Chapter 6
Portfolio Allocation with Multi-Asset
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. Sec-
ond, even long-term investors are assumed to evaluate their port-
folios 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).
The fact that equities are too risky in short and medium-term horizons
then pushes institutional investors to diversify their portfolios, by including
sovereign and corporate bonds and alternative investments such as commodi-
ties and hedge funds.
This is particularly true for pension funds which face liability constraints.
Indeed, pension liabilities modify asset allocation decisions, because the
matching of asset and liability durations leads to investment in bonds. In
this context, it is not surprising to observe a wide dispersion of the asset allo-
cation between equities and bonds (Antolin, 2008). This dispersion is effective
270 Introduction to Risk Parity and Budgeting
between countries, but also within a country. Even when pension funds have
the same constraints and objectives, the stock/bond asset mix policies dif-
fer. Nevertheless, some portfolio references have emerged over the past thirty
years. Indeed, the 60/40 equity/bond portfolio is an anchor point for many
Anglo-Saxon pension funds (Ambachtsheer, 1987). However, with the recent
crisis, this constant-mix portfolio has suffered and institutional investors are
trying to find a more robust asset mix policy.
The choice of stock/bond allocation is all the more important as many
studies have shown that most of the differences in pension fund performances
are caused by the asset allocation policy. Brinson et al. (1986, 1991) estimate
that its contribution is larger than 90%. Ibbotson and Kaplan (2000) find
similar levels when they consider the variability in the returns of pension
funds over time. In a more recent study, Blake et al. (1999) conclude that
strategic asset allocation accounts for most of the time-series variation in
portfolio returns, while market timing and asset selection appear to have been
far less important”. Among the different components of a long-term policy,
i.e. strategic asset allocation, tactical asset allocation, market timing and asset
selection, the reference portfolio is the key choice. In a sense, the risk budgeting
approach embodies both of the first two steps. Risk parity portfolio policies
may also be an alternative of constant-mix portfolio policies.
Risk parity with multi-asset classes is not limited to the design of diver-
sified funds or strategic asset allocation. In fact, it was first used by hedge
funds to build absolute return strategies. The success of Bridgewater’s All
Weather fund, which is a global macro hedge fund, has led the asset manage-
ment industry to propose absolute return funds built around the risk parity
In this chapter, we consider these different topics. The first section is ded-
icated to the construction of diversified funds. The second section deals with
long-term investment policy and the third section shows how to use risk parity
to develop absolute return strategies.
6.1 Construction of diversified funds
6.1.1 Stock/bond asset mix policy
The diversified funds business has suffered a lot of criticism, both from a
theoretical and a practical point of view. In chapter one, we have seen that
mean-variance portfolios of risky assets define the set of efficient portfolios.
If we introduce a risk-free asset, the efficient frontier becomes a straight line
called the capital market line. Along this frontier, optimal portfolios corre-
spond to a combination of the risk-free asset and the tangency portfolio. The
separation theorem states that all the investors hold the tangency portfolio.

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