Question

Need assistance with part B

Consider the following table:

   

		Stock Fund	Bond Fund
Scenario	Probability	Rate of Return	Rate of Return
Severe recession	0.05	−27%	−12%
Mild recession	0.25	−7%	18%
Normal growth	0.40	12%	11%
Boom	0.30	17%	−8%

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.)  

Mean return		6.80 %
Variance		146.76 %-Squared

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.)

Covariance ________ %-Squared

Answer 1

Covariance between two assets, X and Y can be calculated as:

where r_Xi is the return for asset X, r_Yi is the return for asset Y

ERPx and ERPy are the expected returns (mean returns) for X and Y

p_i is the probability for a given state i, and

N is the number of states.

Scenario	Probability (p)	Rate of Return (rs)	Rate of Return (rb)	rs-E(rs)	rb-E(rb)	(rs-E(rs))^2	(rs-E(rs))(rb-E(rb))	p*(rs-E(rs))(rb-E(rb))
Severe recession	0.05	-27%	-12%	-0.3380	-0.1790	0.1142440	0.06050	0.0030251
Mild recession	0.25	-7%	18%	-0.1380	0.1210	0.0190440	-0.01670	-0.0041745
Normal growth	0.40	12%	11%	0.0520	0.0510	0.0027040	0.00265	0.0010608
Boom	0.30	17%	-8%	0.1020	-0.1390	0.0104040	-0.01418	-0.0042534
Expected return		6.80%	5.90%				Covariance	-0.0043420

Covariance = -43.42 %-Squared