# Which riskfree rate to use for Maximum Sharpe Ratio Portfolio?

I am conducting out of sample backtests of the MV framework. But how exactly do I derive the Maximum Sharpe Ratio portfolio for this? The standard forumula of the Sharpe Ratio is given by:

$$\frac{(w r - r_f)}{\sqrt{w Σ w'}}$$

Lets say I have an estimation window of 60 monthly returns on whose basis I derive the optimal portfolio weights. Which risk free rate $$r_f$$ would I have to use here or would I have to use any at all?

I'd appreciate any help!

To impose a more realistic borrowing constraint, you could follow the approach in Black (1972) by constructing a mean-variance efficient portfolio uncorrelated with the market portfolio. Let's call the returns on this portfolio by $$r_z$$, then $$\mathbb{E} r_z$$ represents the shadow cost of borrowing and you can simply replace $$r_f$$ with $$\mathbb{E} r_z$$.
• The purpose of the risk-free rate/excess returns is for your own optimization purposes (i.e. to factor in risk-free opportunity cost). The LIBOR is a good measure of risk-free rates, but is generally not possible for investors to borrow/lend at inter-bank rates so excess returns will be overinflated. If you don't plan on including a risk-free asset in your investment strategy, just set $r_f = 0$.