Chapter 18 – Derivatives and Risk Management

Chapter 18 – Derivatives and Risk Management

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Risk Management • Risk Management has gradually evolved from a narrow insurance-based discipline to traditional financial activities. • Risk Management involves the management of unpredictable events that have adverse consequences for the firm.

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History of Risk Management – “Insurance” • 2100 B.C. – “Bottomry” – from the Code of Hammurabi. (A form of naval insurance whereby the owner of the vessel can borrow money to buy cargo, and does not pay the debt if the ship is lost at sea – Pledging the boat’s bottom to the lender). • 17th to 18th Century – Insurance developed rapidly with the growth of British commerce. • 1735 – The first insurance company in the American colonies was established. • 1787 – Fire insurance corporations in NYC; 1794 – in Philadelphia. • 1880’s – Appearance of Public Liability Insurance • 1897 – Workmen’s Compensation Act in Britain (required employers to insure employees against industrial accidents). • Late 19th Century – Insurance that safeguards workers against sickness and disability, old age, and unemployment. • 1905-1912 – Worker’s Compensation Laws introduced in the USA. Social insurance schemes proliferated worldwide. • 1938 – Federal Crop Insurance Act • After 1944 – Supervision and regulation of insurance corporations. • Till then, insurance was still the main way companies manage risk. JQY

History of Risk Management • 1956 – When exploration of the idea of risk management began. HBR published “Risk Management: A new phase of cost control” by Russell Gallagher. (Dr. Wayne Snider: “the professional insurance manager should be a risk manager). • 1960s and 1970s – First Age of Risk Management. Businesses considered only the non-entrepreneurial risk (e.g. Security, fire, pollution, fraud) Risk is treated reactively, like using insurance. But insurance is only one way to protect the company. There are many others. • 1970s and 1980s – Second Age of Risk Management. Quality assurance is introduced, heralded by the British Standards Institution (BSI). Risk is treated in a proactive or preventable way. • 1980s – Environmental risks is taken into account. • 1995 – Third Age of Risk Management. Non-entrepreneurial and Entrepreneurial risks (risks that a company is exposed to when it engages in business) are considered. JQY

Ages of Risk Management

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Source: Kit Sadgrove, The Complete Guide to Business Risk Management, 2nd edition

Why might stockholders be indifferent to whether or not a firm reduces the volatility of its cash flows? • Diversified shareholders may already be hedged against various types of risk. • Reducing volatility increases firm value only if it leads to higher expected cash flows and/or a reduced WACC.

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Risk Management – Does it add value to SHs? • If the general premise that most investors hold well-diversified portfolio is true, then the answer is theoretically NO. • Recall the Corporate Value Model (page 326). Market Value of the Company = PV of expected future FCF • MV = FCF1/(1+WACC)^1 + FCFN/(1+WACC)^N • Therefore, MV of shares depends on 2 variables, FCF and WACC. If and only if risk management can increase expected FCF or decrease WACC can the market value of the stock increase. • Suppose that you are in the business of buying and selling apples. The price now is P20 per apple. You expect that the price is going to increase 10% for the next 5 years. So to manage risk, you entered into an agreement with the supplier to buy apples at P20.50 per apple for the next 5 years. • You have reduced risk, but have you added shareholders’ value? Remember that since 20.50 is already known and therefore expected, The absolute amount of FCF won’t change. • Recall that WACC = cost of debt + cost of preferred stock + cost of RE or common stock. If there is no change in any of these components, or the capital structure remains the same, WACC will remain the same. For cost of debt: If the supposed increase in the price of apples won’t cause bankruptcy (if bankruptcy is imminent, kd must be reduced). For cost of equity: most investors hold well diversified portfolios, so the relevant risk is non-diversified (systematic) risk. So even if an increase in price of apples will lower your stock price, if you hold a well diversified portfolio, any changes won’t be too significant. Thus, stock value won’t change significantly.

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Reasons why Companies Manage Risks • Reduced volatility allows more Debt Capacity – to be able to take on more debt. Reduces CF volatility and probability of bankruptcy, interest tax savings lead to higher stock price. Remember that kd is less than ke or ks due to tax savings, which leads to higher stock price. • Maintaining optimal capital budget over time. Strive for the lowest WACC by taking on more kd and cost of RE to avoid flotation costs. • Reduced volatility minimize financial distress – CFs can fall below expected levels. Risk management can alleviate this concern (through price tie-ups). • Comparative advantages (in contrast with individual investor) in hedging – lower transaction costs, asymmetric information, specialized skills and knowledge • Reduced volatility results to the reduction of borrowing costs (particularly on swaps) • Tax effects. Reduced volatility reduces the higher taxes that result from fluctuating earnings. Stable earnings generally pay lower taxes than companies with volatile earnings. (Tax credits, carryforward, carrybacks). • For managers – they will try to employ risk management for earnings to stabilize, so their bonuses will also be stable. Certain compensation schemes reward managers for achieving stable earnings. JQY

