# Tail Risk

Most of the literature in market risk management is dedicated to explaining the methods which are used in the management of regular market risk. This means that importance is rightly given to the management of the cases which are likely to occur 99% of the time. However, the recent past has shown us that there are some severe events that can happen 1% of the time.

For instance, the subprime mortgage crisis, as well as the coronavirus pandemic, are two severe events that have taken place over the course of a decade! If these infrequent but high-impact events are not managed in an appropriate manner, they could threaten the very existence of the firm. The risk which these unforeseen events pose to the organization is called tail risk. In this article, we will have a closer look at what tail risk is and how it can be used to manage risks better.

### What is Tail Risk?

In simple words, tail risk is the risk of loss that may arise when a highly improbable event occurs. They are often called “black swan” events in reference to the term black swan which was coined by Nicholas Nassem Taleb.

The more technical definition of tail risk is that it is the risk arising from three standard deviations away from the mean. This means that if we assume a normal distribution, almost 99.7% of the values will be within three standard deviations from the mean. Hence, the risk arising from the balance of 0.3% of the values is called tail risk.

It needs to be understood that the approach used to manage tail risks is different from the approach used to manage the other risks. This is because of the fact that it is impossible to predict tail risk. This is the reason that no attempt is made to predict the black swan events as opposed to the other risk events. Instead, it is assumed that these events will take place infrequently and there must be a mechanism in place in order to manage the risk better.

### The Possibility of a Fat Tail

In the above definition, we have assumed that the returns follow a normal distribution. However, in reality, that may not be the case. There are many statisticians who have observed that the returns seem to have more values towards the extreme left and extreme right end than a normal curve. This is colloquially referred to as a fat tail. Over the years, statisticians have developed a different type of distribution called the fat-tailed distribution in order to be able to manage these situations better.

### How Can Tail Risks Be Managed?

Tail risks are generally managed by hedging these risks. There are several ways in which this hedging is done. For instance, the investors can buy an option that allows them to sell their securities at a higher price if the value of these securities goes below a certain price. This price is the price that is three standard deviations away from the mean. Since the probability of this event happening is extremely low i.e. 0.3%, the options are quite cheap.

In most of the years, the options will be out of the money and hence it may appear like a waste of resources to continue buying them. However, one must not forget that the risk being covered is rare but has a huge impact. Hence, it is advisable to continue buying the options unabated.

There are certainly other strategies that are also used to hedge tail risk. For instance, firms can deliberately reduce the amount they invest in highly volatile sectors.

Alternatively, derivatives such as swaps can also be used. However, whenever derivatives are involved, the complexity of the instruments increases rapidly. Monitoring and mitigating risks become even more important since it may be possible to lose more than the initial investment which was made.

### Is Hedging Tail Risks Expensive?

Many experts believe that hedging tail risks can be quite expensive. This may be true particularly when fat tails are being hedged. However, leaving the fat tails unhedged would be like taking a huge risk. Everything will work fine for a long period of time until one day when it suddenly doesn’t!

There are several benefits that are realized as a result of this hedging.

1. The company is protected from adverse events which can threaten its existence

2. Since the organization is protected from the vagaries of these adverse events, it has excess cash flow. This excess cash flow can be a valuable tool to buy up assets on the cheap since the market has just witnessed a massive downturn

3. Under normal circumstances, the organization is assured that its tail risks are covered. Hence, they can afford to take more risks elsewhere without exceeding their total risk threshold.

If we consider all these advantages, it may in fact be much more expensive to not hedge the tail risks particularly when the option premiums required for this protection may be paltry.

To sum it up, tail risks are not covered under the value at risk (VaR) model. They need to be calculated separately. Hedging is the only way to mitigate them since anticipating such risks is almost impossible.

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