Question

North Around, Inc. stock is expected to return 22 percent in a boom, 13 percent in a normal economy, and −15 percent in a recession. The probabilities of a boom, normal economy, and a recession are 6 percent, 92 percent, and 2 percent, respectively. What is the standard deviation of the returns on this stock?

Answer 1

Answer:

4.53%

Explanation:

Data provided in the question:

Expected return = ∑ (Return × probability)

Thus,

Expected return = (0.06 × 22) + (0.92 × 13) + (0.02 × (-15))

= 12.98%

Now,

Probability       Return        Probability × (Return-Expected Return)²

0.06                  22                   0.06 × (22% - 12.98%)² = 4.8816

0.92                  13                    0.92 × (13% - 12.98%)² = 0.000368

0.02                  -15                   0.02 × (-15% - 12.98%)² = 5.657608

========================================================

                                                                            Total = 20.5396%

Standard deviation = $\sqrt{\frac{\text{Total probability}\times(\text{Return-Expected Return})^2}{\text{Total probability}}$

= √(20.5396)

= 4.53%