Question

Consider the following table:

			Stock Fund			Bond Fund
Scenario	Probability		Rate of Return			Rate of Return
Severe recession	0.05		–31	%		–10	%
Mild recession	0.25		–11	%		16	%
Normal growth	0.40		16	%		9	%
Boom	0.30		21	%		–6	%

a.Calculate the values of mean return and variance for the stock fund. (Do not round intermediate calculations. Round "Mean return" value to 1 decimal place and "Variance" to 2 decimal places.)

b.Calculate the value of the covariance between the stock and bond funds. (Negative value should be indicated by a minus sign. Do not round intermediate calculations. Round your answer to 2 decimal places.)

Answer 1

Question - (a)

Let P = Probabilities as given and " X " represents the returns.

Mean = Sum of the product of probability and returns = sum ( X * P ) = 8.40 ( see the table )

Dx = Deviation from mean = X - 8.40. Thus deduct 8.40 from each of the " X " values.

Dx² = Dx * Dx

Variance = Total of the product of probabilities and squared deviations. = 242.44 ( see the table below)

Scenario	P	X	X * P	Dx	Dx2	P * Dx2
Severe	0.05	-31	-1.55	-39.4	1552.36	77.618
Mild	0.25	-11	-2.75	-19.4	376.36	94.09
Normal	0.4	16	6.4	7.6	57.76	23.104
Boom	0.3	21	6.3	12.6	158.76	47.628
		Mean =	8.4	Variance =		242.44

Question - (b)

Here ......... Y = Bond returns.

P = Probability

Mean return for Bond stock =

Sum of the products of Y and P = ( - 10 * 0.05) + ( 16 * 0.25 ) + ( 9 * 0.40 ) + ( - 6 * 0.30) = 5.30

Dy = Deviation in Y from its mean. That means, deduct .......... 5.30 from each of the " Y " values.

Scenario	P	Dx	Dy	P * Dx *DY
Severe	0.05	-39.4	-15.3	30.141
Mild	0.25	-19.4	10.7	-51.895
Normal	0.4	7.6	3.7	11.248
Boom	0.3	12.6	-11.3	-42.714
				-53.22

Co-Variance between stock returns and bond returns = - 53.22