Question

Consider the following table:

   

		Stock Fund	Bond Fund
Scenario	Probability	Rate of Return	Rate of Return
Severe recession	0.05	−44%	−13%
Mild recession	0.25	−16%	11%
Normal growth	0.40	10%	4%
Boom	0.30	30%	3%

   

b.	Calculate the values of expected return and variance for the stock fund. (Do not round intermediate calculations. Enter "Expected return" value as a percentage rounded to 1 decimal place and "Variance" as decimal number rounded to 4 decimal places.)

       

Expected return	%
Variance

c.	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. Enter your answer as a decimal number rounded to 4 decimal places.)

Covariance

Answer 1

	Stock Fund:
	Scenario	Probability of scenario [p]	Rate of return [%]	E[r] = p*r	d = r-E[r]	d^2	p*d^2
	Severe recession	0.05	-0.44	-0.0220	-0.5080	0.2581	0.0129
	Mild recession	0.25	-0.16	-0.0400	-0.2280	0.0520	0.0130
	Normal growth	0.40	0.10	0.0400	0.0320	0.0010	0.0004
	Boom	0.30	0.30	0.0900	0.2320	0.0538	0.0161
				0.0680			0.0425
	Expected return			6.8%
	Variance			0.0425
	SD			20.60%
	Coefficient of variation		3.03
	Bond Fund:
	Scenario	Probability of Scenario [p]	Rate of return [%]	E[r] = p*r	d = r-E[r]	d^2	p*d^2
	Severe recession	0.05	-0.13	-0.0065	-0.1760	0.0310	0.0015488
	Mild recession	0.25	0.11	0.0275	0.0640	0.0041	0.0010240
	Normal growth	0.40	0.04	0.0160	-0.0060	0.0000	0.0000144
	Boom	0.30	0.03	0.0090	-0.0160	0.0003	0.0000768
				0.0460			0.0026640
	Expected return			4.60%
	Variance			0.0027
	SD			5.16%
	Coefficient of variation		1.12
	Correlation [A,B]:
	Scenario	Probability of Scenario [p]	ds*db	ds*db*p
	Severe recession	0.05	0.089408	0.0045
	Mild recession	0.25	-0.014592	-0.0036
	Normal growth	0.40	-0.000192	-0.0001
	Boom	0.30	-0.003712	-0.0011
	Covariance [Stock,Bond]			-0.0004
a]	STOCK FUND:
	Expected return	6.80%
	Variance	0.0425
b]	BOND FUND:
	Expected return	4.60%
	Variance	0.0027
c]	Covariance [Stock,Bond]	-0.0004