Fluent Essays

Help with Investment Analysis (1) Problems related to Chapter 20 (Options Markets: Introduction) 1. Assume that the stock of XYZ Inc. is trading for $37 per share. A call option and a put option are available for a given date at a strike price of $33. Which one is more valuable, the call or the put? SOLUTION: The put option is out-of-the money. The right to sell at $33 is not very attractive when the stock is selling at $37 in the market. The call option is in-the-money, so the right to buy at $33, when the stock is trading at $37 is attractive. Therefore, call option has more value. 2. An investor bought 200 shares of a stock at $40 per share and writes 200 call options at a strike price of $45 for a premium of $1.50 each. The option will expire in four months. What is the dollar return of this covered call position if the strike price at expiration is $38, $42 or $47? SOLUTION: The dollar return comes from both the stock and the call option positions. Stock price Return from stock position Return from option Total dollar return $38 = ($38 - $40) × 200 = -$200 =200×$1.5 =$3001 =-$200 + $300 = $100 $42 =($42 – $40) × 200 =$400 =200×$1.5 =$3002 =$400 + $300 =$700 $47 =($47 – $40) × 200 =$1400 =200×$1.5 – ($47 - $45) × 200 =$300 - $400 = - $100 =$1400 - $100 =$1300 3. A call option is selling at $2.20 with 30 days maturity and a strike price of $10. If the spot price of underlying stock is $12 and the risk-free rate is 5\% per annum, calculate the put option premium (assume put-call parity holds and the stock does not pay any dividend) SOLUTION: We can solve this problem using the put-call parity equation as follows: ( ) ( ) 0 0 1 , 1 S r X CPOr PS r X C T f T f − + += += + + 1 Since stock price is less than the strike price, call option will not be exercised. The return to the call writer is the premium received by writing the call. 2 Since stock price is less than the strike price, call option will not be exercised. The return to the call writer is the premium received by writing the call. (2) Given: C = $2.20 X = $10 rf = 5\% T = 30/365 S0= $12 Plugging in these values in the above equation we get ( ) 16.0$ 12$96.9$20.2$ 12$ 05.1 10$ 20.2$ 365 30 = −+= −+=P 4. Calculate the call premium from the information given below. Assume put-call parity holds and the stock does not pay any dividend. Put premium $0.10 Expiry 2 months Risk-free rate 5\% p.a. Spot price of stock $11 Strike price $10 SOLUTION: We can solve this problem using the put-call parity equation as follows: ( ) ( )T f T f r X PSCOr PS r X C + −+= += + + 1 , 1 0 0 Given: P = $0.10 X = $10 rf = 5\% T = 60/365 S0= $11 Now we plug these values in the above equation: ( ) ( ) 18.1$ 92.9$10.11$ 05.1 10$ 10.0$11$ 1 12 2 0 = −= −+= + −+= T f r X PSC (3) 5. The premium of a put option with strike price $21.50 and 60 days time to maturity is $2. The call option premium with same strike price and maturity is $1.50. The underlying asset price and risk-free rate are $21.50 and 5\% p.a. respectively. Is possible to make an arbitrage profit using Put-call parity? If so, show your calculation. SOLUTION: First we calculate the costs of each portfolio. ( ) ( ) 828.22$328.21$50.1$ 05.1 50.21$ 50.1$ r1 X C :portfolio Call 365 60 f =+=+= + + T 50.23$2$50.21$S :portfolioPut 0 =+=+ P Costs of two portfolios are not same. Put-Call parity does not hold. One can make arbitrage profit equal to $23.50 - $22.828 = $0.672. This can be achieved by selling the expensive portfolio (Put portfolio: $23.50) and purchasing cheaper portfolio (Call portfolio: $22.828) Strategy Position Immediate cash flows Cash flow in 60 days ST < $21.50 ST ≥ $21.50 Sell put portfolio Short stock $21.50 -ST -ST Sell put $2.00 -($21.50 – ST) 0 Purchase call portfolio Purchase call -$1.50 0 ST - $21.50 Invest $21.50/1.0560/365 =$21.328 -$21.328 $21.50 $21.50 