Coherent Risk Measure: Types - Advantages & Disadvantages

In the subject of finance and economics, it is very crucial to choose an appropriate risk measurement technique achieving desired results. Among various risk measurement techniques, the most commonly used was Value at Risk (VaR) measure. But, due to the failure of this method to consider extreme events, it became imperative to develop an effective method. This is the reason marketers came up with the method of Coherent Risk Measure. Here you will learn about all the aspects of this technique educating you to tackle some of the most extreme challenges.

What is a Coherent Risk Measure?

Before elucidating the technique of coherent risk measure, you need to understand the significance of this subject in financial economics. A coherent risk measure is a method used to estimate the profitability of a business depending on the risk taken. In this discipline, the amount of risk involved in a business is directly proportioning to the profits earned. The demand for this technique emerged after encountering the shortcomings and drawbacks of the method of Value at Risk. Correctly, in the discipline of actuarial science and financial economics, the method of coherent risk measure plays a vital role. It considers all the extreme events lying under the shortcomings of VaR measure making it suitable while analyzing risk.

The method of coherent risk measure works on the principle of Expected Tail Loss helping marketers to estimate the risks accurately. Also, for a risk measure to be coherent, it should satisfy specific mathematical properties possessing a strong significance in risk measurement. Thus, this method satisfies the properties of monotonicity, sub-additivity, positive homogeneity, and translation invariance.

What Are the Different Types of Coherence?

Coherence risk measure follows a set of relevant criteria needed to measure the risk involved in earning profits of a business. To estimate the profitability of a business, you need to consider the factors involved in risk measurement like; p(X) where X is a set of outcomes.

4 Types of Coherence Risk Measurement

Monotonicity: It implies that an increase in return in all future sales of security leads to a decrease in the risk of loss. On comparing the portfolios of both the factors, it can be observed that for a factor possessing greater values than another; the chances of risk tends to decrease in business. The mathematical operation of this measurement can be shown as follows:

If X < Y for each scenario, p(X) > p(Y).

Sub-additivity: This type of measurement is also known as the Diversification principle as it contributes to the diversification of risk involved in the business. It educates you regarding the risks involved if you add two portfolios together and adding the two separately. The mathematical explanation of this method is given as p(X + Y) < p(X) + p(Y).
Positive homogeneity: According to this measurement, if you double the capital asset of a portfolio, then the risk associated with it also gets doubled. It can be given as, for X > 0, p(XX) = Xp(X).
Translation variance: It states that if a sum of cash c is added to a portfolio, then the risk is reduced by the given amount. In simple terms, you can add cash to a portfolio reducing the risks associated with your business. In mathematical terms,

p(X + c) = p(X) - c

The method of Value at Risk got nullified as it failed to satisfy the condition of sub-additivity. Suppose, you have two portfolios X and Y, then the benefits can be given as:

p(X) + p(Y) - p(X + Y)

Therefore, risk measurement can be considered as coherent if it satisfies all the four factors described above.

Why is Value at Risk Not a Coherent Risk Measure?

Value at Risk (VaR) is an old technique of actuarial science and financial economics used to estimate the risks involved in the business. But, the reason that this theory lost popularity in the market was due to its failure to satisfy the conditions of the sub-additivity axiom. Moreover, the technique of VaR failed in considering extreme events making it more challenging for a business to estimate the risks. It is imperative for any organization to evaluate the risks involved to provide it with an adequate measure contributing to its promotion. Therefore, the primary reason for the failure of this method was its incapacity to consider all the crucial factors.

Advantages and Disadvantages of Coherent Risk Measures

Advantages

It helps to determine the risks involved in a business and estimating the profitability more accurately.
It contributes majorly to a decrease in the risk of loss for business by boosting the return for all future sales.
This method contributes to the diversification of risk involved in the business as it categorizes the portfolios separately.
It allows you to add cash to your portfolio and reducing the risk associated with it contributing to the development of your business.

Disadvantages

Being considered as the most popular method to determine the risk involved in a business, it does not guarantee 100% accuracy.
A deficiency of sub-additivity in the risk measurement of business can be exploited leading to a form of regulatory arbitrage.

Is Expected Shortfall a Coherent Risk Measure?

Expected shortfall is calculated as an average of the total losses having a value greater than or equal to VaR. It estimates the future value of an investment in the worst possibilities of any case. Therefore, the technique of expected shortfall is considered as an effective, coherent risk measure widely known by marketers globally. It is also known as the conditional value at risk (CVaR), average value at risk (AVaR), and expected tail loss (ETL).

Expected Shortfall - A Coherent Risk Measure

This method concentrates on the less favorable outcomes estimating the risks involved in an investment in a materialistic way.
It ignores the remote possibilities of maximum profits for higher values of quantile (q). On the contrary, it focuses on maximum losses for a small value of quantile (q).
This method is a well-known coherent risk measure possessing stronger significance than the technique of value at risk (VaR).
Expected shortfall is the mean loss in a value given that a loss is occurring at or below the quantile. Also, it contributes majorly to the estimation of quantile-level (q) more accurately helping marketers to calculate the profits earned.

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