Problem 4

With a Investement Capital of : $1,000,000. It is possible to invest it in the following three assets: 10-year US Treasury bond with coupon rate 4.5%, Blandy and Gourmange stocks, which have the following historical annual returns:

Year Blandy Gourmange

1 26.0% 47.0%

2 15.0% -54.0%

3 -14.0% 15.0%

4 -15.0% 7.0%

5 2.0% -28.0%

6 -10.0% 40.0%

7 22.0% 17.0%

8 30.0% -23.0%

9 -32.0% -4.0%

10 28.0% 75.0%

11 28.6% 51.7%

12 16.5% -59.4%

13 -15.4% 16.5%

14 -16.5% 7.7%

15 2.2% -30.8%

16 -11.0% 44.0%

17 62.2% 18.7%

18 33.0% -25.3%

19 -35.2% -4.4%

20 50.8% 82.5%

21 23.4% 42.3%

22 13.5% -48.6%

23 -12.6% 13.5%

24 -13.5% 6.3%

25 1.8% -25.2%

26 -9.0% 36.0%

27 18.8% 15.3%

28 27.0% -20.7%

29 -28.8% -3.6%

30 25.2% 67.5%

The goal is to have the expected annual return of 7.6% with a minimum portfolio risk. How much money should be allocated to these three assets? What is the minimum portfolio risk (i.e., the standard deviation)?