Different Risks a firm may be exposed to • Pure risks – risks that offer ONLY the prospect of a loss. There is no possibility that a gain may occur. For example, fire hazard risk • Speculative risks – there is a chance of a gain but there’s also a chance of a loss. For example, investments in new projects. • Demand risks – risk that demand for a firm’s products or services will go down. • Input risks – risks that input costs will increase, and that these costs cannot be transferred to the customer. • Financial risks – risks resulting from financial transactions. For example, the risks of interest rate fluctuation or exchange rate fluctuation. • Property risks – risks that productive assets will be destroyed. • Personnel risks – risks resulting from the actions of employees. For example, strikes, theft, fraud. • Environmental risks – risks of public outcry in case of pollution • Liability risks – risks associated with product, service, or employee actions (that may or may not lead to lawsuits) • Insurable risks – risks that can be covered/mitigated by insurance (generally – property, personnel, environmental, and liability)

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Process for managing risks • Identify the risks faced by the firm • Measure the potential effect of each risk • Decide how to handle each relevant risk ▫ Transfer risk to the insurance company ▫ Transfer function that produces risk to a third party (agency) ▫ Purchase derivative contracts to reduce risk (hedge risks) ▫ Reduce probability of adverse events ▫ If adverse events do occur, reduce magnitude of the loss ▫ Totally avoid the activity that gives rise to the risk (discontinue products that may be subject to potential lawsuits). JQY

Derivatives • Financial innovation that allows investors to manage risks. • Securities whose values are determined by the market price or interest rate of some other asset (underlying asset) • Common underlying assets: – Equities – Indexes – Bonds – Physical Assets – Interest Rates • May be used to hedge risk or to profit from speculation. • Potentially risky, especially for inexperienced investors. JQY

Types of Derivatives: • Forward Commitments – represents a commitment or a binding promise to buy or sell an asset or make a payment in the future – Forward Contracts – Futures Contracts – Swaps

• Contingent Claims – payoffs occur if a specific event occurs. It represents a right to buy or sell. It only has value if some future event takes place (EG: if asset price > specified price) – Callable and/or Convertible Bonds – Warrants – Options

• Standard Options – based on assets • Exotic Options – based on futures or other derivatives • Common types of options: – Based on interest rate – Asset-backed security

2 Broad Groups of Derivatives: • Exchange-traded derivatives

– These are transacted via specialized derivatives exchanges (CME Group, Korea Exchange, Eurex) – Examples: Futures contracts and most options – They are standardized, regulated, and backed by a clearinghouse. – They have relatively low default risk as such is shouldered by the clearinghouse.

• Over-the-counter derivatives

– Traded/created by dealers and financial institutions in a market with no central location. – Examples: Forward contracts, swaps, and some options (bond options) – They are largely customized, unregulated and each contract has a counterparty. They expose the owner of a derivative to default risk (in case the counterparty does not honor his commitment).

Classification of Derivatives

Common Derivatives in the Philippines • HSBC Philippines: ▫ Cross-Currency Swaps ▫ Currency Options ▫ Interest Rate Swaps

• BDO ▫ Interest Rate Derivatives ▫ Credit Derivatives

• Metrobank ▫ Swaps ▫ Options ▫ Credit Derivatives

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Derivatives to be studied: ▫ ▫ ▫ ▫ ▫ ▫ ▫

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Forward Contracts Futures Contracts Swaps Options Structured Notes Inverse Floaters Other Exotic Contracts

Forward Contracts • Forward Contract ▫ A bilateral private contract under which one party agrees to buy a commodity at a specific price (agreed today) on a specific future date; and the other party agrees to make the sale. ▫ Not traded in an exchange. It is traded over-the-counter. ▫ Physical delivery occurs ▫ Underlying assets can be anything, or any instrument (eg: bonds, equities, indices, or portfolio of those already stated) ▫ Entail both market risk and credit risk

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Forward Contracts • Deliverable Forward Contract ▫ It specifies that the long (buyer) will pay a certain amount at a future date to the short (seller), who will deliver a certain amount of an asset.

• Forward Contract with Cash Settlement ▫ Does not require delivery of the underlying asset. Cash payment is made at settlement date from one counterparty to the other, based on the contract price and market price of the asset at settlement.

