A Mean-Variance Approach to Fixed Income Portfolio Allocation

Abstract:     
Long term investments in bonds offer known returns, but with risks corresponding to defaults of the underwriters. The excess return for a risky bond is measured by the spread between the expected yield and the risk-free rate. Similarly, the risk can be expressed in the form of a default yield, measuring the difference between the yield when no default occurs and the expected yield. For zero coupon bonds and for actual market data, the default yield is proportional to the probability of default per year. The analysis of market data shows that the yield spread scales as the square root of the default yield. This relation expresses the risk premium over the risk-free rate that the bond market offers, similarly to the risk premium for equities. With these measures for risk and return, an optimal bond allocation scheme can be build following a mean/variance utility function. Straight forward computations allow to obtain the optimal portfolio, depending on a pre-set risk aversion level. As for equities, the optimal portfolio is a linear combination of one risk-free bond and a risky portfolio. Using the scaling law for the default yield allows to obtain simple expressions for the value, yield and risk of the optimal portfolio.

Number of Pages in PDF File: 22

Keywords: bond yield, default spread, risk/return scaling, mean-variance portfolio allocation

JEL Classification: C00, G11

working papers series