Lisa has $100,000 to invest in 10 mutual fund alternatives. She has some self-im

Question

Lisa has $100,000 to invest in 10 mutual fund alternatives. She has some self-imposed restrictions for her investment strategy. First, she must invest all of the $100,000. For diversification, no more than $25,000 can be invested in any fund. However, if a fund is chosen for investment, then at least $10,000 must be invested in it. No more than two funds can be pure growth funds. At least one pure bond fund must be selected. The total amount invested in pure bond funds must be at least as much as the amount invested in pure growth funds.

Formulate and solve a model that will maximize Lisa’s expected annual return.

How much do you invest in Fund 1 (round to the nearest whole dollar)?

Explanation / Answer

Among all the funds, fund 3 (growth)gives highest returns i.e 8.45%. So we can invest the maximum possible amount I'm fund 3 i.e, $ 25,000.

Now we are left with $75,000. Fund 4 (growth) provides next best returns i.e, 7.45%. But with investment in fund 4 which is also a growth fund, we will be forced to invest balance in pure bond funds, which gives lowest returns. Hence, investment in fund 4 is not advisable.

As we have invested $25,000 in fund 3 which is a pure growth fund, we shall invest atleast $25,000 in pure bond funds. So we will invest $25,000 in fund 9 because it gives high returns i.e , 5.15% when compared to fund 10 which gives 5.08%.

So with investment in fund 9 we are left with $50,000 to be invested among other funds. The balance $ 50,000 should not be invested in any of the pure growth fund as it would force us to invest in pure bond funds which is not advisable. So, we are left with $50,000 and 5 funds i.e, fund 5,6,7,8,10.

Among those 5 funds, fund 5 and fumd 7 are ranked 1 and 2 based on the returns. So we can invest $25,000 in fund 5 and $25,000 in fund 7.

Hence the portfolio would be:

Fund 3: $25,000

Fund 9: $25,000

Fund 5: $25,000

Fund 7: $25,000

With the above portfolio, expected return would be 6.97%

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