An Asset Allocation Puzzle: Comment

01 March 2001
By Dr. James Jordan with Department of Finance, George Washington University Professor Isabelle Bajeux-Besnainou and CNAM and ESSEC Finance Chair Roland Portait

Should the proportions of risky assets in the risky part of an investor's portfolio depend on the investor's risk aversion? According to basic financial theory, in particular the mutual fund separation theorem with a riskless asset, the answer is no. The theorem says that rational investors should divide their assets between a riskless asset and a risky mutual fund, the composition of which is the same for all investors. Risk aversion affects only the allocation between the riskless asset and the fund.

Niko Canner, N. Gregory Mankiw and David N. Weil (CMW) (1997), however, observe that popular investment advice does not conform to this theory. They report the stocks, bonds, and cash allocations recommended by four advisors for conservative, moderate, and aggressive investors. The advisors recommend a bond/stock ratio that varies directly with risk aversion.

In this paper we provide theoretical support for the popular advice. The two key insights are that the investor's horizon may exceed the maturity of the cash asset and that the investor rebalances the portfolio as time passes. If the investor's horizon exceeds the maturity of cash, which might be a money market security with maturity of one to six months, then cash is not the riskless asset as is commonly assumed in the basic theory. In a theory allowing portfolio rebalancing, as opposed to a buy-and-hold framework, it is not unreasonable to assume that the investor can synthesize a riskless asset (a zero-coupon bond maturing at the horizon) using a bond fund and cash. Then bonds will be in both the (synthetic) riskless asset and in the risky mutual fund, and we show that in this case the theoretical bond-stock ratio varies directly with risk aversion for any HARA investor. As an example of the type of results that a specific model can produce, we provide a continuous-time model with closed-form solutions which produces theoretical bond-stock ratios similar to the popular advice.

This paper was published in the September 2001 issue of The American Economic Review.