This last chapter is dedicated to the allocation problem when the investment universe is a set of asset classes. In fact, the roots of risk parity come from this asset mix policy problem. What relative proportion of equities and bonds must be held by an institutional investor, for instance a pension fund? If we refer to performances over the past century, a portfolio fully invested in equities offers the best performance (Ibbotson Associates, 2010). However, this high equity risk premium combined with a low risk-free rate and smooth consumption is difficult to reconcile with the typical risk aversion of investors (Mehra and Prescott, 1985). Numerous explanations have been put forward to solve this paradox, known as the equity premium puzzle (see e.g. Odean, 1998; Rabin, 1998; Hirshleifer, 2001; Barberis and Thaler, 2003). One of the main arguments is that time accounting differs from time preference. Many long-term investors evaluate their allocation policy on a yearly basis, which explains why they are more sensitive to losses than gains:

“The equity premium puzzle refers to the empirical fact that stocks have outperformed bonds over the last century by a surprisingly large margin. We offer a new explanation based on two behavioral concepts. First, investors are assumed to be ‘loss averse’, meaning that they are distinctly more sensitive to losses than to gains. Second, even long-term investors are assumed to evaluate their portfolios frequently. We dub this combination ‘myopic loss aversion’. Using simulations, we find that the size of the equity premium is consistent with the previously estimated parameters of prospect theory if investors evaluate their portfolios annually” (Benartzi and Thaler, 1995).