• Early Termination ▫ Entering into a new forward contract with the opposite position, at the then-current expected forward price ▫ May be done with the existing counterparty (eliminates default risk) or a new counterparty (must consider default risk)

Forward Contracts • End Users of Forward Contracts ▫ Often a corporation hedging an existing risk

• Dealers of Forward Contracts ▫ Usually brokers, banks, or financial institutions originate then, taking a long side in some contracts and a short side in others. ▫ They always allow for a spread in pricing to compensate for actual cost, bearing default risk, and any unhedged price risk.

• Using bonds as the underlying asset ▫ Bonds have a maturity date, so the forward contract must be settled before the bond matures. ▫ Quotations:  Quoted in terms of the discount on zero-coupon bonds (T-bills)  Quoted in terms of the YTM on coupon bonds (exclusive of accrued interest)

▫ Corporate bonds: must contain special provisions to deal with possibility of default and any call or conversion features

Bond Forward Contract Illustration: • A forward contract covering a $10 million face value of T-bills that will have 100 days to maturity at contract settlement is priced at 1.96 on a discount yield basis. Compute the dollar amount the long must pay at settlement for the T-bills. When market interest rate increase, discount increase and Tbill prices fall. Thus, if interest rates rise, the short gains, and the long will have losses on the forward contract. If interest rates fall, the long will gain on the forward contract, and the short loses.

Equity Forward Contracts • The underlying asset is a single stock, portfolio of stocks, or stock index. • Treatment is the same as other forward contracts. • Portfolio of stocks as the underlying asset: ▫ The difference between a forward contract with one portfolio of stocks as the underlying asset and several forward contracts with each covering a single stock is that it has better pricing (because overall administration/origination costs will be less for the portfolio forward contract)

• Stock index as the underlying asset: ▫ Similar to that of a single stock as the underlying asset, except that the contract will be based on a notional amount and will be very likely a cash-settlement contract.

Equity Index Forward Contract Illustration: • A portfolio manager desires to generate $10 million 100 days from now from a portfolio that is quite similar in composition to the S&P 100 index. She requests a quote on a short position in a 100 day forward contract based on the index with a notional amount of $10 million and gets a quote of 525.2. If the index level at the settlement date is 535.7, calculate the amount the manager will pay or receive to settle the contract.

Eurodollar, LIBOR, and EURIBOR • Eurodollar deposits ▫ Deposits in large banks outside the USA, denominated in USD. ▫ Quoted as an add-on yield rather than on a discount basis.

• LIBOR ▫ ▫ ▫ ▫

“London Interbank Offered Rate” The lending rate on dollar-denominated loans between banks. Quoted as an annualized rate based on a 360-day year Used as an international reference rate for floating rate USD denominated loans worldwide, quoted in 30-day, 60-day, 90-day, 180-day, or 360-day terms

• EURIBOR ▫ “Europe Interbank Offered Rate” ▫ Equivalent for short-term Euro denominated bank deposits (loans to banks)

LIBOR-based Loan Illustration: • Compute the amount that must be repaid on a $1 million loan for 30 days if 30-day LIBOR is quoted at 6%.

Forward Rate Agreement (FRA) • A forward contract to borrow/lend money at a certain rate at some future date. • Cash settlement, but no actual loan is made at settlement date. • Serve to hedge the uncertainty about short-term rates (eg: 30, 60, or 90 day LIBOR) that will prevail in the future. • If reference rates rise, the long (borrower) gains and the short loses. • If reference rates fall, the short (lender) gains and the long loses.

Reading FRAs • 60-day FRA on a 90-day LIBOR ▫ Settlement or expiration is 60 days from now ▫ Payment at settlement is based on 90-day LIBOR, 60 days from now. ▫ Is also referred to as 2-by-5 FRA or 2x5 FRA

Payment from the short to the long at settlement on an FRA:

• Numerator = interest savings in percent • Denominator = discount factor

FRA Cash Settlement Illustration: • Consider an FRA that: ▫ ▫ ▫ ▫

Expires or settles in 30 days. Is based on a notional principal amount of $1 million. Is based on 90-day LIBOR. Specifies a forward rate of 5%

Assume that the actual 90-day LIBOR 30 days from now (at expiration) is 6%. Compute the cash settlement payment at expiration, and identify which party makes the payment.

Currency Forward Contracts • Specifies that one party will deliver a certain amount of one currency at the settlement date in exchange for a certain amount of another currency. • A single cash payment is made at settlement based on the difference between the exchange rate fixed in the contract and the market exchange rate at the settlement date.

Currency Forwards Illustration: • Velvet expects to receive EUR 50 million 3 months from now and enters into a cash settlement currency forward to exchange these euros for USD at USD 1.23 per euro. If the market exchange rate USD 1.25 per euro at settlement, what is the amount of the payment to be received or paid by Velvet?

