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# Investment Strategies

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on 10 December 2014

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#### Transcript of Investment Strategies

Thank You!
Our Optimal Solution
{Z= 1.118, G =.311, I = .2, M = .4889}
Original LP model:
max P = (1.18G + 1.125I + 1.075M)x
such that
G + I + M ≤ 1
(.10)G + (.07)I + (.01)M ≤ .05.
.20 ≤ G ≤ .40
.20 ≤ I ≤ .50
.30 ≤ M
Not too much money in growth fund
Investment amount: \$500
Maximum Risk Tolerance: .05

First Year Yield:
\$559.00
Fifth Year Yield:
\$976.34

By: Adam Coppock, Greg Yerkes, Sunny Mitra
Investment Strategies
G + I + M ≤ 1
(.10) G + (.07) I + (.01) M ≤ .05
.20 ≤ G ≤ .40
.20 ≤ I ≤ .50
.30 ≤ M
Design a Linear Programming model for J.D. Williams Inc.

Help maximize the yields of their clients’ financial portfolios.
J.D. Williams Inc.
Asset-Allocation Model:
Invests clients money into multiple funds
Three Types of Funds
Growth Fund
Main goal of capital appreciation
Has little to no dividend payout for the investor
Requires the highest tolerance for risk
Associated risk:
.10
Annual yield:
18%
Income Fund
Primary focus on the current income
Income made at varying intervals (monthly, annually, etc.)
Associated risk:
.07
Annual yield:
12.5%
Money-Market Funds
similar to a saving account
returns higher interest rates
Manages more than \$120 million
Meet our investor:
Would like to invest:
\$800,000
Maximum risk tolerance:
.05
Associated risk:
.01
Annual yield:
7.5%
Objective Function:
G
= Percentage invested in growth funds

I
= Percentage invested in income funds

M
= Percentage invested in money­ market funds
Maximize p = (1.18 G + 1.125 I + 1.075 M) x
Constraints:
\$248,800 into growth funds
\$160,000 into income funds
\$391,200 into money­-market funds
Re-assessing Risk Index
(.10)G+(.07)I+(.01)M ≤
.055
{Z= 1.118, G =.311, I = .2, M = .4889}
○ \$293,360 into growth funds
○ \$160,000 into income funds
○ \$346,640 into money-­market funds
Annual Yield: \$899,200
Revision of Yield from Growth Fund
Yield of 16%
Yield of 14%
max Z =
( )
G + 1.125 I + 1.075 M
{Z= 1.111, G =.31, I = .2, M = .49}
○ \$248,800 into growth funds
○ \$160,000 into income funds
○ \$391,200 into money-­market funds
{Z= 1.106, G =.30, I = .3667, M = .4333}
○ \$160,000 into growth funds
○ \$293,360 into income funds
○ \$346,640 into money-­market fund
Annual Yield: \$884,800
\$213,360 into growth funds
\$213,360 into income funds, and
\$373,280 into money-market funds
Annual Yield: \$888,800
Annual Yield: \$894,400
Annual Yield: \$892,800
G ≤ I
Revising the Yields
One at a Time
All Together

The optimal distribution of investment remains the same when:

Growth Fund:
Yield > 15%

Income Fund:
Yield < 14.5%

Money Market Fund:
1.5% < Yield < 18%

g
= Annual yield for growth fund
i
= Annual yield for income fund
m
= Annual yield for money market fund
Multiple conditions due to free variables,
some can be eliminated subject to
g
,
i
,
m
>1
m
is minimum
Binding condition:
g <= 10m
i <= 0.67 g + 0.33 m
m > 0
Modifying to Suit Every Client
The optimal basic feasible set remains the same under the following condition:
(not necessarily the same optimal investment distribution)
0.04 < Risk Index < 0.058
Modified LP model:
max Z = 1.18G + 1.125I + 1.075M
such that
G + I + M ≤ 1
(.10)G + (.07)I + (.01)M ≤ .05.
.20 ≤ G ≤ .40
.20 ≤ I ≤ .50
.30 ≤ M
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