Also need the Value at risk: Assume that the economy can experience high growth,

ID: 2817761 • Letter: A

Question

Also need the Value at risk:

Assume that the economy can experience high growth, normal growth, or recession. Under these conditions, you expect the following stock market returns for the coming year: Probabilit 0.2 0.7 0.1 State of the Eco Hich Growth Normal Growth Recession Return 50 22% 58 a. Compute the expected value of a $1,000 investment over the coming year. If you invest $1,000 today, how much money do you expect to have next year? What is the percentage expected rate of return? Instructions: Enter dollar values rounded to the nearest whole dollar and percentages rounded to one decimal place The expected value is $ b. Compute the standard deviation of the percentage return over the coming year. Standard deviation = 1% c. If the risk-free return is 7 percent, what is the risk premium for a stock market investment? Risk premium = % and the expected rate of return is

Explanation / Answer

State of Economy

Probability = P

Return = R

Product = P x R

High growth

0.20

50.00%

10.00000%

Normal

0.70

22.00%

15.40000%

Recession

0.10

-5.00%

-0.50000%

Average Return = Total =

24.90000%

Expected return = 24.9%

Expected value = 1000 x (1+24.9%) = $1,249

Standard deviation of return = [Sum (Probability x (Return - Average return)]^0.5

Standard deviation of return = (0.2*(50%-24.9%)^2+0.7*(22%-24.9%)^2+0.1*(-5%-24.9%)^2)^0.5

Standard deviation =

14.9%

Risk premium = Expected return - risk free return

Risk premium = 24.9%-7%

Risk premium = 17.9%

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Note:

For value at risk we need confidence level:

Just ---- Assuming confidence level of 95% the Z-value = 1.65

Value at risk in % = - Expected return + Z-value x Standard deviation

Value at risk in % = - 24.90% + 1.65 x 14.88% = -0.35%