Futures Contracts ▫ Similar to a forward contract, but it is a standardized contract traded through the futures exchange. There is a third party – “clearinghouse” that acts as counterparty on all contracts. ▫ Regulated by the government ▫ More liquid than forward contracts ▫ Lower transaction costs than forward contracts ▫ Usually done for commodities (underlying asset) ▫ “Marked to market” on a daily basis, and entails virtually no physical delivery ▫ Entail only market risk. Credit risk is passed on to the clearinghouse. Clearinghouse doesn’t take market risk as it only takes offsetting positions.

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Futures Contract can be • Either deliverable or cash settlement • Zero value at time the contract is entered into Exchange sets minimum price fluctuation called “TICKS”. They also set daily price limit, setting the maximum price movement allowed in a single day.

Futures Contracts: Delivery Open Month

High

Low

Settle

Change

High

Low

Open Interest

Sept. Sept.

109-00 109-00

110-04 110-04

108-27 108-27

110-02 110-02

37 37

112-12 112-12

96-07 96-07

367,016 367,016

Dec.

107-30 107-30

108-29 108-29

107-27 107-27

108-28 108-28

37 37

111-04 111-04

96-06 96-06

96,216 96,216

Dec.

Consider a 20 year semi-annual payment, 6% coupon rate 100,000 t-bonds. Required: 1. Compute for the price of the bond one day ago. 2. Compute for the total value of the bonds. 3. Compute for the nominal interest rate of the bond today and one day ago. 4. Compute the value of the contract if interest rates fall by 0.3%, 2 months later. 5. Compute for the profit or loss (increase or decrease of contract value)

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Requirements: • • • • •

1: Compute for the PV of the bonds today and one day ago. 2: Compute for the total value of the bonds. 3: Compute for the nominal annual interest rate today and one day ago. 4: Compute for the PV of the bonds using the new interest rate. 5: Compute for the profit/loss if interest rates fall by 0.3%.

Note: • For Requirement 1, do Step 1. • For Requirement 2, do Steps 1 and 2. • For Requirement 3, do Steps 1 and 3. • For Requirement 4, do Steps 3 and 4. • For Requirement 5, do Steps 1, 3, 4, and 5.

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Solution: • Step 1: Compute for the PV of the bonds today and one day ago.

Delivery Month

Settle

Change

Open Interest

Dec.

108-28

37

96,216

PV of Bond Today = {[108 + (28/32)]/100} x 100,000 = 108,875 Change in Bond Value = (37/32)/100 x 100,000 = 1,156.25 PV of Bond One Day Ago = 108,875 – 1,156.25 = 107,718.75 (REQ. 1) • Step 2: Compute for the total value of the bonds. Total Value of the Bonds = PV x No. of contracts outstanding Total Value of the Bonds = 108,875 x 96,216 = 10,476 billion (REQ. 2) • Step 3a: Compute for the nominal annual interest rate today. (Use YTM Equation) YTM = {{Annual PMT + [(FV – PV)/Annual N]} / [(40% x FV) + (60% x PV)]}} YTM = {{6,000 + [(100,000 – 108,875)/20]} / (40% x 100,000) + (60% x 108,875)]}} YTM = 5.28% or 5.3%

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Solution: • Step 3b: Compute for the nominal annual interest rate one day ago. (Use YTM Equation) YTM = {{Annual PMT + [(FV – PV)/Annual N]} / [(40% x FV) + (60% x PV)]}} YTM = {{6,000 + [(100,000 – 107,718.75)/20]} / (40% x 100,000) + (60% x 107,718.75)]}} YTM = 5.37% (REQ. 3) • Step 4. Compute for the PV of the bonds using the new interest rate. (Use YTM Equation) YTM = {{Annual PMT + [(FV – PV)/Annual N]} / [(40% x FV) + (60% x PV)]}} (YTM Today – Change in Interest Rate) = {{6,000 + [(100,000 – PV)/20]} / (40% x 100,000) + (60% x PV)]}} (5.3% – 0.3%) = {{6,000 + [(100,000 – PV)/20]} / (40% x 100,000) + (60% x PV)]}} 3% PV – [(100,000 – PV)/20] = 4,000; 60% PV – 100,000 + PV = 80,000 160% PV = 180,000; PV = 112,500 (REQ. 4) JQY

Solution: • Step 5: Compute for the profit/loss if interest rate falls by 0.3% • Profit(Loss) = PV of bonds using new interest rate – PV of bonds using original interest rate • Profit(Loss) = 112,500 – 108,875 = 3,625 Gain (REQ. 5)

