Vineer Bhansali, managing director and portfolio manager at Pimco, says there has been a shift in asset allocation modelling away from reliance on a single mean point, towards multiple points of equilibrium.
Implications for Portfolio Construction and Hedging
How does this bimodality apply to portfolio construction in the world of high volatility and multiple equilibria that we see today? Here is what we find when we apply it to two problems of finance: optimal asset allocation and option pricing.
Optimal Allocation to Risky Assets: If we start with an assumption that we would allocate 50% of the portfolio to equities in the unimodal case, what would the optimal allocation be in the bimodal case, assuming our risk preferences are unchanged? By following a very traditional portfolio optimization exercise which involves a little bit of math, the answer turns out to be that the optimalallocation would be only 10%! In other words, one would have to de-risk by almost 80% from the current optimal allocation to arrive at the mathematically optimal result (see disclosures at the end of this article for a more detailed explanation of our computations). The prospect of being trapped in a low return, low probability event requires us to, as Mohamed El-Erian would say, “generally play defense and selectively play offense.”
Pricing of Options on Tails: If we started with an assumption of unimodality and the real distribution turned out to be the bimodal one, how mispriced would put options on the tails be in retrospect? Our research shows that a typical unimodal distribution just cannot be tweaked large enough to make it come out with the price of a put option one would likely get if the real world turned out to be bimodal. A portfolio manager pricing such tail options armed with traditional unimodal distributions would wrongly think that the tail options were “expensive” (tail options will generally tend to be underpriced when based on a unimodal distribution but significantly higher when derived from bimodal distributions).
(Again, for the mathematically inclined we priced the options by mathematically summing the put payoff over all the probability-weighed outcomes from the two distributions.) These two illustrations show that the very possibility of a bimodal outcome forces you to de-risk directly, i.e. by reducing the allocation to risky assets; or to build in tail hedging, which might look expensive by traditional measures, but may turn out to actually be “cheap” in a bimodal world.
For all these reasons, we believe that the core building blocks of asset allocation and option pricing should incorporate the possibility of multimodality. To follow a traditional approach in a world that is so exposed to the possibility of multiple equilibria is to ignore the reality of today’s markets.