Question

60. 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:

Price	Rate of Return	Probability
$16	–20%	0.25
$20	0%	0.30
$24	+20%	0.25
$28	+40%	0.20

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

Answer 1

Ans : Coefficient of variation for the rate of return on Phoenix stock = b) 2.68

Step 1: Calculation of Expected Return & Standard Deviation of Stock

Price	Return (Rs)	Probability	Rs * Probability	Deviation (D)	D^2	D^2 * Probability
16	-20%	25%	-0.05	-0.28	0.0784	0.01960
20	0%	30%	0.00	-0.08	0.0064	0.00192
24	20%	25%	0.05	0.12	0.0144	0.00360
28	40%	20%	0.08	0.32	0.1024	0.02048
		Total	0.08		Total	0.0456

a. Calculation of Expected return of Stock

where Rs = Return of Stock

ER(s) = 0.08 or 8%

b. Calculation of Standard Deviation of Stock

where D = Rs - ER(S)

0.213542 or 21.3542%

Step 2: Calculation of Coefficient of variance (COV)

COV = 0.213542 / 0.08
COV = 2.67 (approx)