We study a simple model in which arbitrageurs trade assets in infinitely repeated stages and a financial crisis may occur due to redemption requests of investors on arbitrageurs. If the asset is undervalued, the arbitrageurs buy the asset to make profits. But the mispricing may become even larger in the next period and the arbitrageurs will take huge losses temporarily. Even though the asset price will recover its fundamental value in the end, the temporary losses of the arbitrageurs can force the arbitrageurs to liquidate the funds due to the redemption requests and stay away from the market in all the subsequent stages. Thus, patience of arbitrageurs (the relative weight to the future profits) affects possibility of a financial crisis. This paper shows two properties on the discount factor. First, a financial crisis without external shocks can arise only when arbitrageurs are impatient, and second, if such a crisis may arise, high patience of arbitrageurs mitigates the crisis but enlarges the pre-crisis mispricing. The model setup mimics the modern financial markets and some of them may be viewed as market frictions which prohibit market efficiency. The simplicity of the model allows a closed-form solution.

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Many theories, experiments, and survey studies suggest that investors are ambiguityaverse, thereby implying the existence of a positive ambiguity premium [Please check whether this revision conveys your intended meaning. If not, please suggest a suitable alternative.]. However, some empirical studies suggest contradictory results. Baltussen, Bekkum, and Grient (2018) use the volatility of implied volatility as a proxy for ambiguity and find a negative correlation between the volatility of implied volatility and expected returns. This negative correlation is inconsistent with the theories of Epstein and Schneider (2008) and Klibanoff, Marinacci, and Mukerji (2005),which state that investors’ demand for ambiguity premiums in the stock market depends on their ambiguity avoidance. That is, while most extant theoretical studies on ambiguity suggest a positive correlation between ambiguity and expected returns on stocks, most empirical studies rarely prove this relationship. This study analyzes whether there is a significant correlation between ambiguity and expected stock returns in the Korean stock market and also empirically analyzes whether there exists a positive ambiguity premium. In the financial sector, asset-pricing models such as a capital asset -pricing model (CAPM) are based on various assumptions about the distribution of stock returns. For example, a CAPM assumes that stock returns follow a multivariate normal distribution. Many empirical studies, however, question the type of probability distributions of stock returns (Fama, 1965; Rosenberg, 1974; Tsay, 2010); they suggest that the probability distribution of stock returns does not follow a normal distribution, and are even skeptical about whether such a distribution exists. In particular, Knight (1921) argues that ambiguity is defined as the uncertainty about the location and shape of a probability distribution. Ellsberg (1961) and Camerer and Weber (1992) also note that Knightian uncertainty or ambiguity is generally defined as uncertainty about distribution. Thus, the degree of uncertainty in a distribution is directly related to Knight’s (1921) ambiguity definition. If the recent distribution of stock returns unexpectedly differ from those in the past, the investor must pay a higher cost to better understand the difference between the recent and the past probability distribution of returns. Therefore, he/she will require higher premiums to hold these stocks. The main goal of this study is to empirically analyze whether there is a premium for the ambiguity of stock returns at the individual firm-level. To estimate investors’ difficulties in understanding distributions of stock returns, this study presents the Kolmogorov-Smirnov (KS) and Kuiper (K) statistics, which measure the difference between the probability distribution of recent stock returns and those of past returns as a proxy for the ambiguity of stock returns. The results show that high-ambiguity stocks in the probability distribution of returns earn, on average, higher returns. An investor who is averse to high-ambiguity stocks demands a premium for that stock, thereby increasing his/her expected returns of the stock. This study examines whether such an ambiguity premium exists in the Korean stock market, and demonstrates that high-ambiguity stocks in return distributions lead to, on average, higher returns. We also find that the difference between the returns for portfolios with the highest and lowest distribution uncertainty is significantly positive. The bottom decile portfolio (S) by KS shows expected average monthly returns of 0.11%, and the top decile, 3.26%. When forming decile portfolios by K, stocks (S) with the least distribution uncertainty provide 0.07% of the expected average monthly average returns, and the stocks (B) with the most distribution uncertainty, 3.22%. In terms of value-weighted average returns, the V-W average returns for portfolios with the most distribution uncertainty are substantially higher. Using Fama and French’s (2015) five-factor model, we show that our measures for distribution uncertainty are highly correlated with alphas estimated from five-factor specifications. The magnitude of the alphas is positively related to the level of distribution uncertainty, implying that high distribution uncertainty portfolios earn more positive abnormal returns. The alphas of the B-S spread are significantly positive. As a result, the Kolmogorov-Smirnov (KS) statistic and the Kuiper (K) statistic are correlated with future stock returns. To determine the robustness of the empirical results, we extensively investigate whether the effect of distribution uncertainty persists after controlling for firm characteristics such as beta, size, book-to-market ratio, momentum, short-term reversal, and illiquidity. Overall, the results from these robustness tests using alternative measures of distribution uncertainty still support our hypothesis. Moreover, the results remain significant even after controlling for the characteristics of the distribution of returns, such as intrinsic volatility, skewness, kurtosis, and maximum returns. Next, we examine the cross-sectional relationship between distribution uncertainty and expected stock returns at the firm level using Fama-MacBeth (1973) regressions. The results show a significant correlation between the degree of distribution uncertainty and expected returns even after controlling for a variety of other firm-level variables. Our findings demonstrate the existence of ambiguity premiums in the Korean stock market.

