2023/02/17 by Smerlak, Matteo
#FOS: Economics and business #FOS: Physical sciences #General Finance (q-fin.GN) #Physics and Society (physics.soc-ph) #Portfolio Management (q-fin.PM) #Statistical Finance (q-fin.ST)
paper · doi:10.48550/arxiv.2302.08829
Returns distributions are heavy-tailed across asset classes. In this note, I examine the implications of this well-known stylized fact for the joint statistics of performance (absolute return) and Sharpe ratio (risk-adjusted return). Using both synthetic and real data, I show that, all other things being equal, the investments with the best in-sample performance are never associated with the best in-sample Sharpe ratios (and vice versa). This counter-intuitive effect is unrelated to the risk-return tradeoff familiar from portfolio theory: it is, rather, a consequence of asymptotic correlations between the sample mean and sample standard deviation of heavy-tailed variables. In addition to its large sample noise, this non-monotonic association of the Sharpe ratio with performance puts into question its status as the gold standard metric of investment quality.