Question

Suppose you have a portfolio worth $10000. Assuming normally distributed portfolio returns, calculate the 5% Dollar VaR for the portfolio if the expected return is 31% and variance 25%. VaR5%​=Rexpected ​+−1.64485+σ Caclculate the solution to two decimal points of accuracy.

Answer 1

The 5% Dollar Value at Risk for a portfolio with an expected return of 31% and a variance of 25% is $11,324.25.

Step-by-step explanation:

The question asks for the calculation of the 5% Dollar Value at Risk (VaR) for a portfolio that has normally distributed returns. The expected return is 31% and the variance is 25%. The VaR formula is: VaR5% = Rexpected - Zscore(5%) × σ, where the Zscore(5%) for a one-tailed normal distribution is -1.64485.

Firstly, to find the standard deviation (σ), we take the square root of the variance:

σ = √25% = 0.5 or 50%.

Now apply the given values into the VaR formula:

VaR5% = 31% - (-1.64485 × 50%) = 31% - (-82.2425%) = 31% + 82.2425% = 113.2425%.

The Dollar VaR is obtained by multiplying the percentage VaR by the portfolio value:

$10,000 × 113.2425% = $11,324.25.

So the 5% Dollar VaR for the portfolio is $11,324.25.