Question

You are considering purchasing a stock. In a growing economy, the potential return is 20 percent, but if the economy stagnates, the potential return is only 7 percent. In the case of a recession, you could sustain a loss since the anticipated return is

-8 percent. The probability of economic growth is 60 percent, while the probability of stagnation and recession are 30 percent and 10 percent respectively.

 

Assume the risk-free rate and the Security’s risk premium were 7 percent and 8 percent, respectively.

Answer 1

1) The expected return can be calculated using the respective probability.

(0.6 * 0.2) + (0.3 * 0.07) + (0.1 * (-0.08))
= 0.12 + 0.021 - 0.008
= 0.133

2) The expected volatility can be found by following formula
(Mean Return - Nominal Return) ^ 2

(0.133 - 0.2) ^ 2 + (0.133 - 0.08) ^ 2 + (0.133 + 0.08) ^ 2
0.004489 + 0.003969 + 0.045369
= 0.053827

(0.053827 / 3) * 100 = 1.7942%

3) The required rate of return is calculated by adding the risk premium of the asset class or security to the risk free rate of return.

Required Rate of Return = Risk Free Rate + Risk Premium

7% + 8% = 15%

4) The expected rate of return for this security is 15% but the expected return after taking into account the probability of each scenario is 13.3%. This is lower than the required rate so the stock should be avoided.