Investment Strategy Case

INVESTMENT STRATEGY CASE

AMIT KUMAR (PGDMA-1001)

J.D.WILLIAM, INC.O Investment advisory firm

O Managing $120 million funds for its clients

ASSET ALLOCATION MODEL

Growth stock

fund(GF)

Income fund(IF)

Money market

fund(MMF)

Amount

Invested

20-40% of Total Portfolio

20-50% of Total Portfolio

>=(at least) 30% of Total

Portfolio

RISK 0.10 0.07 0.01

Annual YIELD

18% of GF(0.18GF)

12.5% of IF(0.125IF)

7.5% of MMF(0.075MMF)

O Overall portfolio risk index=weighted avg. of the risk rating for the 3 funds.

O R=O W1= , R1=0.1O W2= , R2=0.07O W3= , R3=0.01

Contracted with a client, having $ 8,00,000 to invest

Problem- To allocate $8lakh among the growth, income

&Money market funds. To develop an L.P model that provide maximum

yield for the portfolio. To develop a managerial report on the L.P model.

O Decision Variables- GF, IF, MMFO Objective function- To maximize the total yield for the portfolioO Max 0.18GF + 0.125IF +0.075MMFO Maximum Risk index given=0.05

Model Formulation

Constraints-I. 1GF + 1IF + 1MMF <= 800,000 ($ amount

available to invest)II. GF >= 0.2* (GF+IF+MMF)

0.80GF -0.20IF -0.20MMF >= 0 (Min growth fund)III. GF <= 0.4* (GF+IF+MMF)

0.60GF -0.40IF -0.40MMF <= 0 (Max growth fund)IV. IF >= 0.2* (GF+IF+MMF)

-0.20GF +0.80IF -0.20MMF > 0 (Min income fund)V. IF <= 0.5* (GF+IF+MMF)

-0.50&F +0.50IF -0.50MMF <= 0 (Max income fund)

VI. MMF >= 0.3* (GF+IF+MMF)-0.30GF -0.30IF +0.70MMF >= 0 (Min money market fund)

VII.0.1*GF+0.07*IF+0.01*MMF <= 0.05* (GF+IF+MMF)0.05GF +0.021F -0.04MMF <= 0 (Max risk),GF,IF,MMF >= 0

OQ1.) solution-

Fund Allocation-

GF IF MMF SUM TOTAL

$248888.8889 $160000 $391111.1111 $800000

Yield = $94133

Yield (in %) = = 11.8 %.

RISK YIELDlowerlimit upper limit

GF 20% 40% 0.1 18%IF 20% 50% 0.07 12.50%MMF 30% 0.01 7.50%

Total Fund $8,00,000Total risk 0.050

MaX. Yield 94133.33333

GF IF MMF SUMTOTAL248888.8889 160000 391111.1111 800000

GF+IF+MMF 800000 <= $8,00,000GF 88888.89 >= 0GF -71111.1 <= 0IF 0 >= 0IF -240000 <= 0MMF 151111.1 >= 0

Amount invested(in%)

INVESTMENT STRATEGY CASE

objective function

Constraints

Decision Variables

OQ2) solution-if the client's Risk index were increased by 0.05%,(from 0.05 to 0.055), the annual yield on investment would increase by $4,667, from the original optimal estimation of $94,133 to a new projection of $98,800.

Fund Allocation-GF IF MMF

SUMTOTAL

$293333.33 $160000 $346666.67 $800000

Annual yield in (%) = = 12.35%

Amount invested(in%) RISK YIELDlowerlimitupper limit

GF 0.2 0.4 0.1 0.18IF 0.2 0.5 0.07 0.125MMF 0.3 0.01 0.075

Total Fund 800000Total risk 0.055

objective function Change in yieldMaX. Yield 98800 4667

Decision Variables


ConstraintsGF+IF+MMF 800000 <= 800000GF 133333.3 >= 0GF -26666.67 <= 0IF 0 >= 0IF -240000 <= 0MMF 106666.7 >= 0RISK 0 <= 0

