Investments with Downside Insurance and the Issue of Time Diversification

Abstract

Of two insurance policies that guarantee the same minimum rate of return on a portfolio and differ only in their time horizons, which is riskier? This study shows that if the minimum rate is lower than the risk-free rate, and if the risk is measured by the cost of insurance, then the degree of risk is not a monotonic function of the policy's time horizon. For every positive level of concession rate—defined as the risk-free rate minus the insured rate—the cost of such insurance peaks at a finite time horizon. This peak cost horizon is typically between 5 and 15 years. The higher the concession rate (or the lower the volatility of the insured portfolio), the shorter this peak-cost time horizon is. Thus, although a 5-year insurance policy can be much riskier than a 1-year policy, it can also be riskier than a 30-year policy.