strategies are able to <beat the market= systematically. 

 

All the findings are against the basics concepts of normative finance. Practically all the findings 

indicate evidence against efficiency and suggest that textbook efficiency is the anomaly, not the 

other way around. Therefore, it seems that there is a huge gap between the descriptive reality 

of the markets and normative finance textbook statements to the contrary.  

 

KEYWORDS: Efficient Market Hypothesis, Arbitrage Theory, Normative Finance, Market Tim-

ing, Closed-End Funds, Mispricing 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 



Contents 

1 Introduction 1 

1.1 Purpose of the study 2 

1.2 Structure of the study 4 

2 Efficient market hypothesis 6 

2.1 Degrees of efficient market hypothesis 6 

2.1.1 Weak form market efficiency, random walk, and noise 7 

2.1.2 Semi-strong form market efficiency 7 

2.1.3 Strong form market efficiency 8 

2.2 Concept of arbitrage 9 

2.3 Joint hypothesis issue 11 

2.4 Critic of normative finance 12 

2.4.1 Evidence against weak form market efficiency 13 

2.4.2 Evidence against semi-strong form market efficiency 14 

2.4.3 Evidence against strong form market efficiency 15 

3 CEFs´ an unambiguous violation of EMH 16 

3.1 Overview of CEFs 16 

3.2 CEFs mispricing 17 

3.3 CEFs mispricing and EMH 19 

4 Market timing 22 

4.1 Overview of market timing 22 

4.2 Market timing and EMH 23 

4.3 Market timing and mean reversion 24 

4.4 Market timing and joint hypothesis 25 

5 Data 26 

5.1 Selected CEFs 26 

5.2 Variables 26 

5.3 Data validation and outliers 27 

6 Methodology 30 



6.1 Mispricing analysis and formulas 30 

6.2 Mispricing regression model and variables 32 

6.3 Trading analysis and trading rules 36 

6.4 Trading analysis formulas and variables 39 

6.5 Trading analysis financial indicators and regression model 41 

6.6 Robustness checks 41 

7 Mispricing analysis results 44 

7.1 Descriptive statistics 44 

7.2 Time analysis of mispricing 48 

7.3 CEFs correlation distribution and correlation matrix 50 

7.4 Mispricing regression results 53 

7.5 Robustness checks results for mispricing analysis 60 

8 Trading analysis results 64 

8.1 Long and short positions results 64 

8.2 Results for market tactic strategies and market strategies 67 

8.3 Robustness checks results for trading analysis 72 

8.4 Additional consideration about trading analysis 76 

9 Conclusions 78 

Appendix 80 

References 87 

 

 

 

 

 

 

 

 

 

 

 

 

 



Figures 

 

Figure 1 Individual CEFs mispricing correlation distribution 80 

 

Tables 

 

Table 1 Development of CEFs´ (Statista, 2023) 17 

Table 2 Trading rules 37 

Table 3 Overview of the 3 market tactic strategies and 3 market strategies 38 

Table 4 Descriptive statistics for CEFs mispricing 44 

Table 5 CEFs mispricing time analysis 49 

Table 6 Correlation matrix with variables used in mispricing regression 51 

Table 7 OLS regression of CEFs mispricing (2002-2019) 54 

Table 8 Long positions returns 65 

Table 9 Short positions returns 66 

Table 10 Returns of the market tactic strategies and market strategies 67 

Table 11 Summary of market tactic strategies statistical significance 70 

Table 12 Trading analysis robustness indicators summary 73 

Table 13 Weekly data robustness test 74 

Table 14 EMH based trading strategy 75 

Table 15 Regression model with weekly data 81 

Table 16 Mispricing regression with a different time sample 81 

Table 17 Newey-West standard error correction 82 

Table 18 Autocorrelation corrected regression model 82 

Table 19 VIF tests 83 

Table 20 Tactics vs market (No TCs) 83 

Table 21 Trading analysis OLS regression (Tactic 1) 84 

Table 22 Trading analysis OLS regression (Tactic 2) 84 

Table 23 Trading analysis OLS regression (Tactic 3) 85 

Table 24 Returns with different trading rules 85 

Table 25 List of selected CEFs 86 

 



 

Abbreviations 

 

Closed-end funds (CEFs) 

Efficient market hypothesis (EMH) 

Law of one price (LOOP) 

Purchasing power parity (PPP) 

Net asset value (NAV) 

Mispricing (Relative mispricing) 

Initial public offering (IPO) 

Arbitrage pricing theory (ATP) 

Seasonal affective disorder (SAD) 

Market value (MV) 

Portfolio manager (PM) 

Holding period return (HPR) 

Small minus Big (SMB) 

Value-weighted index (VWD) 

Durbin-Watson-test (DWT) 

Variance inflation factor (VFI) 

Breusch-Pagan (BP) 

Newey-West (NW) 



1 

1 Introduction 

The relative mispricing of Closed-End Funds (<CEFs=) is closely related to the Efficient 

Market Hypothesis (<EMH=) (i.e., market-based pricing relative to model-based pricing). 

The current textbook version of the EMH was invented by Samuelsson and Fama in the 

1970s and is still considered to be one of the cornerstones of finance, if not its primary 

cornerstone. According to the EMH active competition should lead to 8efficient9 and right 

prices, and arbitrage should remove the possibility of excess returns. Nevertheless, the 

evidence from the financial markets speaks directly against this key concept of academic 

finance. 

 

Furthermore, it should be noted that in reality no one actually knows what the <right= 

price should be and therefore at least the possibility of <free meals= is then logically 

available in the financial markets. That is, for example, if nobody knows exactly what the 

common share price of IBM should be at all times and in all markets that trade common 

shares of IBM, then how is it possible to achieve no arbitrage conditions for shares of 

IBM? In other words, how can you eliminate pricing arbitrage for something you are not 

even confident of its price? 

 

Critics have questioned the unrealistic assumptions of the EMH, such as no taxes or 

transaction costs. However, a more recent subfield of study within finance has made 

some effort in explaining away the deviations from efficiency with more behavioral ex-

planations of why prices deviate, namely what is often referred to more recently as <be-

havioral finance=. For example, Kahneman and Tversky (1979, pp. 2633265) presented 

Prospect Theory (<PT=) as an alternative to standard Expected Utility Theory (<EUT=) for 

decision making under uncertainty. For example, when comparing things like PT vs. EUT, 

as time has passed it would seem that more and more agents in the field of finance are 

aware of the contradictions between normative and descriptive finance. Given that nor-

mative finance explains how agents should behave while descriptive finance explains 

how agents actually behave (Kahneman & Tversky, 1979, p. 265, 277; Allais 1997, p. 4), 

we should at least now be more careful before exclaiming that <prices are right=.  



2 

Furthermore, and given the divide between normative finance theory and the descrip-

tive reality of the financial markets, it is my conclusion that agents should focus more on 

the practical part of finance as there are numerous ways to demonstrate that markets 

are inefficient and excess returns are possible. For example, the concept of the Law Of 

One Price (<LOOP=) is claimed to be true, but empirical evidence shows that in practice 

the LOOP does not hold for anything (see, e.g., Ardeni, 1989, p. 661, 662). For example, 

the <Big Mac index= shows unambiguous evidence against the concept of the LOOP as 

Bic Macs have different prices in different countries (i.e., after adjusting for currency dif-

ferences). Differences in taxes, goods, transaction costs and time make the LOOP practi-

cally impossible to realize in practice. The same applies to Purchasing Power Parity 

(<PPP=), which is essentially the LOOP applied to whole economies. Overall, the magni-

tude of contradictions and issues linked to the basic concepts of finance is alarming. If 

we cannot rely on whether prices or interest rates are <right=, what then can we rely on 

to be empirically verifiable? Furthermore, normative finance has even made testing the 

EMH virtually impossible due to the joint hypothesis issue (Fama, 1970, p. 414). 

 

1.1 Purpose of the study 

The primary purpose of this study is to research whether the chosen 108 CEFs listed in 

US exchanges were efficiently priced relative to their Net Asset Value (<NAV=) during the 

studied period of 200232019. The value of a CEF NAV should be equal to the price of a 

CEF at any given time, and therefore any deviation between them is a clear sign of rela-

tive inefficiency (relative mispricing is referred as <mispricing= from this onwards). The 

CEF NAV is the only indicator we know for certain and on the contrary, no one knows 

what the <right= price of a CEF should be. Therefore, the research of the CEFs mispricing 

is based on relative values and the results are only relative indicators of efficiency. The 

results from the analyses are suggestions based on the relative values and their assump-

tions, instead of absolute values. Overall, the NAV, price and mispricing are the 3 most 

important indicators of this study. The NAV per share of a CEF is calculated by dividing 

the difference between assets and liabilities with the number of shares outstanding. The 

mispricing describes the difference between the CEF price and NAV.   



3 

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CEFs are funds initially issued at a fixed amount of shares through an Initial Public Offer-

ing (<IPO=) to finance their operations (Brealey, et al., 2020, p. 80, 380). CEFs are almost 

a perfect subject to research relative pricing efficiency since even a single deviation from 

market efficiency is unambiguous evidence against the EMH and the joint hypothesis 

issue does not apply to CEFs (Pontiff, 1996, pp. 113531136). In reality CEFs commonly 

trade at a <discount= (i.e., market price is less than NAV) or <premium= (i.e., market price 

is greater than NAV) for long periods of time in relation to their NAV. In addition, and in 

fact, CEF IPO underwriters would not even have an incentive to launch CEF IPOs if there 

would not be any mispricing. 

 

The second purpose of this study is to research whether it is possible to systematically 

<beat the market= using simple, or not so simple, market timing strategies based on the 

simple observation that CEFs9 mispricing mean reverts. The market timing analysis is a 

test of whether money is made or loss with the used assumptions of CEFs mispricing 

mean reversion. Market timing refers to beating the market by predicting its movements 

(see, e.g., Merton 1981, p. 363; and Baker & Wurgler, 2002, p. 1). The EMH states that 

market timing is not possible; therefore, the results from a trading analysis can be used 

as evidence of inefficiency. Although, it should be noted that this type of evidence, and 

as opposed to the primary relative pricing analysis of market prices vs. NAV, does have 

the joint hypothesis issue (e.g., we must accept the model of mean reversion is correct).  

