On the Time Dimension of Investing

Abstract

This paper explores how to structure choices for personal investment accounts that have a well-defined set of target dates. Key examples are investing for retirement or for a child's college education. We show that if the investor's objective is to minimize the ex ante cost of hitting specific targets at specific dates, the optimal portfolio strategy is to match the portfolio's payoffs to the time profile of those targets and not take any risk. Therefore to accommodate risk-averse investors with diverse time horizons, financial institutions ought to provide their clients with a term structure of risk-free investments to serve as clear points of reference.

In structuring choices with different degrees of risk and reward, an important set of reference points is a term structure of exchange-traded index options and the corresponding set of implied volatilities. In framing the time dimension in this fashion, one avoids the need for explicit forecasts of the term structure of equity risk premia, which are notoriously difficult to forecast. Our approach is not vulnerable to the potential biases inherent in the use of historical time series, such as survivorship bias.

Our approach and the mean-variance efficient frontier approach should be seen as complements rather than as substitutes. We view ours as a natural first step in structuring the time dimension of investment choice in personal investment accounts. Subsequent steps should include econometric modeling and some kind of tailoring to the preferences and circumstances of the end user.

Keywords: matching, efficient diversification, term structure, implied volatility

JEL Classification: G11