Investment Manager Max Gaines Has Several Clients Who Wish to Own

question 25

Essay

Investment manager Max Gaines has several clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the S&P 500 stock index. His task is to determine what proportion of the portfolio should be invested in each of the five mutual funds listed below so that the portfolio most closely mimics the performance of the S&P 500 index. Formulate the appropriate nonlinear program. $\text { Annual Returns (Flanning Scenarios) }$
$\begin{array}{c|rrrr}\text { Mutual Fund } & \text { Year } 1 & \text { Year 2 } & \text { Year } 3 & \text { Year 4 }\\\hline\text { International Stock } & 26.73 & 22.37 & 6.46 & -3.19 \\\text { Large-Cap Blend } & 18.61 & 14.88 & 10.52 & 5.25 \\\text { Mid-Cap Blend } & 18.04 & 19.45 & 15.91 & -1.94 \\\text { Small-Cap Blend } & 11.33 & 13.79 & -2.07 & 6.85 \\\text { Intermediate Bond } & 8.05 & 7.29 & 9.18 & 3.92 \\\hline \text { S\&P 500 Index } & 21.00 & 19.00 & 12.00 & 4.00\end{array}$

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Definitions:

Service Failure

A situation where a service does not meet the customer's expectations, leading to dissatisfaction and potentially damage to the service provider's reputation.

Services Gap

The discrepancy between customers’ expectations of service quality and their actual experiences.

Service Expectations

The preconceived notions or standards that customers have regarding the levels of service they should receive.

Perishability

A characteristic of a service.