Question

1. You are a conservative investor.  You hold only a total market index mutual fund and Treasury-bills.  Currently the market index has an expected return of 10% and a standard deviation of 24% and the T-bills promise a 3% return.  You are evaluating the desirability of three different portfolios, 100% in the market index, 75% in the index and 25% in T-bills, and 50% in each.
   
   1. What is the expected return and standard deviation of each of the three portfolios?

2. What is the beta of each of the three portfolios?

3. What is the risk premium on the index portfolio?

4. What criterion would you use to choose between the three candidates?

5. BONUS: What are the expected return, standard deviation, and beta of your portfolio if you have $100,000 of your own to invest and you borrow another $100,000 at the risk free rate so you can buy $200,000 of the market index?
   
                                Use the table below for (A), (B) and (E)
   

	Expected Portfolio Return	Portfolio Standard Deviation	Portfolio Beta
100% in Market Index 0% in Treasury-Bills	? ? ?	? ? ?	? ? ?
75% in Market Index 25% in Treasury-Bills	? ? ?	? ? ?	? ? ?
50% in Market Index 50% in Treasury-Bills	? ? ?	? ? ?	? ? ?
+200% in Market Index -100% in Treasury-Bills	? ? ?	? ? ?	? ? ?

Answer 1

Formulas to be used:

1. Portfolio return: Wx * Rx + Wy * Ry

where W is the weight of each asset & R is the expected return of each asset

2. Portfolio standard deviation:

represents the standard deviation.

3. Portfolio beta: Wx * Betax + Wy * Betay

Note that, by definition, the beta of market index is always = 1.

Using these formulas, we complete the given table as shown below:

Formula view for table calculations:

The values for first 3 parts of the question are as calculated in the table above.

Part 4:

As we are conservative investors, we should choose the portfolio having lowest risk (as indicated by SD or beta) among the given alternatives. So the portfolio having 50% of each should be selected as it has minimum beta among these alternatives.

Part 5: Required values are shown in the table.

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