 

In the mispricing analysis, the objective is to show that CEFs are systematically mispriced, 

which, again, if true, directly contradicts the EMH. Furthermore, to research whether 

there are any specific factors affecting CEFs mispricing would also contradict related the-

ory. In fact, it would seem that actual fundamental factors include CEF specific and 



4 

macroeconomic factors (i.e., not just macroeconomic). Furthermore, if the null hypoth-

esis (i.e., essentially there is no mispricing) of this study can be rejected without a joint 

hypothesis issue and if the evidence confirms that timing strategies result in statistically 

significant mispricing, then this study will strongly confirm that market inefficiency exists. 

 

Furthermore, and again, in a larger context the purpose of this study is to update and 

revise the current perception of normative finance and the EMH. Possibly the results of 

this study would enable financial markets agents to understand the differences between 

reality in the financial markets vs. what is in modern finance textbooks and taught in 

classrooms. Potentially, agents should realize the importance of considering descriptive 

financial market reality rather than believing blindly in the pronouncements of norma-

tive finance that lack scientific merit. By exploiting the actual facts of the markets, agents 

could avoid making common mistakes. Hopefully, this would also assist finance to trans-

form more towards teaching descriptive reality, and away from purely normative theory. 

 

The hypotheses of this study are the following: 

H0 : There is no statistically significant mispricing within the CEF market. 

H1 : There are no CEF market timing strategies that are able to beat the market. 

 

As already stated, the hypotheses are intended to clarify firstly whether the CEF markets 

are efficient and secondly if there any possibilities to take advantage of relative ineffi-

ciency with market timing strategies based on mean reversion. All the researched mate-

rial and data analysis indicates that the null hypothesis does not hold, and that there are 

possibilities to take advantage of these inefficiencies. Essentially, the remainder of this 

thesis after this section is intended to support the rejection of the null hypothesis. 

 

1.2 Structure of the study 

The thesis is divided into nine main sections. The first section is the Introduction, and it 

presents the topic, some background and the hypotheses. Section two presents the core 

theory section of the study, concentrating on the EMH. Section three introduces CEFs to 



5 

the reader. In section four the concept of market timing is presented to the reader. Data 

and the variables used in the study are presented in section five. Section six introduces 

the methodology used and related formulas. Section seven and eight present the results 

for the mispricing and trading strategy analyses. Conclusion are covered in the last sec-

tion. 

 



6 

2 Efficient market hypothesis 

The relative mispricing of Closed-End Funds (<CEFs=) is closely related to the Efficient 

Market Hypothesis (<EMH=) (i.e., market-based pricing relative to model-based pricing). 

The current textbook version of the EMH was invented by Samuelsson (1965, p. 41) and 

Fama (1970, pp.383-384) in the 1970s and is still considered to be one of the corner-

stones of finance, if not its primary cornerstone. According to the EMH active competi-

tion should lead to 8efficient9 and right prices, and arbitrage should remove the possibil-

ity of excess returns (Brealey et al., 2020, pp. 3403342; Bodie et al, 2021, pp.3323333). 

In the EMH prices are assumed to reflect all the available fundamental information about 

the financial markets and agents are assumed to be price takers who have no effect to 

market price. Other assumptions of the EMH are perfect competition, no transaction 

costs, and rational behavior of agents. Despite the EMH includes many unrealistic as-

sumptions it is still widely taught in textbooks and believed to hold true in practice.  

 

2.1 Degrees of efficient market hypothesis 

The degrees of the EMH are weak, semi-strong, and strong. The 3 different degrees of 

the EMH are classified according to the market efficiency (i.e., how well prices reflect 

fundamental information. The degrees of the EMH are based on a study published by 

Fama (1970) in the 1970s,but also many other academics have researched the topic e.g., 

Malkiel (2014) has presented his owns visions about the degrees in his book called <A 

random walk down the street=. The EMH assumes that only fundamental information 

has an effect to prices but in reality, also non-fundamental information has an effect to 

prices. Fundamental information refers to a situation where e.g., a positive change in 

company earnings increases the stock price of a company. Non-fundamental information 

refers to a situation where e.g., the company changes its name, and it has a positive 

effect to the stock price of a company. In reality usually the non-fundamental infor-

mation has a more significant effect to price than the fundamental information.  



7 

2.1.1 Weak form market efficiency, random walk, and noise 

In the weak form of market efficiency information is based on historical asset prices 

(Fama, 1970, pp. 383-384; Malkiel, 2014, p. 26, 140, 183; Brealey et al, 2020, p. 340). 

The weak form does not believe in the use of technical or fundamental analyses and 

beating the market is considered impossible. Since there should not be any significant 

differences in returns random portfolio is preferred over active trading. The weak form 

is based on the idea that prices seem to follow a random walk (Kendall, 1953). Kendall 

found out that overall, the prices tend to be independent and uncorrelated from each 

other (i.e., the price today does not indicate any information about the price in future) 

instead of certain price patterns. The view of the weak form aligns with the EMH since 

agents are not allowed to have <free lunches= and arbitrage should balance the price.  

 

The concept of random walk has been actively researched after the Kendall´s study and 

the academics have concluded that it mostly works, but there are some detectable price 

patterns (Malkiel, 2014, pp. 1413142; Brealey et al, 2020, pp. 3423343; Bodie et al, 2021, 

pp. 3473348). Academics have detected these price patterns e.g., in stocks having high 

momentum and volatility. The findings suggest that momentum seems to effect future 

prices in both positive and negative ways. Also, stocks including high volatility include 

clearly detectable price cycles. Furthermore, also noise is often considered to have an 

effect on price changes. Usually, the random walk is seen as a process, and noise as a 

describing factor behind the changes. Noise is always included in the agents expectations, 

and it can be positive or negative depending on the return expectations (Brealey et al, 

2020, p. 210). Noise is tricky since it is important, but no one knows what it really is.  

 

2.1.2 Semi-strong form market efficiency 

In the semi-strong form of market efficiency, the prices reflect all public and past infor-

mation available (Fama, 1970, pp. 383-384; Malkiel, 2014, pp. 1823184; Brealey et al, 

2020, p. 340, 343; Bodie et al, 2021, p. 336). Usually, the semi-strong form is considered 

to be the most practical degree of the EMH. The public information refers to sources 



8 

such as, news, social media, and financial report and past information to the historical 

asset prices. In the semi-strong form prices should reflect the public information in-

stantly and as there is no inside information available there should be no use for funda-

mental or technical analyses. Recently the amount of information and the amount of 

information sources has substantially increased compared to the time of publishing the 

theory. Overall, the importance of finding the relevant information has increased. Usu-

ally, the semi-strong form is considered to be the most practical form of EMH. 

 

To test whether the semi-strong form holds in practice academics have used fundamen-

tal analyses to research stock price reactions to information (Brealey et al, 2020, pp. 

3433344; Bodie et al, 2021, p. 3493350). Evaluating whether the reaction is <right= and 

considering all information is a more challenging analysis due to the joint hypothesis 

issue which practically removes the ability to test the EMH. In addition to stock price 

reactions academics have published studies focusing on abnormal returns (i.e., differ-

ence between actual and expected return). These studies have tested the reactions of 

specific stock groups facing the same news. The results from the abnormal tests argue 

that the price reactions to new information are immediate and in right amount, e.g., in 

the Enron scandal in 2001 as the fraud became public the stock price of Enron decreased 

shortly to zero and the company claimed bankruptcy.  

 

2.1.3 Strong form market efficiency 

In the strong form of market efficiency prices reflect all available information (i.e., all 

available past, public and private) on the market (Fama, 1970, pp. 383-384; Malkiel, 2014, 

pp. 1823184; Brealey et al, 2020, p. 340, 345; Bodie et al, p. 336). The strong form creates 

a situation where there can be winners and losers but due to fierce competition no one 

is able to achieve constant excess returns. Therefore, beating the market is possible but 

to constantly do it is hard or impossible, and even inside information does not inevitably 

lead to excess returns.  



9 

2.2 Concept of arbitrage 

The term of arbitrage refers to <riskless profit= (Malkiel, 2014, p. 231; Brealey et al, 2020 

p. 59; Bodie et al, p. 311). The concept of arbitrage is based on the Arbitrage Pricing 

Theory (ATP) which was introduced by Ross in 1976. The ATP shares mostly the same 

assumptions as the EMH but the ATP assumes that the returns are affected by macroe-

conomic factors and noise which lead to the right price (Ross, 1976, p. 355; Brealey et al, 

p. 213). The factors and their sensitivity cannot be predetermined since they vary be-

tween the used assets. The ATP assumes two kinds of risks, systematic risk, and unsys-

tematic risk. The textbook arbitrage assumes arbitrage to be only relative instead of ab-

solute, i.e., no one knows what the right price should be. Therefore, models such as 

Black-Scholes option pricing model are built on the relative arbitrage assumptions.  

 

The term riskless profit can be e.g., achieved by the following chain of events: Suppose 

in Helsinki you can trade Swedish crowns at ten cent exchange rates, while in Stockholm 

you can trade euros for Swedish crowns at a twelve-cent exchange rate. In order to make 

arbitrary riskless wins, one would buy Swedish crowns at Helsinki at ten cent rate and 

then immediately sell them at Stockholm with twelve cent rate resulting in two cent 

riskless profit per crown. The profit might seem low, but it might lead to significant 

amounts as the arbitrageurs are using significant amount of capital. Other well-known 

arbitrage strategies are e.g., covered interest arbitrage and triangular arbitrage, which 

are both based on the concept to exploit interest rate differences. 

 

The relationships between the EMH and the ATP can be confusing since the EMH high-

lights the role of fundamental information behind efficiency, while the ATP highlights the 

role of price deviation corrections behind efficiency (Brealey et al, 2020, pp. 213, 3403

342). Regardless the differences, the so-called textbook arbitrage is more complex than 

it may sound. In reality arbitrage is never risk-free since there are always limits to arbi-

trage (Brealey, 2020, pp. 3513353; Schleifer & Vishny, 1997, p.54). Arbitrage is always 

influenced by at least two types of costs: transaction and holding costs. (Pontiff, 1996, 

pp. 113831139). Transaction costs refer to the cost of opening or closing the trade and 



10 

holding costs refer to costs occurring during the investment period. Both of these costs 

differ between individual and institutional operators. Both of these costs should be pos-

itively correlated with efficiency deviations since otherwise there would not be an incen-

tive to reduce them. Therefore, the amount of costs is linked to the inefficiency and if 

there are no incentives to reduce them inefficiency might remain. Arbitrage is often 

linked to buying low and selling high it is usually executed with the opposite strategy of 

buying high and selling low. In shorting the holding costs can be unpredictable if the 

mispricing takes long to balance. For certain agents shorting is not even possible due to 

high margin requirements. Also, sometimes agents are not able to find stocks to borrow 

or they are not able to find stocks to buy them back, resulting in losses.  

