em Investment Strategy J. D. Williams, Inc. is an investment advisory firm that

ID: 2718286 • Letter: E

Question

em Investment Strategy J. D. Williams, Inc. is an investment advisory firm that manages more than $120 million in funds for its numerous clients. The company uses an asset allocation model that rec- ommends the portion of each client's portfolio to be invested in a growth stock fund, an income fund, and a money market fund. To maintain diversity in each client's portfolio, the firm places limits on the percentage of each portfolio that may be invested in each of the three funds. General guidelines indicate that the amount invested in the growth fund must be between 20 and 40 percent of the total portfolio value. Similar percentages for the other two funds stipulate that between 20 and 50 percent of the total portfolio value must

Explanation / Answer

Answer:

Asset allocation model:

Growth stock fund

Income fund

Money market fund

Amount Invested

20-40%

20-50%

At least 30%

Risk

0.1

0.07

0.011

Yield

18% of GF = 0.18GF

12.5% of IF = 0.125IF

7.5% of MMF = 0.075MMF

Overall portfolio risk index = weighted average of risk rating for the 3 funds

R = (w1R1 + w2R2 + w3R3)/(w1 + w2 + w3)

W1 = GF / (GF + IF + MMF) ; R1 = 0.1

W2 = IF / (GF + IF + MMF) ; R2 = 0.07

W3 = MMF / (GF + IF + MMF) ; R3 = 0.01

Contracted with client, have to invest $8,00,000

Model formulation:

Decision variables = GF, IF and MMF

Object function : to maximize yield of the portfolio.

MAX : 0.18GF + 0.125IF + 0.075MMF

Maximum risk index given = 0.05

Constraints:

0.8GF-0.2IF-0.2MMF>=0 (min growth fund)

0.6GF-0.4IF-0.4MMF>=0 (max growth fund)

-0.2GF+0.8IF-0.2MMF>=0 (min income fund)

-0.5GF+0.5IF-0.5MMF<=0 (max income fund)

-0.3GF-0.3IF+0.7MMF>=0 (min money market fund)

Solution-1

Fund allocation:

GF = $248888.889

IF = $160000

MMF = $391111.11

Total = $800,000

Yield = $94133

Yield in % = $94133/800,000 = 11.8%

Solution-2

If the client risk index changes from 0.05% t0 0.055% ie by 0.05% then the annual yield would get increased by $4667.

Fund allocation:

GF = $293333.33

IF = $160000

MMF = $346666.67

Total = $800,000

Annual yield = $98,800/800,000 = 12.35%

Growth fund revised downward to 14%

Limit for growth fund = 0.18

Since 0.16 is in objective coefficient range for the growth fund return there would be no change in allocation.

However the return would decrease by $94133 - $89155 = $4978