Question

Consider the total returns between Southeast Utilities and Precision Instruments for the different market trends. The summary statistics for these two stocks are as follows:

POSSIBLE OUTCOMES	PROBABILITY	RETURNS
		SOUTHEAST	PRECISION
Bullish Trend	0.25	13%	16%
Normal Trend	0.50	5%	11%
Recession	0.25	(7)%	13%

Calculate the risk for both the company’s stock and comment which is better and less risky?

Answer 1

Given probabilities and stocks returns for two stocks namely Southeast Utilities(S) and Precision Instruments(P)

Note: that probabilities always add upto one

0.25+0.50+0.25 = 1

In order to calculate the risk we need to find out the standard deviation.

Calculating the expected return for the stocks S and P,

We know that the expected return of stock R is given by the formula,

E(R) = Σ(pi*Ri)

Where E(R) is the expected return of the stock

pi = probability of stock R

Ri = return on the stock R

By using this formula, we calculate the expected returns for stocks S and P as follows,

E(S) = (0.25*0.13) + (0.50*0.05) + (0.25*(-0.07))

E(S) = 0.0325 + 0.025 + (-0.0175)

E(S) = 0.04 or 4%

E(P) = (0.25*0.16) + (0.50*0.11) + (0.25*0.13)

E(P) = 0.04 + 0.055 + 0.0325

E(P) = 0.1275 or 12.75%

using these expected return values for stocks S and P, we need to calculate the standard deviation or the risk of the stocks

SD(R) = σ =  Σ pi *(Ri - E(Ri))^2

where E(Ri) is expected return of stock

pi = probability of stock R

Ri = return on the stock R

Now substituting the values of stocks S and P, we get

SD(S) = 0.25(0.13-0.04)^2 + 0.50(0.05-0.04)^2 + 0.25(-0.07-0.04)^2

= 0.25(0.09)^2 + 0.50(0.01)^2 + 0.25(-0.11)^2

= 0.25*0.0081 + 0.50*0.0001 + 0.25*0.0121

= 0.002025 + 0.00005 + 0.003025

= 0.0051 OR 0.51%

SD(P) = 0.25(0.16-0.1275)^2 + 0.50(0.11-0.1275)^2 + 0.25(0.13-0.1275)^2

= 0.25(0.0325)^2 + 0.50(-0.0175)^2 + 0.25(0.0025)^2

= 0.25*0.00105625 + 0.50*0.00030625 + 0.25*0.00000625

= 0.00026406 + 0.00015312 + 0.00000156

= 0.00041874 OR 0.0418%

In our case, we can choose stock P i.e., Precision Instruments since the standard deviation which is the measure of risk is lower when compared with that of standard deviation of stock S, Southeast Utilities.

The lower the standard deviation the less risky is the stock.