Say I'm running a few backtests, say 1980-now, 2000-now and 2010-2015. When I'm calculating the Sharpe ratio of these backtests, do I use the risk-free rates associated with those time periods? or should I use the current risk-free rate for all of them?
My concern is that is that it might misleading to compare the Sharpe ratios of these different backtests to assess the viability of the different trading strategies I'm backtesting, because the Sharpe will be dependent on, say, what the T-bills at the time were looking like at the time of the backtest and not necessarily how profitable the trades are. However, if I use the current risk-free rate for all of them it will (I think) suggest what their risk-adjusted returns would be in the current market.
Is this a valid concern? Or should I just be using the historical risk-free rate for the times I'm backtesting. Thanks in advance!