 

Information asymmetry is present in the financial markets as some agents possess more 

information than others (Shleifer & Vishny, 1997, pp, 36337). Usually, the agents with 

the additional information are the ones with the most capital and leverage, such as banks, 

institutions, and governments. The ability to exploit arbitrage opportunities varies be-

tween agents. More importantly, detecting inefficiencies are not guarantees of profit 

(Brealey et al, 2020, p. 343). In 1970 Akerlof (p. 489, 493) described the issues of infor-

mation asymmetry using a car example. If agents are not confident about the right price 

the information asymmetry causes adverse selection and moral hazard. The agents with-

out the information have to bear all the costs associated but on contrary the information 

holder faces moral hazard. Information asymmetry is present and can lead to artificially 

high prices until and (if) the market corrects the situation.  

 

The argument of agents acting rationally contradict with the empirical findings from fi-

nancial markets. The findings show that agents cause the asset prices to diverge from 

their fair values. (Brealey et al, 2020, pp. 3493350). The well-known term <irrational ex-

uberance= by Alan Greenspan is based on this phenomenon and referring to a situation 

where assets prices are driven too high or low. The expectation of agents always acting 

rationally is nonsense since most of the agents are amateurs. For example, Kahneman 

and Tversky (1979, pp. 2633264, 280) stated that agents tend to have strong risk aversion. 



11 

Agents are not particularly interested in the current situation of their portfolio, but the 

overall gains or losses will rather dictate the direction of their investment strategy. If the 

portfolio overall is positive a riskier strategy is applied and vice versa. Overall, agents 

tend to have overconfidence of their own skills.  

 

2.3 Joint hypothesis issue 

The normative finance argues that researching market efficiency is problematic or even 

impossible due to the joint hypothesis issue (Fama, 1970, p. 414; Bodie et al, 2021, p. 

349. The joint hypothesis issue refers to a situation where we cannot be sure what we 

are testing, and therefore what do the results imply. The normative finance claims that 

the joint hypothesis issue is constructed when typical asset pricing models and assump-

tions linked to them are used. This leads to a situation where the results can imply: 1. 

market inefficiency 2. misleading returns (wrong model) or 3. both. Nevertheless, in the 

case of CEFs the joint hypothesis issue does not apply, since we know the value of NAV 

and therefore the mispricing tests of the CEFs are solely tests of market efficiency.  

 

In the 1970s Fama stated that market efficiency cannot be tested before knowing how 

the market reflects information and what is the correct equilibrium asset pricing model 

to use. Whether the prices reflect all the available information creates a joint hypothesis 

problem. For example, asset pricing models, like CAPM include fundamental issues, such 

as expected returns are used instead of real returns, and the expected return is assumed 

to be only linked to the assets market risk (beta). As a result, the test of the risk adjusted 

returns are also test of the EMH at the time and all the previously listed 3 outcomes are 

possible (Bodie et al, 2021, p. 349). This leads to a situation where assumptions linked 

to the testing process are questionable and the results cannot be interpreted. All things 

considered the joint hypothesis creates a barrier for testing the market efficiency. In ac-

ademic context the joint hypothesis issue is often ignored due to its absurdity. The EMH 

is one of the most important cornerstones of finance and it cannot even be tested due 

to the nonexistent predictability of CAPM. 

 



12 

The joint hypothesis issue is minimally two folded in the CEFs mispricing analysis of this 

study: researching the market efficiency and the joint hypothesis linked to CEFs. In the 

case of the CEFs we know that the joint hypothesis issue does not apply to them since 

we know the right pricing model for certainty. Therefore, the test of the relative effi-

ciency of the CEFs are solely tests of market efficiency.  

 

2.4 Critic of normative finance 

The irrational assumptions and inapplicability of the EMH has faced significant amount 

of critic since its release. Academics have found direct evidence against all the efficiency 

forms of the EMH and even further. Overall, assumptions and concepts linked to the EMH 

have nothing similar with the reality in the financial markets. In other words, the concept 

of <no free lunch= does not even make any sense since right prices indicate <no free 

lunch= but <no free lunch= does not indicate prices are right (Kihn, 2015; Brealey et al, 

2020, p. 354). Also, the EMH assumption that non-fundamental information has no ef-

fect to prices is absurd. According to a former CEFs manager it may be actually one of 

the key factors behind the CEF mispricing (Kihn, 1996). The findings of Kihn show that 

the mutual fund price changes are mostly due to non-fundamental factors. Furthermore, 

the fund performance can be rather defined by its non-fundamental factors (e.g., mar-

keting, imago, changing name) than fundamental factors (e.g., earnings). In reality, there 

should be no reasons that the mispricing within the CEFs is defined by the fundamental 

risk, and actually the risk of a CEF is mostly due to the non-fundamental factors, which 

can therefore be considered as one of the possible reasons behind the mispricing.  

 

According to the EMH arbitrage should be impossible and never risk-free but it is consid-

ered to preserve efficiency. According to the theory agents should be price takers which 

have no abilities to restore efficiency. Who will the correct the price? Actually, in arbi-

trage no one really knows what the absolute price of a certain asset should be. How is 

then possible to arbitrage the asset and with what strategy? If it is not possible to know 

how to arbitrage then textbook arbitrage does not make any sense from theoretical, 

mathematical, and logical perspectives. Thirdly, the fact that EMH assumes only relative 



13 

arbitrage does not make any sense. The theory also assumes that market inefficiencies 

are opportunities of excess returns. In reality it should be the opposite since market in-

efficiency means that there is fraud within the market, and agents are going to lose 

money. Realistically, whether money is made, or loss is not related to the market effi-

ciency. All things considered it seems that arbitrage causes arbitrage and due to joint 

hypothesis issue it cannot be even tested.  

 

2.4.1 Evidence against weak form market efficiency 

The core idea of the weak form market efficiency is that past prices are not indicators of 

future prices (Fama, 1970, pp. 383-384; Malkiel, 2014, p. 26, 140, 183; Brealey et al, 

2020, p. 340; Bodie et al, 2021, pp. 3343335). However, the academic literature has 

found evidence against this assumption from different time periods (Bodie et al, 2021, 

pp. 3473348). It seems that certain characteristics such as, momentum of volatility of 

assets can be used to predict future prices. In momentum the serial correlation of assets 

can be used to observe asset trends and momentum. On short time periods the correla-

tions are low but as the time is increased the correlation increases and so does the mo-

mentum effect (Jegadeesh and Titman, 1993, p. 65). Overall, in short and intermediate 

periods it is hard to use past stock prices as predictors of future prices, but it is possible.  

 

Fama and French (1988, p. 246) found evidence of negative autocorrelation in the stock 

returns over time. Indicating that todays high (low) returns forecast lower (higher) re-

turns in the future. Also, Fama and French find out that stocks tend to overreact to cer-

tain news, which create short time momentum balancing over time as the expectations 

reduce. The market cycle indicates that an overreaction will first lead to poor perfor-

mance followed by a good performance in the long run. Also, DeBondt & Thaler (1985, 

p. 804) argued that stocks have a reversal effect in which current losers tend to perform 

better in future and vice versa. Seasonal affective disorder (SAD) is an example where a 

time factor is used to predict future returns (Kamstra et al, 2003, p. 340). The SAD illus-

trates the correlation between stock return and the amount of daily light and is a clear 

violation of the EMH. 



14 

 

2.4.2 Evidence against semi-strong form market efficiency 

In the semi-strong form, the question is whether public information can be used to gen-

erate abnormal returns (Bodie, 2021, p. 349). The EMH states that risk adjusted abnor-

mal returns are not possible, and the EMH makes testing practically impossible due to 

the joint hypothesis issue. Regardless of the test results no one knows what the correct 

model is to test the EMH. The joint hypothesis issue is often ignored and tested with 

simplified models which do not contradict with the joint hypothesis issue.  

 

For example, simple tests researching the interest rates mispricing using the Fisher´s 

equation (i.e., nominal interest rate is equal to real interest rate and expected inflation) 

indicated manipulated interest rates by central banks and governments (Kihn, 2015. If 

interest rates are manipulated, what would it mean to the asset prices, since they are 

based on present and future value methods. Also, Basu (1977, p. 668, 680) researched 

mispricing and found evidence of low price to earnings (PE) portfolios producing higher 

returns compared to the high price to earnings portfolios. Thirdly, if two firms share the 

same expected earnings the riskier firm will be cheaper and possess a lower PE ratio 

which will lead to higher expected return (Bodie et al, 2021, p. 350).  

 

De Jong et all (2009, p. 518) researched the topic of mispricing through dual listed funds 

and found significant efficiency deviations between them. Apparently factors like, size, 

volatility etc., can be used to research mispricing and to find the higher return generating 

assets (Bodie et al, 2021, pp. 3513354). In 1993 Fama and French used the factor models 

and detected that market return is not the only explaining factor but also factors such as 

size and value have an effect on stock returns. All things considered, apparently, arbi-

trage is not efficient enough to balance the price deviations. 

 



15 

2.4.3 Evidence against strong form market efficiency 

In the strong form, the question is whether available inside information can be used to 

generate abnormal returns (Bodie, 2021, p. 354). In practice the financial markets are 

not strong format efficient since the governments and institutions regulate and limit in-

side information trading. If inside information and information about the inside trades 

would be available agents should be able imitate them and generate abnormal returns. 

Seyhun (1986, p. 210) researched whether it is rational to imitate inside traders and 

found evidence indicating the opposite. Asset prices tend to rise shortly after the an-

nouncement of inside trading but the rise in price is not high enough to counter the 

transaction costs associated with the trade. As a results, if there are inefficiencies and 

agents are rational, they do not have the incentive to balance the deviation.  

 

Overall, the findings raise serious questions and concerns towards the core center of 

normative finance. The findings from the academic literature show direct evidence 

against all the forms of efficiency, the arbitrage and the EMH itself. The concepts of EMH 

and ATP are contradicting with each other. Arbitrage causes arbitrage itself and none of 

the assumptions related to the EMH actually hold in practice. If we cannot be sure about 

the rightfulness of prices and interest rates, then we cannot be sure about anything re-

lated to normative finance itself. 



