Question

1. Jerome is considering investing $10,000 in a security that has the following distribution of
possible one-year returns:

Probability of
Occurrence 0.10 0.20 0.30 0.30 0.10

Possible
Return -10% 0% 10% 20% 30%
a) What is the expected return in % associated with the investment?

b) Calculate the expected return in DOLLAR AMOUNT for the investment.

c) What is the standard deviation associated with the investment?

Answer 1

(a)-Expected return in % associated with the investment

Expected Return = Sum(Returns x Probability of Occurrence)

= [-10% x 0.10] + 0% x 0.20] + [10% x 0.30] + [20% x 0.30] + [30% x 0.10]

= -1.00% + 0% + 3.00% + 6.00% + 3.00%

= 11.00%

(b)-Expected return in dollar amount for the investment

Expected return in dollar amount = Total amount invested x Expected Rate of Return

= $10,000 x 11%

= $1,100

(c)-Standard deviation associated with the investment

Variance of the Return

Variance = [(-10 - 11)² x 0.10] + [(0 - 11)² x 0.20] + [(10 - 11)² x 0.30] + [(20 - 11)² x 0.30] + [(30 - 11)² x 0.10]

= [441 x 0.10] + [121 x 0.20] + [1 x 0.30] + [81 x 0.30] + [361 x 0.10]

= 44.10 + 24.20 + 0.30 + 24.30 + 36.10

= 129

Standard Deviation of the Returns

The Standard Deviation of the Returns is the Square Root of 129 or [129]^1/2

= 11.36%

“Hence, the Standard deviation associated with the investment would be 11.36%”