VRM1 - Measures of Financial Risk

Question 1

Describe the mean-variance framework and the efficient frontier

Answer 1

Mean-variance framework is the trade-off between risk and return

Efficient frontier created by considering all combinations of risky assets, any combination not on the frontier is not efficient

Question 2

Compare the normal distribution with the typical distribution of returns of risky financial assets such as equities

Answer 2

In practice, financial variables have much fatter tails than the normal distribution

Question 3

Define the VaR measure of risk, describe assumptions about return distributions and explain the limitations of VaR

Answer 3

VaR is the loss level that we do not expect to be exceeded over the time horizon at a specified confidence level

Does not speak to how bad losses may be if they are over VaR level

Question 4

Explain and calculate ES and compare and contrast VaR and ES

Answer 4

Expected shortfall is the expected loss conditional that the loss is greater than the VaR level

ES = mu + sigma * (exp(-u^2 / 2) / ((1 + X)*2pi))
X = confidence level
U = point in normal that has x probability of being exceeded

Question 5

Define the properties of a coherent risk measure and explain the meaning of each property

Answer 5

1. monotonicity: if Pa always worse than Pb, Pa should have a higher risk measure
2. translation invariance: if cash K added to a portfolio, risk measure should decrease by K
3. homogeneity: multiplying all components by lambda means risk measure multiplied by lambda
4. subadditivity: risk measure (A + B) <= risk A + risk B

Question 6

Explain why VaR is not a coherent risk measure

Answer 6

VaR does not have subadditivity