The following tables shows 5 year returns of different funds Mutual Fund Annual
ID: 339053 • Letter: T
Question
The following tables shows 5 year returns of different funds
Mutual Fund
Annual Return (%)
Year 1
Year 2
Year 3
Year 4
Year 5
Stocks
12.01
11.22
13.47
45.42
-21.93
Bonds
17.64
4.25
7.51
-1.33
7.36
Aggressive Growth
32.41
18.71
30.09
41.46
-23.26
Aggressive Value
32.36
20.61
12.93
7.06
-5.37
Moderate Growth
33.44
19.40
6.77
58.68
-9.02
Moderate Value
24.56
25.32
-6.70
5.43
17.31
Let’s assume the minimum return every year across all the funds is M. This means sum of money invested in stock, bonds, aggressive growth, aggressive value, moderate growth and moderate value in any year will return at least M%.
Keep in mind that the total percentage of money allocated across all the funds in any year will be 100%. This means stocks + bonds + …… moderate value = 100% or 1
The objective here is to maximize return in any year. E.g. in year 1 to maximize return, one can invest all the money in moderate growth, but this will not work because in year 2, moderate value returns higher. Therefore, the objective is to come up with an allocation across all the funds such that the return is maximum in the 5 year period.
Mutual Fund
Annual Return (%)
Year 1
Year 2
Year 3
Year 4
Year 5
Stocks
12.01
11.22
13.47
45.42
-21.93
Bonds
17.64
4.25
7.51
-1.33
7.36
Aggressive Growth
32.41
18.71
30.09
41.46
-23.26
Aggressive Value
32.36
20.61
12.93
7.06
-5.37
Moderate Growth
33.44
19.40
6.77
58.68
-9.02
Moderate Value
24.56
25.32
-6.70
5.43
17.31
Explanation / Answer
Let the proportion invested in stocks, bonds, aggressive growth, aggressive value, moderate growth and moderate value be – a,b,c,d,e,f respectively.
Average return of stocks = (12.01+11.22+13.47+45.42-21.9)/5 = 12.038%
Similarly average for bonds = 7.086%, for aggressive growth = 19.882%, for aggressive value = 13.518%, for moderate growth = 21.854% and for moderate value = 13.184%
Objective function = 12.038a+7.086b+19.882c+13.518d+21.854e+13.184f. This has to be maximized.
Constraints are:
1. a+b+c+d+e+f = 1
2. a,b,c,d,e,f>=0 (non negativity)
Solving in excel, using solver, we get the following solution:
Thus the maximized average return is 21.85% and this happens when 100% of the funds is allocated to moderate growth fund.
Fund Proportion invested (as computed by solver) In % Stocks 0.00 0.00 Bonds 0.00 0.00 Aggressive Growth 0.00 0.00 Aggressive Value 0.00 0.00 Moderate Growth 1.00 100.00 Moderate Value 0.00 0.00 Total 1.00 100.00 Formula Total average return 21.85 12.038a+7.086b+19.882c+13.518d+21.854e+13.184f Constraints 1.00 = 1.00 a+b+c+d+e+f = 1Related Questions
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