Question

Suppose the probability of the recession or boom is .30, while the probability of a normal period is .40. Would you expect the variance of returns on these two investments to be higher or lower? Why? Confirm by calculating the standard deviation of the auto stock.

Answer 1

The probability of expected return may changes the outcome and here in following picture we have calculated expected return- Expected return of Auto stock = -2.4+2+5.4=5%. Expected return of gold stock = +6+1.2-6=1.2%.

Situation	Return	Deviation from expected return	square of deviations	Return	Deviation from expected return	squre of deviation
Recession	-2.4	-7.4	54.76	+6	+4.8	23.04
Normal	2	-3	9	+1.2	0	0
Boom	5.4	+0.4	0.16	-6	-7.2	51.84

Variance of auto stock = 1/3(54.76+9+0.16)=63.92/3= 21.30, Variance of gold stock= 1/3(23.04+0+51.84)=74.88/3=24.96.

Standard deviation of auto stock= √21.30= 4.615. Standard deviation of gold stock =√24.96= 4.99.

So we can get from here that the variance is less than earlier where probalities are not same. Variance of stock is lower.