Finance Tutor Help ASAP: a) Why do we need these \"beta\'s\" to construct the po

Question

Finance Tutor Help ASAP:

a) Why do we need these "beta's" to construct the portfolio?

b) If the risk-free rate is given as 2%, what are the required returns for fund 1 and fund 2 if the market rate of return is expected to have 12%?

c) Is it possible to construct a risk-free (or zero-beta) portfolio by combining asset 1 and asset 2? If yes, what is the required return for this portfolio? If the transaction cost for this portfolio requires 2.5% of commission, will you do it?

d) If you'd like to form a portfolio with fund 1 and fund 2 that replicates fund 3’s beta, what are the weights of this portfolio? What are the assumptions needed for the construction of such portfolio?

Thank you very much for the assistance

Explanation / Answer

a)We need these "beta's" to construct the portfolio in order to find out the Beta of the Portfolio i.e Risk of the Portfolio.

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b)Required rate of Return is computed by the CAPM formula

Re = Rf + (Rm-Rf)*Be

Re for Fund-1 = 2 + (12-2)*0.47

Re for Fund-1 = 6.7%

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Re for Fund -2 = 2 + (12-2)*1.83

Re for Fund-2 = 20.30%

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c)Yes , it is possible to construct a risk-free (or zero-beta) portfolio by combining asset 1 and asset 2.

W1*B1 + W2*B2 = 0

W1*0.47 + (1-W1)*1.83 = 0

0.47W1 + 1.83 - 1.83W1 = 0

1.36W1 = 1.83

W1 = 1.35

W2 = -0.35

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Re of this Portfolio = 6.7*1.35 + (-0.35*20.30)

= 9.045 - 7.105

= 1.94%

If the transaction cost for this portfolio requires 2.5% of commission, then i will not construct such a Portfolio since Overall return will be negative (1.94-2.5)

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d)W1*B1 + W2*B2 = B3

W1*0.47 + (1-W1)*1.83 = 0.92

0.47W1 + 1.83 - 1.83W1 = 0.92

1.36W1 = 0.91

W1 = 0.67

W2 = 0.33

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