16 

3 CEFs´ an unambiguous violation of EMH 

This study has already disclosed that testing the EMH can be hard or even impossible 

due to the joint hypothesis issue. According to the joint hypothesis issue we do not know 

what the correct pricing model is to evaluate relative price efficiency or risk associated 

with asset. However, the CEFs pricing efficiency tests do not contradict with the joint 

hypothesis. In the case of the CEFs we know the right relative pricing model for certainty, 

and we do not need to involve standard asset pricing models to research mispricing. 

Therefore, the joint hypothesis issue does not apply to the CEFs, and the mispricing can 

be researched through the relation of CEF NAV and price.  

 

3.1 Overview of CEFs 

a CEF is an investing instrument that raises capital by issuing fixed number of shares to 

market through an IPO (Bodie et al, 2021, p. 96; Brealey et al, 2020, pp. 3793380). CEFs 

are traded in the financial markets mainly like stocks or ETFs, and the shares are non-

redeemable and in fixed numbers. Meaning that they cannot be redeemed against cash 

and at the time of issuance only a certain number of shares are released. The levered 

<CEFs= are an exception as they are not technically CEFs since they allow their number 

of shares to be decreased or increased. Regardless of the difference the behavior of lev-

eraged funds is similar to typical CEFs. Shares of a CEF can only be sold or purchased 

through the market as no new shares are issued. If agents want to sell off their shares 

they have to sell their shares to another investor. The raised capital of a CEF is invested 

into financial assets e.g., stocks or bonds depending on fund strategy. CEFs offer a broad 

choice of different investment strategies. Most of the CEFs invest into common asset 

classes, and bonds have usually accounted for the majority of the CEFs´ total assets. 

 

The table one below describes the development of the CEFs in the USA from 2005 to 

2022 (Statista, 2023). The trend of the number of CEFs has been negative and it seems 

that the popularity of the CEFs has declined while agents have found new alternative 

investment instruments. The amount of the CEFs has decreased over 30 percent during 



17 

the studied period. Also, the total assets within the CEFs have decreased marginally,  e.g.,  

in 2017 the total assets within the CEFs were 277 billion dollars and in 2022 they were 

252 billion dollars (ICI, 2023, p. 64). The trend of the number of the CEFs and the assets 

suggest that large CEFs have become even greater, and some small CEFs have been 

closed. It seems that agents are willing to test new investing instruments instead of CEFs. 

Also, some of the CEFs have lately been liquated, merged or converted into ETFs.  

 

Table 1 Development of CEFs´ (Statista, 2023) 

 

 

3.2 CEFs mispricing 

From the purpose of this study the most important feature of the CEFs is that their mar-

ket value (MV) usually (always) diverges from their NAV (Lee et al, 1991, pp. 113631137; 

Pontiff, 1996, p. 1150). In practice, the CEFs are always trading at a discount or premium 

in relation to their NAV. CEFs are said to be trading at a discount (i.e., negative mispricing) 

when the MV is below the NAV, and when the MV is higher than the NAV they are said 



18 

to be trading at a premium (i.e., positive mispricing). The NAV of a CEF is calculated by 

subtracting the CEF liabilities from the CEF assets, and the NAV per share can be calcu-

lated by dividing the total NAV with the amount of shares outstanding (Pontiff, 1996, p. 

1150; Lee at all, 1991, pp. 113631137). The mispricing of a CEF is calculated by compar-

ing the relation of the CEF NAV and price. The fact that we know the relative efficiency 

pricing model of the CEFs for certain allows us to research the mispricing without con-

tradicting with the joint hypothesis issue. Nevertheless, it has to be highlighted that the 

efficiency tests of mispricing are only research of relative values and their assumptions 

instead of absolute values. In the research only the NAV values are known for certainty, 

and no one knows what the price of a CEF should be.  

 

The CEF efficiency deviation (i.e., mispricing) is based on the relation of the CEF NAV and 

price, which according to the EMH should be always equal zero (Bodie et al, 2021, pp. 

3793380; Lamont & Thaler, 2003, p. 228). Any deviation from the efficiency is a clear 

violation of the EMH, and specially law of additivity which claims that the value of a 

company should be equal to the sum of the values of its different parts at any chosen 

time. The law of additivity should determine the minimum valuation boundaries for 

companies but in practice the boundaries are controlled by supply and demand. A for-

mer CEF manager mentioned that the CEF manager job is to control the NAV of the CEFs. 

He claimed that the deviation between CEF NAV and price can be partially controlled but 

it is virtually impossible the get the NAV and price to match. The agents define the mar-

ket price of the CEFs and therefore whether the CEF is trading at a premium or discount. 

 

In reality, the NAV of CEF often (always) diverges from the market price. On average the 

CEFs are trading at a discount but often at time of issuance the CEFs tend to trade at a 

premium. The finding may sound irrational since why anyone would want to buy a CEF 

at the time of IPO if the price is likely to fall shortly after. On the contrary, the brokers 

are not going to launch new CEFs unless they are mispriced (premium). It seems clear 

that the market cannot add and subtract, and arbitrage is not functioning as the EMH 

claims it should be.  



19 

 

3.3 CEFs mispricing and EMH 

According to the EMH mispricing should not possible since prices are right, agents are 

rational and arbitrage removes pricing inefficiencies (Samuelson, 1965, p. 41; Fama 1970, 

pp. 3833384). Nevertheless, in reality the price inefficiencies are rather a rule than ex-

ception, even in the security classes like CEFs or ETFs which are considered to be effi-

ciently priced security types. The EMH tries to explain the price deviations e.g., by inac-

curate NAV calculations and portfolio manager (PM) irrational behavior related to 

agency costs (Lee et al, 1990, p. 156). These agency costs include components like, lack 

of incentives and pressure to perform. According to Malkiel (1977, pp. 8543855) the 

agency costs related to the CEFs cannot be used as explaining factors of mispricing. CEFs 

facing similar costs do not trade at the same price and the price behavior is not logical.   

 

Secondly related to agency costs, Boudreaux (1973, pp. 5163517) claims that price devi-

ations within the CEFs might reflect managers trading skills since the NAV of the CEFs 

should reflect the expected returns associated. Therefore, the skills of managers are con-

sidered in the NAV of a CEF (Lee et al, 1990, p. 156). If this is true, there is no logic that 

the CEFs are systematically trading at a discount. On contrary, Malkiel (1977, pp. 857-

858) stated that there is no significant relationship with past performance and mispricing. 

According to Malkiel the mispricing tends to be linked to overall market conditions, and 

therefore the discounts tend to decrease in in bear markets and increase in bull markets.  

 

The EMH also argues that restricted stocks might lead to incorrect NAV calculations and 

can therefore cause mispricing within the CEFs (Lee et al, 1990, p. 157). CEFs are claimed 

to be misvalued since they include premium trading restricted stocks which cannot be 

freely sold to the market. Consequently, the CEFs have an incentive to include these 

stocks in their portfolios since they cannot be liquated. Malkiel (1977, p. 854) and Lee et 

all (1991, p. 79) found out that these restricted stocks can be used to explain part of the 

variation in discounts. Despite the findings, some CEFs have no or only a little restricted 

stocks and still trade at a discount (Lee et al, 1990, p. 157).  



20 

The EMH highlights taxes as a possible reason for mispricing (Lee et al, 1990, pp. 157-

158). When CEF assets are sold with a profit the agents has to bear the tax liabilities. 

Furthermore, there is a danger of facing tax payments even if you are a new investor 

without profits if the CEF decides to realize its assets. Moreover, if the CEF is associated 

with substantial capital appreciation the CEF is less attractive for agents since its real 

value is certainly below NAV and trading at a discount. Malkiel (1977, pp. 854-855), and 

Lee et all (1991, p. 80) researched the tax effects and found out that taxes can only ex-

plain a part of mispricing but there was no significant relationship between them.  

 significant relation between taxes and mispricing was not found.  

 

Lee et all (1991) found out that the mispricing behavior of the CEFs includes four differ-

ent detectable cycles which can be used as a guideline for CEFs behavior. The first obser-

vation was that new CEFs tend to trade at premium at time of IPO and shortly after IPO 

they tend to shift quickly to a discount (Lee et al, 1990, p. 154). Agents have to face high 

expectations, cost of becoming public, and transaction costs related to the new CEFs. On 

the contrary, brokers have the incentive to drive the CEF price up. These systematic price 

drops are documented in the empirical literature, and it seems irrational to participate 

in buying the CEFs at time of issuance but shorting them would seem like a viable option. 

The second observation was that the CEFs tend to trade at a discount in comparison to 

their NAV (Lee et al, 1990, p. 155). The empirical evidence indicates that it is rather a 

norm than exception that the CEFs trade at a discount.  

 

The third observation was that pricing mispricing within the CEFs tend to have a high 

degree of variation over time and between CEFs (Lee et al, 1990, p. 155). Empirical evi-

dence has found a high degree of variation within the CEFs, including both premiums 

and discounts. Mispricing variation seems to be positively correlated with price and in-

creasing as time period is lengthened. The discounts and premiums tend to move in the 

same direction. The CEFs variation raises questions of why they variate so much and why 

they move in the same direction. The fourth observation was that when CEFs are shut 

down or shifted to open-end funds the prices tend to revert back to the NAV (Lee et al, 



21 

1990, p. 155). The observation is not surprising since at the time of the liquation the 

assets of CEF should be redeemed at the NAV, and therefore there should not be any 

other possible outcomes. However, some argue that the net assets are reported falsely 

and force the NAV back to market price.   

 

The examples from academic papers imply that the phenomenon of CEFs mispricing is 

complex. Furthermore, the EMH tries to explain the deviations from efficiency with dif-

ferent factors. Most of these factors show only minor explaining significance in relation 

to CEFs mispricing and it seems that mispricing of the CEFs is a phenomenon which is 

more linked to the macroeconomic factors instead of the CEFs specific factors, while a 

large amount of mispricing remains unexplained. Anyway, the stand of the normative 

finance has not changed despite the papers have been able to generate considerable 

evidence in favor of inefficiencies within the CEFs (Bodie et al, 2021, p. 380). The norma-

tive finance is aware of the mispricing but claim mispricing to exist due to combination 

of unexplainable factors and both premiums and discounts within the CEFs are possible.  

