Mastering Risk Measurement Techniques | CFA Level I Portfolio Management

In this lesson, we’ll explore the different ways to measure and quantify risk.

Understanding Probability and Standard Deviation

Probability is the most basic metric associated with risk. For example, estimating the probability of incurring a financial loss from an investment. However, this doesn’t provide much information about the extent of the potential loss.

A more informative and widely-used metric is the standard deviation, which measures the range over which a certain percentage of outcomes are expected to occur. For example, in a normal distribution, about 68% of outcomes lie within ±1 standard deviation of the expected value. Standard deviation is widely used to model the volatility of an asset’s returns.

Limitations of Standard Deviation and Alternative Risk Measures

Standard deviation has some limitations, especially when dealing with non-normal distributions. In these cases, other risk measures like beta for equities, duration for fixed-income instruments, and the Greeks for derivatives are more appropriate.

The Greeks: Delta, Gamma, Vega, and Rho

The Greeks are specialized measures of derivatives risk:

• Delta – Sensitivity of a derivative’s value to a small change in the price of the underlying asset.
• Gamma – Sensitivity of delta to changes in the price of the underlying asset.
• Vega – Sensitivity of a derivative’s value to a change in the price volatility of the underlying asset.
• Rho – Sensitivity of a derivative’s value to changes in interest rates.

Value at Risk (VaR) and Conditional Value-at-Risk (CVaR)

Value at Risk (VaR) is a widely recognized risk measure that focuses on tail or downside risk, estimating the probability of extreme negative outcomes. VaR is applicable across various asset classes, and its measure contains three key elements: a time period, a minimum loss amount stated in units of currency, and a probability.

For instance, a bank might have a one-day VaR of $2 million, with a 5% probability. This means that a loss of at least $2 million in a single day is expected to occur 5% of the time, or once every 20 days. While VaR is widely accepted as a risk measure for banks and used in setting minimum capital requirements, it’s important to note that VaR only specifies the minimum loss over a period, not the maximum loss or an expected value of the loss.

Conditional Value-at-Risk (CVaR), on the other hand, is the expected value of a loss, given that the loss exceeds a minimum amount. Instead of knowing the probability, we get the expected value of the loss if the loss surpasses the minimum. Based on the previous example, the bank’s CVaR might be “if the one-day loss exceeds $2 million, the expected loss is $2.6 million”. In this case, the CVaR would be $2.6 million.

CVaR is similar to the measure of loss severity given default that is used in estimating default risk for debt securities. Both VaR and CVaR have their limitations, and their values can be significantly affected by the inputs and models used for calculation. As such, it’s crucial to use them in conjunction with other risk measures.

Two complementary measures often used alongside VaR are stress testing and scenario analysis. These common-sense approaches examine the effects of specific key variables or multiple variables pushed to extreme values, helping to gauge how a company is affected under different circumstances.

Stress Testing and Scenario Analysis

Stress testing and scenario analysis are common sense approaches to risk measurement:

• Stress testing – Examining the effects when a specific key variable is pushed to an extreme value.
• Scenario analysis – Incorporating changes in multiple variables to analyze the impact on the company.

Measuring Credit Risk, Operational Risk, and Tax and Regulatory Risk

Some risks, like credit risks, operational risks, and tax and regulatory risks, can be very difficult to estimate and quantify:

• Credit risk – Subjective estimates based on the market prices of insurance, derivatives, or other securities to hedge risks.
• Operational risk – Analyzing a large sample of similar firms to estimate the probability and average loss of significant losses due to operational risks.
• Tax and regulatory risk – Subjective estimates, as unexpected changes in tax laws or the regulatory environment are difficult to predict.

It’s important to remember that having a subjective estimate of risk is better than not addressing the risk factor at all.

Conclusion

And there you have it – an overview of various ways to measure risk exposure for an organization. Our last stop on this topic will be on modifying risk exposures.