ECON 1145-Marking Criteria- May 2021 PDF

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EXAMINATION PAPER: ACADEMICSESSION 2020/2021-Marking SchemeCampus Greenwich Maritime/International PartnersFaculty BusinessDepartment International Business and EconomicsCourse Code ECON Course Title PRINCIPLES OF INVESTMENTLevel SIXDuration THREE HOURS (ONLINE)Date May 2021Module Leader:INSTRUCTION...

Description

EXAMINATION PAPER: ACADEMIC SESSION 2020/2021-Marking Scheme Campus

Greenwich Maritime/International Partners

Faculty

Business

Department

International Business and Economics

Course Code ECON1145 Course Title PRINCIPLES OF INVESTMENT Level SIX Duration

THREE HOURS (ONLINE)

Date

May 2021

Module Leader:

INSTRUCTIONS CANDIDATES Answer ALL questions in part A and Select TWO out of FOUR questions in part B

May 2021 Course Title: ECON1145 Course Code: Principles of Investment Page 1 of 14

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PART A- ANSWER ALL QUESTIONS (60 MARKS) Question A1 (13 Marks) A1.1 Explain the Black and Scholes option –pricing model for European call options (6 marks) A1.2 Find the price of a call option that expires in 4 months and has a strike price of $38. The market price of underlying stock is currently $36. The standard deviation is a 50% per year and the risk and risk-free rate is 1.5% (7 marks) Answer to A1.1 • The candidate may say , Used by options traders to try and identify and trade over- and under-valued options, Black and Scholes option-pricing model prices a European call option using the equation:

• S represents the market price of the underlying stock • PV(X) represents the present value of the option’s strike price. • N(d1) and N(d2) are probabilities ranging from 0 to 1; as these probabilities get

•

•

closer and closer to 1.0, the option is more and more likely to be exercised, and hence it is more and more valuable. The Basics of the Black Scholes Model: The initial equation was introduced by Black and Scholes in 1973, the model assumes the price of traded assets follows a geometric Brownian motion with constant drift and volatility. When applied to a stock option, the model incorporates the constant price variation of the stock, the time value of money, the option's strike price, and the time to the option's expiry. It's used to calculate the theoretical value of options using current stock prices, expected dividends, the option's strike price, expected interest rates, time to expiration and expected volatility. The probabilities depend on the numerical values of d and d from these 1 2 equations:

•

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S is stock price X is strike price T is time remaining before expiration (years) σ is the annual standard deviation of the stock’s return r is the annual risk-free interest rate. Once values for d1 and d2 are calculated they are converted into probabilities using the standard normal distribution function. The normal distribution is a bell curve with a mean zero and a standard deviation of 1 . Answer to A1.2

The candidate needs to use the equation presented in A1.1 to calculate the probabilities that represent the likelihood of drawing a number less than or equal to d1 and d2. For the distribution, then use these values of d1 and d2 to obtain the standard normal probabilities using excel N(d 1)= normdist ( ) and N(d2)= normdist ( ), then calculate the call price.

S is stock price=$36 X is strike price=$38 T is time remaining before expiration (years =4 month=0.3333 year σ is the annual standard deviation of the stock’s return=0.5 r is the annual risk-free interest rate=0.015 The candidate needs to calculate the present value of the strike price by discounting $38 at 1.5% for one third of the year. 0.1422 0.50= -0.1464 Using excel ‘=normsdist’ function we have: N() =normsdist ()= 0.5565 N() =normsdist (-)= 0.4418 Call price =$36(0.5565)-[38/(](0.4418)= $3.16 The candidate needs to calculate the present value of the strike price by discounting $38 at 1.5 % for one third of the year. So, according to the Black –Scholes option –pricing model, the call should be priced at $3.16

May 2021 Course Title: ECON1145 Course Code: Principles of Investment Page 3 of 14

Question A2 (8 Marks)   

What is a convertible Debenture? How does a convertible bond differ from a convertible preferred? Identify the equity kicker of a convertible security and explain how it affects the price and behaviour of convertibles?

