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

What is the expected return and standard deviation of each of the three portfolios?

Provided Above = Weight of Market Index * Standard Deviation of Market Index

What is the beta of each of the three portfolios?

Provided Above Beta of Market Index is always equal to 1. Beta = Weight of market index * Beta of Market Index

What is the risk premium on the index portfolio?

Risk Premium = Market Return - Risk Free Rate = 10% - 3% = 7%

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

I would use sharpe ratio to calculate reward to risk ration to choose best stock

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?

Expected Return = Calculated above = 17%

standard deviation = Calculated above = 48%

Beta = calculated above = 2