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Hedging using futures • Recall that when price increases, sellers lose. When price decreases, buyers lose. • Long and short hedges are ways in which an investor can cut his losses. • Long (buy) hedges ▫ Futures contracts are bought in anticipation of (or to guard against) price increases. ▫ You already have a short (sell) position, but you think that price will rise, so you make a buy position to hedge against that risk. ▫ Example: You entered into a futures contract to sell 1000 bushels of wheat at P500k next year. However, since wheat prices start to rise, you anticipated that the price of wheat is going to rise to P800k. So, to hedge that risk, you enter into another contract to buy 1000 bushels of wheat at P600k next year. In case the wheat price becomes P800k. At least you lost only 300k – 200k = 100k. • Short (sell) hedges ▫ Futures contracts are sold to guard against price declines. ▫ You already have a long (buy) position, but you think that price will fall, so you make a sell position to hedge against that risk. ▫ Example: You entered into a futures contract to buy 1000 bushels of wheat at P500k next year. However, since wheat prices start to fall, you anticipated that the price of wheat is going to fall to P300k. So, to hedge that risk, you enter into another contract to sell 1000 bushels of wheat at P400k next year. In case the wheat price becomes P300k. At least you lost only 200k – 100k = 100k.

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Future Contracts “Terms” • Futures margin deposit

▫ Deposits to ensure performance under contract terms. These are not loans.

• Initial margin

•

Set by Feds, ▫ The deposit required to initiate a futures position. may be increased by Maintenance margin brokerage

▫ The minimum margin amount, and when margin falls below this amount, it must be brought back to its initial level (Initial margin)

• Variation margin ▫ Funds needed to bring one’s account back to the initial margin amount

• Margin calculations ▫ Based on daily settlement price , the average of the prices for trades during a closing period set by the exchange.

Marking-to-market • Process of adding gains to or subtracting losses from the margin account daily, based on the change in settlement prices from one day to the next. • Trades cannot take place at prices that differ from the previous day’s settlement price by more than the price limit and are said to be limit down (up) when the new equilibrium price is below (above) the minimum (maximum) price for the day.

Limit Move Illustration • A futures contract has a daily price limit of 5 cents. It settled at $5.53 yesterday. Today, traders wish to trade at $5.60. • No trades will take place today; however, settlement price will be reported as $5.58. This is called a limit move – a limit up. • If traders wish to trade at or below $5.48, the price is said to be limit down. • No trade because of limit move = Locked Limit = a situation where the equilibrium is either above or below the prior day’s settle price by more than the permitted (limit) daily price move.

Margin Balance Computation 1: • On September 1, 2010, A agrees to sell a house to B next year at P5 million. They agreed on cash settlement. On September 2, the market value of the house is P4.8 million. On September 3, the market value of the house is P4.9 million, and on September 4, the market value of the house is P5.1 million. The clearinghouse decides that initial margin will be 10% of the notional principal, and maintenance margin will be 80% of the initial margin. • Calculate the margin balance of A and B for September 2, 3, and 4.

Margin Balance Computation 2: • Consider a long position of five July wheat contracts, each of which covers 5,000 bushels. Assume that the contract price is $2.00 and that each contract requires an initial margin deposit of $150 and a maintenance margin of $100. • Compute the margin balance for this position after a 2 cent decrease in price in Day 1, a 1-cent increase in price in Day 2, and a 1-cent decrease in price on Day 3.

Termination of a Futures Contract: • Offsetting trade (entering into an opposite position in the same contract). The most common method. • Cash Settlement (Cash payment at expiration) • Delivery of the asset specified in the contract (less than 1% of all contract terminations) • An exchange for physicals (asset delivery off the exchange) = an ex-pit transaction; an exception.

Types of Futures Contracts: • Treasury Bill ▫ Based on a $1 million face value 90 day t-bill & settles in cash. One tick is 0.01% ($25 per $1 million contract)

• Eurodollar ▫ Based on 90-day LIBOR ▫ Settles in cash and the minimum price change or one “tick” is 0.01%, ($25 per $1 million contract)

• Treasury Bond ▫ Traded for t-bonds that matures in more than 15 years, is a deliverable contract, have a face value of $100,000 and quoted as percentages or fractions of 1% (1/32nds) of face value ▫ Gives the short a choice of bonds to deliver ▫ Uses conversion factors to adjust the contract price for the bond that is delivered. Long pays the futures price at expiration x conversion factor.

T-bill Futures Contract Illustration: • A t-bill has a price quote of 98.52. How much is the delivery price of the t-bill?

Types of Futures Contracts: • Stock Index ▫ Do not allow for actual delivery. ▫ Have a multiplier that is multiplied by the index to calculate the contract value, and settle in cash. ▫ S&P 500 index future is most popular, settlement is in cash and is based on a multiplier of 250. Dow’s multiplier is 10, NASDAQ is 100 ▫ Example: Suppose the S&P 500 index is at 1,088. A one month futures contract on the index may be quoted at a price of 1,090. Compute for the actual futures price.

