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Investment Analysis & Portfolio Management 1) $17.72 a) Call option X = $17 Price of option = Value of Option at expiry = Overall Net Gain / Loss on Option = b) Put option X = $17 Price of option = Value of Option at expiry = Overall Net Gain / Loss on Option = c) Call option X = $19 Price of option = Value of Option at expiry = Overall Net Gain / Loss on Option = d) Put option X = $19 Price of option = Value of Option at expiry = Overall Net Gain / Loss on Option = e) Call option X = $15 Price of option = Value of Option at expiry = Overall Net Gain / Loss on Option = f) Put option X = $21 Price of option = Value of Option at expiry = Overall Net Gain / Loss on Option = 2 Amount to Invest $10,600 Initial Price per Share $53 Margin Requirement 50% Cost of Borrowed Funds 7% LEAPS $2.50 LEAPS Strike Price $52.50 Interest Earned on T-bills 1% c) Use the entire amount of funds to buy LEAPS call options with the January expiry date. d) Buy options for 200 shares and use the rest of the money to buy government bills paying 1% per year. (hence figure on 6 months of interest). For simplicity ignore any brokerage charges Calculate the net gain or loss from each strategy as of mid January assuming that the price of stock is: Stock Price in Mid January Gain / Loss from Investment in Walmart On June 21, 2011, the GE’s stock closed at $18.81 per share. The accompanying table {at the bottom of the sheet] lists the prices for GE’s exchange-traded options. Using this data, calculate the payoff and the profit for each of the following September expiration options, assuming that: Stock Price at Expiration of Options = It is mid July. You believe that Walmart stock which is currently priced at $53.00 will appreciatesignificantly over the next several months. A long-term equity call option (LEAPS) with an expiry in mid January and a strike price of $52.50 is available at a price of $2.50. You have $10,600 to invest. You consider 4 alternatives: a) Use your entire amount of funds to buy the stock outright b) Use the entire amount to purchase the stock on margin. Assume that the minimum margin requirement is 50% and that you will pay 7% (annually) on borrowed funds. Investment Strategy $45 $50 $55 $60 Stock Outright Stock on Margin All Options Stock & Bills $45 $50 $55 $60 Stock Outright $45 $50 $55 $60 Stock on Margin $45 $50 $55 $60 All Options (LEAPS) $45 $50 $55 $60 Options & Bills 3 One of the financial instruments that attracted so much hostile fire in the analysis of the recent financial crisis were “Synthetic Collateralized Debt Obligations” (synthetic cdos) which used “synthetic debt” as its collateral. A synthetic security is one that has the same payoff (reward / return) and risk characteristics as the security it is mimicking. Describe how you could use a combination of risk free investments and derivatives to create the same pay-off / risk profile as if you were holding a corporate bond, say for IBM. Explain how the pay-off / risk profile is the same (a) if the company remains afloat and pays all of its debt obligations on time or (b) if the company defaults on its debt obligations. In answering this question, don't worry about specific amounts (cost of options, interest rates, etc.) but focus on the basic instruments you'd use and the principles involved. 4 Current Stock Price $50 Int. Rate 10% Strike Price $45 Up Price Down Price $60 $40 Payoff on Option To purchase 1 share of stock now on margin: Borrow Invest Total Value of 1 share of stock in 1 year $60.00 $40.00 Current Stock Price ( S0) $50 Int. Rate ( r ) 10% Strike Price (X) $45 Std Dev of Stock Price 25% Time (T) 1 d1 = d2 = C0 = 5 A stock is currently priced at $50. The risk free interest rate is 10% per year. What is the value of a call option on the stock with a strike price of $45 due in one year? a) Using the Binomial valuation approach, assume that at the end of one year the value of the stock could either have increased to $60 or decreased to $40. Using the Black-Scholes model calculate the value of the call option. Assume that the annual volatility (standard deviation) of the stock price is 25%, the stock price is currently $50, the strike price is $45 and that the risk free rate is 10% Hint: "=Normsdist" is the Excel function used to get the normal distribution for the BlackScholes model and "=exp"is the Excel function to get the natural logrithm On June 29, 2010 the S&P 500 stood at 1308.44. The one year futures price on the index was 1278.7. The 1 year risk free rate was 0.238%. Using the Spot-Futures Parity relationship, calculate the annualized expected dividend yield from the S&P 500 Index. 