I am comparing different asset classes in order to estimate the expected return and the risk of a portfolio. I have historical data (adjusted close price) for my asset classes for the last 5 years with monthly frequency. The goal is to calculate the efficient frontier for my data at original frequency (monthly) and for annualized data.
I firstly need to calculate the excess return of each asset class, so I need to get 5Y average of monthly excess returns and 5Y average of yearly excess returns.
What bothers me is what risk-free rate to use in the calculation of excess return. The only thing clear to me here is that I need to use US Treasury Bonds yields, but of what maturity and why to use a certain maturity (I assume that there is more than one right answer for my question)?
- Do I use T-bonds with 5Y maturity in both cases, because I am doing optimization on historical data for the last 5Y?
- Do I use T-bonds with 1Y maturity for the annualized data and 1 month maturity for the monthly data?
- Is it more reasonable to use the same yield (I assume current yield) for calculating all historical excess returns over the course of 5Y, or to take historical changes in bond yield into account (so, use historical yields for every year to calculate yearly excess returns for the last 5Y)?