Question

1. For this question, use the following data table:

2. 	AT&T	Microsoft
   Expected Return	0.10	0.21
   Standard Deviation	0.15	0.25

   What is the minimum-risk (standard deviation) portfolio allocation of AT&T and Microsoft if the correlation between the two stocks is 0? 0.5? 1? -1? What is the standard deviation of each of these minimum-risk portfolios? (4 pts)

3. What is the optimal combination of these two securities in a portfolio for each of the four given values of the correlation coefficient, assuming the existence of a money market fund that currently pays a risk-free 0.045? (2 pts)

Only need the last question answered -

Answer 1

I am only answering the last part as asked in the question:

To find weightages fo these 2 stocks in optimum portfoili for all the option of correlations we will use below descibed formula:

The tangent portfolio weights(where this tanget touches the efficient portfolio frontier) are calulated as:

WAT$T=1-WMicrofoft;

WMicrofoft;=[(E(RMicrosoft)-Rf)2AT&T-(E(RAT&T)-Rf)xAT&TMicrosoftxAT&TxMicrosoft] divided By(/)

[(E(RMicrosoft)-Rf)2AT&T+(E(RAT&T)-Rf)2Microsoft-(E(RMicrosoft)-Rf+E(RAT&T)-Rf)AT&TMicrosoftxAT&TxMicrosoft]

Now putting the values as per options given:

1) For Correlation:0

WMicrofoft;=[(0.21-0.045)x0.152-(0.10-0.045)X0x0.15x0.25/

[(0.21-0.045)x0.152+(0.10-0.045)X0.202-(0.21-0.045+0.10-0.045)x0x0.15x0.25]

WMicrofoft=0.627907

WAT$T=1-0.627907

WAT$T=0.372093

Now Standard deviation of this portfolio will be:

portfolio=(WAT$T2xAT&T2+WMicrosoft2xMicrosoft2+2xAT&TMicrosoftxAT&TxMicrosoft)1/2

portfolio=(0.3720932x0.152+0.627972x0.252+2x0x0.15x0.25)1/2=0.166604

Similarly you have to put next 3 values for correlation in to the equation to find out optimum weights of these stocks in this optimum portfolio and Standard deviation.

Please let me knoe if you don't get the answer, I'll solve it where ever you are facing problems.

But the formula id explained qute clearly above , I hope by solving by yourself will give you more confidence and clarity;

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