Total $0.672 0 0 6. You are given the following data: • Current stock price $31 • Strike price $30 • Risk-free rate 10\% • 3-month call premium $3 • 3-month put premium $2.25 (a) Does put-call parity hold? (b) If not, how one can make arbitrage profit? (c) Show your calculations SOLUTION: The put-call parity is given by: ( ) PS T += + + 0 f r1 X C :portfolio call ofCost (4) (a) Cost of put portfolio: $31 + $2.25 = $33.25 Cost of call portfolio: Since two payoffs are not equal, put-call parity does not hold. (b) Arbitrage profit can be made by selling the expensive portfolio (put portfolio) and purchasing the cheaper portfolio (call portfolio). Arbitrage profit of $33.25 - $32.29 = $0.96 is possible to make. (c) 7. A call option that has a strike price of $28 and expires in 6 months is priced at $2. The underlying stock price is $27. The put premium for identical maturity and strike price is $3. If the risk-free rate is 10\%, identify if there is any arbitrage profit opportunity. Show your calculations. SOLUTION: In order to identify arbitrage profit opportunity we need to examine the put-call parity relationship. If the parity holds, then there is no arbitrage profit opportunity; however, if the parity does not hold, then there is arbitrage profit opportunity. The put-call parity is given by: ( ) PS T += + + 0 f r1 X C :portfolio call ofCost ( ) ( ) ( ) 697.28$ 10.1 28$ 2$ 10.1 28$ 2$ r1 X C :portfolio call ofCost 5.0 12 6 f =+=+= + + T 30$3$27$S :portfolioput ofCost 0 =+=+ P Since cost of the two portfolios are not same, put-call parity does not hold and there is an opportunity for arbitrage profit. ( ) ( ) 29.32$ 10.1 30$ 3$ 1 12/3 =+= + + T f r X C (5) Arbitrage profit can be made by selling the expensive portfolio (Put portfolio) and purchasing the cheaper portfolio (Call portfolio). By doing so an arbitrageur can make a riskless profit of $1.303 (= $30 - $28.697). Calculations:- Strategy Position Immediate cash flows Cash flow in 60 days ST < $28 ST ≥ $28 Sell put portfolio Short stock $27.00 -ST -ST Sell put $3.00 -($28 – ST) 0 Purchase call portfolio Purchase call -$2.00 0 ST - $28 Invest $28/1.106/12 =$26.697 -$21.328 $28 $28 Total $1.303 0 0 8. A four month call option with $60 strike price is currently selling at $5. The underlying stock price is $59. The risk-free rate is 12\% p.a. The put with same maturity and strike price is selling at $3.5. What opportunity is there for an arbitrageur? SOLUTION: To identify the opportunity for an arbitrageur, we first need to check if the put-call parity holds. The put-call parity is given by: ( ) PS T += + + 0 f r1 X C :portfolio call ofCost ( ) ( ) 776.62$776.57$5$ 12.1 60$ 5$ r1 X C :portfolio call ofCost 12 4 f =+=+= + + T 50.62$5.3$59$S :portfolioput ofCost 0 =+=+ P Since cost of the two portfolios are not same, put-call parity does not hold and there is an opportunity for arbitrage profit. Arbitrage profit can be made by selling the expensive portfolio (Call portfolio) and purchasing the cheaper portfolio (Put portfolio). By doing so an arbitrageur can make a riskless profit of $0.276 (= $62.776 - $59). Calculations:- Strategy Position Immediate cash flows Cash flow in 60 days ST < $60 ST ≥ $60 Purchase put portfolio Buy stock -$59 ST ST Buy put -$3.50 ($60 – ST) 0 Sell call portfolio Sell call $5 0 -(ST - $60) Borrow $60/1.124/12 =$57.776 $57.776 -$60 -$60 Total $0.276 0 0 7/25/2021 1 Revision Questions IA 1 • You are bearish on Telecom and decide to sell  short 100 shares at the current market price  of $50 per share. • (i) How much in cash or securities must you  put into your brokerage account if the broker’s  initial margin requirement is 50\% of the value  of the short position? [Mark: 2] • (ii) You will get a margin call if the price is  above $57.69. What is the maintenance  margin? [Mark: 3] • 2 1 2 7/25/2021 2 • Solution: • Initial margin is 50\% of $5,000, or $2,500. • Let the maintenance margin is X. Then  3 • The government of Dreamland plans to undertake massive  development works in the next fiscal year; however, the tax  revenue will not be large enough to finance the  development works. So, the government will borrow from  the financial system of the country.  