ACTEX FM DVD: ACTEX FM DVD


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives What is a derivative? A financial instrument that has a value derived from the value of something else


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives Uses of Derivatives Risk management Hedging (e.g. farmer with corn forward) Speculation Essentially making bets on the price of something Reduced transaction costs Sometimes cheaper than manipulating cash portfolios Regulatory arbitrage Tax loopholes, etc


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives Perspectives on Derivatives The end-user Use for one or more of the reasons above The market-maker Buy or sell derivatives as dictated by end users Hedge residual positions Make money through bid/offer spread The economic observer Regulators, and other high-level participants


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives Financial Engineering and Security Design Financial engineering The construction of a given financial product from other products Market-making relies upon manufacturing payoffs to hedge risk Creates more customization opportunities Improves intuition about certain derivative products because they are similar or equivalent to something we already understand Enables regulatory arbitrage


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives The Role of the Financial Markets Financial markets impact the lives of average people all the time, whether they realize it or not Employer’s prosperity may be dependent upon financing rates Employer can manage risk in the markets Individuals can invest and save Provide diversification Provide opportunities for risk-sharing/insurance Bank sells off mortgage risk which enables people to get mortgages


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives Risk-Sharing Markets enable risk-sharing by pairing up buyers and sellers Even insurance companies share risk Reinsurance Catastrophe bonds Some argue that even more risk-sharing is possible Home equity insurance Income-linked loans Macro insurance Diversifiable risk vs. non-diversifiable risk Diversifiable risk can be easily shared Non-diversifiable risk can be held by those willing to bear it and potentially earn a profit by doing so


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives Derivatives in Practice Growth in derivatives trading The introduction of derivatives in a given market often coincides with an increase in price risk in that market (i.e. the need to manage risk isn’t prevalent when there is no risk) Volumes are easily tracked in exchange-traded securities, but volume is more difficult to transact in the OTC market


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives Derivatives in Practice How are derivatives used? Basic strategies are easily understood Difficult to get information concerning: What fraction of perceived risk do companies hedge Specific rationale for hedging Different instruments used by different types of firms


Chapter 1: Intro to Derivatives: Chapter 1: Intro to Derivatives Buying and Short-Selling Financial Assets Buying an asset Bid/offer prices Short-selling Short-selling is a way of borrowing money; sell asset and collect money, ultimately buy asset back (“covering the short”) Reasons to short-sell: Speculation Financing Hedging Dividends (and other payments required to be made) are often referred to as the “lease rate” Risk and scarcity in short-selling: Credit risk (generally requires collateral) Scarcity


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Forward Contracts A forward contract is a binding agreement by two parties for the purchase/sale of a specified quantity of an asset at a specified future time for a specified future price


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Forward Contracts Spot price Forward price Expiration date Underlying asset Long or short position Payoff No cash due up-front


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Gain/Loss on Forwards Long position: The payoff to the long is S – F The profit is also S – F (no initial deposit required) Short position: The payoff to the short is F – S The profit is also F – S (no initial deposit required)


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Comparing an outright purchase vs. purchase through forward contract Should be the same once the time value of money is taken into account


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Settlement of Forwards Cash settlement Physical delivery


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Credit risk in Forwards Managed effectively by the exchange Tougher in OTC transactions


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Call Options The holder of the option owns the right but not the obligation to purchase a specified asset at a specified price at a specified future time


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Call option terminology Premium Strike price Expiration Exercise style (European, American, Bermudan) Option writer


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Call option economics For the long: Call payoff = max(0, S-K) Call profit = max(0, S-K) – future value of option premium For the writer (the short): Call payoff = -max(0, S-K) Call profit = -max(0, S-K) + future value of option premium


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Put Options The holder of the option owns the right but not the obligation to sell a specified asset at a specified price at a specified future time


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Put option terminology Premium Strike price Expiration Exercise style (European, American, Bermudan) Option writer


