A Very Simple Goals - and Risk-Based Asset Pricing Model (or Asset Pricing with Heterogeneous Investors)

Abstract

Prof, Andre Perold has shown how the Capital Asset Pricing Model (with implications for asset pricing and risk-adjusted performance) can be derived from maximizing the Sharpe ratio as opposed to the traditional approach of assuming that investors maximize the utility of wealth. More recently, Goals-based Investing (GBI) is becoming the norm for investors and Prof. Robert Merton has suggested that theory needs to accommodate the fact that investors maximize relative (wealth divided by the present value of the goal) and not absolute wealth. Individuals save for a range of goals (e.g., retirement, a child’s college expenses) and each has a unique set of cash flows. The paper first argues for the creation of a new class of relative risk-free fixed income securities for each goal as proposed for a number of countries by Prof. Merton. These instruments will typically be interest-only real bonds (linked to the appropriate inflation index), with a forward start date, and pay coupons for the period required for the respective goal. The second contribution of this paper is to use the Perold approach and show that with two such goals/instruments and the traditional risk-free asset, all risky assets can be priced and optimal asset allocation recommendations derived, without requiring a formal utility function, risk aversion parameter or market portfolio. All that is needed is the assumption that investors maximize risk-adjusted returns relative to the goal-replicating asset and specify risk goals much like traditional investors would specify. The asset pricing model is derived from the simple idea that a relatively risk-free asset for one goal is a risky asset for another, and hence these two assets, plus the absolute risk-free rate allow us to triangulate to establish returns for all other assets. This approach also lends itself easily to an asset pricing model with heterogeneous investors and effective risk-adjusted performance measures.