Question

Universal Corporation is planning to invest in a security that has several possible rates of return. Given the probability distribution of returns in the table below​, what is the expected rate of return on the​ investment? Also compute the standard deviation of the returns. What do the resulting numbers​ represent? a. The expected rate of return on the investment is____%

PROBABILITY   RETURN
0.05    -10%
0.15 10%
0.25 15%
0.55 30%

Answer 1

Probability	Return
0.05	-10%
0.15	10%
0.25	15%
0.55	30%

Expected Return is calculated using below formula:

where p_i is the probability of the ith possible return R_i

Expected Return = E[R] = (0.05*(-10%)) + (0.15*10%) + (0.25*15%) + (0.55*30%) = 21.25%

Variance is calculated using below formula:

Variance = 0.05*(-10%-21.25%)² + 0.15*(10%-21.25%)² + 0.25*(15%-21.25%)² + 0.55*(30%-21.25%)² = 0.01196875

we know that standard deviation is just the square-root of the variance

So, Standard Deviation = (0.01196875)^1/2 = 0.109401782435205 = 10.94%

These numbers represent that the anticipated return or the profit on this security is 21.25% and the risk associated with that security is around 10.94%

Answer

Expected Return = 21.25%

Standard Deviation = 10.94%