Question

Suppose that an investor has a choice between investing in a bond fund (B) and a stock fund (S).

The bond fund has an expected return of E(rB) = 0.06 while the stock fund has an expected return of E(rS) = 0.10. The standard deviation of the bond fund is ?B= 0.12 and the standard deviation of the stock fund is ?S = 0.25.

(a) Calculate the expected return and standard deviation for each of the following portfolio weights. If you are comfortable using EXCEL you can use the “Portfolio Weight Calculator” (located in Cat Courses) to complete the table. When inputting the values do not use decimals (e.g. The expected return of the bond fund is inputted as 6 not 0.06). You do not have to show your calculations.

WS= Portfolio Weight in Equity Fund	WB= Portfolio Weight in Bond Fund	Expected Return of Overall Portfolio	Standard Deviation of Overall Portfolio
0	1
0.1	0.9
0.2	0.8
0.3	0.7
0.4	0.6
0.5	0.5
0.6	0.4
0.7	0.3
0.8	0.2
0.9	0.1
1	0

(b) Plot the expected return and standard deviation of the various portfolios using EXCEL (draw the investment opportunity set). Identify the minimum variance portfolio (MV Portfolio)

(c) Prove that an investor would never choose a portfolio that has a weight of 10% equity fund and 90% bond fund.

Answer 1

Expected return of bond = 6%

Expected return of Stock = 10%

Standard deviation of bond = 12%

Expected return of Stock = 25%

Correlation between Bond and stock = 0.20 (assume)

Expected return and standard deviation of portfolio consisting different weight of each security is calculated in excel and screen shot provided below:

b.

Grapph of expected return and standard deviation of the various portfolios is ploted in excel and screen shot provided below:

c.

investor would never choose a portfolio that has a weight of 10% equity fund and 90% bond fund because expected return compared to risk (standard deviation is lower at this weight.