08 derivatives and risk management

8/19/2019 08 Derivatives and Risk Management

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Derivatives and Risk Management

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Risk Management• In business, risk management involves

identifying events that could have adversefinancial consequences and then taking actionsto prevent and/or minimize the damage caused by those events.

• Risk Management has gradually evolved from anarrow insurance-based discipline to traditionalfinancial activities.

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History of Risk Management – “Insurance”• 2100 B.C. – “Bottomry” – from the Code of Hammurabi.• 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.

Once a discretionary cost, it is now indispensable.JQY


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History of Risk Management• 1956 – When exploration of the idea of risk management began.

HBR published “Risk Management: A new phase of cost control” byRussell Gallagher. (Dr. Wayne Snider: “the professional insurancemanager should be a risk manager).

• 1960s and 1970s – First Age of Risk Management. Businessesconsidered 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 aremany others.

• 1970s and 1980s – Second Age of Risk Management. Qualityassurance 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 itengages in business) are considered.

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Ages of Risk Management

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


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Why might stockholders be indifferent to whether

or not a firm reduces the volatility of its cashflows?

• 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 areduced 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. 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 riskmanagement 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 managerisk, you entered into an agreement with the supplier to buy apples at P20.50 per apple forthe next 5 years.

• You have reduced risk, but have you added shareholders’ value? Remember that since 20.50is 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. Ifthere 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 ofapples won’t cause bankruptcy (if bankruptcy is imminent, rd must be reduced). For cost ofequity: most investors hold well diversified portfolios, so the relevant risk is non-diversified(systematic) risk. So even if an increase in price of apples may affect your stock price, if you

hold a well diversified portfolio, any changes won’t be too significant. Thus, stock value won’tchange significantly.JQY


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Reasons why Companies Manage Risks

• Reduced volatility allows more Debt Capacity – to be able to take on moredebt. Reduces CF volatility and probability of bankruptcy, interest tax savingslead to higher stock price. Remember that kd is less than ke or ks due to taxsavings, which leads to higher stock price.

• Maintaining optimal capital budget over time. Strive for the lowest WACC bytaking on more rd and cost of RE to avoid flotation costs.

• Reduced volatility minimize financial distress – CFs can fall below expectedlevels. Risk management can alleviate this concern (through price tie-ups).

• Comparative advantages (in contrast with individual investor) inhedging – lower transaction costs, asymmetric information, specialized skillsand knowledge

• Reduced volatility results to the reduction of borrowing costs (particularlyon swaps)

• Tax effects. Reduced volatilit y reduces the higher taxes that resultfrom fluctuating earnings. Stable earnings generally pay lower taxes thancompanies 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 schemesreward managers for achieving stable earnings.

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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 betransferred to the customer.

• Financial risks – risks resulting from financial transactions. For example, therisks 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 (hedgerisks)

▫ 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 (discontinueproducts that may be subject to potential lawsuits).

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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 fromspeculation.

• Potentially risky, especially for inexperienced investors.

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Types of Derivatives:•

Forward Commitments – represents a commitment or a binding promise to buy or sell an asset or make a payment inthe 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 somefuture 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

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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 amarket with no central location.

– Examples: Forward contracts, swaps, and some options(bond options)

– They are largely customized, unregulated and each contracthas a counterparty. They expose the owner of a derivative todefault risk (in case the counterparty does not honor his

commitment).JQY


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Derivatives to be studied:

▫ Forward Contracts

▫ Futures Contracts

▫ Swaps

▫ Options▫ Structured Notes

▫ Inverse Floaters

▫ Other Exotic Contracts

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Forward Contracts

• Forward Contract▫ A bilateral private contract under which one party agrees to

buy a commodity at a specific price (agreed today) on aspecific future date; and the other party agrees to make thesale.

▫ 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 amountof 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, basedon 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 defaultrisk) or a new counterparty (must consider default risk)

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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 actualcost, 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 accruedinterest)

▫ Corporate bonds: must contain special provisions to deal withossibilit of default and an call or conversion featuresJQY


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Bond Forward Contract

Illustration:• A forward contract covering a $10 million face value of T-bills that will have 100 days tomaturity at contract settlement is priced at 1.96

on a discount yield basis. Compute the dollaramount the long must pay at settlement for theT-bills.

