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  • 9 July 2021

What is tail risk and how to calculate it

Tail Risk

What is tail risk and how to calculate it

What is tail risk and how to calculate it 800 400 FinScience

written by Valerio Sabelli

What is meant by Tail Risk?

Tail risk (or extreme risk) is the possibility of a loss occurring due to a rare event, as predicted by the probability distribution.

Traditional strategies for building a portfolio are grounded on this theory: the probabilities of obtaining revenues and losses follow a normal distribution (i.e that the probability of having extremely low or extremely high revenues is close to zero). But actually, in the real world we know this is not so true and we must take into account the fact that these distributions come with the so-called “fat tails”: probabilities of extreme losses / gains, calculated through tail risk.

What does Tail mean in Finance?

In order to understand what tail risk is, we should first define what a tail event is: something that can occur with a very low probability, but in case it does happen, it has very heavy implications on the economic and financial markets

This kind of event causes such high volatility, because few traders have been able to predict it.

As a matter of fact, just as it is difficult to predict the event, it is also complicated to estimate the risk for investors: these types of events are quite unique and they create unique, unpredictable correlations among the various investments (despite the existing diversification strategies).

Why is tail risk important?

Because once you acknowledge it, you can start to implement countermeasures to limit damage in case of rare but still possible events.

Casual investors often tend to think: “very rare event” = “impossible event”.

But those who invest in their portfolios more consciously are increasingly in need of a tail risk analysis – especially after financial catastrophic events such as the real estate bubble of American sub-prime mortgages in 2006.

So let’s get to know tail risk better and find out what is the most commonly used strategy to minimize tail risk.

How to calculate Tail Risk

As we said before, tail events happen very infrequently and their impact is different with each new occurrence.

The measure used to understand the effect of these events is the Expected tail loss (ETL)

This is an extension of the so-called VaR (Value at Risk) statistic, which is a defined threshold statistic, basically you calculate the minimum loss for a portfolio, setting a certain probability and a certain time horizon. 

For example, if a certain portfolio has a VaR value of 5% of one million euros, this implies there is a 5% probability that the portfolio will lose that amount of money on a monthly basis. However, we have no indication of how much we would lose if we went beyond the million euros indicated above.

On the contrary, the ETL is instead calculated by averaging the losses that are beyond a certain threshold in the distribution of the revenues of a portfolio. The distribution can be modeled in various ways, but the simplest strategy is to use time series, thus data that has been actually already measured. 

Optimizing the weights between the assets in the portfolio, we can find the combination of investments that minimizes the ETL.

Another way to estimate the tail risk are random walks (also used in physics to simulate random deviations from the starting trend of real data) or Monte Carlo simulations (based on the calculation of linear regressions that estimate the values ​​of the assets through experimental averages).

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What is tail risk strategy?

Tail or Hedging strategies are a way to potentially limit losses in less favorable markets. They can allow investors to maintain their position in difficult times, in a long-term perspective.

How can we protect ourselves from these events? The so-called hedging strategies can be exploited. Basically, you should “spend” part of your revenues each year to “buy” protection – a metaphorical Hedge – against market upheavals.

To get an idea of ​​how it works, here’s an example from everyday life. 

Suppose you have just bought a very expensive house. It could happen – albeit with a very low probability – that your house is destroyed by a fire. In order to mitigate the damage if this could ever happen, you buy home insurance which, in fact, “bets” on that event.

Therefore you agree to lose the insurance premium on a monthly basis, but you know you would be able to manage the “economic disaster” of a fire.  

Applying a hedging mechanism that can protect you from a tail event means using financial instruments or market strategies to reduce the risk of significant economic losses, accepting a slightly lower profit in the activity everyday.