OQ3) solution-Growth fund revised downward to

14%Limit for Growth fund= 0.18 to (“0.18 -

0.03”) = 0.15(N.B : 0.03 is allowable decrease

for GF)Since 0.16 is in the objective coefficient

range for the growth fund return, there would be no change in allocation. However, the return would decrease by(0.02)*($248,889) or ($94133 - $89155) = $4978

Growth fund revised downward to 14%

A decrease to 0.14 is outside the objective function coefficient range . So, we have to resolve the problem. “MAX 0.14GF +0.125IF +0.075MMF”Change in yield = ($94133 - $85066) = $9067


GF 20% 40% 0.1 16%IF 20% 50% 0.07 12.50%MMF 30% 0.01 7.50%


change in yieldMaX. Yield 89155.55556 4978


GF+IF+MMF 800000 <= $8,00,000GF 88888.89 >= 0GF -71111.1 <= 0IF 0 >= 0IF -240000 <= 0MMF 151111.1 >= 0RISK 0 <= 0

INVESTMENT STRATEGY CASEAmount invested(in%)

objective function

Decision Variables

Constraints


GF 20% 40% 0.1 14%IF 20% 50% 0.07 12.50%MMF 30% 0.01 7.50%


change in yieldMaX. Yield 85066.66667 9067

GF IF MMF SUMTOTAL160000 293333.33 346666.6667 800000

GF+IF+MMF 800000 <= $8,00,000GF -1.43831E-07 >= 0GF -160000 <= 0IF 133333.3333 >= 0IF -106666.6667 <= 0MMF 106666.6667 >= 0RISK -5.71163E-09 <= 0


objective function

Decision Variables

Constraints

Q4) solution-Since the current optimal solution has more invested in

the growth fund than the income fund. So, for adding this requirement we have to resolve the problem with a new constraint. Max 0.18GF + 0.125IF +0.075MMFMaximum Risk index given=0.05ConstraintsI. 1GF + 1IF + 1MMF <=

800,000II. 0.80GF -0.20IF -0.20MMF >=

0III. 0.60GF -0.40IF -0.40MMF <=

0IV. -0.20GF +0.80IF -0.20MMF >

0V. -0.50&F +0.50IF -0.50MMF

<= 0VI. -0.30GF -0.30IF +0.70MMF

>= 0VII. 0.05GF +0.021F -0.04MMF

<= 0VIII. 1GF-

1IF <= 0


GF 20% 40% 0.1 18%IF 20% 50% 0.07 12.50%MMF 30% 0.01 7.50%


MaX. Yield 93066.66667

GF IF MMF SUMTOTAL213333.3333 213333.3 373333.3333 800000

GF+IF+MMF 800000 <= $8,00,000GF 53333.3333 >= 0GF -106666.667 <= 0IF 53333.3333 >= 0IF -186666.667 <= 0MMF 133333.333 >= 0RISK -2.2883E-09 <= 0GF-IF -1.85E-08 <= 0


objective function

Decision Variables

Constraints

the value of the solution has decreased from $94,133 to $93,067. This is only a decreaseof 0.2% in yield. Since the yield decrease is so small, We may prefer this portfolio.

OQ5.) solution- we would recommend the use of this

model only when the clients meet the given criteria, i.e., similar objective functions and constraints. since, they are financial investment advisor working for the individual investors according to their need. So, we would not recommend the use of this asset allocation model as a general guide to financial investment.

EXCEL SOLUTION OF THE CASE


GF 20% 40% 0.1 18%IF 20% 50% 0.07 12.50%MMF 30% 0.01 7.50%


MaX. Yield 94133.33333


GF+IF+MMF 800000 <= $8,00,000GF 88888.89 >= 0GF -71111.1 <= 0IF 0 >= 0IF -240000 <= 0MMF 151111.1 >= 0RISK 0 <= 0

Amount invested(in%)

objective function

Constraints

Decision Variables

EXCEL SHEET OF THE CASE

Do right click and open worksheet object.then whole excel will open in separate.

COMPLETE SHEET

Documents

Investment Strategy Case