VRM2 - Calculating and Applying VaR

Question 1

Explain and gives examples of linear and non-linear portfolios

Answer 1

Linear portfolio is linearly dependent on the changes in its underlying assets

Question 2

Describe and explain the historical simulation approach for computing VaR and ES

Answer 2

Identify market variables which effect the value of a portfolio, then look at deltas between day 0-1, 1-2, up to 500 in these variables - use deltas from all of these to create 500 scenarios for 500-501st day

VaR and ES can be calculated from this sample by sorting

Question 3

Describe the delta-normal approach and use it to calculate VaR for non-linear derivatives

Answer 3

Delta-normal gives dP = delta * dS = 0.5 * gamma (dS)^2

ai = di * Si if % change, di if actual
xi = dSi / Si if % change, dSi if actual

then mu_p = sum(i = 1 to n) ai * mu_i
and sigma_p = sum(i = 1 to n) ai^2 * simga_i^2 + 2sum(i>j) ai aj* rho_ij *sigma_i * sigma_j

VaR = mu_p + sigma_p * U

Question 4

Describe limitations with the delta-normal model

Answer 4

Good for both linear and non-linear when gamma is low, answers skew with increasing gamma

Question 5

Explain the structured Monte Carlo method for computing VaR and identify its strengths and weaknesses

Answer 5

• value portfolio using current value of risk factors
• sample from MVNorm to determine new values of risk factors
• calculate the effect this has on the portfolio (one day sim)
• repeat and order to find VaR and ES

Can be computationally expensive

Question 6

Describe implications of correlation breakdown for scenario analysis

Answer 6

In periods of high market stress, correlations do not act in the same way as in normal market conditions - this should be taken into account when calculating VaR and ES

Question 7

Describe worst-case scenario (WCS) analysis and compare WCS to VaR

Answer 7

When repeated trials, can focus on worst-case over a period and perform analysis on that

Tends to be overly pessimistic so doesn’t tend to be used as alternative to VaR