Question

Calculate a stock' standard deviation of its rate of return if there is a 20% chance of a 30% return, a 20% chance of a 12% return and a 60% chance of a 10% rate of return?

		9.48%
		7.84%
		8.81%
		6.12%
		11.14%

Answer 1

Given that probability and it return on a stock as,

Probaility(p)	rate of return(r)	p*r
20%	30%	0.2*0.3 = 0.06
20%	12%	0.2*0.12 = 0.024
60%	10%	0.6*0.1 = 0.06
	Expected return u	0.06 + 0.024 + 0.06 = 0.144

expected return on the stock = 14.40%

standard deviation is calculated in follwoing table:

Probaility(p)	rate of return(r)	u-r	(x-u)^2	p*(x-u)^2
20%	30%	14.4 - 30 = -15.6	243.36	0.2*243.36 = 48.672
20%	12%	14.4-12 = 2.4	5.76	0.2*5.76 = 1.152
60%	10%	14.4-10 = 4.4	19.36	0.6*19.36 = 11.616

So, sum of p*(x-u)^2 is 48.672 + 1.152 + 11.616 = 61.44

standard deviation = sqrt(p*(x-u)^2) = sqrt(61.44) = 7.84%

option B is correct.