Question

Assume that you are providing financial advice to a well-diversified Australian investor, Mr. Rex Sandilands, a full-time biology secondary school teacher and part-time wrestler. Mr. Sandilands is seeking to undertake further investment in any or all of the companies included on the following page, which are each included in the Australian Securities Exchange’s ASX 200 Index. To assist your investment decision-making process, you have been provided the following information:

• the forecast expected return on the Australian Stock Exchange’s ASX 200 Index will be approximately 10% over the next year

• on average, the ASX 200 Index has produced returns approximately 4% in excess of risk-free Australian securities

The relevant Australian companies under consideration are:

• Foxwedge Mining (beta of 1.2) having an expected rate of return of 11.5%

• Sirpinz Holdings (beta of 0.8) having an expected rate of return of 11.5%

• Galilee Trading (beta of 2.0) having an expected rate of return of 12.5%

Required:

1. Given the above information, what is the required rate of return for each of the companies discussed above?
2. In practice, beta values are available from public sources, either at no or at a nominal charge. If you did not however have access to these beta values as given in the question, briefly explain how would you determine such beta values for each of these companies?

Hint: What processes would you use to assess a beta value for each company? (Students should write no more than 100 words for this part of the question).

3. Using all of the information included in this question, would you recommend investment in any or all of the companies discussed above by Mr. Sandilands? Briefly justify your discussion using terminology understandable to Mr. Sandilands, given that, although he is a well-diversified investor, Mr. Sandilands has only a very introductory understanding of finance principles and theory. That is, provide Mr. Sandilands with a convincing argument in favour of / rejection of, the individual companies under consideration.

(Students should write no more than 150 words for this part of the question).

4. Regardless of the advice provided in part c) of this question, assume that Mr. Sandilands subsequently invested $360,000 in a portfolio of the relevant companies comprised as follows:

• Foxwedge Mining $180,000

• Sirpinz Holdings $145,000

• Galilee Trading    $35,000

Under these circumstances what would be Mr. Sandilands: i) portfolio required rate of return? and ii) portfolio beta?

5. Briefly comment on how you might use the calculations undertaken in part d) of this question to assist Mr. Sandilands in the future given his decision to invest in the portfolio. That is, having performed the calculations in part d) of this question, of what use are they as a decision-making tool?

(Students should write no more than 100 words for this part of the question).

6. What is the relevance in this question to the statement that; “Mr. Sandilands is a well-diversified Australian investor”? Hint: How does the above statement allow students to progress with the various calculations / discussion included in this question?

（对于这部分问题，学生应该写不超过75个单词）。（3分）

Answer 1

a.

According to the CAPM:

Ri = Rf + Bi * (Rm – Rf)

Ri is required return of the security i.

Rf is risk free return.

Bi is Systematic risk of the security i.

Rm is market return.

Given,

The forecast expected return on the Australian Stock Exchange’s ASX 200 Index will be approximately 10% over the next year.

So, Rm = 10%

On average, the ASX 200 Index has produced returns approximately 4% in excess of risk-free Australian securities.

So, Rm – Rf = 4%

10% – Rf = 4%

Rf = 6%

Required return for Foxwedge Mining (beta of 1.2):

RFoxwedge = Rf + BFoxwedge* (Rm – Rf) = 6% + 1.2*(4%) = 10.8%.

Required return for Sirpinz Holdings (beta of 0.8):

RSirpinz = Rf + BSirpinz* (Rm – Rf) = 6% + 0.8*(4%) = 9.2%.

Required return for Galilee Trading (beta of 2.0):

RGalilee = Rf + BGalilee* (Rm – Rf) = 6% + 2*(4%) = 14%.

b.

If beta values are not given then we can use the past 5 years daily price data of these companies and market to find the daily past return of these companies and market. Then we need to perform the linear regression of the individual company return data against the market return data to find the beta coefficient that is the slope parameter of the linear regression equation. Alternatively we can also use the formula,

Beta, Bi = (Covariance of past daily returns of security i and past daily market return) / (Variance of past daily market returns).

c.

Foxwedge Mining have a required return of 10.8% according to the underlying systematic risk. So, this stock is under-priced as expected return of 11.5% is higher than 10.8% as market is providing higher return rewards than the risk involved. So, it is recommended to invest in Foxwedge Mining.

Sirpinz Holdings have a required return of 9.2% according to the underlying systematic risk. So, this stock is under-priced as expected return of 11.5% is higher than 9.2%. So, it is recommended to invest in Sirpinz Holdings as it provides higher return relative to undertaken risk.

Galilee Trading have a required return of 14% according to the underlying systematic risk. So, this stock is over-priced as expected return of 12.5% is lower than 14%. So, it is not recommended to invest in Galilee Trading as this stock is expected to provide lower return than the risk involved.

d.

Given,

Mr.Sandilands subsequently invested $360,000 in a portfolio of the relevant companies comprised as follows:

• Foxwedge Mining $180,000

• Sirpinz Holdings $145,000

• Galilee Trading $35,000

i) Portfolio required rate of return.

Portfolio return = Weight average return of the component securities.

Weight of Foxwedge Mining = 180,000/360,000 = 0.5 or 50%.

Weight of Sirpinz Holdings = 145,000/360,000 = 0.402 or 40.2%.

Weight of Gaililee Trading = 35,000/360,000 = 0.098 or 9.8%.

Required return of Foxwedge Mining = 10.8%.

Required return of Sirpinz Holdings = 9.2%.

Required return of Gaililee Trading = 14%.

Portfolio required return = (0.5 * 10.8%) + (0.402 * 9.2%) + (0.098 * 14%) = 10.47%.

ii) Portfolio beta.

Portfolio beta = Weighted average beta of the individual securities.

Beta of Foxwedge Mining = 1.2.

Beta of Sirpinz Holdings = 0.8.

Beta of Gaililee Trading = 2.

Portfolio Beta = (0.5 * 1.2) + (0.402 * 0.8) + (0.098 * 2) = 1.12.

e.

The above calculations tell that the systematic risk of the portfolio is given by beta of 1.12 and the portfolio return is 10.47%. In future we can use this data to compare the expected return of the portfolio with this CAPM required return to check whether the portfolio is under or overpriced and whether we should add long or short positions respectively.

f.

The statement tells that Mr. Sandilands is only concerned with the systematic risk of the given securities as he is already a well diversified investor. So, we do not need to take the total risk of the given securities in the calculations as the undiversified or idiosyncratic risk is already diversified. Otherwise it was not possible to do the calculations using systematic risk as the portfolio of just three securities is not considered a diversified portfolio.