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Futures & SWAPS Financial Derivatives Shanghai Spring 2014 Week 3-4 FINC 5880 Answers Class Assignments.

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Presentation on theme: "Futures & SWAPS Financial Derivatives Shanghai Spring 2014 Week 3-4 FINC 5880 Answers Class Assignments."— Presentation transcript:

1 Futures & SWAPS Financial Derivatives Shanghai Spring 2014 Week 3-4 FINC 5880 Answers Class Assignments

2 Class assignment 1: Margins Suppose the Maintenance Margin on a Wheat Futures contract is 5% (Initial Margin 10%) Current Future Price $2.06 A standard wheat contract is 5000 bushels How many $ cents does the wheat price need to fall to trigger a Margin call on the long position (buyer) ?

3 Answer… Value contract $2.06*5000 bushels=$10,300 so initial margin 10%*$10,300=$1,030 Maintenance margin thus at $515 Every 1$ct price drop triggers $0.01*5000 bushels=$50 margin $515/$50= about 11 $ cents price drop is needed to trigger the margin call…

4 Example You think crude oil prices will increase: You buy oil futures Each contract requires buying 1000 barrels (159 liters) Current Future price (delivery Nov) $52.67 For every $1 price increase of crude oil the long position (buyer) gains $1000 For every $1 price drop the short position (seller) gains $1000 If the spot price is $54.67 at maturity the long side of the contract will benefit $2000 The short side will loose an identical amount…

5 Class Assignment 3: Futures Oil Distributor An oil distributor plans to sell 100,000 barrels of oil in Nov and hedges his price risk with selling 100 (1000 barrels each) futures contracts in November The current price $52.67 Assume the price of oil at maturity can only be $50.67, $52.67 or $54.67 per barrel ; show that the futures contract offers a perfect hedge against the price risk!

6 Answer…no matter the price of oil at maturity the proceeds are the same … P=$50.67P=$52.67P=54.67 Revenues from oil sale 100,000*P= $5,067,000 100,000*P= $5,267,000 100,000*P= $5,467,000 Profit on Futures contract $2*100,000= (Fo-Pt)*100,000 $200,000 $ 0 (Fo-Pt)*100,000 (no difference with buy price) -$2*100,000= (Fo-Pt)*100,000 -$200,000 Total Proceeds$5,267,000

7 Generalizing… Total revenues from the sales of oil by the distributor (class assignment)= Pt (per barrel) being the price at maturity Plus the difference between the future price at moment of buying futures (Fo) and the price at maturity (Pt) Thus Proceeds=Pt+(Fo-Pt)=Fo the position is perfectly hedged against any price movement in the future at the current future price….

8 Class Assignment 4: Futures Electricity Power Company An Electricity Power Company plans to buy 100,000 barrels of oil in Nov; show that if the firm buys 100 futures contracts of oil Nov it can hedge its price risk totally… The current price $52.67 Assume the price of oil at maturity can only be $50.67, $52.67 or $54.67 per barrel

9 Answer…no matter the price of oil at maturity the proceeds are the same … P=$50.67P=$52.67P=54.67 Costs from oil purchase 100,000*P= $5,067,000 100,000*P= $5,267,000 100,000*P= $5,467,000 Profit on Futures contract $2*100,000= (Pt-Fo)*100,000 -$200,000 $ 0 (Pt-Fo)*100,000 (no difference with buy price) -$2*100,000= (Pt-Fo)*100,000 $200,000 Total costs$5,267,000

10 Class assignment 5: Speculation with Futures You hold 100 ounces Gold You also sell one futures gold contract (also 100 ounces) The spot price of gold today is $391 The future price gold (June) is $396 If tomorrow the spread between the spot and futures price narrows to $ 4.50 (Future price $398.50 and spot $394) how can an investor benefit from this?

11 Answer… Gain on holding Gold 1 day $394-$391=$3 Loss on gold future $398.50-$396=$2.50 Net gain is the decrease in the spread ($5 - $4.50)

12 Speculation again… You hold Sept long contract and a June short contract ; the Sept future price increases with 5cts while the June futures price increases with 4cts Will you have a gain?

13 answer Your contract to buy increases in price with 5cts so you gain 5 cts Your contract to sell increases with 4 cts so you loose 4 cts The spread narrows 1ct this is your net gain…

14 Class Assignment 6: Future Pricing… We follow the same reasoning of replication as what we did when we were looking at the valuation of options… We create 2 strategies that have the same pay off…and thus their investments should be equal: Strategy A: buy gold (price= -So) » sell gold at T (price ST) Strategy B: enter long position (no investment today) »Sell at T: (ST-Fo) At same time invest : -Fo/(1+Rf)^T »Growing in T to: Fo Required: show that strategy A and B have the same pay off as a Futures contract and then derive from this Fo=Function(So)

15 Answer: Equivalence… Or in General: Fo(1+Rf)^T=So so Fo=So(1+Rf)^T The price of Future today= spot price today up-rated at the missed (opportunity cost) Risk free rate that we could have made on a T Bill for T periods…so: If gold sells for $400 spot and Rf=0.5% per month then a 6 month maturity futures contract should have a future price Fo of: So(1+Rf)^T=$400(1+0.005)^6=$412.15 A 12 month contract should be priced: So(1+Rf)^T=$400(1+0.005)^12=$424.67 Cash Flow Today Future Pay Off (assuming T=1) Strategy A: Buy Gold - So+St Strategy B: Long (Buy) Future+ Lend Fo/(1+Rf) 0 -Fo/(1+Rf) St-Fo +Fo= +St Implying that:-So=-Fo/(1+Rf) or Fo= So/(1+Rf)