Answer to A2: A convertible debenture is a long-term, unsecured corporate bond carrying the provision that within a stipulated time period, the bond may be converted into a certain number of shares of the issuing corporation’s common stock. A convertible preferred is very similar to a convertible bond except that it is initially issued as a preferred stock and then is convertible into common shares. Thus, a debenture is a bond and a preferred is a stock. Convertible debentures in effect, allow investors to participate in share price appreciation. (3 marks) Another difference between a convertible debenture and convertible preferred is that while the conversion ratio of the debenture generally deals with large multiples of common stock, the conversion ratio of a preferred is generally very small. This is because corporate bonds are sold in $1,000 increments, while convertible preferred sell for $25 to $100. (2 marks) .The equity kicker feature of a convertible security gives the investor an opportunity to participate in the potential price performance of the underlying common stock. When the market price of the common is equal to or greater than the stated conversion price, the equity kicker has value to the investor, and the price of the convertible will move with the common. When the price of the stock goes up, the price of the convertible will increase by a multiple that approximates its conversion ratio; likewise, if the price of the stock falls, the convertible will decline by the same multiple (his subject to the conversion price being less than the stock price). (3 marks)

Question A3 (4 Marks) Calculate the holding period return for the following two investment alternatives. Which, if any, of the return components is likely not to be realized if you continue to hold each of the investments beyond 1 year? Which investment would you prefer, assuming they are of equal risk? Explain. (4 marks) Investment (in $) X Y Cash received 1st quarter 1.00 0 nd 2 quarter 1.20 0 3rd quarter 0 0 4th quarter 2.30 2.00 Investment value Beginning of year 30.00 50.00 End of year 29.00 56.00

May 2021 Course Title: ECON1145 Course Code: Principles of Investment Page 4 of 14

Answer A3 Holding period return (HPR) = Current income  Ending price  Beginning price Beginning price $1.00  $1.20  $0  $2.30  $29.00  $30.00 $3.50  $30.00 $30.00 11.67% $0  $0  $0  $2.00  $56.00  $50.00 $8.00 HPR Y   50.00 $50.00 16% HPRX 

(2 marks) If the investments are held beyond a year, the capital gain (or loss) component would not be realized and would likely change. Assuming they are of equal risk, Investment Y would be preferred since it offers the higher return (16.00% for Y versus 11.67% for X). (1 mark)

Question A4 (4 Marks) A company’s total asset is $ 980 billion, its stockholder’s equity $280,000 million and long term debt $168 billion. What are its Debt-equity ratio and its equity multiplier? Debt-equity ratio= Equity multiplier =

Question A5 (6 Marks) What are the essential parts of a commodity contract? Which parts have a direct bearing on the behaviour of the contract? Answer to A5 The essential elements of a commodities contract are as follows: a) The product: the commodity name, such as No. 2 yellow corn b) The exchange: the exchange where the contract is traded c) The size of the contract: in bushels, pounds, etc. d) The pricing unit: cents per pound, dollars per ton, etc. e) The delivery month: when the contract expires The size of the contract, the price of the underlying commodity, and the pricing unit has the most effect on the contract price. The delivery month also plays a role in the price of the contract.

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Question A6 (15 Marks) A6.1 What the efficient frontier? How is it related to the attainable set of all possible portfolios? How can it be used with an investors ‘utility function to find the optimal portfolio? (3 marks) A6.2 H. Markowitz uses statistical measures to develop a portfolio plan including expected returns and standard deviation of returns for both securities and portfolios and the correlation between returns. a) Develop a Quadratic utility function for wealth to determine the consumer’s choice in situations involving risk in terms of the mean and variance of the outcome. Describe the so- called Modern Portfolio Theory (8 marks) b) Explain the assumptions of the Markowitz model and explain how diversification is achieved. (4 marks) Answer to A6.1 The candidate may say combining securities with less than perfect positive correlation reduces portfolio risk through diversification. By analyzing securities using correlation and beta (which is a statistical measure of the relative volatility of a security or portfolio return as compared to a broadly derived measure of stock market return), the investor attempts to create a portfolio with no diversifiable risk that provides the highest return for a given level of risk. The feasible set refers to all possible combinations (portfolios) of the assets available for the investor. The feasible or attainable set of all possible portfolios refers to the risk-return combinations achievable with all possible portfolios. It is derived by first calculating the return and risk of all possible portfolios and plotting them on a set of risk-return axes. The efficient frontier consists of all efficient portfolios (those that maximize the portfolio’s return for each risk level). Thus, the efficient frontier is part of the feasible set—indeed the most desirable part from an investor’s perspective. All portfolios on the efficient frontier are preferable to the others in the feasible or attainable set. Plotting an investor’s utility function or risk indifference curves on the graph with the feasible or attainable set of portfolios will indicate the investor’s optimal portfolio—the one at which an indifference curve meets the efficient frontier. This represents the highest level of satisfaction for that investor.

