Risk-free rate for ex-post evaluation of investment strategy

Question

When evaluating the strategy ex-post using e.g. Sharpe ratio, what should one use as the risk-free rate? Let's suppose I am using a 1Y sample of weekly returns, sampled between 2012-01-01 and 2012-12-31. Should I use the 1Y risk-free rate as of 2012-01-01, an average of the 1W risk-free rates as of the beginning of each week in 2012, or subtract each 1W risk-free rate from the corresponding strategy return each week before averaging/calculating variance?

My intuition was to do the last, but on the other hand with the interest rates floating, this hardly makes it the "risk-free" option?

Answer 1

seems to me that the rate used depends on the corresponding strategy's grip on funding: that is to say, if the strategy is self-financing, rf=0 when calculating sharpe (in the sense that your costs of funds is zero in construction of the strategy); if it requires an outlay at t_0, an amount which is tied up throughout the time frame of the year, rf should be the 1 yr zero rate as of t0; if the strategy is such that each week the outlay is returned and reinvested the following week, then the rf should be the geometric mean of the return on 1 week t-bills as of 2012-01-01 through 2012-12-31 at any rate see here: see here: http://www.edge-fund.com/Dowd00.pdf