When market interest rate increase, discount increase and T-

bill prices fall . Thus, if interest rates rise, the short gains ,

and the long w i l l have los ses on the forward contract . If

interest rates fall, the long will gain on the forward contract,

and the short loses. JQY


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Equity Forward Contracts

• The underlying asset is a single stock, portfolio ofstocks, 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 witheach covering a single stock is that it has better pricing (becauseoverall administration/origination costs will be less for theportfolio 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 verylikely a cash-settlement contract.

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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 USDdenominated 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)JQY


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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%.

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Forward Rate Agreement (FRA)

• A forward contract to borrow/lend money at a certainrate 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 thefuture.

• If reference rates rise, the long (borrower)gains and the short loses.

• If reference rates fall, the short (lender) gains

and the long loses.JQY


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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

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

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

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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 anothercurrency.

• A single cash payment is made at settlement

based on the difference between the exchangerate fixed in the contract and the marketexchange rate at the settlement date.

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Currency Forwards Illustration:

• Velvet expects to receive EUR 50 million 3months from now and enters into a cashsettlement currency forward to exchange theseeuros for USD at USD 1.23 per euro. If themarket exchange rate USD 1.25 per euro atsettlement, what is the amount of the paymentto be received or paid by Velvet?

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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 nophysical delivery

▫ Entail only market risk. Credit risk is passed on to theclearinghouse. Clearinghouse doesn’t take market risk as itonly takes offsetting positions.

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Futures Contracts “Terms”▫ Commodity Futures

A contract that is used to hedge against price changes for inputmaterials.

▫ Financial Futures

A contract that is used to hedge against fluctuating interest rates,

stock prices, and exchange rates.▫ Speculation

With futures, it involves betting on future price movements.

▫ Hedging

Using transactions to lower risks. Firms or individuals do this toprotect against a price change that would otherwise negativelyaffect profits.

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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 makea buy position to hedge against that risk.

▫ Example: You entered into a futures contract to sell 1000 bushels of wheat at P500knext 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 asell position to hedge against that risk.

▫ Example: You entered into a futures contract to buy 1000 bushels of wheat at P500knext 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 contractto sell 1000 bushels of wheat at P400k next year. In case the wheat price becomesP300k. At least you lost only 200k – 100k = 100k.

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Perfect Hedge = occurs when the gain or loss on the hedged transaction

exactly offsets the loss or gain on the unhedged position.


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Futures Contract can be• Either deliverable or cash settlement

• Zero value at time the contract is entered into

Exchange sets minimumprice fluctuation called

“TICKS”. They also set dailyprice limit, setting themaximum price movement

allowed in a single day.

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DeliveryMonth

Open High Low Settle Change High Low OpenInterest

Sept. 109-00 110-04 108-27 110-02 37 112-12 96-07 367,016

Dec. 107-30 108-29 107-27 108-28 37 111-04 96-06 96,216

DeliveryMonth

Open High Low Settle Change High Low OpenInterest

Sept. 109-00 110-04 108-27 110-02 37 112-12 96-07 367,016

Dec. 107-30 108-29 107-27 108-28 37 111-04 96-06 96,216

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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Futures Contracts:


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Future Contracts “Terms”• Futures margin deposit

▫ Deposits to ensure performance under contract terms. Theseare not loans.

• Initial margin

▫ The deposit required to initiate a futures position.

• Maintenance margin

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

• Variation margin

▫ Funds needed to bring one’s account back to the initialmargin amount

• Margin calculations

▫ Based on daily settlement price , the average of the prices fortrades during a closing period set by the exchange.

Set by Feds,may be

increased by brokerage

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Marking-to-market

• Process of adding gains to or subtracting losses fromthe margin account daily, based on the change insettlement prices from one day to the next.

• Trades cannot take place at prices that differ from theprevious day’s settlement price by more than the pricelimit and are said to be limit down (up) when the newequilibrium price is below (above) the minimum

(maximum) price for the day.

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Margin Balance Computation 1:

• On September 1, 2015, A agrees to sell a house to Bnext year at P5 million. They agreed on cashsettlement. On September 2, the market value of thehouse is P4.8 million. On September 3, the market

value of the house is P4.9 million, and on September4, the market value of the house is P5.1 million. Theclearinghouse 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.

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Margin Balance Computation 2:

• Consider a long position of five July wheat contracts,each of which covers 5,000 bushels. Assume that thecontract price is $2.00 and that each contract requires

an initial margin deposit of $150 and a maintenancemargin of $100.

• Compute the margin balance for this position after a 2cent 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.

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Termination of a Futures Contract:

• Offsetting trade (entering into an opposite positionin the same contract). The most common method.

