Chapter 4: Measures of investment Risk Flashcards
Value at risk
Generalises the likelihood of underperforming by providing a statistical measure of downside risk.
Formula: Value at risk
VaR(X) = -t where P(X < t) = p
Argument for using semi-variance as a risk measure
Most investors do not dislike uncertainty of returns as such; rather, they dislike the possibility of low returns.
4 Arguments against using semi-variance as a risk measure
- not easy to handle mathematically
- takes no account of variability above the mean
- if returns are symmetrically distributed, semi-variance is proportional to variance, so it gives no extra information.
- semi-variance measures downside relative to the mean rather than another benchmark that might be more relevant to the investor.
What can be deduced about and investor’s utility function if the investor makes decisions based on THE VARIANCE OF RETURNS
may imply that the investor has a quadratic utility function
What can be deduced about and investor’s utility function if the investor makes decisions based on the SHORTFALL PROBABILITY OF RETURNS?
This corresponds to a utility function which has a discontinuity at the minimum required return.
5 Measures of investment risk
- Variance of return
- Downside semi-variance of return
- Shortfall probability
- Value at Risk
- Tail value at Risk
Advantages of
Variance of return
- Mathematically tractable
- fits neatly with a mean-variance portfolio construction framework
Disadvantages of “Variance of Return”
- Symmetric measure of risk. The problem of investors is really the downside part of the distribution.
- Credit risky bonds have an asymmetric return distribution and as defaults are often co-dependent on economic downturns, portfolios can have fat tails.
- Neither skewness or kurtosis of returns is captured by a variance measure.
Advantages to Downside Semi-variance of return
- Takes into account the risk of lower returns
- can be decomposed into systematic and non-systematic risk contributions
Disadvantages of downside semi-variance of return
- Semi-variance is not easy to handle mathematically and takes no account of variability above the mean
- if returns on assets are symmetrically distributed, semi-variance is proportional to variance.
- does not capture skewness or kurtosis
Advantages to using “shortfall probability”
- Gives an indication of the possibility of loss below a certain
- It allows a manager to manage risk where returns are not normally distributed
Disadvantages of using “shortfall probability”
- choice of benchmark level is arbitrary
For a portfolio of bonds, the shortfall probability will not give any information on:
- upside returns above the benchmark level
- nor the potential downside of returns when the benchmark level is exceeded.
Advantages to using Value at Risk (VaR)
- VaR generalises the likelihood of underperformance by providing a statistical measure of downside risk
Disadvantages to using Value at Risk
- Portfolios exposed to credit risk, systematic bias or derivatives may exhibit non-normal distributions.
- Usefulness of VaR in these situations depends on modelling skewed or fat-tailed distributions of returns.
- The further one gets out into the “tails” of the distributions, the more lacking the data and, hence, the more arbitrary the choice of the underlying probability distribution becomes.