 

 



22 

4 Market timing 

The market timing is in the center of this study since the second objectictive of this study 

is show that is possible to systematically beat the market index with simplified trading 

strategies based on the CEFs mispricing mean reversion. This section presents the over-

view of market timing and its relationship with the EMH and the joint hypothesis issue.  

 

4.1 Overview of market timing 

In the context of the CEFs mispricing the market timing can be defined as a way to fore-

cast future market movements and to allocate assets in the portfolio according to the 

forecasts in order to make profit. Henrikson and Merton (1981) and Henrikson (1984) 

describe market timing as an option theory related phenomenon, where free call and 

put options are available due to market inefficiencies. In the context of the CEFs mispric-

ing, agents have the possibility to exploit the systematical difference between CEF price 

and NAV. The phenomenon can be considered as an opportunity to buy undervalued call 

or put options and wait for the possible price mean reversion back to  the NAV. The be-

havior of CEFs is asymmetric and on average the CEFs tend to be trading at a discount. 

Therefore, in practice the CEFs mispricing can be mostly exploited through call options.  

 

Market timing can be further divided into two fields: parametric and non-parametric 

market timing (Henrikson & Merton, 1981, p. 514); Henrikson, 1984, p. 74). The para-

metric market timing refers to exploiting efficiency deviations of individual investment 

targets, such as the CEFs. The non-parametric market timing refers to a broader market 

exploiting, where agents allocate their assets between risky and non-risky assets de-

pending on the overall trend of the financial markets.   

 

Market timing sounds attractive and effortless to perform but in reality, at least over 

time it is difficult to perform successfully (Malkiel, 2014, p. 202). For example, behavioral 

finance has denoted that agents tend to overestimate their own skills. Agents rely too 

heavily on their own skills to beat the market, end up facing the high risks associated 



23 

with the strategy. According to the EMH market timing should not be possible, at least 

over time. For example, Malkiel (2014, p. 202) states that active trading increases the 

risk to miss the best return periods since capital is not constantly invested into the mar-

ket. Malkiel also emphasizes that market timing is a fraud which sounds too good to be 

true. He argues that beating the stock market average 9 percent return constantly by 

market timing strategies is impossible, otherwise all others would be also performing it. 

   

4.2 Market timing and EMH 

The EMH argues that market timing is not possible since prices are right, agents are ra-

tional and arbitrage removes pricing inefficiencies (Samuelson, 1965, p. 41; Fama 1970, 

pp. 3833384). As already mentioned, none of the assumption hold true in practice and 

the finance textbooks rarely reflect the reality in the financial markets accurately (Kahne-

man & Tversky, 1979, p. 265, 277; Allais 1997, p. 4). Market timing belongs to the same 

group since it is assumed to be impossible but in reality, it is happening constantly. Cer-

tainly, there might be some kind of restrictions and of course market timing might not 

lead to excess returns but at least opportunities to perform market timing are constantly 

available. It has to also noted that often performing market timing does not need super-

natural trading skills since the market and the agents are behaving irrationally.  

 

The London Gold and Silver Fix is an illustrative example of systematical market timing 

opportunity (Caminschi & Heaney, 2013, p. 1004). In London a certain number of banks 

or specific parties are setting the price of gold and silver at a fixed level according to 

supply and demand. An empirical study was conducted where the returns between buy 

& hold tactic and one specific tactic concentrating on the prices of gold and silver were 

compared. The specific tactic strategy was to buy the morning fix price and sell at the 

evening fix on a daily basis. The price of gold (buy & hold) nearly quadrupled during the 

30-year period, but the tactic generated almost three times higher cumulate returns dur-

ing the period. The price of golf seemed to follow a certain price cycle and if this pattern 

would have been detected a market timing strategy would have led to significant excess 

returns. As governments and public agencies were behind this price pattern the 



24 

credibility of the financial markets could be questioned, and it is foolish to expect this 

was the only case of governmental price manipulation.  

 

In reality there are numerous examples like the previous one and opportunities for mar-

ket timing are constantly available. Nevertheless, despite the mispricing within the CEFs 

may be constantly present taking advantage of might not be so simple. As agents apply 

traditional market timing strategies of buying low (high) and selling (low), there are no 

guarantees of the CEFs mispricing reverting back to their long-time average since the 

premiums or discounts within the CEFs can widen. The uncertainty connected to the 

mispricing reverting duration increases the fundamental risk substantially. The same 

phenomenon can be seen in stocks and e.g., Lee et all (1991, p. 76) found out that the 

discounts within stocks tend be correlated and to move together with the returns of 

small stocks. Also, Pontiff (1996, p. 1136) found out that the CEFs mispricing is negatively 

correlated with the idiosyncratic volatility.  

 

4.3 Market timing and mean reversion  

The used market timing strategy in this study is constructed using the findings from the 

mispricing analysis and academic literature. The core idea of the market timing strategy 

is that the CEFs mispricing tends to follow mean reversion. The idea of mean reversion 

is that on short and intermediate time periods the variation of the market can be high 

but in long run the market tends to revert into its long period average (Malkiel, 1977, p. 

184, 209; Poterba & Summers, 1988, p. 45). The market can undergo short periods of 

high (low) returns but they tend to be followed by periods of low (high) returns. The 

findings from the papers concentrating on the CEFs indicate that the mispricing of CEFs 

can be explained by CEF-specific and macroeconomic factors, but a large share of mis-

pricing remains unexplained. Furthermore, the effects of CEF-specific factors seem lim-

ited and also the macroeconomic factors have only relatively minor effect to mispricing. 

Overall, it seems that there are no factors which can properly explain mispricing within 

the CEFs. The mispricing of a CEF does not seem to depend on the mispricing of other 

funds and is therefore based on mean reversion.  



25 

4.4 Market timing and joint hypothesis 

In the case of the CEFs mispricing analysis we know the correct pricing model to evaluate 

the relative pricing efficiency, and there is no risk of contradicting with the joint hypoth-

esis issue (Lee at all, 1991, pp. 113631137; Pontiff, 1996, p. 1150; Lamont & Thaler, 2003, 

p. 228; Bodie et al, 2021, pp. 3793380; Yang & Gould, 2023, p. 1419). On the contrary 

the market timing analysis of the study includes a joint hypothesis issue since we do not 

know what the correct model is to test the trading strategy.  

 

The trading analysis of this study ignores the joint hypothesis issue and assumes that the 

CEFs mispricing is mean reverting and can be possibly exploited to make significant 

amount of money. Therefore, the trading analysis is rather a tests of whether the CEFs 

mean reversion based trading strategy leads to a loss or profit based on the relative val-

ues. The assumption of mean reversion is based on the mispricing analysis observations, 

where it seems that the relative difference between the market price and the NAV of a 

CEF are mean reverting. In order to conclude that it is possible to beat the market sys-

tematically the returns for the market tactics have to be considerably higher than for the 

market.  



26 

5 Data 

The monthly data of this study concentrates on 108 CEFs listed in the USA exchanges 

during the studied period of 2002-2019, in total 18 years of data. After data filtering and 

validation there are in total 22 862 observations. The core data is retrieved from Bloom-

berg, and it includes information about the CEFs, price, NAV, bid-ask spread, etc. Also, 

some data and information related to used variables is acquired from yahoo finance, 

FRED Economic Data (FED), and CEF-specific brochures. Furthermore, also weekly data 

for the same selected 108 CEFs is retrieved from Bloomberg to enable data comparisons 

between different data intervals. In the weekly data there are 99 066 observations.  

 

5.1 Selected CEFs  

The acquired data from Bloomberg included information about all the listed CEFs in the 

USA, totaling up to over 500 CEFs. The 108 CEFs were selected in the sample based on 3 

conditions: 1. trading data for the selected period of 2002 to 2019, 2. opening year be-

fore 2002 since there were also CEFs with trading data before the official opening date, 

and 3. no consecutive periods with the same price or NAV. The first condition objective 

was to ensure that there are no lengthy periods with missing observations and the sec-

ond condition objective was to avoid included shifted or merged funds in the sample. 

The last condition objective was to ensure that there is no corrupted data. After the con-

ditions were applied the original number of over 500 CEFs decreased to 108 CEFs.  

 

5.2 Variables 

This study includes two different analyses: mispricing analysis and trading analysis. The 

main variables used in the mispricing analysis are mispricing, asset class, premium cycle 

duration, discount cycle duration, VWD, leverage, location, USA 1-year treasury, and SMB. 

These variables were selected based on their use in the OLS regression model in the 

mispricing analysis. Logically, also additional variables were constructed to calculate the 

main variables, e.g., the calculation of SMB factors required data about the CEFs MV and 



27 

NAV, return, and time. The used variables in the trading analysis were partially the same 

as in the mispricing analysis. The main variables in the trading analysis are Z-score, return, 

transaction cost, and financial ratios. These main variables are used to research portfolio 

construction, return calculations, and portfolio return comparisons. In total the number 

of researched variables was over 70. All the main variables used in the analyses are pre-

sented in the upcoming methodology sections.  

 

5.3 Data validation and outliers 

Before data validation and outlier checks, the descriptive statistics and overlook of the 

108 CEFs data indicate the data to be highly skewed to the right with radical tails values. 

The skewness of the data was 2,61 and the kurtosis was 17,53. Despite, 82 percent of 

the observations were within one standard deviation from the mean and overall, the 

distribution had similarities with normal distribution. High kurtosis values can be natural 

characteristics of CEFs data but in order to get the data suitable for the OLS regression 

model the data needed adjustment as OLS is not capable to predict unsymmetric distri-

butions with radical tail values properly. Therefore, different transformations, such as 

logarithmic (LOG) and square root (SQRT) were tested to make the data more suitable 

without distorting the results. The results from the LOG and SQRT transformation were 

limited. Both of the transformations caused distorted the results and were not able to 

decrease the high kurtosis value. Therefore, both of transformations were declined.  

 

After the LOG and SQRT transformations a one percentage modified winsorizing method 

was tested to both of the tails of the distribution. The method generated better results, 

and the high kurtosis value decreased and overall, the distribution became more stable. 

In modified winsorizing the one percentage tail values were deleted from the sample 

instead of replacing the deleted values with boundary values. A total of 446 observations 

(223 observations from both tales) were deleted. The chapters below consider the im-

plications of the deleted observations to ensure that the overall picture of the data did 

not change due to modified winsorizing method.  



