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Nelly Stracke
Nelly StrackeLv2
8 Sep 2019
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The McAlhany Investment Fund has total capital of $500 millioninvested in five stocks:

Stock A: Investment $160 Million Stock's Beta Coefficient 0.5
Stock B: Investment $120 Million Stock's Beta Coefficient 2.0
Stock C: Investment $ 80 Million Stock's Beta Coefficient 4.0
Stock D: Investment $ 80 Million Stock's Beta Coefficient 1.0
Stock E: Investment $ 60 Million Stock's Beta Coefficient 3.0

The Current risk free rate is 8 percent. Market returns have thefollowing estimated probability distribution for the nextperiod:

Probability Market Return
0.1 10%
0.2 12%
0.4 13%
0.2 16%
0.1 17%

A. Compute the expected return for the market
B. Compute the beta coefficient for the investment fund.
C. What is the estimated equation for the security marketline?
D. Compute the fund's required rate of return for the nextperiod
E. Suppose John McAlhany, the president, receives a proposal for anew stock. The investment needed to take a position in the stock is$50 million, it will have an expected return of 18%, and itsestimated beta coefficient is 2.0. Should the firm purchase the newstock? At what expected rate of return should McAlhany beindifferent to purchasing the stock?

Roger McDonald, 55 years old and single, is a dental surgeon and owns a dental practice. Roger has accumulated a SGD2,000,000 investment portfolio with a large concentration in small-cap Singapore equities. Over the last 5 years the portfolio has averaged 15 percent annual total return on investment. Roger does not expect to retire before he is 70 years old. His current income is more than sufficient to meet his expenses. Upon retirement, he plans to sell his medical practice and use the proceeds to purchase an annuity to cover his retirement cash flow needs. He has no additional long term goals or needs.
In consultation with Roger, his investment advisor, Justin Teo has drawn up an investment policy statement with the following elements (Justin’s notes justifying each item are included):
Risk tolerance: Roger has above average risk tolerance.
Justin’s notes:
- Roger’s present investment portfolio and his desire for larger returns indicate a high willingness to take risk.
- His financial situation (largely current asset base, has ample income to cover expenses, lack of need for liquidity or cashflow, and long time horizon) indicates a high ability to assume risk.
Return Objective: The return objective is an average total return of 10 per cent or more with a focus on long-term capital appreciation.
Justin’s notes:
- Roger’s circumstances warrant an above-average return objective that emphasizes capital appreciation for the following reasons:
- Roger has a sizable assert base and ample income to cover his current spending; therefore, the focus should be on growing the portfolio.
- Roger’s low liquidity needs and long time horizon support an emphasis on a long term capital appreciation approach.
- Roger does not rely on the portfolio to meet living expenses.
-The numerical objective of 10 per cent represents an estimate of a target Roger can aim for rather than a minimum return required to meet a specific financial goal.

Liquidity: Roger’s liquidity needs are low.
Justin’s notes:
- Roger has no regular cash flow needs from the portfolio, because the income from his medical practice meets all current spending needs.
- No large, one-time cash needs are stated. However, it could be considered appropriate to keep a small cash reserve for emergencies.
Time Horizon: Roger’s time horizon is long term and consists of 2 stages:
(1) The first stage consists of the time until his retirement, which he expects to be 15 years.
(2) The second consists of his lifetime following retirement, which could range
from 10 to 20 years. Justin has also summarised Roger’s current portfolio in Exhibit 1 below:
Value Total Return Deviation
Short-term Bonds $200,000 10% 4.6% 1.6%
Domestic Large-Cap Equities $600,000 30% 12.4% 19.5%
Domestic Small-Cap $1,200,000 60% 16.0% 29.9%
Total Portfolio $2,000,000 100% 13.8% 23.1%
Exhibit 1: Roger’s Current Investment Portfolio


Roger expects to receive an inheritance of SGD2,000,000 soon. Roger and Justin sit down to discuss its investment in one of the four index funds. Given Roger’s already above average risk tolerance and level of portfolio risk, Roger and Justin have concluded that the risk tolerance description in the current IPS remains valid; they do not want to contemplate further increase in portfolio risk. On the other hand, they do not wish to reduce expected return. Justin is evaluating the four index funds shown in Exhibit 2 below for their ability to produce a portfolio that will meet the following two criteria relative to the current portfolio:
- Maintain or enhance expected return, and
- Maintain or reduce volatility.

