Question

You have invested $12,000 in a portfolio with an annual expected return of 5.6% and standard deviation of 7.1%. Compute your portfolio’s 5% VaR. Express your answer both in percentage and dollar term.

You have invested $12,000 in a portfolio with an annual expected return of 5.6% and standard deviation of 7.1%. Compute your portfolio's 5% VaR. Express your answer both in percentage and dollar term.

Answer 1

The value at risk (VaR) at 5% for the portfolio means alpha is equal to 5% and we have confidence interval 95% and corresponding z value is equal to 1.96

Now

VaR = Mean – z * standard deviation

An annual expected return, mean = 5.6%

And standard deviation of portfolio σ =7.1%

Therefore

VaR = 5.6% - 1.96 * 7.1%

=- 8.316%

Value at risk is -8.316%

Formula to calculate the amount of daily value at risk at the 95% confidence level

VaR of portfolio = V0 * (z *σ)

Where,

V0 is the value of investment = $12,000

Z-score at 95% confidence interval = 1.96

And standard deviation of portfolio σ =7.1%

Therefore

VaR = $12,000* (1.96 *7.1%)

= $12,000* 0.13916

= $1,669.92

Value at risk is a measure of the risk of loss on investments. It estimates that with a given probability, what portion of investments you may loss in a certain time period in a normal market conditions.

Therefore here the meaning of VaR is that at 95% of the time, you will not lose more than $1,669.92 of your investments in a day if market conditions are normal.