16 Like with options… Mispricing leads to arbitrage profits (risk- free) You sell the side that is overpriced You buy the side that is under priced So you make risk free profit…

17 Class assignment 7: Futures Arbitrage (over pricing) Assume that the Future contract 6 months (last slides) was mispriced at $413 instead of $412.15 Recall that the spot of gold now is $400 Recall that Rf=0.5% per month Show that with a zero investment you can make a risk free profit of $0.85 (just the amount of the mispricing)

18 Answer… actionInitial cash flowCash flow at T Borrow $400 and repay with interest at T +$400-$400(1+0.5%)^6=$412,15 Buy gold for $400 (buy under priced side) -$400ST Enter in short future position $413 (sell over priced side) $ 0 (no cash out)$413-ST TOTAL $ 0 (no investment)$ 0.85 riskless

19 Class Assignment 8: Futures Arbitrage (under pricing) If the 6 month future contract in last assignment were under priced at $411 instead $412.15 can you proof that you can make a risk free arbitrage profit of $1.15? Spot gold $400 Rf=0.5% per month…

20 Answer… actionInitial cash flowCash flow at T Lend $400 and receive with interest at T -$400 $400(1+0.5%)^6=$412,15 sell gold for $400 (sell over priced side) $400-ST Enter in long future position $411 (buy under priced side) $ 0 (no cash out)ST-$411 TOTAL $ 0 (no investment)$ 1.15 riskless

21 Future value/Price We have derived that the price of a future contract is: Fo=So(1+Rf)^T indicating the opportunity cost of investing in T Bills If the underlying asset generates an income (dividend on stocks) then the future price changes in: Fo=So(1+Rf-d)^T in which d is the dividend yield on the stocks…

22 Class Assignment 9: Future Contract Pricing for Stock Index The Rf is 0.5% per month The dividend yield on the S&P500 stock index is 0.1% The spot price of the S&P500 is 1200 What should be the 3 month future contract price? And the 6 month? If the S&P500 rises to 1210 what will be the future prices of these contracts?

23 Answer… Fo=So(1+Rf-d)^ T so for 3 month contract: Fo=1200(1.004)^ 3 =1214.46 For 6 month contract: 1200(1.004)^ 6 =1229.09 For 3 month contract if S&P=1210: 1210(1.004)^ 3 =1224.58 For 6 month contract if S&P=1210 1210(1.004)^ 6 =1239.33

24 Swaps: Plain Interest Vanilla Swaps You are manager of a large portfolio of $100 million par value of long term bonds with coupon rate 7%. However you believe looking forward that interest rates will rise and you want to benefit from this! You know it will be extremely expensive in terms of transaction costs to change the portfolio but you know you could SWAP your fixed interest income for a floating rate income if you can find a market party that have interest forecasts opposite to you. A SWAP-dealer (bank) may advertise that it is willing to swap a cash flow based on the 6-month LIBOR rate for one based on a fixed rate of 7%. The portfolio manager thus is expected to enter into a SWAP agreement with the dealer The future will learn if the portfolio manager made the right decision He has exchanged 7% interest on $100 Million for LIBOR*$100M If LIBOR moves to 6.5% the decision to SWAP was wrong since the portfolio manager looses $0.5M interest income but if LIBOR moves up to 7.5% he will gain $0.5M

25 Swaps normally provide benefits for all…(win/win) Assume companies A (triple A rated) and B (triple B rated) Financing conditions: Show that if companies A and B enter into a Swap that both can benefit Company A currently is financed with fixed rate debt and company B with floating rate debt (LIBOR) Note: the Swap dealer want a 0.05% fee… Note: Company B is the weaker party and agreed to pay the fee of the dealer… However assume that both companies will absorb 50% of the benefit from the Swap Company AFixed Rate: 7% Fixed Rate: 7.5% Company BLIBORLIBOR+0.25%

26 Realize from this case…. Company A and B have a very different rating and thus a different cost of debt Company A and B MUST have opposite expectations of future interest rates otherwise they will not enter into the Swap Company A want to Swap to floating rate and thus assumes interest rates will drop Company B want to Swap to fixed rate debt and thus assumes interest rates to rise

27 SWAP DEAL… Pay outside bank-7% Receive from SWAP dealer +7% Pay SWAP dealer-(LIBOR-0.1%) Total PayLIBOR-0.1% Receive from B 7.05% Pay A -7% Receive from A +(LIBOR-0.1%) Pay B -(LIBOR-0.1%) TOTAL FEE 0.05% Company A Company B SWAP Dealer 7% LIBOR+ 0.25% 7%7%+0.05% LIBOR-0.1% Pay outside bank -(LIBOR+0.25%) Receive from SWAP dealer LIBOR-0.1% Pay SWAP dealer -7.05% Total Pay -(7.05%+0.35%)

28 Class Assignment: Plain Vanilla Interest Swap Assume Companies A and B have the following financing conditions: The dealer fee is 0.2% A is initially fixed rate financed and want to SWAP to floating rate B pays the SWAP dealer A and B share the benefit of the SWAP 70:30 Set up the SWAP and show this SWAP has a clear benefit for both A and B…. Company ACompany B Fixed Rate10%14.6% Floating Rate LIBOR+0.3%LIBOR+0.7% The answer is not in the PPT here; we will start with this in session 4!


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