Stock returns are not always from the same distribution: Evidence from the Great Recession
-
DOIhttp://dx.doi.org/10.21511/imfi.17(3).2020.15
-
Article InfoVolume 17 2020, Issue #3, pp. 189-204
- 486 Views
-
119 Downloads
This work is licensed under a
Creative Commons Attribution 4.0 International License
Portfolio allocation strategies, and notably the mean-variance approach, use past returns to assign optimal weights. Even though both past and expected returns should come from the same distribution, a formal test of whether this holds in practice has not been conducted yet. Thus, the study examines if the daily returns of 242 companies with continuous trading in the S&P index come from the same distribution using the Kolmogorov-Smirnov, Cramér-Von Mises, and Wilcoxon rank-sum tests. The tests suggest that generally stock returns do come from the same distribution. However, the hypothesis is rejected during the Great Recession, with the rejection rate increasing as the forecast horizon increased. The rejection rate, using an array of macroeconomic variables, is found to record high levels of persistence. Although macroeconomic variables were not found to be statistically significant determinants of the rejection rate, market distress has a small but significant effect.
- Keywords
-
JEL Classification (Paper profile tab)G11, C14, C58
-
References32
-
Tables4
-
Figures9
-
- Figure 1. Percentage of samples in which distributions were not equal
- Figure 2. One-hundred (100) observations forecast sample
- Figure 3. Fifty (50) and two-hundred (200) observation window
- Figure 4. Percentage of samples in which distributions are not equal using Cramér-von Mises test
- Figure 5. One-hundred (100) observation forecast sample using Cramér-Von Mises test
- Figure 6. Fifty (50) and two-hundred (200) observation forecast sample using Cramér-Von Mises test
- Figure 7. Percentage of samples in which distributions are not equal using Wilcoxon rank-sum test
- Figure 8. One-hundred (100) observation forecast sample using Wilcoxon rank-sum test
- Figure 9. Fifty (50) and two-hundred (200) observation forecast sample using Wilcoxon rank-sum test
-
- Table 1. Average rejection rate in each period
- Table 2. Average rejection rate in each period
- Table 3. Average rejection rate in each period
- Table 4. Estimation results
-
- Alexander, C. (2008). Market Risk Analysis: Pricing, Hedging and Trading Financial Instruments. John Wiley & Sons.
- Andersen, T. G., & Bollerslev, T. (1998). Answering the Skeptics: yes, standard volatility models do provide accurate forecasts. International Economic Review, 39(4), 885-905.
- Anderson, T. W. (1962). On the distribution of the two-sample Cramer-von Mises criterion. Annals of Mathematical Statistics, 1148-1159.
- Andreou, P. C. (2015). Effects of market default risk on index option risk-neutral moments. Quantitative Finance, 15(2), 2021-2040.
- Aparicio, F. M., & Estrada, J. (2001). Empirical distributions of stock returns: European securities markets, 1990–95. European Journal of Finance, 7(1), 1-21.
- Best, M. J., & Grauer, R. R. (1991). On the sensitivity of mean-variance-efficient portfolios to changes in asset means: some analytical and computational results. Review of Financial Studies, 4(2), 315-342.
- Bodie, Z., Kane, A., & Marcus, A. J. (2008). Investments (7th ed.). Boston: McGraw-Hill.
- Bollerslev, T. (1986). Generalized autoregressive conditional heteroscedasticity. Journal of Econometrics, 31(3), 307-327.
- Campbell, J. Y., & Thompson, S. B. (2007). Predicting excess stock returns out of sample: Can anything beat the historical average? Review of Financial Studies, 21(4), 1509-1531.
- Campbell, J. Y., Lo, A. W. C., & MacKinlay, A. C. (1997). The econometrics of financial markets. Princeton, NJ: Princeton University Press.
- Chae, J., & Lee, E. J. (2018). Distribution uncertainty and expected stock returns. Finance Research Letters, 25, 55-61.
- Chopra, V. K., & Ziemba, W. T. (1993). The effect of errors in means, variances, and covariances on optimal portfolio choice. Journal of Portfolio Management, 19, 6-11.
- Cramér, H. (1928). On the composition of elementary errors: First paper: Mathematical deductions. Scandinavian Actuarial Journal, 1, 13-74.
- DeMiguel, V., Garlappi, L., & Uppal, R. (2007). Optimal versus naive diversification: How inefficient is the 1/N portfolio strategy? Review of Financial Studies, 22(5), 1915-1953.
- Egan, W. (2007). The distribution of S&P 500 index returns (Working Paper).
- Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between the expected value and the volatility of the nominal excess return on stocks. Journal of Finance, 48(5), 1779-1801.
- Hansen, P. R., & Lunde, A. (2005). A forecast comparison of volatility models: does anything beat a GARCH (1, 1)? Journal of Applied Econometrics, 20, 873-889.
- Humpe, A., & Macmillan, P. (2009). Can macroeconomic variables explain long-term stock market movements? A comparison of the US and Japan. Applied Financial Economics, 19(2), 111-119.
- Issah, M., & Antwi, S. (2017). Role of macroeconomic variables on firms’ performance: Evidence from the UK. Cogent Economics & Finance, 5(1), 1405581.
- Kim, J. H., Shamsuddin, A., & Lim, K. P. (2011). Stock return predictability and the adaptive markets hypothesis. Evidence from century-long US data. Journal of Empirical Finance, 18(5), 868-879.
- Kirby, C., & Ostdiek, B. (2012). It’s all in the timing: simple active portfolio strategies that outperform naive diversification. Journal of Financial and Quantitative Analysis, 47(2), 437-467.
- Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distribuzione (pp. 83-91). G. Ist. Ital. Attuari.
- Malevergne, Y., Pisarenko, V., & Sornette, D. (2005). Empirical distributions of stock returns: between the stretched exponential and the power law? Quantitative Finance, 5(4), 379-401.
- Markowitz, H. (1952). Portfolio selection. Journal of Finance, 7(1), 77-91.
- Massey, Jr. F. J. (1951). The Kolmogorov-Smirnov test for goodness of fit. Journal of the American Statistical Association, 46(253), 68-78.
- Michail, N. A. (2019). Stock market efficiency 2000–2014: the role of the Great Recession. International Journal of Banking, Accounting and Finance, forthcoming.
- Pesaran, M. H., & Pick, A. (2011). Forecast combination across estimation windows. Journal of Business & Economic Statistics, 29(2), 307-318.
- Smirnov, N. (1948). Table for estimating the goodness of fit of empirical distributions. Annals of Mathematical Statistics, 19(2), 279-281.
- Von Mises, R. (1928). Statistik und wahrheit. Julius Springer.
- Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80-83.
- Yilmaz, K. (2012). Martingale property of exchange rates and central bank interventions. Journal of Business & Economic Statistics, 21(3), 383-395.
- Zaiontz, C. (2015). Real Statistics Resource Pack.