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%

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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%

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,

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%