Since you are buying platinum anyways, the forward will exactly hedge any risk. (a) Which future did you pick? Platinum Futures (b) What is the size of the contract? (Contract Unit under "Specs" tab) 50 troy ounces (c) How is the price quoted? U.S. $ per troy ounce (d) When does trading end? 3 rd last bus. day of month (e) What is the current price of the nearest-to-delivery future? ("Quotes" tab) $930.4/oz (f) What is the current volume? 35,593 (g) What is the current open interest? 69,705 (h) Is this market in Contango, Backwardation, or neither? (Recall how we plotted this in class) Contango, current spot price is lower than the future price, upward curve (i) Given the current open interest, the contract size, and the price of the nearest-to-delivery future, what is the approximate total notional value of this commodity? Total Notional Value = price x contract size x open interest $930.4 x 50 x 69,705 = $3.24B HW #2 -On September 1st you enter 2 forward contracts to buy WTI crude oil on December 1st (3 months later) for a price of $84.42 per barrel. On September 30th, the price of a December 1st forward contract is $85.56. Before the end of the day (Sept 30th), you decide to close out your position by making an offsetting trade. (a) Describe exactly what trade(s) you must make to offset your position. You must enter into 2 short forward contracts for December 1st Delivery. (b) What is your profit or loss per barrel? (St - K) + (F0 - St) = F0 - K $85.56/bbl - $84.42/bbl = $1.14/bbl (c) What is your total profit or loss? $1.14/bbl x 2 contracts x 1,000bbl/contract = $2,280 (d) What happens if you forget and do not make any offsetting trade? You are now the proud owner of 2,000 barrels of oil (and get to deal with any additional delivery costs.) -Tesla (TSLA) is currently trading at S0 = $273/share. A dealer is offering a 3-month forward at a price of F0 = $275/share. One TSLA futures contract is for 100 shares. Assume the interest rate is r = 1.5% p.a. You have no money or financial assets today. However, using your knowledge of forward pricing, you realize you can make an arbitrage profit given this dealer's price! (Assume no margin costs or storage costs.) (a) Name the strategy we discussed in this class to make a riskless profit. Cash and Carry (b) Clearly show each transaction you must make, both today and at time T, to make a riskless profit (c) What is your profit per share? $0.9743/share (d) What is your total profit in dollars, assuming you only use 1 forward contract? $0.9743/share x 1 contract x 100 shares/contract = $97.43 total profit -Some time ago, you entered a forward contract to purchase shares of Advanced Micro Devices, Inc. (AMD) for $32 per share. Your forward contract ends in 6 months and the current spot price of AMD is $29.42 per share. Assume a risk free rate of interest of 1% per year. (a) What is the current price of a forward which ends in 6 months? F0=S0erT = 29.42e(0.01*0.5) = $29.5675/share (b) What is the value of your seasoned forward? f = (F0 - K)e-rT = (29.5675 - 32.00)e(-0.01*0.5) = -$2.42/share Suppose now the current spot price of AMD is $33.42 per share. (c) What is the current price of a forward which ends in 6 months? F0=S0erT = 33.42e(0.01*0.5) = $33.5875/share (d) What is the value of your seasoned forward? f = (F0 - K)e-rT = (33.5875 - 32.00)e(-0.01*0.5) = $1.579/share -You enter a 3-year future contract to purchase gold. The current spot price is $1,716.42 per ounce. It costs the bearer of the gold $15 per ounce to store it each year. Assume an interest rate of 2%. (a) What is the present value per ounce (U) of the storage costs that the gold bearer will incur during the life of the contract? U = $15*(e-r + e2r + e-3r) = $43.24 (b) Using your answer from (a), what is the price on this -Consider a 6-month forward contract on an asset that provides a 1% yield annually to the bearer of the asset. If the current spot price is $25, and assuming a 5.5% annual risk- free interest rate. (a) What is the price on this forward contract? F = S0e(r-q)T = 25e(0.055 - 0.01)(6/12) = $25.5688 (b) What is the price on a similar contract but with a 1-year maturity instead? F = S0e(r-q)T = 25e(0.055 - 0.01)(1) = $26.1507 -The price of a commodity "A" has a standard deviation of $0.42, while the price of a futures contract "B" on that commodity has a standard deviation of $0.84. The two have coefficient of correlation of 0.69. (a) If you want to hedge commodity A using future B, what is the optimal hedge ratio that will minimize your risk ? h = 0.69*(0.42/0.84) = 0.345 (b) You decide to hedge this position by matching quantities. You have 12,000 units of A to hedge, and a futures contract B is for 2,000 units. Using your hedge ratio