Consider the following stocks State Probability Ford Apple recession 0

A)

Expected return = summation(Porbability*Return)

For ford Exp return = 0.2*-0.05 + 0.5*0.10 + 0.3*0.15 = -0.01+0.05+0.045 = 8.5%

For Apple Exp return = 0.2*0.15 + 0.5*0.10 + 0.3*0.10= 0.03+0.05+0.03 = 11%

Standard deviation = Sqrt( Proabability* (Return-Expected Return)^2)

For ford= SQRT( 0.2*(-0.05-0.085)^2+0.5*(0.1-0.085)^2+0.3*(0.15-0.085)^2)

=SQRT(0.2*0.018225+ 0.5*0.000225+0.3*0.004225)

=SQRT(0.005025)

Standard deviation ford= 7.08%

For Apple= SQRT( 0.2*(0.15-0.11)^2+0.5*(0.1-0.11)^2+0.3*(0.10-0.11)^2)

=SQRT(0.2*0.0016+ 0.5*0.0001+0.3*0.0001)

=SQRT(0.0004)

Standard deviation ford= 2.00%

B)

Covariance = SuM(Probability*Product of deviations of ford,Apple))

Deviation= Return-Expected return

Covariance= 0.2*(-0.05-0.085) *(0.15-0.11) + 0.5*(0.1-0.085)*(0.1-0.11) + 0.3*(0.15-0.085)*(0.1-0.11)

=-0.00108-0.000075-0.000195

Covariance= -0.00135

Correlation= Covariance/ Standard deviation of ford* standard deviation of apple

= -0.00135/(0.0708*0.02)

correlation = -0.95

Yes, we are diversifying with these stocks because the negative correlation makes them more efficient risk gets reduced and this will be justified in the next problem

C)

Expected return = Weight1* ford return + weight2* apple return

=0.6*0.085+ 0.4*0.11

=0.051+0.044

Expected return = 9.5%

Standard deviation=(SQRT(Weight1*Standard deviation of ford)^2+(Weight2* standard deviation of apple)^2+(2*weight1*weight2*Covariance))

=SQRT((0.6*0.0708)^2+(0.4*0.02)^2+(2*0.6*0.4*-0.00135))

=SQRT(0.0018045504+0.000064-0.000648)

=SQRT(0.0012205504)

Portfolio standard deviaiton =3.49%

Thus it is proved that risk reduced with the negative correlation and addiiton of weights.