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Using an investor sentiment index and an index of sentiment changes for the Korean stock market, this study examines how investor sentiment affects a cross-section of stock returns. I examine whether more speculative and harder-to-arbitrage stocks are more sensitive to sentiment, that is, whether their returns co-move more with sentiment changes. I also test whether the returns on extremely unspeculative stocks are negatively related to changes in sentiment, that is, whether they have negative sentiment betas. According to studies on behavioral finance (Shleifer and Summers, 1990; Lee, Shleifer, and Thaler, 1991), because a mispricing is the result of an irrational demand shock in the presence of a binding arbitrage constraint, shifts in investor sentiment have cross-sectional effects when sentiment-based demands or arbitrage limits vary across stocks. Consistent with these predictions, prior empirical studies (Baker and Wurgler, 2006, 2007; Kumar and Lee, 2006) report that more speculative and harder-to-arbitrage stocks—smaller, newer, more volatile, unprofitable, non-dividend paying, distressed or those with extreme growth potential—are more likely to be affected by shifts in investor sentiment. However, the effect of sentiment on the aggregate market is somewhat less clear. Brown and Cliff (2004) show that sentiment has little predictive power for near-term future stock returns, and Schmeling (2009) insist that the effect of sentiment on aggregate stock returns is observed only in the countries that are culturally more prone to herd-like behavior. To reconcile the cross-sectional results and the aggregate results, Baker and Wurgler (2007) suggest one possible explanation known as “the sentiment seesaw,” in that if sentiment fluctuations induce demand shifts between speculative stocks and safe stocks, that is, “the flights to quality within the stock market” occur, the low (high) sentiment reduces (increases) the prices of speculative stocks and at the same time increases (decreases) the prices of safe stocks, resulting in no effect of sentiment on aggregate market returns. In line with this idea, this study analyzes the effect of broad-waved sentiment on a cross-section of stock returns in terms of sensitivity to sentiment. Using financial parlance, I investigate whether more speculative and harder-to- arbitrage stocks have higher sentiment betas, and whether extremely unspeculative and easier-to-arbitrage stocks have negative sentiment betas. As in practice, the same securities that are most sensitive to speculative demands also tend to be the costliest to arbitrage, I hypothesize that stocks most sensitive to investor sentiment are those of companies that are smaller, more volatile, have less tangible assets, are unprofitable, are distressed, and have the potential for extreme growth. At first, I construct the monthly sentiment index and the monthly index of sentiment changes for the Korean stock market based on principal component analysis using five key sentiment proxies: the volatility premium, KSE share turnover, IPO volume, IPO first-day returns, and the proportion of companies with seasonal equity offering. To increase the reliability of the indices and their comparability with international research, I develop these sentiment indices in line with those of Baker and Wurgler (2006, 2007). Using these indices and the monthly returns of all of the common stocks of the KOSPI market from 2000 to 2017, I analyze the effect of the changes in investor sentiment on a cross-section of stock returns. I start by forming equalweighted decile portfolios based on several firm characteristics such as firm size, MTB, idiosyncratic volatility, total volatility, asset tangibility, profitability, sales growth, and Rand D ratio, and look for patterns in changes in average returns across deciles when the investor sentiment index changes from +1σ to -1σ. I also consider a regression approach that allows controlling for the Fama-French (1993) factors and the Carhart (1997) momentum factor. I regress the returns of each decile portfolio and the returns of various high-minus-low portfolios on the index of sentiment changes, respectively. Consistent with my prediction, I find that the stocks with high MTB ratio, high volatility, low PPE ratio, low profitability, and low sales growth, respond more sensitively to changes in investor sentiment than the stocks with low MTB ratio, low volatility, high PPE ratio, high profitability, and high sales growth. In other words, the more speculative and harder-to-arbitrage stocks have higher sentiment betas. The returns of stocks with extremely low MTB ratios and low volatilities are negatively related to changes in sentiment. That is, most bond-like stocks appear to have slightly negative sentiment betas. These findings are consistent with those of prior studies. As the Korean stock market is an individual-crowded and highly integrated market, it is a good test bed for studying issues related to investor sentiment. Using Korean stock market data, my findings shed light on the effect of investor sentiment on a cross-section of stock returns in theory and can help practitioners establish a profitable investment strategy using investor sentiment.

