Case Study

J.D. Williams Inc. Part I

J. D. Williams is an investment advisory company that looks after its clients’ $120 million in assets. The company advises clients on how to attain the best possible returns on their investments using a variety of financial techniques. They are listed in the following order:

An Asset Allocation Model

A model of asset allocation that gives each client a personalized investment plan to help them find the best possible investment combinations.

Percentage Limitations

The company strongly recommends investment diversity as a protection of the investor’s assets

A Risk Tolerance Analysis

The business evaluates each investor’s risk tolerance and modifies their portfolios appropriately.

J.D. Williams has signed contracts with new customers recently and wants to know how to best use the $800,000 in available funds for the client’s growth. An overview of the investment advice given to the client is given in the report’s later sections.

II Model Formulation

a.  Decision Variables

GF = $ amount of investment in growth stock fund IF = $ amount of investment in income fund

MMF = $ amount of investment in money market fund

b.  Objective Function Definition Maximize the total return of the portfolio Max 0.18GF+ 0.125+ 0.075MMF

3. Constraint Definition

s.t. 1GF +1IF + 1MMF<= $ 800,000 amount available to invest

.80GF – .20IF – 20MMF>= 0

$ amount invested in the growth fund should be at least 20% of the total portfolio.

.60GF – .40IF – .40MMF<=0 $ amount invested in the growth fund should be at most 40% of the total portfolio.

-.20GF + .80IF – .20MMF>$0 amount invested in the income fund should be at least 20% of total portfolio

-.50&F +.50IF -.50MMF <= 0$ amount invested in the income fund should be at most 50% of total portfolio

-.30GF -.30IF +.70MMF >= 0$ amount invested in the money market fund that should be least 30% of total portfolio

.05GF +.021F -.04MMF <= 0 Investor’s risk tolerance index

III. Key Assumptions

The following table provides information that stipulates the key assumptions taken into consideration in the development of the investment recommendation.

Portfolio Risk Indicators Forecasted Annual Yields

Growth Stock Fund0.100.18 Income Fund0.070.125 Money Market Fund0.010.075

This means that, we assume that the risk indicators and forecasted yields are given as true above. We also assume that the client does not want to consider other investment options. A maximum risk index of 0.05 has been assigned for the new client.

Therefore; Part 1

The optimal portfolio allocation J.D. Williams recommends is as follows:

Growth Fund  = $248,889

Income Fund  = $160,000 Money Market Fund = $391,111 Total = $800,000

The anticipated annual yield is:

Growth Fund  = $248,889 x 0.18 = $44,800 IncomeFund  = $160,000 x 0.125= $20,000 Money Market Fund = $391,111 x .075= $29,333 Total = $94,133

Total Anticipated Annual Yield$ 94,133 = 11.77%


Part 2

In regards to risk tolerance index, if the client’s index were raised by one half of a percentage point, from .05 to .055, the annual yield on investment consequently would increase by $4,667, from $94,133 to $98,800.

The modified asset allocation recommendation and its corresponding projected annual return are as follows:

Fund Allocation  Projected Annual Yield

Growth Fund  =$ 293,333  Growth Fund = $293,333 x 0.18 = $52,800 Income Fund  =$ 160,000  Income Fund = $160,000 x 0.125  = $20,000 M Market Fund =$346,667  M Market Fund=$346,667 x 0.075 =$26,000

Total   =$ 800,000  Total = $98,800

Total Anticipated Annual Yield = $ 98,800/$800,000 =12.35%

Part 3

If the annual yield is changed to 16%, I would not suggest changing the investment advice because that is still within the Range of Optimality. If it were to shift to 14%, though, that would put it over the lower bound. Because of this, the value will drop from $94,133 to $85,067; as a result, we do not advise lowering the percentage below 15%.

A new investment plan for the client would be necessary for any lower index values that are outside the growth fund’s range of optimality under the origins recommendation, as these values alter the initial projected total annual yield value.

Nonetheless, the current advice regarding the growth fund’s investment allocation is predicated on the fund’s specified optimality range, which spans from 15% to an infinite number of annual yield values. This range suggests that any potential increase in this fund’s index, i.e., 16% and above, would not affect the optimal asset allocation in the portfolio just yet, but it would have a positive effect on the total annual yield value of the objective function from the $94,133 initial projection.

On the other hand, possible declines that fall below the 15% annual yield lower limit index for the growth fund would be considered a departure from the initial asset allocation that was advised and its associated projected value of $94,133, since the new value is outside the fund’s optimality range.

Part 4

The goal of financial portfolio theory is to achieve an appropriate ratio of return to risk. A good way to make sure this balance is maintained is by selecting the right constraints.

With the growth fund’s and income fund’s respective risk indices of.10 and.07, the client may decide to take a less aggressive tack by capping the growth fund’s investment amount at a level that matches, but does not exceed, that of the income fund. In contrast to the original, riskier recommendation’s projected annual return of $94,133, this change in investment strategy would yield a lower annual yield of $85,067.

Part 5

J. D. Williams would advise against using this model unless the model’s prospective new clients satisfy the currently specified requirements. However, the company’s goal is to provide expert financial advice that best suits the needs of individual investors. As a result, the business does not advise using this asset allocation model as a general financial investment guide.


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