Holy Grail Distribution 

the missing piece of every investment portfolio

by George Sokoloff, PhD, CFA and Andrew Zaytsev, CFA, CAIA

July 2014


          Recently, markets treated both investment advisors and investment managers favorably. In the first half of 2014 many fund managers, trustees and asset allocators had all the reasons to be proud of the last 5 years of investment returns.

          Most investment portfolios are now in a relatively good shape. In the chart above we post cumulative return of our sample portfolio (50% Public U.S. Equities, 30% U.S. Bonds, 10% U.S. Real Estate, 10% Hedge Funds). This chart should look similar to one representing returns of many other traditional portfolios comprised of public and private equity (domestic and global), government, corporate or even junk bonds, real estate, commodities, hedge funds and many other alternative investments.

          Recent market environment with 5 years of strong equity returns, good bond returns and improving real estate prices helped a lot. At the same time, global interest rates are at historical lows. This regime, favorable to most asset classes is gradually coming to an end.

          One of the well-known problems of traditional investment portfolios is their vulnerability to periodic market performance shocks, or tail risk events.

          Through the life of our sample portfolio over the last 20 years, relatively stable periods are interrupted by periods of high volatility. 

          One does argue and speculate on how far away in the future we will encounter the next volatile period. The question is not IF, but WHEN. With economy and unemployment in the U.S. almost back to long-run averages, extremely low interest rates also have to come back to some regular level.

          Rising interest rates will very likely impact equity, real estate and bond returns. Reduced equity returns in combination with increased market volatility may produce another tail risk event and a portfolio performance shock within the next 2 or 3 years.

          Long-term oriented investors have to invest in equities as one of the best contributors to investment returns. Periodic market crashes disrupt well diversified portfolios and force the total value of traditional portfolios to dive.

          Every investor type has its own problems associated with this portfolio performance pattern. Pension funds may experience significant or severe underfunding and may have to either increase contributions or reduce benefits for current and future beneficiaries.

          Endowments and foundations may have to reduce their support of the cause they serve for.

          High Net Worth individuals may have to postpone some significant life events or re-think their retirement strategy.


          Investment managers might be tempted or forced to make suboptimal investment decisions at the market extremes. For a good portion of portfolio managers tail risk is highly correlated with the career risk.

Needless to say that the fiduciary responsibility of investment managers lies in protecting portfolios they oversee from the impact of tail risk events.


          If we pay attention to one of the commonly used performance metric – 12-month portfolio returns – the problem becomes even more visible. Red areas are the periods of market stress when the traditional diversification fails.

          The underlying cause of this problem is well known.

          In the presence of tail risk events the observed distribution of returns of most asset classes and many investment managers is skewed to the left with a clear fat left tail. These negative fat tails are often observed at the same time – seemingly uncorrelated asset classes suffer simultaneous losses.

          Essentially, during tail risk events some of correlations between asset classes change significantly and go to one, ruining the traditional Asset Allocation framework. This is why portfolios built using traditional Asset Allocation approach suffer from periodic performance shocks.

          Risk Premia Parity (or Risk Parity) approach tries to fix this problem to some extent if implementation takes into account changing correlations of portfolio components.

          An approach derived from Risk Parity, named Tail Risk Parity, addresses this problem directly by balancing risks among asset buckets that behave similarly during tail risk events.


          Tail risk events happen quite regularly. Most investors routinely collect risk premia from various asset classes or investment strategies and then occasionally pay the price in the form of a significant underperformance. Investors have to make a wager and then hope that the worst won’t happen, but “the worst” dies eventually happen.


          The distribution of returns that produces many small gains and few large losses is often referred to as the Taleb distribution. There is no specific formula for the distribution but it is characterized by negative skewness (most of the distribution is left of its peak) and large kurtosis (narrow peak and fat tails). Here’s what this distribution conceptually looks like: positive mean and an oversized negative tail.

          Tail risk events, market performance shocks are represented in this negative long tail. Portfolio of Taleb-like investments with co-located negative fat tails (happening at the same time) is not truly diversified. It suffers from periodic market performance shocks.


          It would be great to have the ability to predict tail risk events, bear markets or significant corrections and move investment portfolios to cash on time. As we well know though, it is impossible for the majority of investors. Investors are the market and any concerted effort to liquidate holdings brings about a market correction.

          If market timing on a consistent basis is out of question, what can investors do to protect themselves from an adverse effect of tail risk events?


           One of the solutions to this problem is a complementary strategy that has a performance pattern that helps reduce the impact of market performance shocks.


          What if we had an instrument with a returns distribution that features a positive mean and a fat right (positive) tail that “happens” right at the time when traditional portfolios take a hit?


          When tail risk events, bear markets or significant market corrections come, portfolio’s negative outcome is compensated by an overlapping strong positive outcome from such an instrument happening at the same moment of time.


          During quiet markets, on the other hand, the instrument is still earning a positive return contributing to the portfolio's overall return.

          Asset allocators would want to hold such an instrument in their investment portfolios on a regular basis, so they could hedge portfolios from tail risk events.

          During the periods of market stress, when traditional diversification fails, sufficient allocation to such an instrument or strategy may solve the problem of periodic portfolio performance shocks.


          The name Holy Grail distribution captures both the elusive nature of finding a strategy with these characteristics and the unique value it provides to an asset allocator.

          The Holy Grail distribution has a positive mean to justify the investment and a “co-located” positive fat tail to add protection to investment portfolios during tail risk events.

          Essentially, Holy Grail distribution is a missing piece in almost every investment portfolio seeking protection from tail risk events combined with positive average returns.

          How hard is it to find strategies following this return distribution? It is hard for many reasons.

          First, any investment strategy that tries to create such a payout profile through the use of derivatives of some kind with an asymmetric positive payout profile is mathematically guaranteed to lose money over time.

          Second, market shocks are always characterized by the lack of liquidity in the markets. These reduced liquidity conditions tend to cause unexpected performance shocks in strategies as price behavior of many assets starts being driven by prevailing capital flows and departs from fundamentals. So strategies that focus on liquidity, volatility or credit risk have the best chance of fulfilling the task. 

          At the same time, allocation to investment instruments and strategies with Holy Grail distribution of returns may provide clear benefits of diversification and protection from periodic equity market performance shocks.


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