Conceptually and mathematically, does increasing holdings of risk free asset in a portfolio increase Sharpe ratio, why or why not?
I can. if the return of the portfolio is less than the RFR - increasing the RFR portion will increase the portolio return while reducing volatility.
I believe the explanation to one of the EOCQs (sorry, don’t remember which reading but in Book 2 or 3) says that adding the risk-free asset has no effect on Sharpe for the portfolio because it has equal impact on the numerator and the denominator. Made sense when I read it, but florinpop makes a good point.
florinpop Wrote: ------------------------------------------------------- > I can. > if the return of the portfolio is less than the > RFR - increasing the RFR portion will increase the > portolio return while reducing volatility. If the return of the portfolio is less than RFR then you would just hold the RFR. You would combine RFr with a portfolio which has a higher rate of return than RFR to reduce volatilty. Sharpe stays the same per CFAI but I have not tried to prove it mathematically
For CFA exam purposes, no, it does not increase the Sharpe. Reason provided is because it decreases return and std dev proportionately.