• Cash Settlement (Cash payment at expiration)

• Delivery of the asset specified in the contract (lessthan 1% of all contract terminations)

• An exchange for physicals (asset delivery off theexchange) = an ex-pit transaction; an exception.

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Types of Futures Contracts:• Treasury Bill

▫ Based on a $1 million face value 90 day t-bill & settles in cash. Onetick 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 aspercentages 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 bondthat is delivered. Long pays the futures price at expiration x

conversion factor.JQY


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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?

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Types of Futures Contracts:• Stock Index

▫ Do not allow for actual delivery.

▫ Have a multiplier that is multiplied by the index to calculate thecontract 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 is100

▫ Example: Suppose the S&P 500 index is at 1,088. A one monthfutures contract on the index may be quoted at a price of 1,090.Compute for the actual futures price.

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Types of Futures Contracts:• Currency

▫ Delivery of standardized amounts of foreign currency.

▫ Are set in foreign currency, and price is stated in USD/unit.

▫ Example: A euro contract covers 125,000 euros and is quotedin dollars per euro. What is the contract price if futures price

is stated as 0.8555 USD?

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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

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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 rateof 6% based on a 360 day year. The floating-ratepayer 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% 90 days from now

▫ 5.0% 180 days from now ▫ 5.5% 270 days from now

▫ 6.0% 360 days from now

Calculate the amount A pays or receives 90, 180, 270, and

360 days from now.JQY


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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 & apayment based on the percentage decline in value.

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Equity Swap Illustration:

• Petunia enters into a 2 year $10 million quarterly swapas the fixed payer and will receive the index return onthe 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.

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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 toforeign land. This is especially applicable for companies that wants to have operations ina foreign land.

• Assume that 1 USD = 2 AUD. Each party goes to his own bank. BB borrows 1m USD at9% (interest of USD90k), and AA borrows 2m AUD at 7% (interest of AUD140k)

• 3 Important Dates:

▫ Swap Initiation- notional principal is swapped at initiation

▫ Swap Interest Payments (to each other)

Borrow USD Borrow AUD

BB (US) 9% 8%

AA (AUS) 10% 7%

BB (US) AA (AUS)

Gives 1m USD

Gives 2m AUD

BB (US) AA (AUS)

Pays AUD 160k (2m x 8%)

Pays USD 100k (1m x 10%)

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How to terminate swaps:• Enter into an offsetting swap, sometimes

through swaption (most common)

• Mutual agreement to terminate the swap (likelyinvolves making or receiving compensation)

• Selling the swap to a 3rd party with consent of

the original counterparty (uncommon)

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Structured Notes

• A debt obligation derived from another debt obligation.

• They are securities whose cash flow characteristics dependupon one or more indices or that have embedded forwardsor options, or securities where an investor’s investmentreturns and issuer’s payment obligations are contingent on,

or highly sensitive to, changes in the value of the underlyingassets, indices, interest rates, or cash flows.

• Example: Collateralized Debt Obligation is a type ofstructured 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% + primerate. 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

• Option writer = seller of an option.

• Call Option

▫ Gives the holder of the call option the right, but not theobligation, to buy an asset at a particular price within aspecified period of time.

• Put Option

▫ Gives the holder of the put option the right, but not theobligation, to sell an asset at a particular price within a

specified period of time.

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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 theunderlying stock.

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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’sexpiration date.

▫ These are more valuable than European options.

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Option Terminologies

• Exercise (or strike) price – the price stated in the optioncontract 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 exercisedtoday (Current stock price - Strike price).

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Option Terminologies

• Covered option – an option written against stock held in aninvestor’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 lessthan the current price of the underlying stock.

• Out-of-the-money call – a call option whose exercise priceexceeds the current stock price.

• Long-term Equity AnticiPation Securities (LEAPS) - similar tonormal options, but they are longer-term options withmaturities 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 isindifferent)

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 theseoptions are in or out of the money.

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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. Exerciseprice is agreed to be $10,000. Suppose that the

market price is $11,500. Compute the gain or loss of Aand B.

