Phoenix Company common stock is currently selling for $20 per share. Security analysts at Smith Blarney have assigned the following probability distribution to the price of (and rate of return on) Phoenix stock one year from now: $$\begin{array} { l l l }
\text { Price } & \text { Rate of Return } & \text { Probability } \
\$ 16 & - 20 \% & 0.25 \
\$ 20 & 0 \% & 0.30 \
\$ 24 & + 20 \% & 0.25 \
\$ 28 & + 40 \% & 0.20
\end{array}$$ Assuming that Phoenix is not expected to pay any dividends during the coming year, determine the coefficient of variation for the rate of return on Phoenix stock.
A) 0.0
B) 2.68
C) 2.61
D) 0.275

Question

Phoenix Company common stock is currently selling for $20 per share. Security analysts at Smith Blarney have assigned the following probability distribution to the price of (and rate of return on) Phoenix stock one year from now: $$\begin{array} { l l l } 
\text { Price } & \text { Rate of Return } & \text { Probability } \
\$ 16 & - 20 \% & 0.25 \
\$ 20 & 0 \% & 0.30 \
\$ 24 & + 20 \% & 0.25 \
\$ 28 & + 40 \% & 0.20
\end{array}$$ Assuming that Phoenix is not expected to pay any dividends during the coming year, determine the coefficient of variation for the rate of return on Phoenix stock.
A) 0.0
B) 2.68
C) 2.61
D) 0.275

Quizplus · Accepted Answer

The coefficient of variation (CV) is calculated by dividing the standard deviation (σ) of the rate of return by the mean (μ) rate of return, and then multiplying by 100 if you want it in percentage form. Here's how to calculate it for Phoenix stock:1. **Calculate the mean rate of return (μ):**$$μ = (-20\% \times 0.25) + (0\% \times 0.30) + (20\% \times 0.25) + (40\% \times 0.20) = -5\% + 0\% + 5\% + 8\% = 8\%$$2. **Calculate the variance:**$$σ^2 = [(0.25 \times (-20\% - 8\%)^2) + (0.30 \times (0\% - 8\%)^2) + (0.25 \times (20\% - 8\%)^2) + (0.20 \times (40\% - 8\%)^2)]$$$$σ^2 = [0.25 \times (-28\%)^2 + 0.30 \times (-8\%)^2 + 0.25 \times (12\%)^2 + 0.20 \times (32\%)^2]$$$$σ^2 = [0.25 \times 0.0784 + 0.30 \times 0.0064 + 0.25 \times 0.0144 + 0.20 \times 0.1024]$$$$σ^2 = [0.0196 + 0.00192 + 0.0036 + 0.02048]$$$$σ^2 = 0.0456$$3. **Calculate the standard deviation (σ):**$$σ = \sqrt{0.0456} = 0.2136 \text{ or } 21.36\%$$4. **Calculate the coefficient of variation (CV):**$$CV = \frac{σ}{μ} = \frac{21.36\%}{8\%} = 2.67$$The calculation shows the coefficient of variation to be approximately 2.67, which is closest to the option B) 2.68. This calculation involves finding the mean and standard deviation of the rate of return, then using these to find the coefficient of variation. The slight discrepancy in the final answer is due to rounding during the calculation process.

Phoenix Company Common Stock Is Currently Selling for $20 Per