• Currency ▫ Delivery of standardized amounts of foreign currency. ▫ Are set in foreign currency, and price is stated in USD/unit.

Swap • Two parties agree to exchange obligations to make specified payment streams. • A series of forward contracts • Not per se, an exchange of one asset for another. Rather, it’s an exchange of obligations. • Are custom instruments, largely unregulated, don’t trade in secondary markets, and are subject to default (counterparty) risk • No money is exchanged at inception, and periodic payments are netted, except currency swaps. • Effects of swaps due to standardized contracts: ▫ Standardized contracts lower the time and effort involved in arranging swaps, thus lowering transaction costs. ▫ Standardized contracts led to a secondary market for swaps, increasing the liquidity and efficiency of the swaps market. • Examples: ▫ Plain Vanilla Interest rate swap ▫ Equity returns swap ▫ Currency swap JQY

Plain Vanilla Interest-rate swap • Fixed-for-floating (or vice versa) interest-rate swap. • Notional principal is generally not swapped • Net payment by the fixed rate payer, based on 360 day year: ▫ (Fixed – Float or LIBOR) x (# of days / 360) x notional principal

• Net payment by the float rate payer, based on 360 day year: ▫ (Float or LIBOR – Fixed) x (# of days / 360) x notional principal

Interest Rate Swap Illustration: • A enters into a $1,000,000 quarterly-pay plain vanilla interest rate swap as the fixed rate payer at a fixed rate of 6% based on a 360 day year. The floating-rate payer agrees to pay 90-day LIBOR plus a 1% margin; 90-day LIBOR is currently 4%. • The first swap payment is known at swap initiation. • 90-day LIBOR rates are: ▫ ▫ ▫ ▫

4.5% 5.0% 5.5% 6.0%

90 days from now 180 days from now 270 days from now 360 days from now

Calculate the amount A pays or receives 90, 180, 270, and 360 days from now.

Equity Swaps • The returns payer makes payments based on returns of a stock, portfolio, or index, in exchange for fixed or floating rate payments. • If stock, PTF, or index declines in value, the returns payer receives the interest payment & a payment based on the percentage decline in value.

Equity Swap Illustration: • Petunia enters into a 2 year $10 million quarterly swap as the fixed payer and will receive the index return on the S&P 500. The fixed rate is 8% and the index is currently 986. At the end of the next three quarters, the index level is 1030, 968, and 989. Calculate the net payment for each of the next three quarters and identify the direction of the payment.

Currency Swap • Used to secure cheaper debt and to hedge against exchange rate fluctuations. • It is less expensive than issuing debt in foreign currency coz own currency is not known to foreign land. This is especially applicable for companies that wants to have operations in a foreign land. Borrow USD

Borrow AUD

BB (US)

9%

8%

AA (AUS)

10%

7%

• Assume that 1 USD = 2 AUD. Each party goes to his own bank. BB borrows 1m USD at 9% (interest of USD90k), and AA borrows 2m AUD at 7% (interest of AUD140k) • 3 Important Dates: ▫ Swap Initiation- notional principal is swapped at initiation Gives 1m USD

BB (US)

AA (AUS) Gives 2m AUD

▫ Swap Interest Payments (to each other) Pays AUD 160k (2m x 8%)

BB (US)

AA (AUS) Pays USD 100k (1m x 10%)

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Currency Swap • 3 Important Dates: ▫ Interest Payments to respective banks  AA pays 140k AUD to Bank, but he gets 160 AUD from BB, so he gains 20,000 AUD  BB pays 90k USD to Bank but he gets 100 USED from AA, so he gains 10,000 USD

▫ Swap Termination Gives 2m AUD

BB (US)

AA (AUS) Gives 1m USD

 AA pays back 2m AUD to the Australian Bank  BB pays back 1m USD to the US Bank

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How to terminate swaps: • Enter into an offsetting swap, sometimes through swaption (most common) • Mutual agreement to terminate the swap (likely involves making or receiving compensation) • Selling the swap to a 3rd party with consent of the original counterparty (uncommon)

Structured Notes • A debt obligation derived from another debt obligation. • They are securities whose cash flow characteristics depend upon one or more indices or that have embedded forwards or options, or securities where an investor’s investment returns and issuer’s payment obligations are contingent on, or highly sensitive to, changes in the value of the underlying assets, indices, interest rates, or cash flows. • Example: Collateralized Debt Obligation is a type of structured asset-backed security.

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Inverse Floaters • A note in which the interest paid moves counter to market rates. • Example: Usually, interest rate on your bond is 1% + prime rate. So if prime rate is 4%, interest rate on your note will be 5%. • For inverse floaters, if interest rate in economy falls, bond yield will rise. (Example: if interest rate of economy is 3%, and bond interest rate is 4%. If economy rate goes to 2%, bond interest rate goes to 5% • Benefits: to enhance yield when economy rates fall.