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The puzzle posed originally by Mehra and Prescott (1985) on the asset pricing model of Lucas (1978) consists of two parts: When asset returns predicted by the model are compared with their historical averages, the equity premium is too small and the risk-free rate too large. These phenomena are referred to as the equity premium puzzle (henceforth, Puzzle I) and the risk-free rate puzzle (henceforth, Puzzle II), respectively. Dokko, Park, and Cho (2001: henceforth, DPC) examine these puzzles in the Korean market using annual data from 1975 to 1999, and conclude that while Puzzle I is very weak, Puzzle II is quite strong. In this paper, we re-examine these issues by extending their study in the following three directions: (i) We use quarterly data instead of annual data to enlarge the sample size. (ii) We use the sample data during the 1999–2017 period, considering that a paradigm shift has taken place in the Korean economy after the 1997 “currency crisis.” (iii) Most importantly, besides the time-additive expected utility and the non-expected utility of Epstein and Zin (1989) used in DPC, we adopt five additional utility functions to explore their usefulness in resolving each puzzle. We take two approaches to this study. First, following Kocherlakota (1996), we perform statistical tests directly on the Euler equation that asset returns must satisfy in equilibrium. Second, we apply a calibration method in which closed-form solutions (or their approximations) of asset returns are compared to their historical averages. The results of the two approaches are, by and large, consistent in each of the cases of the seven utility functions that we consider. We make the following observations. In Mehra and Prescott’s basic model, the existence of Puzzle I in Korea is now apparent in the acceptable range of the relative risk aversion coefficient (2-6). The main reason for this may be that the equity premium has increased sharply over the last twenty years. Puzzle II is even stronger, as the risk-free interest rate has fallen significantly. These results, contrasted with those of DPC, are confirmed by several robustness check analyses. The non-expected utility function of Epstein and Zin (1989), in which relative risk aversion is constant with γ, makes no difference with respect to Puzzle I as the equity premium is determined independently of intertemporal substitution. However, it can alleviate Puzzle II substantially if the intertemporal substitution parameter ρ is small. Our estimation of ρ using Korean data shows that it is between 0.252 and 0.887. In this range, the risk-free rate predicted by the model is close to its historical average. The nonexpected utility function with constant absolute risk aversion (CARA) has the potential to substantially increase the equity premium significantly. As CARA is translated into increasing relative risk aversion, it makes a high degree of relative risk aversion acceptable. For the same reason, it decreases the risk-free rate further, compared with the preceding utility function. The non-expected utility function exhibiting ambiguity aversion can also be useful in explaining both puzzles. Under certain conditions, the ambiguity aversion parameter η replaces the role of γ in the Epstein and Zin utility function. As ambiguity aversion is, by definition, η > γ, it serves to enhance risk aversion if γ is kept reasonably low, which leads to higher equity premiums and lower risk-free rates. However, given that the empirical magnitude of η is unknown, the usefulness of this utility function is quite restrictive. Merits of the habit formation utility function vary with how habits are specified. A multiplicative external habit model using contemporaneous consumption helps explain Puzzle II, because the pricing kernel in this case becomes unity under log utility ( γ = 1). If  equals one, however, it will weaken Puzzle I. A multiplicative external habit model using lagged consumption weakens Puzzle II substantially, while Puzzle I remains intact. Inherently, it has the effect of magnifying the utility discount factor, which reduces the risk-free rate. An additive external habit model using lagged consumption has a channel to resolve both puzzles simultaneously. A strong consumption habit increases the volatility of the pricing kernel, and also its mean, which raises the equity premium and lowers the risk-free rate. This model, however, has one shortcoming, in that the risk-free rate can easily be negative as the mean of the pricing kernel exceeds one if the consumption habit crosses a certain threshold. In sum, except for the time-additive expected utility, each utility function that we consider can be useful for at least a partial resolution of the two puzzles found in Korea. In particular, the non-expected utility with the CARA model, the ambiguity aversion model, and the additive external habit model have the potential to simultaneously alleviate both puzzles. Among these, the non-expected utility with the CARA model seems to be the most successful, as the explanatory power of the remaining models is rather limited.

