Question

The table below shows data on the returns over five 1-year periods for seven mutual funds. A firm's portfolio managers will assume that one of these scenarios will accurately reflect the investing climate over the next 12 months. The probabilities of each of the scenarios occurring are 0.1, 0.3, 0.1, 0.1, and 0.4 for years 1 to 5, respectively.

RETURNS OVER FIVE 1-YEAR PERIODS FOR SEVEN MUTUAL FUNDS
	Planning Scenarios for Next 12 Months
Mutual Funds	Year 1	Year 2	Year 3	Year 4	Year 5
Large-Cap Stock	35.3	20.0	28.3	10.4	-9.3
Mid-Cap Stock	32.3	23.2	-0.9	49.3	-22.8
Small-Cap Stock	20.8	22.5	6.0	33.3	6.1
Energy/Resources Sector	25.3	33.9	-20.5	20.9	-2.5
Health sector	49.1	5.5	29.7	77.7	-24.9
Technology Sector	46.2	21.7	45.7	93.1	-20.1
Real Estate Sector	20.5	44.0	-21.1	2.6	5.1

Develop a portfolio model for investors who are willing to risk a portfolio with a return no lower than 2%. Round your answers to one decimal place. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. If the constant is "1" it must be entered in the box.

To determine the percentage of the portfolio that will be invested in each of the mutual funds we use the following decision variables:

	LS = proportion of portfolio invested in a large-cap stock mutual fund
	MS = proportion of portfolio invested in a mid-cap stock fund
	SS = proportion of portfolio invested in a small-cap growth fund
	ES = proportion of portfolio invested in an energy sector fund
	HS = proportion of portfolio invested in a health sector fund
	TS = proportion of portfolio invested in a technology sector fund
	RS = proportion of portfolio invested in a real estate sector fund

Max

s.t.

LS

+

MS

+

SS

+

ES

+

HS

+

TS

+

RS

LS

+

MS

+

SS

+

ES

+

HS

+

TS

+

RS

≥

LS

+

MS

+

SS

+

ES

+

HS

+

TS

+

RS

≥

LS

+

MS

+

SS

+

ES

+

HS

+

TS

+

RS

≥

LS

+

MS

+

SS

+

ES

+

HS

+

TS

+

RS

≥

LS

+

MS

+

SS

+

ES

+

HS

+

TS

+

RS

≥

LS

+

MS

+

SS

+

ES

+

HS

+

TS

+

RS

=

LS, MS, SS, ES, HS, TS, RS

≥

0

Solve the model in part (a) and recommend a portfolio allocation for the investor with this risk tolerance. Round portfolio return to three decimal places and other answers to one decimal place. If your answer is zero, enter "0".

The recommended allocation is to invest as follows:

__%	of the portfolio in the large-cap stock mutual fund
__%	of the portfolio in the mid-cap stock fund
__%	of the portfolio in the small-cap stock fund
__%	of the portfolio in the energy sector fund
__%	of the portfolio in the health sector fund
__ %	of the portfolio in the technology sector fund
__ %	of the portfolio in the real estate sector fund

The expected portfolio return is ______%

Modify the portfolio model in part (a) and solve it to develop a portfolio for an investor with a risk tolerance of 0%. Round portfolio return to three decimal places and other answers to one decimal place. If your answer is zero, enter "0".

The recommended allocation is to invest as follows:

__ %	of the portfolio in the large-cap stock mutual fund
__ %	of the portfolio in the mid-cap stock fund
__ %	of the portfolio in the small-cap stock fund
__ %	of the portfolio in the energy sector fund
__ %	of the portfolio in the health sector fund
__ %	of the portfolio in the technology sector fund
__%	of the portfolio in the real estate sector fund

The expected portfolio return is _______ %.

Answer 1