28 

The modified winsorizing process of the 446 observations concerns observations from 

37 different CEFs. 33 of the 37 CEFs  have only a few observations to which modified 

winsorizing applies. The total share of these 33 CEFs is equal to 46 percentage. As the 

share of deleted observations is accounted for these 33 different CEFs we can be sure 

that the results do not distort. The remaining 54 percentage of the deleted observations 

is accounted by only 4 different CEFs: RCG US Equity (73 observations / 16 %), CLM US 

Equity (72 observations / 16 %), VFL US Equity (67 observations / 15%), and DNP US 

Equity (47 observations / 11%). For all the 4 CEFs the number of deleted observations 

accounts for a significant amount compared to all the observations.  

 

For the RCG 5 years (2006, 2009, 2010, 2011, and 2012) stand out from the deleted data. 

During all the years there are 10 to 12 deleted observations (i.e., whole year). All of the 

deleted observations are continuous and in discount, and sometimes they can span out 

to last 24 months. The average mispricing of the RCG is about 20 percent and the data 

shows that the RCG is continuously undervalued. Also, for the CLM 3 years (2012, 2013, 

and 2015) stand out from the deleted data. During all these years there are 10 to 12 

deleted observations. Almost all the deleted observations are premiums and for the 

whole period the CLM average mispricing is about 15 percent.  

 

For the VFL and the DNP the deleted observations experience the same characteristics 

as the RCG and the CLM. The VFL has 5 years (2002-2006) where all the observations are 

in substantial premium and deleted. In these deleted observations the price is a on av-

erage almost twice as high as the NAV. The DNP has 2 years (2009 and 2010) where the 

deleted observations concentrate. During these years all the observations are deleted, 

and the DNP undergoes substantial premium. The research on the 4 CEFs shows that 

even though a significant amount of observations are deleted the overall picture of these 

4 CEFs does not change. 

 

The time perspective of the deleted observations is also crucial since if they concentrate 

to a specific time period, they might distort the results. By looking at the data it seems 



29 

that the deleted observations are divided between all the studied years and vary from 6 

to 56 deleted observations on a yearly basis. The amount of observations per year is 

1296 so the amount of deleted observations is insignificant and does not distort the re-

sults. Furthermore, when the deleted observations are considered on month-year basis 

197 unique months stand out. Indicating that the removed observations are well divided 

between different months and their underlying year, and the deleting is approved. 

 

As a results, the modified winsorizing method is approved as it does not distort the re-

sults. On the contrary it seems that modified winsorizing might make the data more re-

liable by deleting the radical tail values. Due to modified winsorizing descriptive statistics 

of the data remain relatively unchanged and the kurtosis significantly decreases. After 

the transformation the data reminds a normal distribution. The effects of modified win-

sorizing are covered more detailed in the upcoming descriptive statistics section.  

 

 



30 

6 Methodology 

The methodology section of this study includes information about two different analyses: 

mispricing analysis and trading analysis. First the methodology to research CEFs (relative) 

mispricing is covered. The methodology includes all the needed information about the 

formulas, variables, and regression model. In the mispricing analysis the formulas used 

to evaluate CEFs NAV, and mispricing are the most important indicators to research mis-

pricing. Conclusions about the null hypothesis can be made based on these simplified 

indicators. The regression analysis of mispricing (additional analysis) objective is to re-

search whether the mispricing of CEFs can be explained with CEF-specific or macroeco-

nomic factors, or is it rather based on specific factors (mean reversion).  

 

The second part concentrates into the trading analysis which will present how trading 

strategies based on CEFs mispricing mean reversion are created. The second section will 

also present the used formulas, variables, and regression model. Lastly robustness 

checks for both analyses are covered. The conclusions about hypothesis 1 are based on 

the returns between the different market tactics and market strategies.  

 

6.1 Mispricing analysis and formulas 

According to Lee et all (1991) and Bodie (2021) mispricing of CEFs can be measured by 

comparing the difference between the CEF price and the CEF NAV. According to the EMH 

the CEF price should be always equal to the CEF NAV (prices are efficient). If the price is 

below (above) the NAV, the CEF is said to trading at a discount (premium). The NAV of a 

CEF is measured by subtracting the liabilities from the assets. NAV per share is calculated 

by dividing the total NAV with the number of shares outstanding.  

 

 ���	���	�/��� = !"#$	&''()'	3!"#$	+,-.,/,),('

0"1.(2	34	56-2('	7")')-#$,#8	
        (1) 

 



31 

The requirements and regulation for CEFs reporting and NAV updating are linked to law. 

According to the SEC (2012, p. 3) CEFs´ are not obligated to update their NAV on a daily 

basis. Nevertheless, most of the CEFs update their NAV on a daily basis. The CEF price 

per share describes the market price of a CEF at the end of the trading day. The CEF 

mispricing is calculated by deducting NAV per share from price per share and dividing it 

by NAV per share. The mispricing is only a relative indicator of efficiency as we only know 

the NAV of a CEF for certainty, but no one knows what the price of a CEF should be 

 

  ���������� = 92,:(	;(2	'6-2(	30&<	;(2	'6-2(

0&<	;(2	'6-2(
  (2) 

 

Further measure of mispricing is NAV-based mispricing, where the CEF size is considered 

and measured by total NAV. In the typical mispricing formula (2) all CEFs mispricing is 

assumed to be equivalent. The NAV-based mispricing is calculated by multiplying the 

mispricing coefficient with the CEF NAV and dividing the result with the NAV of all the 

selected 108 CEFs. The NAV-based mispricing enables to research how mispricing varies 

when the CEF size is considered. In the NAV-based mispricing CEFs with higher NAV val-

ues will have a greater impact on mispricing compared to CEFs with lower NAV values. 

The NAV-based mispricing variable is just an interphase of VWD.  

 

 ��� 2 �����	���������� = =,';2,:,#87!"#$	0&<

&//	!"#$'	0&<
  (3) 

 

The NAV-based mispricing can be further refined to a value-weighted index of mispricing 

(VWD). Lee et all (1991, p. 87) presented this measurement in their study to research 

mispricing of CEFs´. In the VWD the main idea is similar to NAV-based mispricing, but the 

difference is that it includes multiple observations as a sum of NAV-based mispricing. 

The VWD combines all NAV-based mispricing values from a certain time period. In the 

study there are 216 unique time periods (months) so there are also 216 unique VWD 

values. In other words, the VWD of 31st of January 2002 includes 108 individual NAV-

based mispricing values, which are combined to a single VWD value. The VWD illustrates 

the mispricing development of the whole CEFs asset class.  



32 

 ��� = 3 ��� 2 �����	����������)
#

,?@    (4) 

 

The SMB is a second variable where the CEF size is considered. The SMB variable is a 

shared variable between all the CEFs at certain time, and in total there are 216 unique 

SMB values. The variable describes the excess return of small CEFs compared to big CEFs 

at certain time. All the SMB factors are evaluated and calculated based on the CEFs data.  

 

 ��� = @

A
(�� + �� + ��) 2 @

A
(�� + �� + ��)  (5) 

 

Where,  

SV = Small Value, SN = Small Neutral, SG = Small Growth 

BV = Big Value, BN = Big Neutral, BG = Big Value 

 

The durations for the CEF premium and discount cycles are obtained using straightfor-

ward formulas. The formula of discount cycle duration is equal to the consecutive 

months the CEF has been trading at a discount (negative mispricing). The formula for 

premium cycle duration is equal to the consecutive months the CEF has been trading at 

a premium (positive mispricing). If the mispricing unit changes from premium to discount 

or discount to premium the cycle duration starts again from the beginning.  

 

6.2 Mispricing regression model and variables 

The objective of the mispricing analysis is to demonstrate that mispricing within the CEFs 

is a valid and systematic phenomenon. Referring to the null hypothesis of this study: 

<There is no statistically significant mispricing within the CEF market=. Whereas the ob-

jective of the regression analysis is to research whether the CEFs mispricing can be ex-

plained by CEF-specific or macroeconomic factors. The regression analysis is conducted 

using ordinary least squares (OLS) regression. The OLS regression is selected since it is 

simple and effective for the purpose of this study.  



33 

If the null hypothesis of the study can be rejected the OLS regression model is used to 

find possible explanations for the CEFs efficiency deviations. Based on the findings in the 

academic literature, the study expects to find only relatively low coefficients for the ex-

plaining factors of mispricing. According to the academic literature CEFs mispricing 

seems to be caused by a combination of multiple factors, and the mispricing of individual 

CEFs tends develop in their own specific cycles related to mean reversion. Therefore, the 

objective of the mispricing analysis is to find evidence of statistically significant mispric-

ing and possibly to be able to explain it with the used variables in the regression model.  

The formula of the used OLS regression is presented below.  

 

����������,,) = �C + �@�����	�����, + �D�������	�����	��������,,) +

�A��������	�����	��������) + �E���,,) + �F��������,,) + �@��������, +

�@���	��������) + �D���) + �,,)	        (6) 

             

Where, 

Mispricing i,t = CEF i mispricing at time t  

Asset Class i = CEF i asset class (categorical) 

Premium Cycle Duration i,t = CEF i premium mispricing duration at time t 

Discount Cycle Duration i,t = CEF i discount mispricing duration at time t 

VWD t = Value-weighted discount index at time t 

Leverage i, t= CEF i leverage status at time t (categorical) 

Location i = CEF i investment location  (categorical) 

USA Treasury t = 1-year USA Treasury rate at time t   

SMB t = SMB at time t 

÷ I,t = CEF i error term at time t 

³, ·, » = Explaining coefficients for variables 

³0 = Intercept term (Asset Class = Fixed Income, Location = USA, Leverage= Unlevered) 

 

The OLS regression model consists of dependent, independent and control variables. 

Mispricing is used as a dependent variable in the regression model, and it will disclose 



34 

how much the CEF price deviates from its NAV. The selected independent variables are 

asset class, premium cycle duration, discount cycle duration, VWD, and leverage. Each 

of these variables are tied to their own explaining beta coefficient (³). These variables 

illustrate the effect of changing the value of independent variable to dependent variable. 

More detailed, how much will the dependent variable change if the independent varia-

ble is increased by one unit, while all the other independent variables remain constant. 

If the coefficients are positive, they indicate that mispricing increases when variables 

increase, and vice versa.  

 

The asset class (³1) variable demonstrates how the asset class of a CEF affects mispricing. 

