A $600 investment has the following payoff frequency: a quarter of the time it will be $0; three quarters of the time it will pay off $1000. Its standard deviation and value at risk respectively are:
A) $750; $600
B) $433; $600
C) $0; $1,000
D) $433; $1,000

Question

Quizplus · Accepted Answer

To calculate the standard deviation of the investment, we can use the formula:
SD = sqrt[(0-1000)^2(1/4) + (1000-600)^2(3/4)]
This simplifies to SD= $433.

To calculate the value at risk, we need to determine the minimum loss with a certain level of confidence. Let's say we want a 95% confidence level. We can use the formula:
VaR = (expected return) - (z-score)(SD)
The expected return is 3/4(1000) + 1/4(0) = $750.
For a 95% confidence level, the z-score is 1.645.
Plugging in the values, we get:
VaR = 750 - (1.645)(433) = $67. 
So the answer is B, with a standard deviation of $433 and a value at risk of $67.

A $600 Investment Has the Following Payoff Frequency: a Quarter