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Put option economics For the long: Put payoff = max(0, K-S) Put profit = max(0, K-S) – future value of option premium For the writer (the short): Put payoff = -max(0, K-S) Put profit = -max(0, K-S) + future value of option premium


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Moneyness terminology for options: In the Money (“ITM”) Out of the money (“OTM”) At the money (“ATM “)


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Options are Insurance Homeowner’s insurance is a put option Pay premium, get payoff if house gets wrecked (requires that we assume that physical damage is the only thing that can affect the value of the home) Often people assume insurance is prudent and options are risky, but they must be considered in light of the entire portfolio, not in isolation (e.g. buying insurance on your neighbor’s house is risky) Calls can also provide insurance against a rise in the price of something we plan to buy


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Financial Engineering: Equity-Linked CD Example 3yr note Price of 3yr zero is 80 Price of call on equity index is 25 Bank offers ROP + 60% participation in the index growth


Chapter 2: Intro to Forwards / Options: Chapter 2: Intro to Forwards / Options Other issues with options Dividends The OCC may make adjustments to options if stocks pay “unusual” dividends Complicate valuation since stock generally declines by amount of dividend Exercise Cash settled options are generally automatic exercise Otherwise must provide instructions by deadline Commission usually paid upon exercise Might be preferable to sell option instead American options have additional considerations Margins for written options Must post when writing options Taxes


Exercise 2.4(a): Exercise 2.4(a) You enter a long forward contract at a price of 50. What is the payoff in 6 months for prices of $40, $45, $50, $55? 40 – 50 = -10 45 – 50 = -5 50 – 50 = 0 55 – 50 = 5


Exercise 2.4(b): Exercise 2.4(b) What about the payoff from a 6mo call with strike price 50. What is the payoff in 6 months for prices of $40, $45, $50, $55? Max(0, 40 – 50) = 0 Max(0, 45 – 50) = 0 Max(0, 50 – 50) = 0 Max(0, 55 – 50) = 5


Exercise 2.4(c): Exercise 2.4(c) Clearly the price of the call should be more since it never underperforms the long forward and in some cases outperforms it


Exercise 2.9(a): Exercise 2.9(a) Off-market forwards (cash changes hands at inception) Suppose 1yr rate is 10% S(0) = 1000 Consider 1y forwards Verify that if F = 1100 then the profit diagrams are the same for the index and the forward Profit for index = S(1) – 1000(1.10) = S(1) – 1100 Profit for forward = S(1) - 1100


Exercise 2.9(b): Exercise 2.9(b) Off-market forwards (cash changes hands at inception) What is the “premium” of a forward with price 1200 Profit for forward = S(1) – 1200 Rewrite as S(1) –1100 – 100 S(1) – 1100 is a “fair deal” so it requires no premium The rest is an obligation of $100 payable in 1 yr The buyer will need to receive 100 / 1.10 = 90.91 up-front


Exercise 2.9(c): Exercise 2.9(c) Off-market forwards (cash changes hands at inception) What is the “premium” of a forward with price 1000 Profit for forward = S(1) – 1000 Rewrite as S(1) –1100 + 100 S(1) – 1100 is a “fair deal” so it requires no premium The rest is a payment of $100 receivable in 1 yr This will cost 100 / 1.10 = 90.91 to fund


Chapter 3: Options Strategies: Chapter 3: Options Strategies Put/Call Parity Assumes options with same expiration and strike


Chapter 3: Options Strategies: Chapter 3: Options Strategies Put/Call Parity So for a non-dividend paying asset, S + p = c + PV(K)


Chapter 3: Options Strategies: Chapter 3: Options Strategies Insurance Strategies Floors: long stock + long put Caps: short stock + long call Selling insurance Covered writing, option overwriting, selling a covered call Naked writing


Chapter 3: Options Strategies: Chapter 3: Options Strategies Synthetic Forwards Long call + short put = long forward Requires up-front premium (+ or -), price paid is option strike, not forward price