It determines what is the primary investing target of a CEF. The alternatives for asset 

class are equity or fixed income, and as it is a dummy variables the fixed income is se-

lected as reference category and included in the intercept term (³0). The primary invest-

ing asset class of a CEF is obtained from CEF-specific brochures. From the 108 selected 

CEFs 69 CEFs are primarily investing into fixed income, and 39 CEFs are primarily invest-

ing into equity. The asset class is constant for the whole studied period. The upcoming 

section of categorical variables contains more details about the asset class variable.  

 

The premium cycle duration variable (³2) measures consecutive months where CEF mis-

pricing remains in premium. When the CEF mispricing is in discount the value of the 

variable is zero. The variable explains how the duration of premium mispricing will affect 

mispricing. The discount cycle duration variable (³3) measures consecutive months 

where CEF mispricing remains in discount.  

 

The VWD variable (³4) demonstrates how the sum of NAV-based mispricing affects mis-

pricing at certain time. The VWD is a shared coefficient for all the CEFs, and it describes 

the mispricing development of all the selected 108 CEFs. Therefore, it can be considered 

as an overall asset class variable of the selected CEFs. The formulas (3) and (4) demon-

strate how the VWD values are calculated. VWD is an independent variable, but due to 

its characteristics it serves more like a control variable. 



35 

The leverage (³5) variable demonstrates how mispricing varies between the CEFs lever-

age status. It determines whether a CEF uses borrowed capital as a source of funding. 

The alternatives for leverage status are leveraged or unlevered. The leverage status is 

defined based on the leverage date of a CEF, and therefore a CEF can be levered and 

unlevered during the studied period. The selected 108 CEFs are mostly unlevered, and 

all the leverage dates are after the year 2014. In total there are 51 leveraged and 108 

unlevered CEFs. As it is a dummy variable the unlevered category is selected as reference 

category (0) and included in the intercept term (³0) of the regression.  

 

The used control variables in the OLS regression are investment location, USA treasury, 

and SMB. Like independent variables, also control variables have their own coefficients. 

Overall, control variables are factors which may affect mispricing but are not in the cen-

ter of the research. The location (·1) variable demonstrates how mispricing varies be-

tween the CEFs investment location. In other words, how mispricing varies between CEFs 

investing into USA and foreign countries. The location is a categorical dummy variable 

with two alternatives USA and foreign. The CEFs investing to USA are selected as refer-

ence category (0) and included in the intercept term (³0) of the regression. The invest-

ment locations of the CEFs are obtained from CEF-specific brochures. The location clas-

sification is constant for the whole studied period. Meaning, that a CEF can be only in-

cluded in one of the categories during the studied period.  

 

USA Treasury (»1) variable describes how changes in interest rates impact the CEFs mis-

pricing. The 1-year USA treasury includes monthly observations of USA interest rates ob-

tained from Fred (2025). It is added to analysis to include the effect of macroeconomic 

factors. The interest rate values are shared between the CEFs and gathered for 216 indi-

vidual time periods (months).  

 

SMB (»2) variable describes how the difference between small and big CEFs returns af-

fects the mispricing of the CEFs. The SMB factors are calculated for all the individual time 

periods (months) based on the CEFs MV and NAV. Therefore, it is a combined factor for 



36 

all the CEFs at each time t. The role of SMB is to consider the CEF size and to make the 

results of the independent variables more accurate. The size factor is already considered 

in the independent variables through VWD so therefore SMB is left as a control variable.  

 

The categorical variables asset class, leverage, and location are non-continuous variables 

which are coded into either one or zero. These variables enable to analysis the effects of 

non-numerical variables. In each of the categorical variables one category has to be se-

lected as a reference category which is included in the intercept term. The intercept term 

represents the effect when the values of other variables are assumed to be zero. The 

reference categories function as comparison values and do not have their individual ex-

plaining coefficients. The reference categories are selected based on the rule that what 

is the most common observation in the data.  

 

The use of the reference categories is critical and based on the phenomenon called 

dummy trap. The dummy trap refers to a situation where the reference categories are 

ignored, and the regression model leads to full multicollinearity and incorrect estimates. 

The regression model is not able to evaluate the effect of categorical variables if all of 

them are included. In reality there is no need to include all different options for categor-

ical variables, since e.g., a CEF is either investing into USA or to foreign countries. If a 

fund is investing into USA, it does not invest to foreign countries. 

 

The error term (÷ I,t) represents the results which the regression model cannot explain by 

the model factors. Error term signals how the model actually functions.  

 

6.3 Trading analysis and trading rules 

The objective of the trading analysis of this study is to show that the core concepts of 

normative finance are empirically, mathematically, and logically systematically incorrect. 

In this study it refers that the hypothesis one: <There are no CEF market timing strategies 

that are able to beat the market= has to be tested and rejected. The objective is to reject 

the hypothesis one and to show that the market index can be systematically beaten using 



37 

only short and long positions based on the CEFs mispricing mean reversion. The study is 

suggesting that the relative difference between the CEFs market price and the NAV is 

mean reverting. As the trading analysis is contradicting with the joint hypothesis it is 

rather a test of whether the CEFs mean reversion-based market timing strategies lead to 

a profit or loss based on the relative mispricing values. It seems that over time the CEFs 

mispricing variation tends to follow to the long-term mispricing average. The CEFs trade 

occasionally below the long-term average and occasionally above the long-term average. 

These can be called as CEFs mispricing cycles, which usually revert back to the long-term 

average on a relatively short time period.  

 

The test of whether the market index can be systematically beaten with market timing 

strategies are conducted by comparing the results of 3 market tactic strategies and 3 

market strategies performance. The 3 market tactic strategies are constructed based on 

the concept of CEFs mispricing reversion. All the 3 market tactic strategies have the same 

trading rules, but the amount of long and short positions varies between them. The 3 

market strategies are based on the idea of buy and hold and include only long positions. 

The trading rules for the 3 market tactic strategies can be seen below in table 2. The 

trading rules define the positions opening and closing criteria. 

 

Table 2 Trading rules  

 

 

The most important trading rule indicator for the CEFs mispricing mean reversion based 

3 market tactic strategies is the Z-value. The Z-value describes how many standard 



38 

deviations the CEF mispricing is from its long-term average mispricing. The Z-values are 

used as indicators to close and open the trading positions. The long positions are opened 

when the Z-value of a CEF is lower than -1 and the transaction costs are below 5 percent. 

The short positions are opened if the Z-value of a CEF is above 1 and the transaction 

costs are below 5 percent. The long and short position opening is also based on Z-value 

ranking, i.e., lowest (long) and highest (short) Z-value CEFs prioritized in the position 

opening. The maximum amount of long positions is 3 and 2 for short positions, and there 

cannot be duplicate positions simultaneously. As the positions are opened, they are held 

in the portfolio until the position closing criteria is fulfilled. The long positions are closed 

(replaced by a new CEF) when the Z-value is higher than -0,5 and the short positions are 

closed when the Z-value is lower than 0,5.  

 

Table 3 Overview of the 3 market tactic strategies and 3 market strategies 

 

 

The 3 market tactic strategies are constructed based on the trading rules presented in 

table 2, but the amount of long and short positions varies between the 3 strategies. The 

detailed contents of all the strategies can be seen in table 3 above. The tactic 1 includes 

5 constantly active positions (3 long & 2 short). The tactic 2 includes 3 constantly active 

positions (2 long & 1 short). The tactic 3 includes 2 constantly active positions (1 long & 

1 short). The 3 market strategies (buy & forget) are included in the analysis to research 

the returns of the CEFs market. The buy and forget 1 is constructed from all the 108 

selected CEFs and it is used as a market index in this study. The buy and forget 2 is con-

structed from the five best performing (cumulative return) CEFs. The buy and forget 3 is 



39 

constructed from all the CEFs which are used in the 3 market tactic strategies. In all of 

the 3 market tactic strategies and the 3 market strategies the positions are equally 

weighted, i.e., the weight of an asset is calculated by 1 divided by the number of assets. 

 

6.4 Trading analysis formulas and variables 

The trading analysis of the market tactic strategies is based on 4 variables: Z-score, trans-

action costs, returns, and financial indicators. Only the first 3 variables are needed to 

construct the 3 market tactic strategies based on the CEFs mispricing mean reversion 

and the financial indicators are needed to compare the results between the market tactic 

and the market strategies. The Z-value is the most crucial variable of the trading analysis, 

since it is used to define the position opening and closing criteria. In this study the Z-

value variable defines how many standard deviations the CEF mispricing observation is 

from the CEF mispricing long-term average. Therefore, each of the 108 CEFs has a unique 

long-term average mispricing and unique Z-values for all the observations.  

 

  � 2 ����� = GHI

J
       (7) 

 

Where,  

X = Mispricing coefficient 

¿ = Mean (CEF specific) 

à = Standard deviation (CEF specific) 

 

The transaction costs are estimated using the bid-ask spread obtained from the Bloom-

berg data. The bid price represents the demand and ask price represents the supply for 

an asset. The difference between the demand and the supply can be used to estimate 

the transaction cost at time t.  

 

 �����������	����� = &'K	;2,:(HL,$	;2,:(

&'K	;2,:(
    (8) 



40 

The CEFs returns are calculated using the current and original price of the CEF. The re-

turns for short positions are calculated by one divided by the long return. Net returns 

are calculated by deducting transaction costs from returns.  

 

 ������ = MN!	:"22(#)	;2,:(	HMN!	32,8,#-/	;2,:(

MN!	32,8,#-/	;2,:(
   (9) 

 

The financial indicators to compare the results of the 3 market tactic strategies and the 

3 market strategies are cumulative return, average annual return, standard deviation, 

reward to risk ratio, sharpe ratio and alpha. The cumulative returns are calculated by 

multiplying the holding period returns (HPR) of the period. The average annual returns 

are calculated from the yearly cumulative returns. The standard deviation is calculated 

using the HPRs. The reward to risk ratio is evaluated by comparing the average annual 

return and the standard deviation. The key financial indicators to evaluate the strategies 

performance are the sharpe ratio and the alpha. The sharpe ratio is similar to reward risk 

ratio but it takes also the risk-free rate into account. The sharpe ratio describes the risk-

adjusted return of the strategy. The alpha measures the excess return of the strategy in 

comparison to the market index. In all of the alpha calculations the beta coefficients are 

re-evaluated according to the circumstances of the strategy.  