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

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Option example• A call option (option to buy) with an exercise

price of $25, has the following values at theseprices:

Stock price Call option price$25 $ 3.0030 7.50

35 12.0040 16.5045 21.0050 25.50

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Determining call option exercise valueand option premium or time value

Stockprice (S)

Strikeprice (X)

Exercise orIntrinsic value

of option

Market priceof Option

OptionPremium/Time Value

$25.00 $25.00 $0.00 3.00 3.00

30.00 25.00 5.00 7.50 2.50

35.00 25.00 10.00 12.00 2.00

40.00 25.00 15.00 16.50 1.5045.00 25.00 20.00 21.00 1.00

50.00 25.00 25.00 25.50 0.50

JQY


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Determining put option intrinsic valueand option premium or time value

Stockprice (S)

Strikeprice (X)

Exercise orIntrinsic Value

of option

Marketprice of

Option

OptionPremium/

Time Value$30.00 $25.00 $0.00 3.00 3.00

25.00 25.00 0.00 7.50 7.50

20.00 25.00 5.00 12.00 7.00

15.00 25.00 10.00 16.50 6.50

10.00 25.00 15.00 21.00 6.00

5.00 25.00 20.00 25.50 5.50

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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 leverageprovided by options as the underlying stock priceincreases, and the greater loss potential ofoptions 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 calloptions are 5, 4, and 3, respectively.

JQY


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Call premium diagram

Stock

Price

Option

value

30

25

20

15

10

5

Market

price

Exercise

value

5 10 15 20 25 30 35 40 45 50JQY


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Option price depends on:• Stock Price

• Exercise Price

• Term-to-maturity • Variability of the stock price (Volatility)

• Risk-free rate

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OPM – Riskless Hedge• 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 calloption on that stock, ending up with a risklessposition.

• Given: Stock price today = P40 per share;Exercise price next year = P35 per share; Truemarket price = may either be 30 or 50. Assume

that discount interest is 8%.JQY

Steps:


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Steps:1. Find the range.

2. Equalize range of payoffs for both the stock and option

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

Ending Stock Price xfactor

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

JQY

Steps:


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Steps:3. Create a riskless hedged investment (Ending value of total portfolio

= regardless of whether the stock increases or decreases)

4. 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

Ending StockPrice x factor

Ending Value ofStock 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

JQY


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

in 1973.

JQY

What are the assumptions of the Black-Scholes


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What are the assumptions of the Black-ScholesOption Pricing Model?

• The stock underlying the call option pays no dividendsduring 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 thepurchase price at the short-term risk-free interest rate.

• No penalty for short selling and sellers receive immediatelyfull cash proceeds at today’s price. (Short selling ispermitted)

• Option can only be exercised on its expiration date.(European Options)

• Security trading takes place in continuous time, and stockprices move randomly in continuous time.

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Using the Black-Scholes option pricing model

)][N(dXe-)]P[N(dV

tσ-dd

tσ

]t2 [r ln(P/X) d

2

tr -

1

12

2

RF

1

RF

V = Current value of the call optionP = current price

N(d1) = probability that a deviation less than d1 will occur in a standard normal distribution.N(d1) and N(d2) = represent areas under a standard normal distribution function.X = exercise or strike price of an optione = 2.7183kRF = risk-free interest ratet = time until the option expresLn(P/X) = natural logarithm of P/X

SD^2 = variance of the rate of return on the stock

Put-call parity requires that:Put = V - P + Xe-rT

Then the price of a put optionis:Put = Xe-rT N(-d2) - P N(-d1)

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Use the B-S OPM to find the option value of a call optionwith P = $27, X = $25, rRF = 6%, t = 0.5 years, and σ

2 =

0.11.

0.63270.13270.5000 N(0.3391)) N(d

0.71680.21680.5000 N(0.5736)) N(d textbook in theCAppendixFrom

0.3391.7071)(0.3317)(0-0.5736d

0.5736.7071)(0.3317)(0

(0.5))]2

0.11 [(0.06)ln($27/$25 d

2

1

2

1

JQY


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Solving for the call option value

$4.0036 V

[0.6327]$25e-]$27[0.7168 V

)][N(dXe-)]P[N(d V)(0.06)(0.5-

2t-r

1RF

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

Solving for the put option value

JQY


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How do the factors of the B-S OPMaffect a call option’s value?

As the factor increases …

Current stock price

Exercise priceTime to expiration

Risk-free rate

Stock return volatility

The option value …

Increases

DecreasesIncreases

Increases

Increases

JQY


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How do the factors of the B-S OPMaffect a put option’s value?

As the factor increases …

Current stock price

Exercise priceTime to expiration

Risk-free rate

Stock return volatility

The option value …

Decreases

IncreasesIncreases

Decreases

Increases

JQY


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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 arealready able to manage risks.

JQY


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Criticisms of Derivatives:• Likened to “gambling” because of the high

leverage involved in derivatives payoffs.

• Too risky especially to investors with limitedknowledge of complex instruments.

08 derivatives and risk management

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