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There is no single right answer for this one, there are good reasons for and against using cash (either bills or LIBOR widely used) versus terming out the duration to match your equity/risk asset horizons. Whatever would be your default when not invested can never really be too far wrong. Strictly speaking, a treasury bond is not “riskless”. There may be ...

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I would use 3-month bills as a measure of the risk free rate.

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There are a few different views out there in choosing your reference rate. Literature normally uses a T-Bill rate (1 month or 3 months). That's what Fama & French do in their online library. In practice, you're on the right track with matching the maturity of your investment horizon with the maturity of your risk free rate. In theory, you could go a step ...

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Use a rate that's representative of what you'd get on excess cash if you weren't fully invested. For most institutional investors this will be something like either Fed Funds or 1 month LIBOR less a spread (set by your PB / FCM). If you were a corporate treasurer it would likely be roughly equivalent to a money market fund rate. EDIT: LIBOR is unequivocally ...

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The formulas given already explain the substitution you're wondering about, based on standard statistical laws surrounding the distribution of random variables, often focused on the first and second moments of that distribution: the mean $E(\cdot)$ and variance $Var(\cdot)$. You can find these rules being followed in the derivations of many economic models ...

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If they were computed with the same criterion, the Sharpe ratio, you can simply compare the different portfolios' Sharpe ratios with one another: $\frac{\mu_{1}-r_f}{\sigma(r_{1})}$ vs $\frac{\mu_{2}-r_f}{\sigma(r_{2})} \dots$ vs $\frac{\mu_{P}-r_f}{\sigma(r_{P})}$, where $r_p\in\mathbb{R}^{T\times 1}$ is the weighted return time series (vector) for ...

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