1
$\begingroup$

Let's say I have data stemming from date $t_1$ to date $t_2$, I have the annualized return each day during those two dates. Therefore I know the expected return and the standard deviation of the returns between those two dates. But what should I use as risk-free rate in the calculation of the Sharpe ratio: $$ \frac{E(r)-r_f}{\sigma}$$ It seems like to be consistent, it would be natural to use the average 1-year risk-free rate from the Treasury yield curve during dates $t_1$ and $t_2$.

$\endgroup$
1
$\begingroup$

The formula wants to compare the (expected) return of a risky asset with the (known) return of a risk-free alternative. You need therefore to think of $r_f$ as the return of a risk-free asset.

The easiest way to know you're doing it right is to reconstruct this asset on a spreadsheet. To consider a typical case: if you have per annum risk-free rates posted daily, the cumulative value of an initial investment of \$1 would be

$$s_0 = 1, \quad \quad s_{t+1}= s_t \times (1+i_{t+1})^{1/252}$$

where $i_t$ is the interest rate on day $t$. The return on the risk-free asset then would simply be $r_f = s_{t_2 - t_1} -1$.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.