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In economics and finance, a holy grail distribution is a
In economics and finance, a holy grail distribution is a probability distribution
In probability theory and statistics, a probability distribution is a Function (mathematics), function that gives the probabilities of occurrence of possible events for an Experiment (probability theory), experiment. It is a mathematical descri ...
with positive mean
A mean is a quantity representing the "center" of a collection of numbers and is intermediate to the extreme values of the set of numbers. There are several kinds of means (or "measures of central tendency") in mathematics, especially in statist ...
and right fat tail — a returns profile of a hypothetical investment vehicle that produces small returns centered on zero and occasionally exhibits outsized positive returns.
The distribution of historical returns of most asset classes
In finance, an asset class is a group of marketable financial assets that have similar financial characteristics and behave similarly in the marketplace. These instruments can be distinguished as either having to do with real assets or having ...
and investment manager
Investment management (sometimes referred to more generally as financial asset management) is the professional asset management of various securities, including shareholdings, bonds, and other assets, such as real estate, to meet specified inve ...
s is negatively skewed
In probability theory and statistics, skewness is a measure of the asymmetry of the probability distribution of a real-valued random variable about its mean. The skewness value can be positive, zero, negative, or undefined.
For a unimodal ...
and exhibits fat left tail (abnormal negative returns). Asset classes tend to have strong negative returns when stock market crises take place. For example, in October 2008 stocks, most hedge fund
A hedge fund is a Pooling (resource management), pooled investment fund that holds Market liquidity, liquid assets and that makes use of complex trader (finance), trading and risk management techniques to aim to improve investment performance and ...
s, real estate and corporate bonds suffered strong downward price corrections. At the same time vehicles following the Holy Grail distribution such as the US dollar (as a DXY index), treasury bonds
United States Treasury securities, also called Treasuries or Treasurys, are government debt instruments issued by the United States Department of the Treasury to finance government spending as a supplement to taxation. Since 2012, the U.S. ...
and certain hedge fund strategies that bought credit default swaps (CDS) and other derivative instruments had strong positive returns. Market forces that pushed the first category of assets down pulled the latter category up.
Protection of a diversified investment portfolio from market crashes (extreme events) can be achieved by using a tail risk parity Tail risk parity is an extension of the risk parity concept that takes into account the behavior of the Portfolio (finance), portfolio components during tail risk events. The goal of the tail risk parity approach is to protect investment portfolios ...
approach, allocating a piece of the portfolio to a tail risk protection strategy, or to a strategy with Holy grail distribution of returns.
A financial instrument or investment strategy that follows a Holy Grail distribution is a perfect hedge to an instrument that follows the Taleb distribution
In economics and finance, a Taleb distribution is the statistical profile of an investment which normally provides a payoff of small positive returns, while carrying a small but significant risk of catastrophic losses. The term was coined by jou ...
. When a "Taleb" investment vehicle suffers an unusual loss, a perfect hedge exhibits a strong return compensating for that loss (both outliers must take place at the same time).
Practitioners tend to distinguish between a Holy Grail distribution and investment returns that are generated from an inverted Taleb distribution, a “minus-Taleb” distribution. The return series of the former has a positive mean while returns from the latter have a negative mean. For example, maintaining protection from market crashes by maintaining an exposure to an out-of-the-money put option
In finance, a put or put option is a derivative instrument in financial markets that gives the holder (i.e. the purchaser of the put option) the right to sell an asset (the ''underlying''), at a specified price (the ''strike''), by (or on) a ...
on a market index follows a “minus-Taleb” distribution because options premiums have to be paid to maintain the position and options tend to expire worthless in most cases. When a market sells off strongly these options pay back and generate a strong positive outlier that “minus-Taleb” distribution features.
See also
*Financial risk
Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financi ...
*Taleb distribution
In economics and finance, a Taleb distribution is the statistical profile of an investment which normally provides a payoff of small positive returns, while carrying a small but significant risk of catastrophic losses. The term was coined by jou ...
* Kurtosis risk
In statistics and decision theory, kurtosis risk is the risk that results when a statistical model assumes the normal distribution, but is applied to observations that have a tendency to occasionally be much farther (in terms of number of standar ...
* Skewness risk
Skewness risk in forecasting models utilized in the financial field is the risk that results when observations are not spread symmetrically around an average value, but instead have a skewed distribution. As a result, the mean and the median can ...
References
{{reflist, colwidth=35em Financial markets