Financial planner Minnie Margin has a substantial number of clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the Russell 2000 index. Her 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 Russell 2000 index. Annual Returns Year 1Year 2Year 3Year 4International Stock22.3726.734.862.17Large-Cap Value15.4819.6411.50-5.25Mid-Cap Value17.4220.07-4.97-1.69Small-Cap Growth23.1812.363.253.81Short-Term Bond9.268.816.154.04Russell 2000 Index202282 Write out the (non-linear) program that would produce a portfolio that most closely mimics the performance of the Russell 2000 Index.Use Excel's Solver with "GRG Non-Linear" as the solution algorithm: what is the optimal solution, i.e., what percentages should be invested in each of the five funds?

Objective Functions and Constraints: Based on the given details, the objective functions and constraints are Objective Function: Min Z = (R1 – 20) ^2 + (R2 – 22) ^2 + (R3 – 8) ^2 + (R4 – 2) ^2 Decision Variables: R1 – Portfolio return first year R2 – Portfolio return Second year R3 – Portfolio return Third year R4 – Portfolio return fourth year I – International Stock L – Large Cap Value M – Mid Cap Value SC – Small Gap growth ST – Short term growth Constraints: Subject to Year 1: 22.37 I + 15.48 L + 17.42 M + 23.18 SC + 9.26 ST = R1 Year 2: 26.73 I + 19.64 L + 20.07 M + 12.36 SC + 8.81 ST = R2 Year 3: 4.86 I + 11.50 L – 4.67 M + 3.25 SC + 6.15 ST = R3 Year 4: 2.17 I – 5.25 L – 1.69 M + 3.81 SC + 4.04 ST = R4 Maximum: I + L + M + SC + ST = 100% I + L + M + SC + ST ≥ 0Find the calculations below: Solver Declarations: Results:

Answered: Financial planner Minnie Margin has a…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

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Financial planner Minnie Margin has a substantial number of clients who wish to own a mutual fund portfolio that matches, as a whole, the performance of the Russell 2000 index. Her 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 Russell 2000 index.

	Annual Returns
	Year 1	Year 2	Year 3	Year 4
International Stock	22.37	26.73	4.86	2.17
Large-Cap Value	15.48	19.64	11.50	-5.25
Mid-Cap Value	17.42	20.07	-4.97	-1.69
Small-Cap Growth	23.18	12.36	3.25	3.81
Short-Term Bond	9.26	8.81	6.15	4.04
Russell 2000 Index	20	22	8	2

Write out the (non-linear) program that would produce a portfolio that most closely mimics the performance of the Russell 2000 Index.
Use Excel's Solver with "GRG Non-Linear" as the solution algorithm: what is the optimal solution, i.e., what percentages should be invested in each of the five funds?

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