QUESTION 1 [25 marks] This question is compulsory. For this question, that means you lose all 25 possible marks if you do not answer at all.

As an analyst at Smythe Partners, you are considering how to allocate $5,000,000 that the portfolio manager has asked you to invest in the stock market. You start off looking at two companies: Bradfords, a clothing retailer, and Lineas & Co., a drug manufacturer.

Your assessment of their expected returns is tied to the state of the economy (whether the economy is in a boom, in a recession, or is normal), and is summarised next:

The betas of the stocks of the two firms are given next:

Bradfords

0.60

Lineas & Co.

1.20

Required:

a)  Calculate the expected returns and standard deviation for each of Bradfords and      Lineas & Co., as well as the coefficient of correlation between them. Show your fully detailed calculations. Marks are awarded based on final correct figures only.

[5 marks]

b)  Calculate the expected return and standard deviation of your portfolio if you allocate $3,250,000 to Bradfords, and the rest of the money to Lineas & Co. Show your fully detailed calculations.(Marks are available for workings but 2 marks are available for the correct standard deviation i.e. correct figure only.)

[5 marks]

c)  The risk-free rate is equal to 3.1% and that the market (equity) risk premium is equal to 6%. For each of Bradfords and Lineas & Co. determine if the stock is undervalued or overvalued, and compute by how much. Show your fully detailed workings.

[4 marks]

d)  Using the given from Part c) above, calculate the standard deviation of the market portfolio if the slope of the Capital Market Line is 0.30. Show your fully detailed

calculations. (Marks are available for workings but 2 marks are available for the correct standard deviation i.e. correct figure only.)

[3 marks]

e)  You consult with an investment expert about your investment approach and the  prospect of your portfolio. The expert provides you with the following opinion and assessment:

(i)     “The performance of your portfolio depends on the performance of the market.” (ii)     “The Arbitrage Pricing Theory (APT) tells us that a portfolio like yours can have

no alpha, otherwise that would lead to arbitrage.”

(iii)      “According to CAPM, if you want to maximize your returns, allocate more money

to Lineas & Co., because it has the highest beta.”

(iv)      “I cannot comment about the appropriateness of the relative weights of Bradfords

and Lineas & Co. in your portfolio without knowing your investors’ degree of risk aversion.”

Briefly discuss the validity of each of the four parts of the expert’s opinion, making sure you say if each is true or false, while explaining.

[8 marks]

QUESTION 2 [25 marks] This question is compulsory.

You are a portfolio manager at Castor Capital, a bond asset manager, and you are looking at  three  U.S.  Treasury  notes  as  potential  investments  in  your  portfolio.  The  following information is provided about these three notes, all of which pay coupons or compound semi-

annually:

Prices in the above table are expressed as percentages of par value. All three notes have a par value of $1,000.

Required:

a)  Calculate the yield to maturity of Treasury Note 1. Round your answer to two decimal places. Show your fully detailed workings. (Marks are available for workings but 1      mark is available for the correct yield to maturity i.e. correct figure only.)

[3 marks]

b)  Calculate the price of Treasury Note 2, as a percentage of par value. Round your     answer to four decimal places. Show your fully detailed workings. (Marks are             available for workings but 1 mark is available for the correct price of Treasury Note 2 i.e. correct figure only.)

[3 marks]

c)  Calculate the coupon rate for Note 3 that is consistent with the price and yield to     maturity shown in the table above. Show your fully detailed calculations. (Marks are available for workings but 1 mark is available for the correct coupon rate i.e. correct figure only.)

[3 marks]

d)  Calculate the Macaulay duration and the modified duration of Note 2. Show your fully detailed calculations. (Marks are awarded based on correct figures only.)

[6 marks]

e)  Suppose you create a portfolio consisting of Note 1 (60% of the portfolio) and Note 2 (40% of the portfolio). Estimate the percentage change in the value of the portfolio if yields rise by 25 basis points (0.25%). Show your fully detailed calculations. (Marks  are awarded based on correct figures only.)

[4 marks]

Part f) below is independent of Parts a), b), c), d) and e) immediately above.

f)   In relation to the immunization of a portfolio of liabilities, briefly but clearly explain the role of duration, effect of convexity, while ensuring to explain the purpose behind       immunizing liabilities.

