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From: Glyn Holton
Affiliation: Contingency Analysis
Address: glyn@contingencyanalysis.com
Date: 18 Jul 2001
Time: 20:13:11
The issue of symmetry — that market participants need to be able to lend and borrow at the risk-free rate — becomes important if you are employing Sharpe’s ratio within the larger context of portfolio theory. It was James Tobin who introduced a risk-free asset into portfolio theory. Markowitz had demonstrated how to construct an efficient frontier for a universe of risky assets. Tobin demonstrated how to obtain portfolio’s above the efficient frontier by adding a risk-free asset to the universe. Portfolios obtained by leveraging or deleveraging the “super efficient portfolio” (what became the market portfolio in Sharpe’s CAPM) define the capital market line — but these portfolios are only obtainable if market participants actually can leverage or deleverage (borrow or lend) at the risk-free rate. Tobin’s capital market line lead to Sharpe’s CAPM, including such notions as beta, systematic risk and specific risk.
Sharpe’s ratio is just a metric of risk-adjusted performance, and as such, you can define it based upon whatever risk-free rate you find convenient. I agree with Tjemme that T-bill rates are often employed in this context. However, if you are going to use Sharpe’s ratio within the broader context of portfolio theory, consistency requires that it reasonably reflect a risk-free rate at which market participants can borrow and lend. For this purpose, Libor is an imperfect, but reasonable proxy.
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