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This study is the first to thoroughly investigate the effect of subordinated debt issuance on commercial banks’ profitability and insolvency risk as well as the effect of the Basel III capital framework on this relationship. This study empirically examines the subject of interest by using random-effects panel- data models after controlling for potential determinants of bank profitability and insolvency risk. The Basel III framework, established by the Basel Committee on Banking Supervision (BCBS) and first introduced in 2010, provides reinforced regulatory standards on capital requirements, leverage measurements, and liquidity measurements for the banking sector (BCBS, 2010; Eubanks, 2010; Financial Supervisory Service, 2012). Specifically, the capital framework includes increased minimum capital adequacy ratios, and owing to this, the effect and importance of subordinated debt, a type of debt capital recognized as Tier 2 capital, have changed. However, despite this change in the role of subordinated debt in the banking sector, academic and empirical investigations of this debt are lacking. Our study fills this gap. We analyze the relationship between subordinated debt and banks by using a random-effects panel-data analysis method. Our sample data, ranging from 2001 to 2018, are an annually collected dataset from the six commercial banks that currently operate in the Korean banking sector. We proxy bank profitability using the return on assets (ROA) and the return on equity (ROE), and insolvency risk using the distance-toinsolvency Z-score (Boyd and Graham, 1986; Hannan and Hanweck, 1988). We examine the effect of subordinated debt issuance after controlling for other potential determinants of bank profitability and insolvency risk, including banks’ financial ratios, industry- relevant variables, and macroeconomic factors (Athanasoglou et al., 2008). The results of the analyses suggest that subordinated bond issuance negatively affects bank profitability and insolvency risk. The profitability models use either ROA or ROE as the response variable and show that increases in the growth rate of subordinated debt reduce bank profitability. Furthermore, our study considers the interaction between the subordinated debt variable and a dummy variable for Basel III adoption that takes a value of one after 2013, and zero otherwise. We find that the coefficients of the interaction terms are positive for all estimated models, indicating that the negative effect of subordinated debt issuance on bank profitability was substantially mitigated after 2013, when the Basel III accord was first implemented. We also investigate whether the size of previously issued subordinated debt influences the relationship between bank profitability and the issuance of such debt. We measure the relative size of subordinated debt held by a bank as the ratio of subordinated debt to the total debt in period t-1 and sort it into four subgroups based on its quartiles. We find that issuing this debt negatively affects profitability for all subgroups except the subgroup with the largest relative size of subordinated debt, suggesting that banks are not significantly affected by the issuance of additional subordinated debt when they have already issued a sufficiently large amount of subordinated debt relative to their total debt. The Z-score models use the distance-to-insolvency Z-score as the response variable and show that an increase in the growth rate of subordinated debt decreases (increases) the Z-score (insolvency risk). We include the interaction term between subordinated debt issuance and the dummy variable for the adoption of the Basel III regulation in the models. We find that the negative effect of subordinated debt issuance on bank insolvency risk was mitigated after 2013. This finding can be interpreted as resulting from either the enhancement of the integrity of banks’ capital structures after the Basel III regulation or the fact that banks are encouraged to only issue subordinated debt that conforms to reinforced regulation. Finally, we analyze the specific mechanism for the relationship between subordinated debt issuance and bank performance. We find that the growth rate of subordinated debt positively affects banks’ interest costs, indicating that issuing subordinated debt increases banks’ interest costs. We also find that interest costs significantly decrease concurrent profitability and increase concurrent insolvency risk. These results empirically support the hypothesis that subordinated debt issuance incurs costs to banks owing to the relatively high interest rate and can negatively affect bank performance, as prior studies theoretically suggest (Blum, 2002; Kim, 2000). The empirical analyses in this study provide information not only for investors and decision-makers in banks but also for supervisory authorities and policymakers regarding the issuance of subordinated debt. Furthermore, the research methodology used in this study is convenient and practical in that the model uses the financial ratios of banks, industrial variables, and macroeconomic factors that are easily accessible and uses the Z-score as a proxy for bank insolvency risk. Thus, the Z-score can be utilized for insolvency risk analyses in research environments in which the conventional panel logit model is not applicable.

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