 

 �/����	����� = &O(2-8(	-##"-/	2()"2#H2,'K	42((	2-)(

5)-#$-2$	$(O,-),3#
   (10) 

 

 ���/� = �; 2 (�4 + �Q�1 2 �4R)    (11) 

 

Where, 

Rp = Portfolio return 

rf = Risk-free rate 

rm = Market return 

³ = Portfolio beta 



41 

6.5 Trading analysis financial indicators and regression model 

The results of the trading analysis are reviewed using financial indicators and a regres-

sion model. First the financial indicators between the 3 market tactic strategies and the 

3 market strategies are compared to see how the results differ between the CEFs mis-

pricing mean reversion and the buy and hold based strategies. Secondly to research if 

the CEFs mispricing mean reversion-based market tactic strategies are able to generate 

statistically significant and positive alpha in order to reject the hypothesis one.  

 

 ������	�, = 	� + � 7 ������	�, + �, 	    (12) 

 

Where,  

Tactic R = Return from the tactic strategy (dependent variable) 

³ = Intercept (alpha) 

³ = Regression coefficient (measuring market effect to tactic returns) 

Market R = Return from the market index (independent variable) 

 

The statistical significance is evaluated using a simple OLS regression model. Regressions 

are conducted where the HPRs of market tactic strategies are compared to the HPRs of 

market index (buy & forget 1). The objective of the regression model is to find statistically 

significant and positive alpha (intercept) coefficient implying that the returns within the 

market tactic are systematically higher compared to the market index.  

 

6.6 Robustness checks  

The robustness checks of this study include 3 tests: 1. tests with different data intervals 

(weekly data), 2. tests with specific time sample, and 3. tests with robustness indicators. 

All the 3 tests are carried out in both of the analyses. The objective of these tests is to 

ensure the data quality and applicability, and to show that results from the analyses are 

reliable. In the first and the second tests the objective is to generate similar results with 

different data intervals and specific time periods. The robustness indicators role is to 



42 

show that the results from the analyses are reliable. The used robustness indicators are 

Durbin-Watson Test (DWT) to test autocorrelation, Variance Inflation Factor (VIF) to test 

multicollinearity, Newey-West Method (NW) to re-evaluate statistical significance, and 

Breusch-Pagan (BP) to evaluate the heteroskedasticity. In the mispricing analysis the 

used robustness indicators are DWT, VIF, and NW. In the trading analysis the used robust-

ness indicators are DWT, NW and BP. The robustness tests of the trading analysis include 

also an additional test of what returns would an EMH based trading strategy generate. 

 

The error term test of autocorrelation are carried to ensure that the error terms are not 

dependent on time i.e., past time error terms can affect the current time error terms. 

The autocorrelation test is performed by using the Durbin-Watson-test (DWT). The result 

of the test varies between zero and four, and if the result from the test is 2= no autocor-

relation, <2 = positive autocorrelation, >2 negative autocorrelation. If the results is sig-

nificantly divergent from the value of 2 there can be sign of autocorrelation.  

 

  ��� =
3 (( H( )

3 (
      (13) 

 

Where,  

e t = Error (residual) at time t 

et-1 = Error (residual) at previous time  

n = Amount of observations 

  

Multicollinearity tests of variance inflation factor (VFI) are performed to ensure that 

there are no multicollinearity between the independent variables. The VIF test evaluates 

how significantly how significantly the variance of one variable is linked to other varia-

bles in the model. More detailed, a regression is conducted where 1 independent varia-

ble is used as a dependent variable and all the others are used as explaining variables. If 

the VIF is equal to 1= variable is not correlated with other variables, if the VIF >1= varia-

bles is correlated with other variables, and if VIF > 10 = variable is strongly correlated 

with other variables.  



43 

  ���S =
@

@HT
        (14) 

 

In case the robustness tests generate signs of statistically unreliable data, the Newey-

West (NW) corrections are applied to re-evaluate the statistical significance. The NW 

correction formula can be seen below. The NW correction calculates a new standard er-

ror for the data which can be used to re-evaluate the statistical significance.  

 

�� = Q�´�R
H@
Q3 �)D#

)?@ �)�)´ + 23 �S 3 �)�)HS�)�)HS
´#

)?SV@
+
S?@ RQ�´�R

H@
 (15) 

 

The heteroskedasticity is evaluated using Breusch-Pagan (BP) tests. The BP tests are ap-

plied to detect the error term variance variation since heteroskedasticity can lead to un-

reliable statistical significance.  

 

  �� = �	�	�D        (16) 

 

Where,  

n = amount of observations 

R2 = regression r-square 

 

The EMH based trading strategy is built on the assumptions of the EMH, and it includes 

the same characteristics as the other market tactics. The positions are opened based on 

the highest mispricing value and positions are closed as the mispricing reverts to zero as 

the EMH claims. The EMH based strategy will face significant issues as there are basically 

none 0 mispricing values, since the concept of the EMH does not work in practice. There-

fore, to simplify if the mispricing coefficient of a CEF reverts from negative to premium 

or vice versa the position is closed. The strategy includes only long positions as the EMH 

expects the mispricing always to recover back to zero.  



44 

7 Mispricing analysis results 

This section reviews the results for the CEFs mispricing analysis. The objective of the 

analysis is to show that the CEFs are systematically mispriced, and to reject the null hy-

pothesis: <There is no statistically significant mispricing within the CEF market=. Secondly 

if the null hypothesis can be rejected to research if there are any CEF-specific or macro-

economic factors which can explain the mispricing of the CEFs. In the end the statistical 

significance of the findings is tested by robustness tests.  

 

7.1 Descriptive statistics 

The descriptive statistics of the CEFs mispricing are presented below in table 4. The de-

scriptive statistics are based on the monthly data of the 108 US listed CEFs during the 

studied period of 2002-2019. The data is based on the values after the one percent mod-

ified winsorizing. In the table 4 the CEFs are arranged to categories based on the used 

CEF-specific variables of the study. The used variables are all CEFs, asset class, leverage 

status, and location.  

 

Table 4 Descriptive statistics for CEFs mispricing 

 

 



45 

The mean refers to the average mispricing of the CEFs. The mean is negative for all the 

categories indicating significant discounts among the CEFs. For all the CEFs the mean is  

-5,11 percent. From the categories the equity CEFs have the lowest mean of -7,27 per-

cent and the fixed income CEFs have the highest mean of -3,94 percent. Overall, the 

statistics for mean did not change substantially due to the modified winsorizing process. 

Before the modified winsorizing process, the mean ranged from -3,53 percent to -7,00 

percent, being -4,78 percentage for all the CEFs.  

 

Based on the means in table 4 it seems that there are differences between different 

categories mispricing. A simple two-tailed t-test applied to research if there are statisti-

cally significant differences between the three variables mispricing. The t-test generated 

statistically significant p-values for all the three groups at 0,1 percent significance level. 

Indicating that in there are significant differences between the variables mispricing, 

which is a good sign for the upcoming explaining factors regression model analysis. The 

difference in the means seems logical since e.g., the equity CEFs can be viewed more 

riskier compared to fixed income CEFs.  Also, the CEFs investing to foreign countries can 

be more discounted than the CEFs investing to USA since foreign financial markets can 

be viewed more riskier and less transparent compared to the liquid US financial markets.  

 

Also, the median is negative for all the categories, being -6,28 percent for all the CEFs. 

The range of median is from -4,90 percent to -9,50 percent. The relation between the 

mean and the median is interesting since all the medians are 1-2 percents lower than 

the means. Implying that most of the observations locate close to median and are lower 

than the mean but there are also higher values which increase the mean compared to 

the median. The sample median did not change radically after the modified winsorizing.  

 

The standard deviation ranges from 0,07 to 0,09 between the categories. For all the CEFs 

the standard deviation is 0,08. Referring that the observations differ on average 8 per-

cents from the mean. The relatively high standard deviation compared to the mean in-

dicates that mispricing varies considerably between the CEFs. The variation of standard 



46 

deviations between the categories is low, implying that the variation is not linked to CEF-

specific factors but rather to market factors or CEFs mean reversion. The modified win-

sorizing decreased the standard deviation for all the categories. In the original data the 

standard deviation for all the CEFs was 0,10. In normal distribution 68 percent of the 

observations are within one standard deviation from the mean, the equivalent number 

for the CEFs mispricing data 72 percent. Overall, the observations in the CEFs data re-

semble normal distribution. 70 percent of the observations have values between -13 

percent and 3 percent. Prior to the modified winsorizing the distribution was more cen-

tralized, and 80 percent of the values were within one standard deviation from the mean. 

After the transformation the distribution is better and suitable for the regression model. 

 

The minimum values for the categories vary from -23,94 percent to -18,35 percent and 

the maximum values for the categories vary from 30,90 percent to 31,14 percent. Mini-

mum and maximum values illustrate that the mispricing varies significantly in all the cat-

egories, but the radical values are similar between the categories. Prior to modified win-

sorizing the minimum and maximum values were substantially higher. As the one per-

centage tail values were deleted from the data these figures naturally decreased.  

 

The skewness indicates whether the distribution is asymmetric and to which direction. 

The skewness ranged from 0,84 to 1,97, being 0,91 for all the CEFs. The positive values 

for skewness indicate asymmetric distribution where the right tale is a bit longer and 

includes more diverging values compared to the left side. The skewness is relatively close 

to normal distribution. As all the means for different categories were negative the finding 

that the distribution is skewed to the right is logical. Since the skewness is positive also 

the mean should be higher than the median. Prior to modified winsorizing the skewness 

variables ranged from 1,85 to 3,97, being 2,61 for all the CEFs. With the transformation 

the values of skewness decreased, but the original direction of skewness was maintained.  

 

The kurtosis indicates how sharply pointed or flat the distribution is compared to the 

normal distribution. The range for kurtosis is from 1,41 to 5,96, being 1,65 for all the 



47 

CEFs. The excess kurtosis for all the CEFs is slightly negative, but relatively close to the 

equivalent value of normal distribution. The low positive kurtosis denotes that the dis-

tribution has wider tails and lower peak compared to normal distribution. As the obser-

vations are viewed visually the distribution reminds a copy of normal distribution. In the 

original data kurtosis was substantially higher and one of the main reasons to execute 

the transformation. In the original data the range of kurtosis between the categories was 

from 7,18 to 33,42, being 17,53 for all the CEFSs. The fact that leveraged CEFs still have 

a relatively high kurtosis has to be accepted and it is due to the low observation amount.   

 

Overall, the most important finding from the descriptive statistics and examples from 

the data is that the CEFs are on ave