## Past Issues

Asian Review of Financial Research / November 2010 Vol. 23 No. 4

### The Effect of Macroeconomic Characteristics on Credit Risk : A Case of Small and Medium Sized Enterprises

Asian Review of Financial Research :: Vol.23 No.4 pp.327-366

AbstractIn line with Basel Ⅱ capital guidelines financial institutions have developed internal credit rating systems to mainly assess credit risk. Meanwhile, ever since introduced in Ohlson(1980)'s seminal paper, conditional default probability models, such as logit and probit, have been universally adopted as a standard credit risk model while neglecting significant theoretical progresses that have been made in this field in the recent years. Further, for nearly half a century since Altman(1968) the older model has been also actively utilized in evaluating firms' financial information as a way to gauge the default risk. Meanwhile, credit theories claim that credit risk is likely to be influenced by macroeconomic environments. In fact, a large body of literature has provided evidence that credit risk is closely related to the state of an economy. If it is really so, then we should take into account salient macroeconomic characteristics as the determinants of credit risk in order to accurately evaluate systematic risk. However, it is difficult for a static default probability model based merely on cross-sectional accounting information to fully account for credit risk dynamics affected by volatile business cycles. Moreover, there has been no consensus established on what financial ratios should be benchmarked in making default prediction in spite of empirical evidences. For these reasons, this paper empirically examines how macroeconomic characteristics as well as firm-specific factors are being used to evaluate credit risk through random effect probit model. To do this, we looked into an unbalanced panel data set of small and medium-sized enterprises(henceforth, SMEs) for a 10 year period of 1997 to 2006. In addition, it is important to note that previous research has not fully delved into the effect of firm age on credit risk while credit risk is known to be largely dependent on firm duration. In this regard, the default probability model can be useful in identifying default and non-default firms as well as the factors contributing to firm failures; however, such framework does not reveal much information about the timing of a default. To improve on these potential short comings, the Cox proportional hazard model and the Kaplan-Meier survival analysis were performed to demonstrate whether credit risk would actually depend on firm duration. However, the Cox model is still vulnerable to the censored data problem. Thus, Cox regression was applied to start- up firms' sub-samples from 2000 to 2006. The accounting dataset is obtained by Korea Credit Guarantee Fund and Korea Enterprise Data Co., Ltd. The main results of empirical analysis can be summarized as follows: First, utilizing quarterly data for the period between 1990Q1 and 2008Q4 we estimated cross-correlation coefficients, which is to shed light on the relation between macroeconomic variables and loan default. Loan default is proxied by the default amount of loans guaranteed by Korea Credit Guarantee Fund. We found out that loan interest rates, government bond yields, and term structures rather than inflation and unemployment rates are closely related to loan default. Second, most financial data pertaining to idiosyncratic risk factors appear to be statistically significant in both probit and Cox regressions, including: sales growth; cash ratio calculated as cash and cash equivalents divided by total assets less cash and cash equivalents; profitability ratio defined as EBIT divided by total assets; and solvency ratio proxied by equity capital as a percentage of total assets. They are, in fact negatively related to default probability even after controlling for firm size and industry as well as time effects. This result suggests that companies with healthier financial status are less likely to go default on their debts. Third, some of macroeconomic factors which are often blamed for being drivers of systematic risk fail to properly function in the assessment of default probability for SMEs. Nevertheless, empirical results revealed that models with variables representing financial market conditions, such as government bond yields, loan interest rates, KOSPI, and foreign exchange rates, are more significant factors for estimating default probability than other macroeconomic factors such as real GDP and inflation proxied by growth rate of consumer price index. The results using lagged macroeconomic variables are fairly similar to the former. In short, macroeconomic characteristics appear to be salient in assessing macroeconomic condition but probit models with macroeconomic variables are inferior to those with time dummy variables as compared with pseudo R-squared. Fourth, we find that there exists a negative relationship between credit risk for SMEs and their firm ages in Korea. The Kaplan-Meier analysis shows that a hazard rate steeply increases over time during the first 4 years of a firm life. Afterwards, hazard rate decreases, resulting in a hump‐shaped curve with time. Through the survival analysis we could also find out that a non-linear relationship exists between hazard rate and firm age. This evidence supports the empirical results of Bonfim(2009). Finally, the larger firm size is or/and the more collateral increases, the less credit risk increases. Firm size is defined as the logarithm of total assets and collateral as the share of tangible assets on firms' total assets. Empirical results from the Cox model show that profitability ratios and collaterals are more useful than macroeconomic factors on default probability measurement of start-up firms. Of other factors, government bond yield is positively correlated with credit risk in start-up SMEs. From these findings, it may be safer for us to conclude that both macroeconomic characteristics and firm- specific factors play important roles in estimating default probabilities for SMEs. It is worthwhile to note that our study resulting from an extensive accounting data set of more than 21,000 SMEs minimizes the likelihood of sample selection bias which is one of the drawbacks of prior default prediction models.