The monetary  authority foresees an upward pressure on the real interest  rate caused by the planned budget deficit, which will  hinder private investment. In response to proposed budget  deficit the monetary policy needs to be formulated in such  a way that keeps the real interest rate unchanged. What  monetary policy will be undertaken to keep the interest  rate unchanged?  • Diagrammatically show how the proposed fiscal action  (budget deficit) and monetary policy will affect the  positions of demand & supply of fund curves and the real  interest rate. Please make sure that X and Y axes and all  curves/lines are correctly labelled. [Mark: 2 for drawing the  graph appropriately + 3 for explaining the appropriately] 4 3 4 7/25/2021 3 • Solution:  Government will borrow from the financial system,  so demand for loanable fund will go up, demand  curve will move from D1 to D2 position. • According to the question interest rate will  remain unchanged, so monetary authority will  take expansionary monetary policy. Supply of  loanable fund will increase. Supply loanable fund  curve will move from S1 to S2 position in a way  that will keep interest rate unchanged. 5 • Suppose, expected return [E(rp)] and risk (σp)  of a risky portfolio P are 15\% and 22\%  respectively. Risk‐free rate (rf) is 8\%. An  investor invests 125\% of his fund in the risky  portfolio by borrowing, fortunately, at 7\% risk‐ free rate.  • (i) Draw the appropriate kinked Capital  Allocation Line (CAL) [Mark:2] • (ii) Calculate the slopes for the two segments  of the CAL. [Mark: 1.5 + 1.5 = 3] 6 5 6 7/25/2021 4 7 8 Slope of the CAL (with lending):   3182.0 \%22 \%8\%15      p fp rrE  Slope of the CAL (with borrowing):   3636.0 \%22 \%7\%15      p fp rrE  7 8 7/25/2021 5 • Two investors, Mr. X and Mrs Y. They have  different risk aversion coefficients. Mr. X’s risk  aversion coefficient is 2 and Mrs Y’s risk  aversion coefficient is 5.  • Draw the indifference curves of these two  investors that reflect their risk aversion (make  sure that the graph is appropriately labelled)  [Mark: 2.5] • Explain with the help of the graph drawn in (i)  above how these two investors are different  along their indifference curves in terms of  their risk‐return preferences? [Mark: 2.5] 9 10 9 10 7/25/2021 6 • Use the information given in the table below and calculate  • (i) The expected rates of return for Stock A and Stock B [2]  • (ii) The standard deviations of returns on Stock A and Stock B [3] • • State of the economy  Probability  Stock A  Stock B  • Boom  0.30  50\%  10\%  • Normal  0.50  18\%  20\%  • Recession  0.20  ‐20\%  ‐15\%  11 • (i) Expected return  • Stock A: [0.2 × (−20\%)] + [0.5 × 18\%] + [0.3 × 50\%] =20\% [1 mark]  • Stock B: [0.2 × (−15\%)] + [0.5 × 20\%] + [0.3 × 10\%] =10\% [1 mark]  • (ii) Standard deviation  • Stock A: variance= [0.2 × (– 20 – 20)2] + [0.5 × (18 – 20) 2] + [0.3 × (50 – 20) 2] = 592  • SD of A = √592 = 24.33\% [1.5 mark]  • Stock B: variance = [0.2 × (– 15 – 10) 2] + [0.5 × (20 – 10) 2] + [0.3 × (10 – 10) 2] = 175  • SD of B = √175 = 13.23\% [1.5 mark]  12 11 12 7/25/2021 7 • Mr. Robert manages a risky portfolio with  expected rate of return of 18\%. One of his clients  Ms. Lawra choses to invest 70\% of her portfolio in  Mr. Robert’s fund and 30\% in a T‐bill money  market fund.  • (i) Calculate the T‐bill rate if the expected rate of  return on Ms. Lawra’s portfolio is 15\% [2]  • (ii) What is the standard deviation of Ms. Lawra’s portfolio if Mr. Robert’s reward‐to‐volatility is  0.35714? [3]  13 • Let, T‐bill rate is x\%.  • (i) 15\% = (0.7 × 18\%) + (0.3 × x\%) [2 mark]  • x\% = (15\% ‐ 12.60\%)/0.3 = 8\%  • (ii)0.035714  = (0.18 – 0.08 ) / SD • SD = 28\% [2 mark]  • Standard deviation of Ms Lawra’s portfolio is:  0.7×28\% = 19.60\% [1 mark]  14 13 14 7/25/2021 8 • Suppose stock A (with expected return 10\% and  standard deviation 5\%) and stock B (with  expected return 15\% and standard deviation  10\%) are perfectly negatively correlated. If it is  possible to borrow at the risk free rate,  • (i) what is the standard deviation of the portfolio  formed with stock A and B? [1]  • (ii) what are the weights of stock A and stock B in  the portfolio? [2]  • (iii) what must be the value of the risk‐free rate?  [2]  15 • Since Stock A and Stock B are perfectly negatively correlated, a risk‐ free portfolio can be created and the rate of return for this  portfolio, in equilibrium, will be the risk‐free rate. To find the  proportions of this portfolio [with the proportion wA invested in  Stock A and wB = (1 – wA ) invested in Stock B], set the standard  deviation equal to zero. With perfect negative correlation, the  portfolio standard deviation is:  • σP = Absolute value [wAσA ‐ wBσB]  • 0 = 5 × wA − [10 × (1 – wA)]  • wA = 0.6667  • The expected rate of return for this risk‐free portfolio is:  • E(r) = (0.6667 × 10) + (0.3333 × 15) = 11.667\%  • Therefore, the risk‐free rate is: 11.667\%  16 15 16 7/25/2021 9 • Suppose you buy (i) a January 2016 expiration  call option with exercise price $180, which  cost you $12.58 and (ii) a January 2016  expiration put option with exercise price $185,  which cost you $9.75.  • At what stock prices in January 2016 you will  just break‐even (i.e. no profit, no loss)? [5]  17 • Total investment now = $12.58 + $9.75 =  $22.33. Therefore, stock price in January be  either $180+$22.33 = $202.33 (so Call will be  exercised) or $185 ‐ $22.33 = $162.67 (so Put  will be exercised) and net profit will be zero. 18 17 18 7/25/2021 10 • If stock price in January 2016 is 202.22:‐ • Profit from Call: $202.22 ‐ $180 = $22.33  • Less cost of call $12.58  • cost of put $9.75  • $22.33  • Net profit $00.00  19 • If stock price in January 2016 is 162.67  • Profit from Put: $185 ‐ $162.67= $22.33  • Less cost of call $12.58  • cost of put $9.75  • $22.33  • Net profit $00.00  • =====  20 19 20 7/25/2021 11 • The risk aversion index of Mr Brown is 4. He  holds all his wealth in a risk‐free portfolio. The  yield of this risk‐free portfolio is 5\%. Now  suppose Mr Brown wants to invest in a risk  portfolio. The standard deviation of this risky  portfolio is 1.20\%. What must be the expected  return of this portfolio if Mr Brown wants to  maintain the level of utility identical to his  risk‐free portfolio? (5 marks) 21 • Since standard deviation of risk‐free portfolio is zero, utility of  this portfolio is equal to its risk‐free return, i.e. 5\% = 0.05.  Plugging in this value in risky‐portfolio utility function we get  22 21 22 7/25/2021 12 • An issue of shares in the Eddie & Co. is to be sold to the  public soon and a corporate analyst has just completed  a careful check of the company. The final report  includes a typographical error that suggests an  estimated standard deviation in the share price returns  of 100\%. The manager believes it is highly unlikely  given the general information provided about the  company. One diagram includes an equally weighted  portfolio of this company’s share and a risk‐free asset  with the portfolio variance set at 0.04 p.a. Is the  variance estimate of 100\% correct given the data in the  diagram was correct? Show all calculation steps. (5  marks) 23 • Variance of two‐asset (one risky asset, r, and one risk‐free asset,  rf) portfolio is:  • Since variance