Table 1. Efficiency of explaining and predicting risk premium in different samples.

Risk measure
Standard deviation	7.83%	33.9%	36.7%	7.94%	9.7%	0.75	0.65
Beta	6.17%	36.7%	43.7%	13.31%	6.45%	0.98	1.02
Shannon entropy	12.98%	43.5%	39.6%	13.38%	10.15%	0.69	0.64
Rényi entropy	15.71%	42.4%	38.6%	12.82%	9.34%	0.63	0.62

Note: The table summarizes the explanatory power (in sample R ²) of the investigated risk measures in different samples. We estimate risk measures of 150 random securities using standard deviation, CAPM beta, Shannon- and Rényi entropy risk estimation methods for (1) long term, from 1985 to the end of 2011 (1985–2011); (2) long term on upward trends (bull market), (3) long term on downward trends (bear market), (4) 18 10-year periods shifting by one year from period (1985–1994) to period (2002–2011), split into two 5-5 year periods for each. Both types of entropy functions are calculated by histogram based density function estimation, with 175 bins for Shannon entropy and 50 bins for Rényi entropy. The shows the explanatory power of risk measures for long term, the , and summarizes the explanatory power on upward and downward trends, respectively, stands for the average explanatory power of risk measured in the first 5 years of 10-year shorter periods in sample, and shows the average predicting power of risk measures (out of sample R ²) calculated by estimating risk in the first 5 years and evaluating them on the other 5 years in each 10-year periods. The last two columns show the relative standard deviation of the explanatory and predicting power based on the 18 shorter periods for the investigated risk measures.