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### Value at Risk Using Generalized Extreme Value Distribution Implied in the KOSPI 200 Index Options

Asian Review of Financial Research :: Vol.23 No.4 pp.367-404

AbstractBased on Harrison and Pliska(1981)'s no arbitrage equilibrium theory, Markose and Alentorn(2005) introduced an original analytical closed form solution for generalized extreme value distribution (GEV) in the European options. They showed that the three parameter GEV based risk-neutral density function for asset returns has great flexibility in defining the tail shape implied by traded option price data. They also found that the GEV option pricing model not only accurately captures the negative skewness and higher kurtosis of the implied risk neutral density but also delivers the market implied tail index that governs the tail shape. Hence, the model allows accurate estimation of the risk neutral density function by including extreme values and fat tails. Meanwhile, Aït-sahalia and Lo(2000) and Panigirtzoglou and Skiadopoulos(2004) have argued that Economic VaR, calculated under the option market risk neutral density, is a more relevant measure of risk than historically based VaR. Economic VaR can be seen as a forward looking measure to quantify market sentiment about the future course of financial asset prices whereas historical or statistically based VaR is backward looking based on the historical data. Thus, in this paper adjusting Markose and Alentorn (2005)'s closed form solution to improve the model stability for in-sample-fit and out-of-sampling pricing, we empirically investigate the usefulness of the adjusted GEV model implied in the KOSPI 200 index options prices in terms of effectiveness for value at risk(VaR). As benchmark models, we use two-lognormal mixture model(TLM) and variance-gamma model(VG) as well as Black-Scholes model(BS). Because TLM is the weighted sum of two Black-Scholes solutions, the model can relax the assumption of the lognormal distribution. And variance gamma process is obtained by evaluating the Brownian motion at a random time change given by a gamma process. So variance-gamma model can relax the assumption of the geometric Browian motion. As time-series model for comparative analysis, we use not only normal model but also GJR-GARCH model which can reflect the presence of excessively fatter tails and pronounced skewness, reflecting strong volatility clustering. To estimate parameters for each option pricing model, the non-linear least squares approach is applied to minimize the sum of squared errors between the model and the market prices. As for the back-testing of value at risk, we examine the number of violations, mean violation, and maximum violation. For the statistical testing of the performance, the frequency tests of Christoffersen's conditional back-testing procedures are examined. The Christoffersen approach enables us to test both coverage and independence hypotheses at the same time. Moreover, if the model fails a test of both hypotheses combined, this approach enables us to test each hypothesis separately so as to establish where the model failure arises. The hypothesis of unconditional coverage means that the expected frequency of observed violations is precisely equal to observed violation. The hypothesis of independence means that if the model of VaR calculation is valid, then violations must be distributed independently. We also wonder whether it is helpful to eliminate the non-tail information, in which case we consider the whole return distribution equality tests by using the Berkowitz methodology. In this way, we aim to investigate whether the estimated densities are equal to the true densities not only in the tails of the density but also in the full range area of the density. Back-testing results of VaR show that, of all the models, GEV yields the least number of violations for the industry standard for 10 day VaR at the high confidence level of 99%. Because the risk-neutrality assumption was strongly rejected by the market data due to the second state variables such as the negative risk premium for the stochastic volatility and jump fear, the preference for moments of higher order than the variance, heterogeneous beliefs and risk preferences and market inefficiency and imperfections, call option prices are not perfectly correlated with put option prices and the information contents of the call option price are different from those of put options market price. So, under the non-complete market and the limited arbitrage, we examine whether the information implied in call(or put) option market price is more useful than that which is inferred from both call and put option market prices. The results show that for the non-complete put option market, the performance of GEV is improved much more incrementally than that of the other models. However, in the entire density forecast evaluation, GEV is not as useful as it is for the performance in the tail portions of the implied distribution.