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Options • A contract that gives its holder the right, but not the obligation, to buy (or sell) an asset at some predetermined price within a specified period of time. • It’s important to remember: ▫ It does not obligate its owner to take action. ▫ It merely gives the owner the right to buy or sell an asset. JQY

Options • Option writer = seller of an option. • Call Option ▫ Gives the holder of the call option the right, but not the obligation, to buy an asset at a particular price within a specified period of time.

• Put Option ▫ Gives the holder of the put option the right, but not the obligation, to sell an asset at a particular price within a specified period of time.

Options: • Four possible Options: ▫ ▫ ▫ ▫

Long Call – buyer (holder) of a call option Short Call – seller (writer) of a call option Long Put – buyer (holder) of a put option Short Put – seller (writer) of a put option

• Option Premium – the price paid for the option. • Moneyness – determined by the difference between the strike or exercise price and the market price of the underlying stock.

Kinds of Options: • European Options ▫ Can be exercised only at the option’s expiration date.

• American Options ▫ Can be exercised at any time up to the option’s expiration date. ▫ These are more valuable than European options.

Option Terminologies • Exercise (or strike) price – the price stated in the option contract at which the security can be bought or sold. • Option price – option contract’s market price. • Expiration date – the date the option matures. • Exercise value – the value of an option if it were exercised today (Current stock price - Strike price).

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Option Terminologies • Covered option – an option written against stock held in an investor’s portfolio. • Naked (uncovered) option – an option written without the stock to back it up. • In-the-money call – a call option whose exercise price is less than the current price of the underlying stock. • Out-of-the-money call – a call option whose exercise price exceeds the current stock price. • Long-term Equity AnticiPation Securities (LEAPS) - similar to normal options, but they are longer-term options with maturities of up to 2 1/2 years.

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Option’s Moneyness: CALL OPTION

PUT OPTION

In the money (Option holder WILL Exercise)

Stock/Market Price > Strike/Exercise Price

Stock/Market Price < Strike/Exercise Price

At the money (Option holder is indifferent)

Stock/Market Price = Strike/Exercise Price

Stock/Market Price = Strike/Exercise Price

Out of the money (Option holder WILL NOT exercise)

Stock/Market Price < Strike/Exercise Price

Stock/Market Price > Strike/Exercise Price

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Moneyness Illustration: • Consider a September 40 call and a September 40 put, both on a stock that is currently selling for $37 a share. Calculate how much these options are in or out of the money.

Option Simple Illustration: • A, the writer of a call option, has a contract with B. The price paid for the option is set at $800. Exercise price is agreed to be $10,000. Suppose that the market price is $11,500. Compute the gain or loss of A and B. • A, the writer of a call option, has a contract with B. The price paid for the option is set at $800. Exercise price is agreed to be $11,500. Suppose that the market price is $10,000. Compute the gain or loss of A and B.

Option example • A call option (option to buy) with an exercise price of $25, has the following values at these prices: Stock price $25 30 35 40 45 50 JQY

Call option price $ 3.00 7.50 12.00 16.50 21.00 25.50

Determining call option exercise value and option premium or time value Stock Strike price (S) price (X)

Exercise or Intrinsic value of option

Market price of Option

Option Premium/ Time Value

$25.00 30.00

$25.00 25.00

$0.00 5.00

3.00 7.50

3.00 2.50

35.00 40.00 45.00 50.00

25.00 25.00 25.00 25.00

10.00 15.00 20.00 25.00

12.00 16.50 21.00 25.50

2.00 1.50 1.00 0.50

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Determining put option intrinsic value and option premium or time value Stock Strike Exercise or price (S) price (X) Intrinsic Value of option $30.00 $25.00 $0.00

25.00 20.00 15.00 10.00 5.00 JQY

25.00 25.00 25.00 25.00 25.00

0.00 5.00 10.00 15.00 20.00

Market price of Option 3.00

7.50 12.00 16.50 21.00 25.50

Option Premium/ Time Value 3.00

7.50 7.00 6.50 6.00 5.50

How does the option premium change as the stock price increases? • The premium of the option price over the exercise value declines as the stock price increases. • This is due to the declining degree of leverage provided by options as the underlying stock price increases, and the greater loss potential of options at higher option prices.

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Intrinsic Value Illustration: • Consider a call option with a strike price of $50. Compute the intrinsic value of this option for stock prices $55, $50, and $45 • Compute for the option premium under the three scenarios, if market price of the call options are 5, 4, and 3, respectively.