from (a), how many contracts should you enter ? N = h* 12,000units / 2,000 units = 0.345 * 6 = 2.07 or approximately 2 contracts -You are a fund manager in charge of a 50-million-dollar portfolio. Your portfolio has a beta of 1.25 relative to the S&P500. The S&P500 Index is currently 3,942. One S&P500 futures contract has a value of $250 * the index level. (1.00 points) (a) Assume you want to remove S&P500 risk from your portfolio. Do you use long or short contracts? Your portfolio is naturally long the S&P500, you hedge this by shorting S&P500 index futures. (b) What is the optimal number of S&P500 futures contracts that you need to remove all S&P500 risk from your portfolio? N = Beta * Total Value / Forward Contract Value Forward Contract Value = $250 * Index Level = $250 * 3,942 = $985,500 N = 1.25 * ($50,000,000/$985,500) = 1.25 * 50.7356 N = 63.4196 or short approximately 63 contracts. HW #3 -Mili Pharmaceuticals is based in New Delhi, India, and has a 4-year contract to produce chemicals at a production facility located in Delaware, United States of America. Mili received $80,000 per year and is concerned about the exchange risk she will bear exchanging US Dollars (USD) to Indian Rupees (INR) over this period. Luckily, Neel Aeronautics, a US firm doing business with India, has the exact opposite currency exposure. Mili and Neel agree to a currency swap in order to hedge their exchange risk. Assume the US risk free rate is 2%, the Indian risk-free rate is 2.8%, and the exchange rate between USD ($) and INR ( ) is 80.00 /$ (80.00 Rupees can be exchanged for 1 USD). rus = 0.02 , rin = 0.028 , S0 = 80.00 /$ a) What is the present value of Mili's 4-year cash flow in USD, compounded continuously? PV = 80,000e^(-0.02 x 4) = $304.469.52 b) Next, Mili wants to borrow this amount of USD, convert it to INR at today's spot rate, and lend it to Neel. What is her loan to Neel in INR? $304,469.52 x 80 INR/USD = 24,357,566.55 INR c) Neel will repay her loan with 4 even payments in INR. What is the value of one of his yearly payments? (Hint: you are solving for the coupon) 24,357,566.55 / (e^-0.028 + e^(- 0.028 x 2) + e^(-0.028^3) + e^(-0.028^4)) = 6,527,722 INR d) What is Mili's net cash flow at the start of the contract, time zero? Zero cost e) What is Mili's net cash flow during a given year? 6,527,722 f) Explain briefly how this has hedged Mili's foreign exchange risk. The formula above is similar to a short forward on the INR to USD exchange rate. Mili has made a forward position while hedging her exchange risk. Now, she receives a fixed amount of INR per year rather than having to rely on the exchange rate. You spend many sleepless nights building cash flow models of Facebook Inc. (FB) and are convinced they are undervalued. The current spot price of FB is $204/share. You predict that in 6 months they will reach $240/share. Assume a 2% interest rate per annum. b) Under what circumstances will you make money? K + Ce^rt = breakeven $230 + 5.20e^(0.02 x 0.5) = $235.252 If stock prices strike, we will make money because stock prices will go up HW #1 -Despite Tesla's poor performance recently, you believe it can go lower still. You decide to short a single share of Tesla stock (TSLA). It is currently valued at $123.22 per share. In 1 month, TSLA will have their next earnings announcement, and you are hoping they will not meet analysts' expectations. Assume you have an interest rate of r = 0.045 (4.5%) per annum, and that all interest is compounded continuously. (b) On the earnings call, what price does TSLA need to reach for you to break even? 0 = ST - S0erT = ST - 123.22*e(0.045*1/12) ST = $123.68 breakeven price (c) Rising lithium prices cause TSLA's earnings to plummet. Their share price is currently $112.42. What is your payoff and what is your profit? Payoff = - ST = - $112.42/share Profit = S0erT - ST = $123.68 - $112.42 = $11.26/share (d) Ellon Musk tweets that Tesla will now accept Dogecoin as payment and the internet goes wild. TSLA price jumps to 133.69 per share. What is your total payoff and total profit? Payoff = - ST = - $133.69/share Profit = S0erT - ST = $123.68 - $133.69 = - $10.01/share -Bed Bath and Beyond (BBBY), once a popular meme stock, has recently been ignored. Currently trading at $3.49 per share, you believe the stock is undervalued and decide to buy 10 shares. One month later, the stock price rises to $9.42. Assume an interest rate of r = 0.01 (1%) per annum. -(b) What is your breakeven price? 