Question

NAB shares have a monthly average return of 1% and a monthly return standard deviation of 5%. Returns are assumed to be normally distributed.

1. Calculate the stock’s Value-at-Risk (VaR) at the 95% level over the 1 month horizon.
2. Calculate the stock’s Value-at-Risk (VaR) at the 95% level over the 1 year horizon

Answer 1

standard deviation Monthly (σ Monthly) = 05%

Now standard deviation  Yearly (σ Yearly ) =

σ Yearly = σ Monthly * sqrt(12) = 05% * sqrt (12) = 05% * 3.4641 = 17.3205 %

monthly average return of (RM) = 01%

Yearly  average return of (RY) = RM * 12 = 01% * 12 = 12%

Value-at-Risk (VaR) at the 95%  level over the 1-month horizon. =

P(z) * RM*  σ Monthly = P(95%) * 01% * 0.05 = 1.65 * 1% * 0.05 = 0.0825%

Value-at-Risk (VaR) at the 95%  level over the 1-month horizon. =   0.0825% (Ans)

Value-at-Risk (VaR) at the 95%  level over the 1 Year horizon. =

P(z) * RY*  σ Yearly = P(95%) * 12% * 0.05 = 1.65 * 12 % * 0.173205 = 3.429%

Value-at-Risk (VaR) at the 95% level over the 1 Year horizon. = 3.429% (Ans)