Investment Strategy Case
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Transcript of 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
GF IF MMF SUMTOTAL293333.33 160000 346666.6667 800000
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
RISK YIELDlowerlimit upper limit
GF 20% 40% 0.1 16%IF 20% 50% 0.07 12.50%MMF 30% 0.01 7.50%
Total Fund $8,00,000Total risk 0.050
change in yieldMaX. Yield 89155.55556 4978
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 >= 0RISK 0 <= 0
INVESTMENT STRATEGY CASEAmount invested(in%)
objective function
Decision Variables
Constraints
RISK YIELDlowerlimit upper limit
GF 20% 40% 0.1 14%IF 20% 50% 0.07 12.50%MMF 30% 0.01 7.50%
Total Fund $8,00,000Total risk 0.050
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
INVESTMENT STRATEGY CASEAmount invested(in%)
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
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 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
INVESTMENT STRATEGY CASEAmount invested(in%)
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
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 >= 0RISK 0 <= 0
Amount invested(in%)
objective function
Constraints
Decision Variables
EXCEL SHEET OF THE CASE
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COMPLETE SHEET