Chapter 3: Options Strategies: Chapter 3: Options Strategies Spreads and collars Bull spreads (anticipate growth) Bear spreads (anticipate decline) Box spreads Using options to create synthetic long at one strike and synthetic short at another strike Guarantees a certain cash flow in the future The price must be the PV of the cash flow (no risk) Ratio spreads Buy m options at one strike and selling n options at another Collars Long collar = buy put, sell call (call has higher price) Can create a zero-cost collar by shifting strikes


Chapter 3: Options Strategies: Chapter 3: Options Strategies Speculating on Volatility Straddles Long call and long put with same strike, generally ATM strikes Strangle Long call and long put with spread between strikes Lower cost than straddle but larger move required for breakeven Butterfly spreads Buy protection against written straddle, or sell wings of long straddle


Exercise 3.9: Exercise 3.9 Option pricing problem S(0) = 1000 F = 1020 for a six-month horizon 6mo interest rate = 2% Subset of option prices as follows: Strike Call Put 950 120.405 51.777 1000 93.809 74.201 1020 84.470 84.470 Verify that long 950-strike call and short 1000-strike call produces the same profit as long 950-strike put and short 1000-strike put


Exercise 3.9: Exercise 3.9


Chapter 4: Risk Management: Chapter 4: Risk Management Risk management Using derivatives and other techniques to alter risk and protect profitability


Chapter 4: Risk Management: Chapter 4: Risk Management The Producer’s Perspective A firm that produces goods with the goal of selling them at some point in the future is exposed to price risk Example: Gold Mine Suppose total costs are $380 The producer effectively has a long position in the underlying asset Unhedged profit is S – 380


Chapter 4: Risk Management: Chapter 4: Risk Management Potential hedges for producer Short forward Long put Short call (maybe) Can tweak hedges by adjusting “insurance” Lower strike puts Sell off some upside


Chapter 4: Risk Management: Chapter 4: Risk Management The Buyer’s Perspective Exposed to price risk Potential hedges: Long forward Call option Sell put (maybe)


Chapter 4: Risk Management: Chapter 4: Risk Management Why do firms manage risk? As we saw, hedging shifts the distribution of dollars received in various states of the world But assuming derivatives are fairly priced and ignoring frictions, hedging does not change the expected value of cash flows So why hedge?


Chapter 4: Risk Management: Chapter 4: Risk Management


Chapter 4: Risk Management: Chapter 4: Risk Management


Chapter 4: Risk Management: Chapter 4: Risk Management Reasons to hedge: Taxes Treatment of losses Capital gains taxation (defer taxation of capital gains) Differential taxation across countries (shift income across countries) Bankruptcy and distress costs Costly external financing Increase debt capacity Reducing riskiness of future cash flows may enable the firm to borrow more money Managerial risk aversion Nonfinancial risk management Incorporates a series of decisions into the business strategy


Chapter 4: Risk Management: Chapter 4: Risk Management Reasons not to hedge: Transactions costs in derivatives Requires derivatives expertise which is costly Managerial controls Tax and accounting consequences


Chapter 4: Risk Management: Chapter 4: Risk Management Empirical evidence on hedging FAS133 requires derivatives to be bifurcated and marked to market (but doesn’t necessarily reveal alot about hedging activity) Tough to learn alot about hedging activity from public info General findings About half of nonfinancial firms use derivatives Less than 25% of perceived risk is hedged Firms with more investment opportunities more likely to hedge Firms using derivatives have higher MVs and more leverage


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Alternative Ways to Buy a Stock Outright purchase (buy now, get stock now) Fully leveraged purchase (borrow money to buy stock now, repay at T) Prepaid forward contract (buy stock now, but get it at T) Forward contract (pay for and receive stock at T)


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Prepaid Forwards Prepaid forward price on stock = today’s price (if no dividends) Prepaid forward price on stock = today’ price – PV of future dividends:


