Question

You can invest your money either in risk-free government bonds that yield 3% per year, or you can buy a well- diversified index fund that has an expected return of 10% and a standard deviation of 25%. Since the index fund resembles the market portfolio, assume that the beta of this fund is 1.

a) Suppose you want to create a portfolio with an expected return of 8% (by investing in government bonds and the index fund). What would be the standard deviation and the beta of such a portfolio?

Select one:

The portfolio standard deviation is 17.9%; the beta of the portfolio is 0.71

The portfolio standard deviation is 12.5%; the beta of the portfolio is 0.50

The portfolio standard deviation is 7.1%; the beta of the portfolio is 0.29

The portfolio standard deviation is 3.2%; the beta of the portfolio is 0.71

The portfolio standard deviation is 3.2%; the beta of the portfolio is 0.50

The portfolio standard deviation is 13.9%; the beta of the portfolio is 0.49

The portfolio standard deviation is 50%; the beta of the portfolio is 2.00

The portfolio standard deviation is 0%; the beta of the portfolio is 0

b) If you have $10,000 to invest and you want to create a portfolio consisting of government bonds and index funds that has half the systematic risk of the market portfolio, what would be the expected return and standard deviation of your portfolio?

Select one:

The expected return is 10%; the standard deviation is 25%

The expected return is 5%; the standard deviation is 12.5%

The expected return is 8%; the standard deviation is 12.5%

The expected return is 6.5%; the standard deviation is 12.5%

The expected return is 10%; the standard deviation is 20%

The expected return is 8%; the standard deviation is 25%

The expected return is 6.5%; the standard deviation is 25%

The expected return is 10%; the standard deviation is 0%

Answer 1

1.
Let proportion in index fund be w and in government bonds be 1-w
Hence,
w*10%+(1-w)*3%=8%
=>w=5/7

Standard Deviation=5/7*25%=17.8571429%

Beta=5/7*1=0.714285714

The portfolio standard deviation is 17.9%; the beta of the portfolio is 0.71

2.
Let proportion in index fund be w and in government bonds be 1-w
Hence,
w*1=0.5*1
=>w=0.5

Expected returns=0.5*10%+0.5*3%=6.5%
Standard Deviation=0.5*25%=12.5%

The expected return is 6.5%; the standard deviation is 12.5%