In this article, the author reminds us again that return mean and variance are not enough. Appropriate investment risk-bearing scales with surplus over future withdrawal commitments, as well as with investment return characteristics. This framework provides for the integration of financial planning and investment decision-making. Its time-varying risk aversion with the ratio of investments to surplus also provides an opportunity for use of dynamic strategies, though speculative bubbles require compensating inputs to avoid excessive allocation extremes. Appropriate risk-bearing can also scale with functions of shortfall probability to deal with time-specific funding requirements. The probability of avoiding shortfall from an initial surplus over longer time horizons may scale close to the square root of time, creating an illusion of time diversification. In contrast, from an initial surplus deficit, minimizing shortfall probability is akin to playing Russian roulette. Allocations based on minimized shortfall probability can be usefully blended with mean–variance allocations, especially for 5- to 15-year time horizons.
Relative arbitrage: Sharp time horizons and motion by curvature
