1 / 28

Futures & SWAPS Financial Derivatives

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

rico
Télécharger la présentation

Futures & SWAPS Financial Derivatives

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Futures & SWAPSFinancial 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 …

  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 …

  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

  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…

  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…

  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

  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… 7% 7%+0.05% LIBOR+0.25% 7% SWAP Dealer Company A Company B LIBOR-0.1% LIBOR-0.1%

  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…. The answer is not in the PPT here; we will start with this in session 4!

More Related