of risk‐free asset is zero, the above variance  equation reduces to   • If the diagram related data are correct, then from the above  equation we get variance of risky asset (i.e., company’s share) as  follows (w=0.50 since equally weighted portfolio): • Therefore, the correct standard deviation is 40\%, not 100\% 24 23 24 7/25/2021 13 • During the period of severe inflation, a bond  offered a nominal HPR of 80\% per year. The  inflation rate was 70\% per year. • What was the real HPR on the bond over the  year? • Compare this real HPR to the approximation  • (4 marks: 2+2) 25 26 Clearly, the approximation gives a real HPR that is too high. 25 26 7/25/2021 14 • A closed‐end fund starts the year with a net asset value  of $12.00. By year‐end, NAV equals $12.10. at the  beginning of the year, the fund was selling at a 2\%  premium to NAV. By the end of the year, the fund is  selling at a 7\% discount to NAV. The fund paid year‐end  distributions of income and capital gains of $1.50. • What is the rate of return to an investor in the fund  during the year? • What would have been the rate of return to an investor  who had the same securities as the fund manager  during the year? • (6 marks: 3+3) 27 • Start‐of‐year price: P0 = $12.00 × 1.02 =  $12.24 • End‐of‐year price: P1 = $12.10 × 0.93 = $11.25 • Although NAV increased by $0.10, the price of  the fund decreased by $0.99. • Rate of return =  28 27 28 7/25/2021 15 • An investor holding the same securities as the  fund manager would have earned a rate of  return based on the increase in the NAV of the  portfolio: 29 • Suppose risk‐free rate is 7\%, expected return  and standard deviation of risky portfolio are  15\% and 22\% respectively. Calculate the risk  aversion coefficient of an investor who wants  to invest 41\% in risky portfolio and 59\% in risk‐ free asset. Also calculate the expected return  of the complete portfolio. (5 marks)  30 29 30 7/25/2021 16 31 • Expected return of the completed portfolio • = (0.41x15) + (0.59x7) • = 10.28\% 32 31 32 7/25/2021 17 • Using information given in the following table  calculate the standard deviation of the  optimal risky portfolio formed with debt (D)  and equity (E). assume risk‐free rate is 5\%. (5  marks)  33 34 33 34 7/25/2021 18 • During the period of severe inflation, a bond  offered a nominal HPR of 80\% per year. The  inflation rate was 70\% per year.  • (a) What was the real HPR on the bond over  the year?  • (b) Compare this real HPR to the  approximation rr = rn ‐ 1 • (4 marks: 2+2)  35 36 35 36 7/25/2021 19 • Consider a fund with $100 million in assets at  the start of the year and with 10 million  shares outstanding. The fund invests in a  portfolio of stocks that provides no income;  however, increases in value by 10\%. The  expense ratio, including 12b‐1 fees, is 1\%.  Calculate net asset value (NAV) and the rate of  return for an investor in the fund at the end of  the year? (6 marks)  37 38 37 38 7/25/2021 20 39 An investor purchased shares of XYZ Co. at $36 per share using a 50\% margin. At what price the investor would face a 30\% maintenance margin call? (Mark: 3) 40 Solution: Equity is (P - $18). So the investor will receive a margin call when: )(71.25$ 70.0 18$ 18$70.0 18$30.0 30.018$ 30.0 18$ AnsP P PP PP P P       39 40 7/25/2021 21 • Suppose you bought a stock for $15. The next  year it jumped to $30, but you sold it when it  fell back to $15 in the following year. Compute  the arithmetic and geometric mean returns  for your two‐year holding period. (Mark: 2) 41 Geometric mean (1 mark) Arithmetic mean (1 mark) 42 \%100 15$ 15$30$ 1   r \%50 30$ 30$15$ 2   r              0 11 15.02 1\%501\%1001 111g 2 1 2 1 1 21      Nrr   \%25 2 \%50 2 \%50\%100     41 42 7/25/2021 22 43 You are planning to invest in financial instruments. You can either invest in two risky