Question

Since you became an expert in Corporate Finance and CAPM, now you want to make some money by investing in stocks. Instead of buying one stock, you will make a diversified portfolio using several stocks. Suppose that there are only 3 stocks in the market, and expected return, standard deviation, and correlations are as follows

Stocks Expected Return Standard Deviation

Stock A    5% 5%

Stock B    7% 10%

Stock C 10%    20%

Correlations Stock A Stock B Stock C

Stock A 1    0.4 -0.3

Stock B 0.4 1 0.7

Stock C -0.3 0.7 1

*Calculate Expected Return and Standard Deviation of Each Portfolio:
Portfolio 1: 30% in Stock A + 70% in Stock B
Portfolio 2: 60% in Stock B + 40% in Stock C
Portfolio 3: 50% in Stock A + 50% in Stock C

Answer 1

1.Calcuation of Expected Return of Portfolio(Er)

Portfolio 1

Er=Expected return of Stock A*Weight of Stock A+Expected return of Stock B*Weight of Stock B

=5%*.30+7%*.70

=1.5%+4.9%

=6.4%

Portfolio 2

Er=Expected return of Stock B*Weight of Stock B+Expected return of Stock C*Weight of Stock C

=7%*.60+10%*.40

=4.2%+4%

=8.2%

Portfolio3

Er=Expected return of Stock A*Weight of Stock A+Expected return of Stock C*Weight of Stock C

=5%*.50+10%*.50

=2.5%+5%

=7.5%

2.Calculation of Standard deviation of Portfolio(Sdp)

Sd=Sqrt[(SdA)^2*(WA)^2+(SdB)^2*(WB)^2+2*WA*WB*CA,B]

Where,

SdA=Standard Deviation of Stock A

SdB=Standard Deviation of Stock B

WA=Weight of Stock A

WB=Weight of Stock B

CA,B=Correlation of Stock A and Stock B

Portfolio 1

Sdp=Sqrt[(5)^2*(.30)^2+(10)^2+(.70)^2+(2*.30*.70*5*10*0.4)]

=Sqrt(2.25+49+8.4)

=7.72%

Portfolio 2

Sdp=Sqrt[(10)^2*(.60)^2+(20)^2+(.40)^2+(2*.60*.40*10*20*.7)]

=Sqrt[36+64+67.2]

=12.93%

Portfolio 3

Sdp=Sqrt[(5)^2*(.50)^2+(20)^2*(.50)^2+(2*.50*.50*5*20*-0.3)

=SQRT[6.25+100-15]

=9.55%