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A while ago, we adressed the following question: A portfolio manager knows that his strategy can, on average, outperform the benchmark index by 3% annually. His portfolio has an annual volatility (standard deviation) of 25% against the index's 15%. Assuming that the correlation between the returns of the portfolio and the returns of the index is 0.9, how many years would it take to outperform the index with 90% probability?

The correct answer is a whopping 300 years! (apply the Itô-Döblin formula)

Today somebody asked me if I could run a couple of simulations to get a better understanding of the result. What I did was plot 20 simulations of log(Portfolio/Index) for varying correlations. For ρ = 0.9 2 out of 20 (10%) are--as expected--below zero:
skillluckparadox

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