Question

Drexel Investments manages portfolios for a number of wealthy clients. They consider three investment types for their clients: a growth stock fund, an income fund, and a money market fund. For diversification purposes, they impose the following minimum and maximum percentages for each type of investment in each portfolio:

Investment Type	Minimum %	Maximum %
Growth Stock Fund	20%	40%
Income Fund	20%	50%
Money Market Fund	30%	60%

The risk index and the annual yield forecast for each type of investment are as follows:

Investment Type	Risk Index	Annual Yield
Growth Stock Fund	0.1	18.0%
Income Fund	0.07	12.5%
Money Market Fund	0.01	7.5%

Drexel has a new client with $800,000 to invest, and he would like the weighted average risk index of his portfolio to be no more than 0.05. Help Drexel come up with an investment plan that maximizes the expected annual yield of this client's portfolio.

a) If the client's risk index is increased to 0.055, how would the portfolio yield be affected?

b) If the annual yield for the growth stock fund decreased to 16%, how would the portfolio allocation be affected?

c) The client wants to add a constraint to ensure that the amount in the growth stock fund is no more than the amount invested in the income fund. Would this change the portfolio allocation - if so, how?

d) If the risk index of the income fund is revised downward to 0.06, how would this affect the portfolio yield?

Answer 1

A) IF Drexel has to ensure that risk index is no more than 0.05, the investment allocation should be as follows.

Investment Type	Risk Index	Annual Yield	Investment Allocation %	Weighted Risk Index(Risk Index x Investment allocation %)	Expected Return
Growth Stock Fund	0.10	18.00%	40.00%	0.0400	7.20%
Income Fund	0.07	12.50%	6.67%	0.0047	0.83%
Money Market Fund	0.01	7.50%	53.33%	0.0053	4.00%
Total				0.0500	12.03%

Here maximum allocation as per limits is done to Growth Stock fund since the Annual Yield of this fund is the highest among all category. The balance allocation is done to ensure that the risk index stays within 0.05 as required. The allocation is done between Income Fund and Money Market Fund on trial and error basis to finally arrive at Weighted Average Risk Index of 0.05, Using the above allocation, the client portfolio gives the highest return.

B) If the client yield risk index is increased to 0.055, the investment allocation will be modified as follows.

Investment Type	Risk Index	Annual Yield	Investment Allocation %	Weighted Risk Index(Risk Index x Investment allocation %)	Expected Return
Growth Stock Fund	0.10	18.00%	40.00%	0.0400	7.20%
Income Fund	0.07	12.50%	15.00%	0.0105	1.88%
Money Market Fund	0.01	7.50%	45.00%	0.0045	3.38%
Total				0.0550	12.45%

Here also maximum allocation is done to Growth Stock fund since it gives the highest category returns. Thereafter again through trial and error method higher allocation is done to Income fund which gives the second highest category returns. The allocation is done in such a manner that Weighted Average Risk Index (WAR Index) remains within 0.055. This change results in higher yield at 12.45% as against 12.03% return when the WAR index is at 0.5.

C)

IF the growth fund yield decreases to 16%, the portfolio allocation will not be affected since the Growth stock fund still gives the highest category returns, However the overall returns for the client portfolio will be affected due to this change.

D) IF the client wants to add a constraint to ensure that the amount in the growth stock fund is no more than the amount invested in the income fund, this would impact the asset allocation. It is also assumed that the client wants the Weighted Average Risk Index to be at 0.05. In this case the best allocation derived through trial and error method is as below. Here equal allocation is done to both Growth Stock Fund and Income Fund and at the same time the clients required Weighted Average Risk Index of 0.05 is maintained. This is the best allocation possible within the required Risk Index ratio.

Investment Type	Risk Index	Annual Yield	Investment plan %	Risk Index X Investment plan %	Expected Return
Growth Stock Fund	0.10	18.00%	26.67%	0.0267	4.80%
Income Fund	0.07	12.50%	26.67%	0.0187	3.33%
Money Market Fund	0.01	7.50%	46.67%	0.0047	3.50%
Total				0.0500	11.63%

E) If the risk index of the income fund is revised downward to 0.06 and if Weighted Average Risk Index is to be maintained at 0.05 level as originally required, this would lead to change in portfolio mix. This allows Drexel to make further allocation of investment to Income Fund as this will improve the overall yield. When the risk index was at 0.07 the Investment that could be allocated was only 6.67%, whereas now 8% can be allocated due to lower risk index.

Investment Type	Risk Index	Annual Yield	Investment plan %	Risk Index X Investment plan %	Expected Return
Growth Stock Fund	0.10	18.00%	40.00%	0.0400	7.20%
Income Fund	0.06	12.50%	8.00%	0.0048	1.00%
Money Market Fund	0.01	7.50%	52.00%	0.0052	3.90%
Total				0.0500	12.10%