Question

1. (a) Suppose the rates of return of the bond portfolio in the four scenarios of the below spreadsheet are -10% in a mild recession, 7% in a normal period, and 2% in a Boom. The stock returns in the four scenarios are -37%, -11%, and 30%. What are the covariance and correlations coefficient between the rates of return on the two portfolios?

1			Bond Fund	Stock Fund
2	Scenario	Probability	Rate of Return	Rate of Return
3	Severe Recession	0.05	-10%	-37%
4	Mild Recession	0.25	10%	-11%
5	Normal Growth	0.40	7%	14%
6	Boom	0.30	2%	30%

(b). A portfolio’s expected return is 12%, its standard deviation is 20%,

and the risk-free rate is 4%. Which of the following would make for the greatest increase in the portfolio’s Sharpe ratio?

1. An increase of 1% in expected return.

2. A decrease of 1% IN THE Risk-free rate.

3. A decrease of 1% in its standard deviation.

(c). In forming a portfolio of two risky assets, what must be true of the correlation coefficient between their returns if there are to be gains from diversification? Explain

(d). When adding a risky asset to a portfolio of many assets, which property of the asset is more important, its standard deviation or its covariance with the other assets? Explain

Answer 1

	BOND FUND
		p	R1	A=R1*p	B1=R1-5.4	C=(B1^2)	D=C*p
	Scenario	Probability	Rate of Return(Percent)	(Return)*(Probability)	Deviation from   expected	Deviation Squared	(Deviationsquared)*(Probability)
	Severe Recession	0.05	-10	-0.5	-15.4	237.16	11.858
	Mild Recession	0.25	10	2.5	4.6	21.16	5.29
	NormalGrowth	0.40	7	2.8	1.6	2.56	1.024
	Boom	0.30	2	0.6	-3.4	11.56	3.468
			TOTAL	5.4		Total	21.64
	Expected Return of Bond Fund(Percent)	5.4
	Variance of return of Bond fund	21.64
	Stadardard Deviation=Square Root (Variance)
	Standard Deviation of Bond Fund(Percent)	4.65188134	SQRT(21.64)
	STOCK FUND
		p	R2	A=R2*p	B2=R2-10	C=(B2^2)	D=C*p
	Scenario	Probability	Rate of Return(Percent)	(Return)*(Probability)	Deviation from   expected	Deviation Squared	(Deviationsquared)*(Probability)
	Severe Recession	0.05	-37	-1.85	-47	2209	110.45
	Mild Recession	0.25	-11	-2.75	-21	441	110.25
	NormalGrowth	0.40	14	5.6	4	16	6.4
	Boom	0.30	30	9	20	400	120
			TOTAL	10		Total	347.1
	Expected Return of Bond Fund(Percent)	10
	Variance of return of Bond fund	347.1
	Stadardard Deviation=Square Root (Variance)
	Standard Deviation of Bond Fund(Percent)	18.63061996	SQRT(347.1)
	COVARIANCE OF BOND AND STOCK
		p	B1	B2	E=B1*B2	F=E*p
	Scenario	Probability	Deviation from   expected BondFund	Deviation from   expected Stock Fund	(Deviation Bond)*(Deviation (Stock)	(Dev Bond)*(Dev Stock)*Probability
	Severe Recession	0.05	-15.4	-47	723.8	36.19
	Mild Recession	0.25	4.6	-21	-96.6	-24.15
	NormalGrowth	0.40	1.6	4	6.4	2.56
	Boom	0.30	-3.4	20	-68	-20.4
					Sum	-5.8
	Covariance between return of Bond and Stock	-5.8
	Correlation Coefficient=Covariance/((Std Deviation of Bond)*(Standard Deviation of Stock))
	Correlation Coefficient =	-0.066922485	(-5.8/(4.65*18.63))
(b)	Sharp Ratio=(Return-Risk free Rate)/Standard Deviation
	Sharp ratio	0.4	(12-4)/20
	Sharp ratio with 1% increase in return	0.406	((12*(1.01))-4)/20
	Sharp ratio with 1% increase in risk free rate	0.398	((12-(4*1.01)))/20
	Sharp ratio with 1% Decrease in Standard Dev.	0.404	(12-4)/(20*(1-0.01))
	ANSWER:
	I:An increase of 1% in expected return
.(c)
	Portfolio Variance=(w1^2)*(S1^2)+(w2^2)(S2^2)+2*w1*w2*Cov(1,2)
	w1=weight of asset 1 in the portfolio
	w2=weight of asset 2 in the portfolio
	S1=Standard Deviation of asset 1
	S2=Standard Deviation of asset 2
	Cov(1,2)=Covariance of asset 1 and 2
	Cov(1,2)=Correlation (1,2)*(S1*S2)
	If there is to be gain in diversification,
	Portfolio Variance need to be minimum
	Hence Cov(1.2) should be minimum
	Correlation Coefficient should be minimum
	It is better if Correlation is negative
	This will reduce Variance and Risk
(d)	Covariance with other asset is more important
	It plays significant part in objective of diversification ,which is reducing risk