Measures of Investment Risk

Question 1

Comment on the usefulness of downside semi-variance as a measure of investment
risk.

Answer 1

• Ignores risk (variance) above the mean.
• Consistent with an investor who is risk-neutral above the mean (an unlikely scenario).
• The mean may not be an appropriate benchmark for a particular investor (it is an
  arbitrary benchmark).
• Gives the same results as using the variance if returns are symmetrical.
• Much less easy to use for calculations/modelling than variance (less mathematically
  tractable)

Question 2

Advantages and Disadvantages of Variance of return

Answer 2

• Variance is mathematically tractable.
• Variance fits neatly with a mean-variance portfolio construction framework.
• Variance is a symmetric measure of risk. The problem of investors is really the downside part of the distribution.
• Neither skewness nor kurtosis of returns is captured by a variance measure.

Question 3

Advantages and Disadvantages of Downside semi-variance of return

Answer 3

• Semi-variance is not easy to handle mathematically and it takes no account of variability above the mean.
• Furthermore if returns on assets are symmetrically distributed semi-variance is
  proportional to variance.
• As with variance of return, semi-variance does not capture skewness or kurtosis.
• It takes into account the risk of lower returns.

Question 4

Advantages and Disadvantages of Shortfall probability

Answer 4

• The 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.
• It gives an indication of the possibility of loss below a certain level.
• It allows a manager to manage risk where returns are not normally distributed.

Question 5

Advantages and Disadvantages of Value at Risk

Answer 5

• VaR generalises the likelihood of underperformance by providing a statistical measure of downside risk.
• Portfolios exposed to credit risk, systematic bias or derivatives may exhibit non-normal distributions.
• The 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.

Question 6

Advantages and Disadvantages of Tail Value at Risk (TailVaR)

Answer 6

• Relative to VaR, TailVaR provides much more information on how bad returns can be when the benchmark level is exceeded.
• It has the same modelling issues as VaR in terms of sparse data, but captures more information on tail of the non-normal distribution.