If you have a portfolio that's growing over a long period of time; and you keep reinvesting all the PNLs; if the total cumulative capital is upward going, your standard deviation of daily PNL is also growing, as well as the mean of daily PNL... ---------------- You would hope that the growth of the portfolio capital as well as reinvesting don't impact the Sharpe Ratio, but unfortunately that's not the case, the Sharpe Ratio is impacted: when you don't reinvest the PNLs at all, your Sharpe ratio is actually higher than that of when you do reinvest all the PNLs into the portfolio.... Any thoughts?
No only Sharpe ratio, but also all the ratios such as Sortino and Calmar, etc., as well as the year-to-date cumulative PNL and the 15 yr cumulative PNL, (under the assumption that the risk as measured by daily standard deviation of PNL is kept the same)... all improved when we don't reinvest the PNLs... interesting...
Sharp ratio does not favor volatility. It means that your system experiences greater volatility on the "right" side of the equity. Namely, at the beginning volatility was lower but through the time it grown up. When you do not reinvest while the equity still goes up, the volatility automatically goes down. It because your investment portion as compared to the equity is lower than it was before.
So what can we conclude from this? It looks like since my end goal is to keep daily risk limit to be a constant, for example, risking $500K (one standard deviation), I should use the non-reinvestment approach, instead of the fully-reinvesting-all-pnl approach?