[6 marks]

QUESTION 3 [25 marks] This question is compulsory.

Iconic Enterprises has just reported annual earnings per share (EPS) of $4 and paid out a dividend of $1.60 per share. The company will grow its earnings at a rate of 12% a year   over the next five years (i.e. Years 1, 2, 3, 4, and 5) while maintaining the same retention ratio as in the year that just ended. Starting year 5, it is believed that the firm’s plowback  ratio will be 25% and its ROE will be 20% in perpetuity.

Jubilee Industries is a comparable firm to Iconic Enterprises, is in the same industry and     has the same systematic risk attributes. Jubilee Industries has just earned $2.50 per share (EPS) for the year that just ended, is trading at $15, has a constant dividend payout ratio of 60%, and grows its earnings at 4% in perpetuity. Jubilee Industries is believed to be fairly   valued.

Assume dividends are paid out annually, at the end of the year for both companies.

Required:

a)  Using the information provided about Jubilee Industries, compute the cost of equity of Iconic Enterprises. Show your fully detailed calculations. (Marks are awarded     based on correct figures only.)

[3 marks]

b)  Using the Dividend Discount Model (DDM), calculate the fair price of a share of       Iconic Enterprises today. Show your fully detailed calculations. (Marks are available for workings but 1 mark is available for the correct coupon rate i.e. correct figure     only.)

[8 marks]

c)  Calculate the Present Value of Growth Opportunities (PVGO) of Jubilee Industries, and briefly comment on your finding. Show your fully detailed calculations. (Marks  are awarded based on correct figures only.)

[5 marks]

d)  Calculate the ROE of Jubilee Industries and briefly comment on how your answer relates to the answer to Part c) immediately above. Show your fully detailed         calculations. (The marking scheme awards 2 marks for the correct ROE – correct figure only, and up to 3 marks for correct/appropriate comments.)

[5 marks]

Part e) below is independent of Parts a), b), c), and d) immediately above.

e)  Critique and comment on the following statements, making sure to justify your assessment.

“In comparing value to growth companies, value companies typically command a lower PE (price to earnings) ratio than growth companies. Consequently, value   companies will provide higher returns to investors than growth companies in a    perfectly efficient market.

[4 marks]

QUESTION 4 [25 marks] This question is compulsory.

You wish to price two European put option on two different stocks for an investor who wishes to hedge their long position.

The stocks in question are: Sphericus Technology, a developer of a fintech app, currently trading at $80 per share, and Oates Inc., a maker of earth-moving equipment, currently   trading at $120 per share.

The put option on on Sphericus Technology has a strike of $75, and expires in six months, at which time Sphericus Technology can either be trading at $65 or $95.

The annualized standard deviation of returns (volatility) on Oates Inc. stock is 30% per

year. The strike of the put you need to price is $110, and it expires in six months. The risk-free rate is 4% for all maturities (continuously compounded).

Required:

a)  In relation to the six-month put option on Sphericus Technology, and using the two- state model for option pricing applied to one (1) time step:

i.     Compute the hedge ratio for the option. Show your fully detailed calculations. (Marks are awarded based on correct figures only.)

[3 marks]

ii.     Explain the concept of a hedged or instantaneously riskless portfolio in the     context of pricing options and apply that concept to compute the value the put option on Sphericus Technology. Show your fully detailed workings.

[5 marks]

iii.     Using the answer from sub part ii. immediately above, calculate the risk-    neutral probability of an up-move p in the one-step binomial six-month put pricing model on Sphericus Technology to four decimal figures. Show your fully detailed workings. (Marks are awarded based on correct figures only.)

[3 marks]

b)  In relation to the six-month put option on Oats Inc., and using the binomial tree model for option pricing applied to two (2) time steps:

i.     Compute up step size, u, and the down step size, d to four decimals. Show your fully detailed workings.

[2 marks]

ii.     Calculate the risk-neutral probability of an up-move p to four decimals. Show your fully detailed workings. (Marks are awarded based on correct figures     only.)

[2 marks]