Answer to A6.2 (a) (8 MARKS) The candidate needs to argue that the portfolio theory is concerned with allocation of an individual’s wealth among the various available assets and May 2021 Course Title: ECON1145 Course Code: Principles of Investment Page 6 of 14

construct a portfolio to specify the individual’s utility function. The calculation of expected utility may then be used to determine the consumer’s choice in situations involving risk. Modern portfolio theory (MPT) is based on the use of statistical measures including mathematical concepts such as correlation (of rates of return) and beta. Combining securities with negative or low positive correlation reduces risk through statistical diversification. By analyzing securities using correlation and beta (which is a statistical measure of the relative volatility of a security or portfolio return as compared to a broadly derived measure of stock market return), the investor attempts to create a portfolio with minimum diversifiable risk that provides the highest return for a given level of acceptable diversifiable risk. Plotting an investor’s utility function or risk indifference curves on the graph with the feasible or attainable set of portfolios will indicate the investor’s optimal portfolio—the one at which an indifference curve meets the efficient frontier. This represents the highest level of satisfaction for that investor.  Quadratic utility function: (1)



Applying expectation operator to the equation (1 ):



(2) Since

(3)

o Expressing the utility function merely in terms of the mean and variance of the outcome: (4)



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Investment decisions are based on the concept of return rather than wealth. A quadratic utility function can be specified in terms of rate of return : (5) The expected return of a portfolio comprising of securities in terms of weighted average

of the expected return of each security in the portfolio: (6)



Variance of return of each security and covariance of returns between each pair of securities:



The correlation of returns between the two securities and their returns:

(7) (8) Where ρ is the correlation coefficient between returns of securities i and j. 

The variance of return of a portfolio is determined by the correlation of returns between each pair of securities as well as the variance of each security (9)

The variance of return of a portfolio is determined by the correlation of returns between each pair of securities as well as the variance of return of each security. 

In the two –asset portfolio : (10)

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Answer to A6.2 (b) (4 MARKS) The assumptions underlying the Markowitz model are  The return of an investment adequately summarizes the outcome of the investment.  Investor’s estimated risk are proportionate to the variance of return  The investors are willing to base their decision on just two parameters of the probability distribution function: the expected return and variance of return.  The investor exhibits risk aversion: for a given expected return he/she prefers minimum risk.

Question A7 (10 Marks) The Ben Hashem (B) and Patel (P) Corporations have the following expected risk and return inputs for the next year

The portfolio risk for a portfolio of 50% in each asset is 23.8844 %. Determine the correlation coefficient that will be to reduce the level of portfolio risk by 35 percent. (8 Marks) What is the expected return of equally weighted portfolio? (2 Marks) Answer to A7 A thirty five % reduction in risk is (0.35) (23.8844) = 8.35954 %. Therefore the new level of risk will be 15.52486

-0.29458 (2 marks) PART B : PLEASE CHOOSE 2 OUT OF 4 QUESTIONS B1, B2, B3&B4 . (20 MARKS EACH) May 2021 Course Title: ECON1145 Course Code: Principles of Investment Page 8 of 14

Question B1 (20 marks) B1.1 The Kumar (K) and the Wong (W) Corporations have the following joint probability distribution of returns for next year: STATE

PROBABILITY

Boom Recession Normal Recovery Slow growth

RETURN Kumar %

0.1 0.2 0.4 0.1 0.2

RETURN Wong %

14 -5 10 9 12

20 -2 9 14 18

B1.1.1 Determine the expected covariance of returns for the Kumar and Wong Corporations. (5 marks) B1.1.2 what is the correlation of returns between the Kumar and Wong Corporations? (5 marks) Answer B1.1: The candidate should determine the expected return for Kumar and Wongs Corporations . Expected return can be determined using the equation below

E(rk)=(0.1)(14)+(0.2)(-5)+(0.4)(10)+(.1)(9)+(0.2)(12)=7.7% E(rw)=(0.1)(20)+(0.2)(-2)+(0.4)(9)+(.1)(14)+(0.2)(18)=10.2%