assets, X & Y or in a risk- free asset. Returns from asset X and Y are 4\% and 7\%respectively. If the return from risk-free rate is 5\%, what combinations of the two risky assets will give you returns that exceed the risk-free rate? (mark: 4) 44    xxp wwrE  1\%7\%4  prE   67.0 \%3 \%2 \%2\%3 \%3\%2 \%3\%5\%7 \%5\%3\%7 \%5\%7\%7\%4 \%51\%7\%4         x x x x x x xx xx w w w w w w ww ww Let wx is the proportion invested in X; therefore (1 – wx) is the proportion invested in Y. expected return of this portfolio is: According to the question, should be greater than 5\%. Therefore, Therefore, all portfolios those have less than 67\% in asset X will give an expected return greater than exceed the risk-free return. 43 44 7/25/2021 23 XYZ Co. ABC Co. Expected return 2.28\% 5.64\% Standard deviation 5.56\% 12.01\% Correlation between XYZ Co. and ABC Co. 0.45 45   marks) (1.5\%30.4 60.0\%64.540.028.2  rE 295.71 423.14926.51946.4 01.1256.545.060.040.0260.001.1240.056.5 22222    marks) (2.5 443.8295.71  •Suppose an investor formed a portfolio comprising 40\% in the common stock of XYZ Co. and 60\% in the common stock ABC Co. Use the data provided below to calculate the portfolio’s expected return and standard deviation. (Mark: 4) Solution: Expected return Standard deviation X 10\% 20\% Y 30\% 60\% Z 5\% 0\% 46                              6818.0 60202.05305202053060510 60202.053060510 ,Cov ,Cov 22 2 22 2        YXYXXYYX YXYYX X RRRERERERE RREERE w             mark) 1(\%36.16 303182.0106818.0    YYXXp rEwrEwrE           mark) (1 \%13.21 60202.03182.06818.02603182.0206818.0 ,2 2 1 2222 2 1 2222    YXYXYYXXp rrCovwwww  •Mr. Stuart is given the investment choices as described in the table below. If his risk aversion coefficient is 5, calculate his optimal investment proportion in each of the assets. Assume that the correlation coefficient between X and Y is -0.20 (Mark: 7) Solution: Therefore, wy = 1 – 0.6818 = 0.3182 (2 marks for calculating these weights) Expected return of this optimal risky portfolio is: Standard deviation of this optimal risky portfolio is: 45 46 7/25/2021 24 47 Given a risk aversion coefficient of 5, the proportion invested in optimal risky portfolio is: Therefore, proportions in optimal complete portfolio are (1.5 marks): Asset X: 0.5089×68.18 = 34.70\% Asset Y: 0.5089×31.82 = 16.19\% Asset Z: 1 – 0.5089 = 49.11\% Total = 100\%   5089.0 2113.05 05.01636.0 22       p fp A rrE y  48 [a] ‘Stop-buy orders often accompany short sales’ – explain this statement with example (Mark 3) [b] You are bearish on Telecom and decide to sell short 100 shares at the current market price of $50 per share: (i) How much in cash or securities must you put into your brokerage account if the broker’s initial margin requirement is 50\% of the value of the short position? (Mark 1) (ii) You will get a margin call if the price is above $57.69. What is the maintenance margin? (Mark 2) 47 48 7/25/2021 25 49 (a) Stop-buy orders often accompany short sales to provide protection to the short seller if the share price moves up. Let you short-sell XYZ’s share when it is selling at $100 per share. If the share price falls, you will profit from the short sale. On the other hand if the share price rises, let’s say to $130, you will lose $30 per share. But suppose that when you initiate the short sale, you also enter a stop- buy order at $120. The order will be executed if the share price surpasses $120, thereby limiting your losses to $20 per share. (b)(i)Initial margin is 50\% of $5,000, or $2,500. (b)(ii) Let the maintenance margin is X. Then \%30 10069.57$ 10069.57$500,7$    X 50 The end-of-year cash flow derived from a risky portfolio will be either $70,000 (with probability 0.65) or $200,000 (with probability 0.35). The alternative risk- free investment in T-bills pays 6\% per year. (a) If you require