Risk Measurements

Question 1

Calculate Standard Deviation of Multiple Asset Portfolio (with portfolio weights)

Answer 1

On formula on sheet; but two summations symbols are confusing: simplifies to this with two assets:

σp =(Wa x Wb x covariance of AB) ^(1/2)

Question 2

Which would have higher standard deviations…..annual returns

or monthly returns?

Answer 2

Annual returns have a higher standard deviation. Intuitively most would probably guess that monthly returns should have a higher standard deviation because monthly returns appear to jump around more than annual returns. But actually, standard deviations are higher over longer periods of time as more can happen (i.e., there is greater variability over time).

Question 3

Downside Deviation

Answer 3

Downside deviation, like standard deviation, measures the price volatility of financial instruments. The key difference is that downside deviation, or downside risk, focuses only on the price movement to the downside of a minimally accepted return (MAR).

The min in the Downside Deviation formula provided in the CIMA Formula Sheet refers to minimum, which means that as you go through all the n observations, you’ll sum the square of each of the smaller (minimum) of either 0 or Rt-MAR. The effect of this approach is to use 0 instead of Rt-MAR whenever the observation R t exceeds the MAR.

Don’t expect to calculate it

Question 4

Semi-Variance

Answer 4

• Measures data that is below the mean or target value of a data set.
• Considered a better measurement of downside risk.
• Semi-variance is the average of the squared deviations of all values less than the average or mean.
Think of semi variance as a specific version of downside deviation. Both relate to the standard deviation using only observations below some minimal level. In an investment theory capacity, that level is called: the minimally accepted return (MAR)), with downside deviation, which could be the average return, the risk free rate or some benchmark or index return; and the average or mean return, with semi-variance.

Question 5

Delta Normal Method (Value at Risk)

Answer 5

VaR is a measure of risk that quantifies potential loss (e.g., $1 million), the
probability of the potential loss (e.g., 3%), and the time frame for potential loss (e.g.,
three months). Assumes returns are normally distributed
• Advantages
• Easy to understand
• Not computationally difficult
• Disadvantages
• Returns not normal kurtosis (fat tails)
• Correlation not constant

Question 6

Value at Risk z-scores

Answer 6

z = -1.00 (i.e., 1 std dev left) covers 15.87% or about 16% which is why the area within 1 std deviation of a mean represents 68% of the outcomes
z = -2.00 covers 2.28% so +/ 2 std dev represents about 95%
z = -3.00 covers 0.13% so +/ 3 std dev represents about 99%
z = -1.65 covers 5.0% (useful for VaR)
z = -2.33 covers 1.0% (useful for VaR)

Question 7

Alternate Value at Risk Formula

Answer 7

VaR = -[Expected Return + (Z-score x SDEV)] * Portfolio Value