= (14-7.7)(20-10.2)(0.1)+ (-5-7.7)(-2-10.2)(0.2)+ (10-7.7)(910.2)(0.4)+ (9-7.7)(14-10.2)(0.1)+ (12-7.7)(18-10.2)(0.2) =43.26

(0.1)(14-7.7)2 +(0.2)(-5-7.7)2+(0.4)(10-7.7)2+(0.1)(9-7.7)2+(0.2)(12-7.7)2 = 42.21 6.50% (0.1)(20-10.2)2 +(0.2)(-2-10.2)2+(0.4)(9-10.2)2+(0.1)(14-10.2)2+(0.2)(18-10.2)2 = 53.56 =7.318% May 2021 Course Title: ECON1145 Course Code: Principles of Investment Page 9 of 14

=

B1.2 The major news affecting the financial markets is the change in expectations of future interest rates. Discuss the interest rate risk to investors. (10 Marks) Answer to B1.2 a) Securities are especially affected by interest rate risk. This is particularly true for those securities that offer purchasers a fixed periodic return. Interest rate risk is the chance that changes in interest rates will adversely affect a security’s value. The interest rate changes themselves result from changes in the general relationship between the supply of and the demand for money. As interest rates change, the prices of many securities fluctuate. The prices of fixed-income securities (bonds and preferred stock) typically drop when interest rates rise. As interest rates rise, new securities become available in the market, and those new securities pay the new, higher rates. Securities that are already outstanding make cash payments that reflect lower market rates from the past, so they are not competitive in the higher rate environment. Investors sell them, and their prices fall. The opposite occurs when interest rates fall: Prices of outstanding securities that make cash payments above the current market become more attractive, and their prices rise. (3 marks) b) A second, more subtle aspect of interest rate risk is associated with reinvestment of income. Only if you can earn the initial rate of return on income received from an investment can you achieve a fully compounded rate of return equal to the initial rate of return. In other words, if a bond pays 8% annual interest, you must be able to earn 8% on the interest received during the bond’s holding period in order to earn a fully compounded 8% rate of return over that period. This same aspect of interest rate risk applies to reinvestment of the proceeds received from an investment at its maturity or sale. (4 marks) c) A final aspect of interest rate risk is related to investment in short-term securities such as U.S. Treasury bills and certificates of deposit. Investors face the risk that when short-term securities mature, they may have to invest those proceeds in lower-yielding, new short-term securities. By initially making a long-term investment, you can lock in a return for a period of years rather than face the risk of declines in short-term interest rates. Clearly, when interest rates are declining, the rates from investing in short-term securities are adversely affected. (On the other hand, interest rate increases have a positive impact on such a strategy.) The chance that interest rates will decline is therefore the interest rate risk of a strategy of investing in short-term securities. (3 marks ) May 2021 Course Title: ECON1145 Course Code: Principles of Investment Page 10 of 14

Question B2 (20 marks) Angela sold her business and bought a portfolio of American blue-chip stocks worth $56.592 million. She wants to hedge her position with six-month futures contracts on the Dow Jones Industrial Average, which are currently trading at 32,960. B2.1 why would she choose to hedge her portfolio with the DJIA rather than the S&P 500? (3 marks) B2.2 given that Angela wants to cover the full $56.592 million in her portfolio, describe how she would go about setting up this hedge. (5 marks) B2.3 if each contract required a margin deposit of $20,875, how much money would she need to set up her hedge? (3 marks) B2.4 Assume that over the next six months, stock prices do fall and the value of Angela’s portfolio drops to $50.3 million. If DJIA futures contracts are trading at 31,400, how much will she make (or loose) on the futures hedge? Is it enough to offset the loss in her portfolio? That is, what is her net profit or loss on the hedge? (6 marks) B2.5 Will she now get her margin deposit back, or is that a “sunk cost” (lost forever)? (3 marks) Answer to question B2 B2.1 Since Angela’s portfolio consists of blue chip stocks—stocks of major, wellestablished companies—the Dow Jones Industrial Average Index would track her stock portfolio better than the S&P 500. B2.2 The value of Angela’s portfolio is $56,592,000. One DJIA futures contract is worth $329,600 (32960X 10). To cover her entire portfolio, she has to short sell 20 futures contracts ($56,960,000 divided by %329,600). B2.3 Since the margin deposit is $20,875, she needs to invest 417,500 ($20,875x 20) initially to set up this hedge. B2.4 Loss in Angela’s portfolio value is $6,292,000 ($5...