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### The Study on the Fair Valuation of ESOs

Asian Review of Financial Research :: Vol.23 No.4 pp.405-436

AbstractEmployee stock options have been the representative compensation system since they were adopted in 1997 in Korea with the change into the performance culture. Recently fair valuation of employee stock options(ESOs) has become a significant issue not only because they can measure their incentive effects but also because the Accounting Standards require ESOs value to be expensed for documenting financial statements. ESOs, which are inalienable and forfeitable, exhibit different exercise patterns from standard options. Prior researches related with empirical exercise patterns of ESOs exhibit that ESOs are prematurely exercised soon after the vesting period is over and the early exercise patterns are influenced particularly by risk aversion(Huddart and Lang, 1996; Carpenter, 1998; Bettis et al., 2005; Boyd et al., 2007). Kim and Jung (2009) analyzed the Korean ESOs and showed that stock options are exercised approximately 3.15 years after being granted, and these early exercise patterns were found to be influenced by risk aversion, profitability through exercise and firm characteristics. There are ESO valuation models reflecting these ESOs features such as extended American option model(Carpenter, 1998) and Utility-maximization model(Huddart, 1994; Kulatilaka and Marcus, 1994). The one adjusted the simple American option model by adding an exogenous parameter, ‘stopping state', in which the employees or executives automatically exercise or forfeit the option. The other adopted the employee's utility function of CRRA(constant relative risk aversion). Employees exercise their stock options when their expected utility, influenced by their risk aversion and outside wealth as well as stopping state, is maximized. But, generally, accounting practitioner estimate the fair valuation of ESOs using just either the modified Black-Scholes model, which adjusts the option's life to the expected life and subtracts the cancelation, or typical American option model, which can be exercised prior to maturity. The aim of this study is both to look for an ESO valuation model that can best predict the actual exercise pattern. Furthermore, we are to review whether the expected life of ESOs that are currently posted on the financial statements fits the actual exercise pattern. This analysis helps us know if accounting practitioner estimate the expected life of ESOs appropriately considering the ESOs' features and the correlation between stock price and the timing of exercise. The process of analysis is like followings; First, we have to calibrate some unobserved parameters; stopping state in extended American option model and risk aversion, outside wealth, and stopping state in utility-maximization model according to the method of Carpenter (1998) and Bettis et al. (2005). To do this, we set the mean exercise pattern of sample the base exercise pattern, searching the best unobserved parameters showing the closest to the base exercise pattern through the grid-search method. Second, we calculate the expected exercise pattern of each firm using calibrated parameters(stopping state, risk aversion, outside wealth) and observed parameters of its own; volatility, dividend rate, vesting date, risk-free rate, expected return. Third, we evaluate which option model forecasts most accurately among models; modified Black-Scholes model, American option model, extended American option model, Utility-maximization model. Also we analyze whether the expected life of ESOs that is currently posted on the financial statements forecast properly by comparing the forecast error such as the mean error, the percentage error, the mean absolute error, and the square root of the mean squared percentage error, and by the regressions of the actual exercise variable on the model forecast. We analyzed a total of 159 exercised employee stock options for the years between 2000 and 2008. We limited the sample to ones that we can obtain the characteristics of stock option grant and exercise and the firm specifies the estimates of the characteristics of ESOs on the footnote of financial statement such as expected life of their own. The results are like followings; First, the analysis of 159 stock options in this study indicates that among many theoretical ESO models, the extended American option model appears to be the best valuation model in predicting the expected stock-to-strike ratio and the expected life of ESOs. This result is encouraging and practicable because extend American option model doesn't assume the risk aversion which is very difficult to observe and presume. So, we can estimate the fair valuation of ESOs without using the elaborate model such as utility-maximization model. Second, the officially posted estimate on the financial statements, on the other hand, didn't have as good a predictability as the model, and the correlation with the actual exercise period was not even close to the statistics. Consequently, proper measures should be taken in order to estimate the expected life based on the ESOs features such as early exercise and forfeiture rate in the process of fair valuation of ESOs for documenting financial statements.