Each Fund in Exhibit 2 is invested in an asset class that is not substantially represented in the current portfolio shown in Exhibit 1. Exhibit 2 presents statistics on those index
funds.
Expected Expected Correlation of
Index Annual Annual Standard Returns with Current
Fund Return Deviation Portfolio’s Return
Fund A 15% 25% +0.80
Fund B 11% 22% +0.60
Fund C 16% 25% +0.90
Fund D 14% 22% +0.65
Exhibit 2: Expected Risk, Return and Correlation of 4 Index Funds under Consideration

Question 1
(a) Recommend the most appropriate index fund to add to Roger’s portfolio. Justify your recommendations by describing how your chosen fund best meets both of the stated criteria. (No calculations are required.)

(b) Twenty years later, Roger is meeting with you, his new financial advisor. You are evaluating if Roger’s investment policy remains appropriate for his changed circumstances.
- Roger is now 75 years old and retired. His spending requirements are expected to increase with the rate of general inflation, which is expected to average 3.0 per cent annually.
- Roger estimates his current living expenses at SGD150,000 annually. An annuity, purchased with the proceeds from the sale of his medical practice, provides SGD20,000 of this amount. The annuity is adjusted for inflation annually using a national price index.
- Because of poor investment performance and a high level of spending, Roger’s asset base has declined to SGD1,200,000 exclusive of the value of the annuity.
- Roger sold all of his small-cap investment last year and invested the proceeds in domestic bonds.
- Because his international equity investments have performed poorly, Roger has become markedly uncomfortable holding international equities.
-Roger plans to donate SGD60,000 to a charity in three months.

Discuss how each of the following components of Roger’s investment policy statement should now reflect the changes in his (note that the observations should focus on but not limited to the direction and magnitude of change in each component rather than on a specific numeric change):
(i) Risk tolerance
(ii) Return requirement
(iii) Liquidity needs
(iv) Time horizon

(c) Roger’s investment portfolio at 75 years old is summarised in Exhibit 3 below:
Current Expected Expected
Allocation Return Standard Deviation
Cash equivalents 2% 5% 3%
Fixed Income 75% 7% 8%
Domestic Equities 10% 10% 16%
International Equities 3% 12% 22%
Domestic Real Estate 10% 10% 17%
_______________________________________________________________
Exhibit 3: Roger’s Investment Portfolio at Age 75 Years Old


Given Roger’s changed circumstances, state whether the current allocation to each asset class should be lower, the same, or higher. Justify your response with one reason for each asset class. No calculations are required and responses should be based only on Roger’s changed circumstances and the information in
Exhibit 3.
(i) Cash Equivalents
(ii) Fixed Income
(iii) Domestic Equities
(iv) International Equities
(v) Domestic Real Estate

(d) Explain one (1) way in which Roger might seek to reduce the tension between his current return requirement and his current risk tolerance.

  1. RON Ltd has the following capital structure components.

    Five million shares issued with a current market price of 5. Equity holders require a 13% return.

    10,000, 6%, $1000 Corporate bonds outstanding which are currently priced at par. Coupons are paid annually.

    If the firm faces a corporate tax rate of 30%, compute RON Ltd's Weighted Average Cost of Capital (WACC). Enter your answer in decimal form to FOUR decimal places. For example 10.34%, would be entered as 0.1034.____________

  2. Assume that the economy has three types of people. 20% are fad followers, 75% are passive investors, and 5% are informed traders. The portfolio consisting of all informed traders has a beta of 1.4 and an alpha of 4.98%. The market has an expected return of 10% and the risk-free rate is 4 %.

    What is the alpha for the fad followers? Enter your answer as a percentage to two decimal places (i.e. 0.12% rather than 0.0012; the percent sign is not necessary)._____________

  3. Which of the following statements is FALSE?

    The largest alphas occur in the smallest size deciles.

    When considering portfolios formed based on the market-to-book ratio, most of the portfolios plot below the security market line.

    The size effect is the observation that small stocks have positive alphas.

    When considering portfolios formed based on size, although the portfolios with the higher betas yield higher returns, most size portfolios plot above the security market line.

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