The following annual returns for Stock E are projected over the next year for three possible states of the economy. What is the stock's expected return and standard deviation of returns? E (R) = 8.5% σ = 22.70%

The question is incomplete. Here is the complete question:

The following annual returns for Stock E are projected over the next year for three possible states of the economy. What is the stock's expected return and standard deviation of returns? E (R) = 8.5%; σ = 22.70%; mean = $7.50; standard deviation = $2.50

State Prob E (R)

Boom 10% 40%

Normal 60% 20%

Recession 30% - 25%

Answer:

The expected return of the stock E (R) is 8.5%.

The standard deviation of the returns is 22.7%

Explanation:

Expected return

The expected return of the stock can be calculated by multiplying the stock's expected return E (R) in each state of economy by the probability of that state.

The expected return E (R) = (0.4 * 0.1) + (0.2 * 0.6) + (-0.25 * 0.3)

The expected return E (R) = 0.04 + 0.12 - 0.075 = 0.085 or 8.5%

Standard Deviation of returns

The standard deviation is a measure of total risk. It measures the volatility of the stock's expected return. The standard deviation (SD) of a stock's return can be calculated by using the following formula:

SD = √ (rA - E (R)) ² * (pA) + (rB - E (R)) ² * (pB) + ... + (rN - E (R)) ² * (pN)

Where,

rA, rB to rN is the return under event A, B to N. pA, pB to pN is the probability of these events to occur E (R) is the expected return of the stock

Here, the events are the state of economy.

So, SD = √ (0.4 - 0.085) ² * (0.1) + (0.2 - 0.085) ² * (0.6) + (-0.25 - 0.085) ² * (0.3)

SD = 0.22699 or 22.699% rounded off to 22.70%