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### Equity Fund Performance and Cash Flows : Structural Changes, and Start-up and Survivorship Biases

Asian Review of Financial Research :: Vol.23 No.4 pp.437-468

AbstractThe relationship between fund performance and cash flows is very important to fund investors, fund managers, and management companies alike. As is the case in the U. S., many studies have shown that better-performing funds have larger cash flows. This study investigates the relationship between fund performance and cash flows in Korean equity fund markets, and shows the behavior of investors in response to fund performance. Very few studies have considered Korean fund market's unique features. In 2005, the Korean fund markets and industry have faced structural changes that affected the behavior of investors. Based on the structural changes, we show the relationship between fund performance and cash flows. Since 2000, Korea has witnessed great capital influx due to great market expansion. Investors began to be aware of the risk and reward relation of equity funds, and are able to distinguish equity funds from bond funds and bank savings. At the same time, nominal interest rates have drastically declined. As a consequence, the equity fund market has started to attract investors seeking higher returns on their investments. In line with the changing climate of financial markets, the Korean government has allowed commercial banks to conduct fund sales business using their extensive retail networks. As expected, sales businesses by commercial banks have helped accelerate the rapid growth of equity funds. To meet growing investors' demands, investment management companies have devised dollar cost averaging techniques for equity mutual fund investments. They could succeed in launching a host of new equity funds that were designed specifically for dollar cost averaging investments. As a result of these adjustments, by the end of 2004, the demand base of equity funds was further strengthened with much larger market share. Moreover, the assets under management of equity funds following the preponderant dollar cost averaging investments have also begun to grow rapidly, which has provoked structural changes in the Korean mutual fund market. By fully taking into account such unique features and developments in the Korean fund markets, we investigate the relationship between fund performance and cash flows. For this study, fund data are generously provided by Zeroin and FN Guide, Korean financial data providers. The period for empirical analysis runs from January 2001 through December 2007. A total of 223 equity funds are selected among 1,117 public equity funds which have total net assets over 50 billion Korean won on average. One thing that should be noted here is ways in which class funds are handled to make sure to prevent the problems of fund replication. Nowadays, like in the U. S., most funds in Korea are established as class funds which can be included in the same portfolio but with different fee structures. For the purpose of empirical analysis, hence, just a fund should be selected among the same class funds. In this study, in order to prevent the replication bias, only the largest class fund is selected. To investigate the effect of equity fund performance on fund flows, we regress fund flows on equity fund performance and other control variables. According to the previous literature, control variables include standard deviation of past fund returns, past fund flows, market flows, log of total net assets, fund age, and some related dummy variables. Additionally, we employ a switching regression model to reflect the effect of structural changes of fund markets on the relationship between fund performance and flows. The overall results are as follows. First, as expected from the previous U.S. studies, better-performing funds have larger monthly cash flows than the other worse-performing funds. That is to say, investors base their fund investment decisions on the performance. Second, we find that fund performance and cash flows are positively related only for the period of 2005∼2007, based on which we conclude that the structural changes of the fund market affect the performance-flow relationship. Third, we observe the effect of start- up funds caused by enormous cash flows into start-up funds, but it does not affect the conclusion of this study. Also, we do not find any survivorship bias in the Korean fund market. To empirically prove the absence of start-up fund and survivorship biases, we employ both the direct and indirect approaches. Fourth, the best-performing funds in general induce greater cash inflows than do the worst-performing funds. As is the case in the U. S., therefore, we conclude that there exists an asymmetric relationship between fund performance and cash flows for the Korean equity fund markets. We also find evidence supporting the effect of structural changes on the relationship between fund performance and cash flows. Unfortunately in Korea, due to its relatively short history of fund markets and lack of data availability thereof, sufficient studies have not been conducted to fully understand the behavior of fund investors. The increasing number of behavioral finance analyses underlines the importance of understanding the behavior of fund investors for both protecting fund investors and further advancing fund industry. Therefore, we believe that this study could effectively stimulate further research.

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