6 Contract Size (lbs) 25000 Spot Price Today per pound $4.204 Futures Price Today per $4.321 Initial Margin per contract $5,738 Maintenance Margin per contr $4,250 Spot Price at Maturity $4.25 $4.30 $4.35 $4.40 Spot Value of 1 contract at Maturity Futures price of 1 contract (today) Initial Investment (Margin) Net Gain / Loss 6 month rate of return Annualized Rate of Return (Bond Equivalent Rate) Annualize Rate of Return (Effective Interest Rate) 6 Current Spot Price: $120 Futures Price (1 Year): $125 Interest Rate (1 Year): 8% Initial Margin (to purchase the Futures) $7.50 b) Calculate the arbitrage profit Initial Cash Flow (time 0) 116 120 124 128 132 Total Net Cash Flow (profit) c) Verify the arbitrage profit by calculating the initial cash flows (when the transactions are entered into) and the profits for each of the spot prices at time T indicated below: Joan Tam, CFA, believes she has identified an arbitrage opportunity (meaning that she will stand to gain regardless of the spot price in the future) for a commodity as indicated by the following information: Spot price at time T a) Describe the strategy and transactions that Joan should use to take advantage of this arbitrage opportunity. (Hint: First determine if the Future is over priced or under priced based Futures contracts for copper are traded on the COMEX exchange. The standard contract is 25000 pounds. The initial margin is $5738 per contract and the maintenance margin is $4250 per contract. The 6 month futures price is $4.321 per pound. The spot price today is $4.204. What will be the annualized rate of return for an investor purchasing copper futures under the following spot prices at maturity? This is easiest to calculate on the basis of one contract. The spot value of the contract at maturity will be the spot price (e.g. $4.25) times 25000 lbs., hence $106,250. The acquisition price will be the same for all scenarios, the futures price $4.321 times 25000 lbs. The gain or loss is the difference between the two, so $106250 less $108025 for a loss of $1775. The 6 month rate of return is the gain or loss divided by the initial margin (the amount invested when the futures contract is purchased), so if the price is $4.24 at maturity -1775 / 5738 = -30.93%. Annualizing this – bond equivalent method =2 x 30.9% = 61.9% or using the effective interest rate method ={[(1-.309)^2] -1} = -52.3% Expiration Volume Open Volume Open Interest Interest Dec 10 ... ... ... 0.08 217 3322 Sep 13 ... ... 870 0.06 20 6070 Dec 13 ... ... ... 0.15 8 2114 Jul 14 4.6 29 827 ... ... 204 Jul 15 3.7 1 1 0.02 210 15799 Sep 15 4 1 1280 ... ... 13893 Dec 15 4 1 409 0.3 380 3581 Jul 16 ... ... 542 0.03 222 3347 Aug 16 ... ... 597 0.12 191 1932 Sep 16 3.04 353 1919 0.2 375 78449 Dec 16 ... ... 250 0.49 690 4915 Jul 17 1.95 86 2503 0.06 124 11300 Aug 17 2.08 25 1150 0.23 362 21499 Sep 17 2.18 349 4196 0.34 1089 29426 Dec 17 2.45 15 479 0.72 105 16755 Jul 18 0.99 3537 7192 0.17 11672 26979 Aug 18 1.3 626 4138 0.41 1773 12694 Sep 18 1.38 376 12832 0.58 2698 40944 Dec 18 1.79 120 2683 1.03 2594 10423 Jul 19 0.35 36899 61396 0.53 9103 32734 Aug 19 0.65 2031 16488 0.78 3856 21731 Sep 19 0.77 4565 25395 0.96 101 64748 Dec 19 1.22 274 7206 1.51 1046 13989 Jul 20 0.06 4781 22943 1.19 222 19283 Aug 20 0.25 4649 28705 1.47 15 17267 Sep 20 0.38 4856 31045 1.56 32 36015 Dec 20 0.76 962 11433 2.06 67 9845 Jul 21 0.01 169 25400 2.15 20 2592 Aug 21 0.08 348 10613 ... ... 1990 Sep 21 0.15 786 24122 2.41 509 9623 Dec 21 0.45 2224 11789 2.87 1 1250 Jul 22 0.01 1318 9329 ... ... 592 Aug 22 0.03 195 3487 3.18 1 1189 Dec 22 0.24 909 7256 ... ... 948 Sep 22.5 0.04 417 34725 3.75 4 20599 Jul 23 ... ... 3399 4.21 2 904 Aug 23 0.02 25 1712 ... ... 441 Dec 23 0.12 590 12298 ... ... 977 Sep 24 0.02 118 7820 ... ... 1069 Dec 24 0.07 20 3177 5.35 1 1454 Aug 25 ... ... 92 6.4 10 ... Sep 25 ... ... 7223 6.36 186 1088 Dec 25 0.04 250 5511 ... ... 602 Sep 30 ... ... 2756 11.35 76 1240 GE Exchange Traded Options Strike Price Call Put Source: Wall Street Journal Option Price Option Price

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Investment Analysis and Portfolio Management
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