Question

A trader has invested equal amounts in Stock A and Stock B and knows the following:

• Stock A’s daily average return is 0% and its daily standard deviation is 2%.
• Stock B’s daily average return is 0% and its daily standard deviation is 3%.
• The stocks have a correlation of 0.4.

If returns are assumed to be normally distributed, calculate the 10 day Value-at-Risk (VaR) for this portfolio at the 99% level

Answer 1

Please note the concept tested in the question is Value at risk.

1) Concept

VAR = Invested Amount * Z * Standard deviation of portfolio

2) Calculation

Standard deviatiion of portfolio =

Standard Deviation = [ (0.5)2 * (0.02)2 + (0.5)2 * (0.03)2 + 2 * (0.5 * 0.5) * (0.02 * 0.03) * 0.4 ] 1/2

                                     = 1.67 %

10 days standard deviation of portfolio = (10)1/2 * 1.67

                                                               = 5.281 %

VAR = 100000 * 5.281 % * ( 2.33) [ Z at 99% confidence level = 2.33]

           = $ 12304.74 Answer