a risk premium of 7\%, how much will you be willing to pay for the portfolio? [Mark 2] (b) Suppose that the portfolio can be purchased for the amount you found in (a). What will be the expected rate of return on the portfolio? [Mark 2] (c) Now suppose you are willing to pay $101,315 for the portfolio. What is your risk premium now? [Mark 2] 49 50 7/25/2021 26 51 a. The expected cash flow is: (0.65 × $70,000) + (0.35 × 200,000) = $115,500. With a risk premium of 7\% over the risk-free rate of 6\%, the required rate of return is 13\%. Therefore, the present value of the portfolio is: $115,500/1.13 = $102,212.389 ≈$102,212 52 b. If the portfolio is purchased for $102,212 and provides expected cash inflow of $115,500, then the expected rate of return [E(r)] is as follows: $102,212 × [1 + E(r)] = $115,5000 Therefore, E(r) = 13\%. The portfolio price is set to equate the expected rate of return with the required rate of return. 51 52 7/25/2021 27 53 c. If the risk premium over T-bills is now X\%, then the required return is: (X+6)\% The present value of the portfolio is now: $115,500/1+0.0X+0.06 = $101,315 1.06+X = $115,500/$101,315 1.06+X = 1.14 X = 1.14 – 1.06 X= 8\% The risk premium you are asking is 8\% 54 •Assume that two securities constitute the market portfolio. Those securities have the following expected returns, standard deviations, and their weights in the … Chapter 8- Index Model Concept Check 8.1 if the market return is expected to be 14\%, a stock has a beta of 1.2, and the T-bill rate is 6\%, The expected returns for XYZ = 12\%. But the fair returns (based on CAPM) should be 11\% BUY asset XYZ Alpha = 12-11 =1\% OPTIONS – Chapter 20 Option – Gives HOLDER the rights but not the obligation Call option: option to BUY the asset at the exercise price (X) PUT option: option to SELL the asset at the exercise price (X) HOLDER BUYS the option by paying a premium. Writer sells the option by receiving the premium. X = exercise price S = spot price C = call premium P = put premium Call option with X = $100 If S = 120, holder will exercise the option. The call option is IN THE MONEY If S = 90, option will NOT be exercised. Option is OUT of Money If S = 100, option is AT the money Call option with X = $100 Call Premium = C = $10 If S = 120, holder will exercise the option. The call option is IN THE MONEY Payoff= 120 – 100 = S – X = 20 Gain/loss = payoff – premium = 20 – 10 =10 Loss for the writer = 10 If S = 90, option will NOT be exercised. Option is OUT of Money Payoff = 0 Loss = payoff – premium = 0-10 = 10 If S = 100, option is AT the money Payoff = 0 Loss = 0-10 = 10 If S = 108, option is in the money Payoff = 108-100 = 8 Loss = 8-10 = 2 PUT option with X = 100 If S = 120, will not exercise the option. Option expires OUT of money If S = 90, option will be exercised. Option is IN the money If S = 100, option is AT the money PUT option with X = 100 Put premium = P =10 If S = 120, will not exercise the option. Option expires OUT of money Payoff: 0 Gain/loss = 0-10 = -10 If S = 90, option will be exercised. Option is IN the money Payoff: 100 -90 = 10 = (X -S) Gain/loss = 10-10= 0 If S = 100, option is AT the money Payoff = 0 Gain/loss = 0-10 = -10 PUT CALL PARITY PROTECTIVE PUT Buy an asset (share) and buy a PUT option If S > X, PUT is NOT Exercised Payoff: S + 0 = S If S < X, PUT will be exercised Payoff: S + (X – S) = X FIDUCIARY CALL: Buy a CALL option and buy a zero-coupon bond with face value = X If S > X, call option is exercised Payoff: (S – X) + X = S If S < X, call option is not exercised Payoff: 0 + X = X The payoffs of the two strategies- Protective PUT and Fiduciary Call- are the same. The initial investment for both the strategies should be same. Exercise price of put = exercise price of call = face value of bond Maturity of put = maturity of call = maturity of bond