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures For prepaid forwards on an index, assume the dividend rate is d, then the dividend paid in any given day is d/365 x S If we reinvest the dividend into the index, one share will grow to more than one share over time Since indices pay dividends on a large number of days it is a reasonable approximation to assume dividends are reinvested continuously Therefore one share grows to exp(dT) shares by time T So the price of a prepaid forward contract on an index is


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Forwards The forward price is just the future value of the prepaid forward price Discrete or no dividends: Continuous dividends:


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Other definitions Forward premium: Annualized forward premium:


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Theoretically arbitrage is possible if the forward price is too high or too low relative to the stock/bond combination: If forward price is too high, sell forward and buy stock (cash-and-carry arbitrage) If forward price is too low, buy forward and sell stock (reverse-cash-and-carry arbitrage)


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures No-Arbitrage Bounds with Transaction Costs In practice there are transactions costs, bid/offer spreads, different interest rates depending on whether borrowing or lending, and the possibility that buying or selling the stock will move the market This means that rather than a specific forward price, arbitrage will not be possible when the forward price is inside of a certain range


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures An Interpretation of the Forward Pricing Formula “Cost of carry” is r-d since that is what it would cost you to borrow money and buy the index The “lease rate” is d Interpretation of forward price = spot price + interest to carry asset – asset lease rate


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Futures Contracts Basically exchange-traded forwards Standardized terms Traded electronically or via open outcry Clearinghouse matches buys and sells, keeps track of clearing members Positions are marked-to-market daily Leads to difference in the prices of futures and forwards Liquid since easy to exit position Mitigates credit risk Daily price limits and trading halts


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures S&P 500 Futures Multiplier of 250 Cash-settled contract Notional = contracts x 250 x index price Open interest = total number of open positions (every buyer has a seller) Costless to transact (apart from bid/offer spread) Must maintain margin; margin call ensues if margin is insufficient Amount of margin required varies by asset and is based upon the volatility of the underlying asset


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Since futures settle every day rather than at the end (like forwards), gains/losses get magnified due to interest/financing: If rates are positively correlated with the futures price then the futures price should be higher than the forward price Vice versa if the correlation is negative


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Arbitrage in Practice Textbook examples demonstrates the uncertainties associated with index arbitrage: What interest rate to use? What will future dividends be? Transaction costs (bid/offer spreads) Execution and basis risk when buying or selling the index


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Quanto Index Contracts Some contracts allow investors to get exposure to foreign assets without taking currency risk; this is referred to as a quanto Pricing formulas do not apply, more work needs to be done to get those prices


Chapter 5: Forwards and Futures: Chapter 5: Forwards and Futures Daily marking to market of futures has the effect of magnifying gains and losses If we desire to use futures to hedge a cash position in the underlying instrument, matching notionals is not sufficient: A $1 change in the asset price will result in a $1 change in value for the cash position but a change in value of exp(rT) for the futures Therefore we need fewer futures contracts to hedge the cash position We need to multiple the notional by to account for the extra volatility


Exercise 5.10(a): Exercise 5.10(a) Index price is 1100 Risk-free rate is 5% continuous 9m forward price = 1129.257 What is the dividend yield implied by this price?


Exercise 5.10(b): Exercise 5.10(b) If we though the dividend yield was going to be only 0.5% over the next 9 months, what would we do? Forward price is too low relative to our view Buy forward price, short stock In 9 months, we will have 1100*exp(.05(.75)) = 1142.033 Buy back our short for 1129.257 We are left with 12.7762 to pay dividends


Chapter 8: Swaps: Chapter 8: Swaps The examples in the previous chapters showed examples of pricing and hedging single cash flows that were to take place in the future But it may be the case that payment streams are expected in the future, as opposed to single cash flows One possible solution is to execute a series of forward contracts, one corresponding to each cash flow that is to be received A swap is a contract that calls for an exchange of payments over time; it provides a means to hedge a stream of risky cash flows


