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A century ago, life expectancy was roughly 40 years, hence all income could be consumed, as for most people, there was no need to save for retirement. Today, things have drastically changed: Life expectancy exceeds 80 years in many countries, and one should expect to live and consume many years after retirement. Thus, we have many investors with various investment horizons, where the length of the investment horizon becomes a crucial factor in determining the best investment diversification.This book analyzes the effect of the investment horizon on the optimal diversification, specifically between stocks and bonds: Should a young investor and an older investor have the same portfolio? Is it recommended to savers for retirement to change the asset allocation between stocks and bonds as they grow older, as life cycle mutual funds do in practice? Is the idiom "stocks for the long run" backed by scientific evidence? We analyze for which horizons it is recommended to employ the popular Mean–Variance rule and for which horizons employing this rule induces an economic distortion, hence a loss to the investors. It is shown that all relevant parameters for investment choice (means, variances, and correlations) change in a non-linear way with the horizon, a fact that makes the investment horizon crucial for investment choices. Similarly, the popular Sharpe, Treynor, and Jensen performance indices vary with the assumed horizon even in the case of independence over time. To analyze all the above issues, we employ the Mean–Variance rule and Stochastic Dominance rules, as well as direct expected utility calculations.
Introduction
Asset Allocation and the Horizon: The Ongoing Disputes
The Distribution of Returns and the Horizon
Mean–Variance, Stochastic Dominance, and the Investment Horizon
Performance Indices and the Investment Horizon
Stocks Versus Bonds: Mean–Variance and Expected Utility Paradigms
Risk and the Horizon: The Discounting Cash-Flows Approach with Rothschild and Stiglitz’s Definition of Risk
Stock Risk: Do Historical Crashes Tell the Whole Story? The Black Swan Hypothesis
Discrete and Continuous Returns and the Investment Horizon
Almost Stochastic Dominance Rules and the Horizon
Prospect Theory and the Horizon
The Change in the Relative Attractiveness of Stocks and Bonds with the Horizon with a Riskless Asset