Question

You are an investment manager considering investments in a Stock fund and a bond fund. You forecast the following scenario probabilities and returns for the two assets:

Scenario	Probability	Stock fund Return (%)	Bond fund Return (%)
Recession	1/3	-15%	-9%
Normal growth	1/3	6%	15%
Boom	1/3	30%	9%

Which of the following is closest to the volatility (standard deviation) of the Stock fund return?

10%

18%

3%

20%

14%

Based on the data in Question #22, which of the following is closest to the covariance between the returns on the Stock and Bond funds?

0.015

0.017

0.013

0.011

0.019

Answer 1

	Return
Probability	stock(x)	p*x	bond(y)	p*y	∑p(x-∑px)^2	∑p(y-∑py)^2	∑p(x-∑px)(y-∑py)
0.33	-15	-5	-9	-3	161.33	65.33	102.67
0.33	6	2	15	5	0.33	33.33	-3.33
0.33	30	10	9	3	176.33	5.33	30.67
	∑px	7	∑py	5	338	104	130
Standard deviation of stock(%)=	(∑p(x-∑px)^2)^(1/2)
	18.38	(338^(1/2))
Hence the standard deviation is closest to 18%
Covariance(percent sq)=	∑p(x-∑px)(y-∑py)
Since covariance is in percent square so to arrive at the absolute value of covariance we need to divide our value calculated above by 100^2
so our covariance is 0.013