نبذة مختصرة : The paper is dedicated to empirical analysis of the asymptotic properties of the sample estimator of the risk aversion coefficient of the portfolio with the maximum Sharpe ratio. Because the mathematical expectation of the sample estimators of the weights, expected return and variance of this portfolio do not exist its practical use is questionable. We propose to solve this problem by substituting instead of the maximum Sharpe ratio portfolio statistically equivalent portfolio with the maximum expected utility. It is done by considering distributional properties of the sample estimator of the investor’s risk aversion coefficient of the portfolio with the maximum Sharpe ratio. Using Monte Carlo method with 100000 repetitions and the data based on the returns of 30 stocks included into the Dow Jones index for the period from 01.01.2019 to 31.12.2019 (251 observation) we provide empirical distributions of the sample estimator of the corresponding investor’s risk aversion coefficient and investigate the convergence of these distributions to the corresponding asymptotic one. We make use of two assumptions concerning asset returns vector distribution: multivariate normal distribution or multivariate t distribution with 5 degrees of freedom. We conclude that convergence of empirical distributions to corresponding asymptotic is fast enough in both cases. Even for portfolio with 30 assets and t distributed returns a good approximation is reached for moderate sample size of historical values (n=4000). We make use of this result to investigate the degree of maximum Sharpe ratio portfolio risk. Using the rolling window of size n=2000 we show that this portfolio was very risky during 2018-2019 years by considering asymptotic confidence interval of its risk aversion coefficient. We observe that in all considered cases the upper limit of 99 % confidence interval is smaller than 0.2.Keywords: Sharpe ratio, risk aversion coefficient, asymptotic distribution, confidence interval, elliptical distribution, Monte Carlo method. ...
Processing Request
No Comments.