Asset A has an expected return of 10% and standard deviation of 20%. Asset B has

Question

Asset A has an expected return of 10% and standard deviation of 20%. Asset B has an expected return of 16% and a standard deviaiton of 40%. The correlation between A and B is 0.35. Portfolio C is composed of 30% asset A and 70% asset B.

Portfolio C: Expected return= 14.2% Standard deviaiton= 30.62%

Question:

A)Plot the attainable portfolios for a correlation of 0.35. Now plot the attainable portfolios for correlatio of +1.0 and -1.0.

B) Suppose a risk-free rate has an exdpected return of 5%. By definiton, its standard deviation is zero, and its correlation with another asset is also zero. Using only asset Aand the risk-free asset, plot the attainable portfolios.

Explanation / Answer

Attainable portfolio at correlation 1 is

Expected return = weight of asset A * expected return on asset A + weight on asset B * expected return on asset B

                          = 0.30*10+0.70*16

                          = 14.2%

Standard deviation of portfolio at correlation of +1

= [(Weight of A)^2* (SD of A)^2 + (Weight of B)^2 * (sd of B)^2 +( 2 * Correlation coefficient * weight of A* weight of B * SD of A * SD of B)]^1/2

= (0.30^2)(20^2) + (0.70^2)(40^2) + 2*1 *0.30*0.7*20*40

= [36+784+336]^1/2

=34%

The portfolio will have same return of 14.2% and standard deviation of 34% at correlation of +1

When correlation is -1

The return remains same

The Standard deviation changes

= [(Wa^2)(SD of A^^2) +(Wb ^2)(SD of B ^2) +2 * -1* Wa Wb* SD of A * SD of B]^1/2

=(0.3^2)(20)^2 + (0.70^2)(40^2) + 2*-1*0.30*0.70*20*40

= 36+784-336

=(484)^1/2

= 22%

When risk free asset is used

Expected return = 0.30*10+.70*5

                          = 6.5%

Since , risk free asset does not have any risk of its own,

The portfolio will only have risk of it risky asset

= weight of A * SD of A

= 0.30* 20 =6%

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