# Level 1 CFA® Exam:

Risk Metrics

Probability is the simplest metric of risk.

Standard deviation and variance are basic risk metrics. Standard deviation is a square root of variance and it tells us what is an average deviation from the mean for a given probability distribution. Standard deviation may not be an appropriate risk measure for non-normal probability distributions.

Beta is a measure of systematic risk, so we can use it for both (i) well-diversified portfolios and (ii) single securities (the latter is true if we assume that investors are rational, in which case non-systematic risk shouldn’t be priced).

Beta tells us how much the rate of return for a stock / portfolio will change if the market return changes by 1 percentage point. By the definition, the beta of the market is equal to 1. Very often for defensive stocks beta is lower than 1. On the other hand, cyclical stocks are very often characterized by beta higher than 1.

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Tells us how much a price of a bond will change if the interest rate changes by 1 percentage point. Duration is the first-order risk, whereas convexity (which we discussed in the Fixed Income topic) is the second-order risk.

Value at Risk is a measure of downside risk because it is the measure that informs us about the minimal amount of money we can lose with a given probability, e.g.

If 5% VaR for a portfolio is USD 500,000 for 1 month >> there is a 5% probability that losses will exceed USD 500,000 in one month

Together with VaR, we very often use scenario analysis and stress testing.

A big drawback of VaR is that it doesn’t give us information about what the loss will be if we exceed the threshold. For the example given above, we know that there is a 5% probability that losses will exceed USD 500,000 in one month but we don’t know whether in this adverse case we should expect USD 1,000,000 of loss or maybe USD 10,000,000 or any other value.

This drawback of value at risk is mitigated by conditional value at risk.

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Measures of credit risk include: credit ratings, ratios (liquidity, solvency, profitability ratios), credit VaR, probability of default, expected loss given default, and probability of credit rating change.

Bondholders very often pay attention to prices of CDSs and based on them estimate the probability of default for an issuer. Also, the pricing of other derivatives can tell us a lot about the probability of adverse and extreme events perceived by the market.

- Standard deviation is a square root of variance and it tells us what is an average deviation from the mean for a given probability distribution.
- Beta tells us how much the rate of return for a stock / portfolio will change if the market return changes by 1 percentage point.
- The Greeks tell us how the price of an option or other derivative reacts to changes in some related variables.
- Value at Risk is a measure of downside risk because it is the measure that informs us about the minimal amount of money we can lose with a given probability.
- For a given probability distribution, conditional VaR (CVaR) measures weighted average loss for losses that exceed the VaR loss.
- Standard deviation, variance, beta, the Greeks, duration, VaR, and CVaR are market-related risk metrics.
- Measures of credit risk include: credit ratings, ratios (liquidity, solvency, profitability ratios), credit VaR, probability of default, expected loss given default, and probability of credit rating change.