Chapter 8: Swaps: Chapter 8: Swaps Consider this example in which a company needs to buy oil in 1 year and then again in 2 years The forward prices of oil are 20 and 21 respectively


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps *Cash flows are on a per-barrel basis; in actuality these would be multiplied by the notional amount The swap price is not $20.50 (the average of the forward prices) since the cash flows are made at different times and therefore is a time-value-of-money component. The equivalency must be on a PV basis and not an “absolute dollars” basis


Chapter 8: Swaps: Chapter 8: Swaps The counterparty to the swap will typically be a dealer In the dealer’s ideal scenario, they find someone else to take the other side of the swap; i.e. they find someone who wishes to sell the oil at a fixed price in the swap, and match buyer and seller (price paid by buyer is higher than price received by the seller, the dealer keeps the difference) Otherwise the dealer must hedge the position The hedge must consist of both price hedges (the dealer is short oil) and interest rate hedges


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps The Market Value of a Swap Ignoring commissions and bid/offer spreads, the market value of a swap is zero at inception (that is why no cash changes hands) The swap consists of a strip of forward contracts and an implicit interest rate loan, all of which are executed at fair market levels


Chapter 8: Swaps: Chapter 8: Swaps But the value of the swap will change after execution: Oil prices can change Interest rates can change Swap has level payments which are fair in the aggregate; however after the first payment is made this balance will be disturbed


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps Interest rate swaps Interest rate swaps are similar to the commodity swap examples described above, except that the pricing is based solely upon the levels of interest rates prevailing in the market. They are used to hedge interest rate exposure


Chapter 8: Swaps: Chapter 8: Swaps LIBOR LIBOR stands for “London Interbank Offered Rate” and is a composite view of interest rates required for borrowing and lending by large banks in London  LIBOR are the floating rates most commonly referenced by an interest rate swap


Chapter 8: Swaps: Chapter 8: Swaps Interest rate swap schematic


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps One more way to write the swap rate


Chapter 8: Swaps: Chapter 8: Swaps


Chapter 8: Swaps: Chapter 8: Swaps The swap rate is just the par rate on a fixed bond In fact the swap can be viewed as the exchange of a fixed rate bond for a floating rate bond


Chapter 8: Swaps: Chapter 8: Swaps The Swap Curve The Eurodollar futures contract is a futures contract on 3m LIBOR rates  It can used to infer all the values of R for up to 10 years, and therefore it is possible to calculate fixed swap rates directly from this curve The difference between a swap rate and a Treasury rate for a given tenor is known as a swap spread


Chapter 8: Swaps: Chapter 8: Swaps Swap implicit loan balance In an upward sloping yield curve the fixed swap rate will be lower than forward short-term rates in the beginning of the swap and higher than forward short-term rates at the end of the swap Implicitly therefore, the fixed rate payer is lending money in the beginning of the swap and receiving it back at the end


Chapter 8: Swaps: Chapter 8: Swaps Deferred swaps Also known as forward-starting swaps, these are swaps that do not begin until k periods in the future


Chapter 8: Swaps: Chapter 8: Swaps Why Swap Interest Rates? Swaps permit the separation of interest rate and credit risk A company may want to borrow at short-term interest rates but it may be unable to do that in enough size Instead it can issue long-term bonds and swap debt back to floating, financing its borrowing at short-term rates


Chapter 8: Swaps: Chapter 8: Swaps Amortizing and Accreting Swaps These are just swaps where the notional value declines (amortizing) or expands (accreting) over time


Exercise 8.2(a,b): Exercise 8.2(a,b) Interest rates are 6%, 6.5%, and 7% for years 1, 2, and 3 Forward oil prices are 20, 21, and 22 respectively What is the 3yr swap price? What is the 2yr swap price beginning in 1 year?


Exercise 8.2(a): Exercise 8.2(a)


Exercise 8.2(b): Exercise 8.2(b)