Value at Risk - statistics/economics

Question

Sophie is a moderate investor who maintains her portfolio of U$50,000.00 with an average daily return of 0.1% and a daily standard deviation of 1.2%.

Under these conditions, the maximum daily loss estimate, with a confidence level of 95%, taking as a measure of the parametric VaR is approximate:

a) U$ 510,00

b) U$ 750,00.

c) U$ 940,00.

d) U$ 1150,00.

Answer 1

The general formula for calculating VaR at a given confidence level is:

VaR ​ = portfolio_value * [ average return - (z-score * standard deviation) ].

The z-score corresponding the one-sided p= 95% confidence interval is obtained from P(Z > z ) = 0.05, or z=1.65. Therefore VaR= 50000 *[(0.001 - 1.65*0.012)] = -$937, which is close to answer c) $940.

Since everything is calculated daily, no further conversion is needed.