0 = ST - S0erT = ST - 3.49*e(0.01*1/12) ST = $3.49 breakeven price (c) What is your payoff and profit per share in this scenario? Payoff = ST = $9.42/share Profit = ST - S0erT = $9.42 - $3.49 = $5.93/share -People say we are in a recession, but you don't believe them. You think the recession is almost over and that the price of gold will drop soon. You decide to short 2 gold futures contracts at a price of $1886.50 per ounce, expiring in 3 months. Assume an interest rate of r = 0.03 (3%). (Hint: 1 gold futures contract covers 100 ounces of gold). (a) If the price of gold drops to $1833.42 per ounce, what is your total profit? Total Profit = (1886.5 - 1833.42) x2 x100 = $10,616.00 (b) If the price of gold rises to $1900.42 per ounce, what is your total profit? Total Profit = (1886.5 - 1900.42) x2 x100 = - $2,784.00 You work for Cao Chemical International, and your company regularly uses platinum as a catalyst for chemical reactions. To hedge your exposure to the price of platinum, you convince your boss to let you use futures contracts. Your company expects that it will need 1,000 troy ounces of platinum in 3 months. The price on a 3-month platinum future contract is $1084.42 per troy ounce. A platinum futures contract is for 50 troy ounces- (a) How many contracts will you need to cover your exposure, and what will it cost you initially? 1000 / 50 = 20 contracts Initial cost = $0.00 (Futures cost $0 up front!)- (c) In 3 months, the spot price of platinum is $900.42/oz. What is your total profit assuming you close the position and do not take delivery? Total Profit = (900.42 - 1084.42) x 20 x 50 = - $184,000 (d) If the spot price is $800/oz what is your total profit? Total Profit = (900.42 - 1084.42) x 20 x 50 = - $284,420 (e) Does it matter if your futures contracts earn a profit? Since, you are buying platinum anyways, the forward will exactly hedge any price risk.
Chipotle (CMG) is currently trading at $1607/share. You heard someone say there was another e. coli outbreak at one of their restaurants. Hoping to make a quick profit you sell a 2-day call option with a strike price of $1600/share for a price of $13.00/share. Assume a 3.5% interest rate per annum. (1 point) b) To your horror, over the next two days CMG jumps to $1675/share. What is your total profit or loss? 1600 + 13e^(0.035)(2/365) = 1613 Ce^rt = 13 Profit = Ce^rt - max[0, St - K] = 13e^(0.035 x (2/365)) - max [0, 1675-1600] = -$62/share x 100 = $6200 (Loss) Definitions Hedgers : take a position in futures market to reduce risk. A producer enters short futures, A consumer enters long futures Speculators : take position in futures market to take-on Risk. Enter long if they think market price is rising, Enter short if they think market price is falling Arbitrageurs: take simultaneous positions in multiple markets for a riskless profit. Useful for market efficiency Opportunities are small and short-lived. The spot price is the price at which the purchase/sale of an asset transaction for immediate delivery occurs "Payoff" refers to cash flow incurred unwinding position "Profit" is payoff net of costs or receipts incurred (need to account for timing) Volume counts trades Open interest counts number of open contracts a trade to open a futures position will increase volume and increase open interest by 1. a trade to offset a position will increase volume and and decrease open interest by 1. Offset is taking opposite side of trade with same delivery date Gold=100 troy ounces ($1341.2*100= $134,120/contract) Oil = 1,000 barrels ($48.90*1000 = $48,900/contract) S&P500 = $250 * Index Level -If the current spot price is below the futures price we will see an upward sloping forward curve. The market is said to be in "Contango" where futures are trading at a premium. Reasons for contango in physically delivered goods are related to the "cost to carry" -If the current spot price is above the futures price, we will see a downward sloping forward curve. The market is said to be in " Backwardation " where futures are trading at a discount. Reasons for backwardation in physically delivered contacts are due to " convenience yield " Perfect hedge all risk eliminated with perfect timing, asset match, and quantity match (so they are rare) Basis risk Spot prices not moving as expected with futures prices Direct hedge Asset underlying derivative contract matches the asset you want to hedge Cross-hedge Asset underlying derivative contract doesn't match the asset you want to hedge Hedge-and-forget one trade is all that is needed to hedge "Business risk" or "Natural exposure" relation of profit/payoff to an asset (long or short) Short hedge Derivative position is short (natural long exposure) Long hedge Derivative position is long (natural short exposure) Hedge ratio Size of derivative position relative asset being hedged Uses 1 st column (year t) and 3 rd column (Rc %) to figure out the 6 th column numbers
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