Question

were you c which of the geometric average. The Actual Returns of Company A for the Past 3 months were IS20 25% and 5 ro company B 18%, 24% and -1%. In case of portfolio, there will be equal investment a) calculate the expected return of company A using arithmetic average b) Calculate the expected standard deviation Company B 2 companies will invest in? d) Find the covariance between the rates of return. e find the correlation coefficient between the return. Find the expected portfolio return if you equally in the 2 companies. I find the weighted Standard deviation of the portfolie. 6 Find the standard deviation of the portfolio using the Correlation coefficient found in (Ques. e). i) At what correlation coefficient is the maximum risk. reduction obtained from diversification? ;) calculate the expected return of company B using rates of invest

Answer 1

Company A	Period	ReturnA	Ai-mean(A)	ReturnB	Bi-Mean(B)	(Ai-mean(A))*(Bi-Mean(B))
	1	15%	3%	18%	4%	0.14%
	2	25%	13%	24%	10%	1.38%
	3	-5%	-17%	-1%	-15%	2.44%
Average	(R1+R2+R3)/3	12%		14%		3.97%
Standard Deviation	Average/(n-1)	0.152752523		0.130511813
Sharpe ratio	return per unit of risk	0.763762616		1.047159361
Covariance	((Ai-mean(A))*(Bi-Mean(B)))/(n-1)					0.019833333
Correlation	covariance/SDevA*SDevB					0.994849751
Geometric Average	((1+r1)*(1+r2)*(1+r3))^1/n - 1			0.131478473

	Wa	Ra	Wb	Rb	SDevA	SDevB
	0.5	12%	0.5	14%	0.152753	0.130511813
Expected portfolio return	Wa*Ra+Wb*Rb	0.126666667
Standard deviation	((Wa*Sdeva)^2 +(Wb*Sdevb)^2+2*corr*Wa*Sdeva*Wb*Sdevb)^(0.5)	0.141450816
Wighted standard deviation	Wa*SDeva+Wb*Sdevb	0.141632168
Correlation coeff = -1		0.011120355

Qns 1	12%
Qns 2	0.130511813
Qns 3	Company B
Qns 4	0.019833333
Qns 5	0.994849751
Qns 6	0.126666667
Qns7	0.141632168
Qns 8	0.141450816
Qns 9	0.011120355	When Coeff = -1
Qns 10	0.131478473