Option value

Call premium diagram

30

25 20

15 Market price

10

Stock

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10

15

20

25

30

Exercise value 35 40 45

Price 50

Option price depends on: • • • • •

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Stock Price Exercise Price Term-to-maturity Variability of the stock price (Volatility) Risk-free rate

OPM – Riskless Hedge

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• We are to find the value of an option assuming a riskless hedge. • Riskless Hedge – a hedge where an investor buys a stock and simultaneously sells a call option on that stock, ending up with a riskless position. • Given: Stock price today = P40 per share; Exercise price next year = P35 per share; True market price = may either be 30 or 50. Assume that discount interest is 8%.

Steps:

1. Find the range. Ending Stock Price

Minus Strike Price

Exercise Value of the Option

30

35

0

50

35

15

20

15 (computed as 15/20)

0.75

2. Equalize range of payoffs for both the stock and option Ending Stock Price x factor

Ending Stock Value

Exercise Value of the Option (Ending Value)

30 x 0.75

22.50

0.00

50 x 0.75

37.50

15.00

15.00

15.00

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Steps: 3.

4.

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Create a riskless hedged investment (Ending value of total portfolio = regardless of whether the stock increases or decreases) Ending Stock Price x factor

Ending Value of Stock in PTF

MINUS Ending Value of Option in PTF

Ending Total Value of the PTF

30 x 0.75

22.50

0

22.50

50 x 0.75

37.50

15.00

22.50

Pricing the call option PV of the Portfolio = 22.50 / (1.08)^1 = 20.83 Remember, stock NOW is worth P40.00. Cost of stock is P30.00, because it costs 0.75(40) = 30 to purchase ¾ of a share. Price of Option = Cost of Stock – PV Portfolio Price of Option = P30.00 – P20.83 = 9.17

Black-Scholes Option Pricing Model • Developed by Fischer Black and Myron Scholes in 1973.

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What are the assumptions of the Black-Scholes Option Pricing Model? • The stock underlying the call option pays no dividends during the call option’s life. • There are no transactions costs for the sale/purchase of either the stock or the option. • The short-term, risk-free interest rate (rRF) is known and is constant during the life of the option. • Any purchaser of a security may borrow any fraction of the purchase price at the short-term risk-free interest rate. • No penalty for short selling and sellers receive immediately full cash proceeds at today’s price. (Short selling is permitted) • Option can only be exercised on its expiration date. (European Options) • Security trading takes place in continuous time, and stock prices move randomly in continuous time. JQY

Using the Black-Scholes option pricing model  2   t] ln(P/X)  [rRF   2   d1  σ t d 2  d1 - σ t

Put-call parity requires that: Put = V - P + Xe-rT Then the price of a put option is: Put = Xe-rT N(-d2) - P N(-d1)

V  P[N(d1 )] - Xe-rRFt [N(d2 )]

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V = Current value of the call option P = current price N(d1) = probability that a deviation less than d1 will occur in a standard normal distribution. N(d1) and N(32) = represent areas under a standard normal distribution function. X = exercise or strike price of an option e = 2.7183 kRF = risk-free interest rate t = time until the option expres Ln(P/X) = natural logarithm of P/X SD^2 = variance of the rate of return on the stock

Use the B-S OPM to find the option value of a call option with P = $27, X = $25, rRF = 6%, t = 0.5 years, and σ2 = 0.11. ln($27/$25)  [(0.06  0.11 )] (0.5) 2 d1   0.5736 (0.3317)(0.7071) d 2  0.5736 - (0.3317)(0.7071)  0.3391 From Appendix A in the textbook N(d1 )  N(0.5736) 0.5000  0.2168  0.7168 N(d2 )  N(0.3391) 0.5000  0.1327  0.6327 JQY

Solving for the call option value V  P[N(d1 )] - Xe

-rRFt

[N(d 2 )] -(0.06)(0.5 )

V  $27[0.7168] - $25e

[0.6327]

V  $4.0036

Solving for the put option value Put = Xe-rT N(-d2) - P N(-d1) Put = [$25e^(-0.06x0.5)] x 0.3673) – ($27 x 0.2832) Put = $8.9111 – $7.6464 = $1.2647 JQY

How do the factors of the B-S OPM affect a call option’s value? As the factor increases … The option value … Current stock price Increases Exercise price Decreases Time to expiration Increases Risk-free rate Increases Stock return volatility Increases

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How do the factors of the B-S OPM affect a put option’s value? As the factor increases … The option value … Current stock price Decreases Exercise price Increases Time to expiration Increases Risk-free rate Decreases Stock return volatility Increases

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Benefits of Derivatives: • Provide price information (price discovery). • Allows risk to be managed and shifted among market participants. • Reduce transaction costs because investors are already able to manage risks.

Criticisms of Derivatives: • Likened to “gambling” because of the high leverage involved in derivatives payoffs. • Too risky especially to investors with limited knowledge of complex instruments.