금융변수의 주가수익률 예측력 검정

In this paper, we examine stock return predictability in the Korean stock market using the random time Cauchy estimator. Various financial variables have been tested for stock return predictability, but the results remain inconclusive. In the Korean stock market, Kim and Kim (2004), Kim and Park (2009) and Chung and Kim (2010) try to find evidence of return predictability using the dividend-price ratio, earnings-price ratio, and interest rates, but their conclusions are mixed. More recently, Choi et al. (2016) propose a robust test of stock return predictability which combines the time-change method with a Cauchy estimator. They show that the random time Cauchy test has an exact size of test and comparable power to Campbell and Yogo (2006) and Chen and Deo (2009)’s tests. We apply this new methodology to the KOSPI index and report the empirical results, providing comparison with other widely used tests for return predictability. Stock returns have nearly nonstationary stochastic volatility, and this causes substantial size distortions on standard tests relying on constant variance. To handle this nonstationary stochastic volatility in returns, we implement a simple time change. For the required time change, “we wait for volatility to reach a certain threshold before collecting each observation such that there is a constant level of volatility across all observations in our sample.”(Campbell and Yogo, 2006) Using the daily KOSPI index, we first test the presence of discrete jumps in our sample. We detect a total of 15 jumps between January 2001 and December 2014 with the windows size 16 and a 5% significance level, using Lee and Mykland (2008) test. Depending on the presence of discrete jumps, we measure the realized variance and realized bi-power variation. When we allow for only the continuous martingale in the regression error, we remove the detected daily jumps and compute the total realized variance by squaring and summing up daily excess returns. When we allow our continuous time regression model to have discrete jumps, we compute the realized total bi-power variation without removing detected jumps. We have a total of 168 months in our sample span. The computed total realized variance (TQV) and total realized bi-power variation (TBPV) are then divided by the number of months and we set this as our volatility threshold  and  for a time change with QV and a time change with BPV, respectively. Using the given volatility threshold, we add up daily squared excess returns until it hits our set  and resample our regression variables on that date and repeat the process until we reach the TQV and TBPV. After correcting for stochastic volatility in returns, we implement a Cauchy estimator to handle the persistent endogeneity of covariates. The Cauchy estimator uses the sign transform of a covariate as an instrumental variable. “The advantage of using a Cauchy estimator is that the asymptotic normality of the Cauchy t-ratio holds regardless of any statistical ano- malies in covariates including nonstationarity, fat-tailed innovations, struc- tural breaks, and jumps.” (Choi et al., 2016) Thus, it is well suited for testing return predictability in cases where many commonly used covariates are highly persistent and correlated with the regression residuals. Infe- rences using the Cauchy t-ratio are also valid even in the presence of structural breaks and jumps. We test for stock return predictability in the Korean market using the log of dividend-price ratio, the log of earnings-price ratio, the risk- free rate, and short-term, medium-term and long-term yield gaps. For the dividend-price ratio, conventional OLS t-test over-rejects the null hypothesis of no predictability. We could not find evidence for predictability using other tests except the random time Cauchy with BPV. For the ear- nings-price ratio, none of our tests reject the null. The coefficients of risk-free rates are insignificant except for Campbell and Yogo (2006)’s BQ test where its 90% confidence interval does not include zero value. Using the Amihud and Hurvich (2004) and Campbell and Yogo (2006)’s test, short- term yield gap has predictive power. But using the Chen and Deo (2009)’s chi-square 1 and random time Cauchy t-test, we could not reject the null. After correcting for persistent endogeneity in the medium-term yield gap, evidence for return predictability disappears, and all our tests except for OLS t-test cannot reject the null. Finally, we could not find any evidence for predictability using the long-term yield gap.