Financial Products and MarketsFRM Level 1 Part 3
Source Material ‐ https://www.garp.org/#!/frm
Introduction to Futures and Options Markets
LO30
Futures and Options Markets• The futures market initially provided contracts for on agricultural commodities, but
has since expanded to include financial instruments, other commodities such as raw materials, oil, copper…etc
• Risks that can be mitigated via futures and options include locking in prices but also include
– Improved quality from laws and regulations that inspect storage units and variation in quality– Standardization of payment terms– Ability to off‐set transactions– Liquid, standardized contracts– Reduced counterparty risk from using an exchange
• Key features of futures contracts– Buyers are “long” while sellers are “short” the contract– “Offsetting transactions” can close the futures position– Settlement can be “physical” or in cash– Futures can trade on more than one exchange
• Futures Contract Terms– Underlying instrument (i.e. “spot instrument” or just “underlying”)– Size– Settlement mechanism (physical or cash)– Delivery date– Grade or Quality
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Futures vs Equity SecuritiesCriteria Futures Contracts Equity Securities
Primary Purpose Risk Transfer and Price Discovery
Capital Formation
Shorting Common Less common
Limits on price moves and position sizes Yes No
Limit on number of contracts/shares No Yes
Time horizon Finite Infinite
Margin classification Earnest money Down payment
Electronic vs floor presence Substantial floor presence
More electronic
Regulator CFTC SEC
LO30
Key terms• Volume vs Open Interest
– Volume is the total purchases or sales during a trading session– Open interest is the total number of contracts (not parties) that
remain open at the end of a trading session (i.e. contracts not yet liquidated either by offsetting futures market transaction or delivery)
• Hedgers vs Speculators– Hedgers are generally the “producers” or consumers” of various
products who wish to reduce price risk– Speculators are those who are willing to take the price risk from
hedgers, and are looking for profitable trading opportunities• Arbitrage ensures prices are “fair” and in balance
LO30
Example: Volume and Open InterestLO30
Successful Futures Market
• Available underlying cash market• Transparency• Standardization• Efficient delivery infrastructure• Unique contract specifications
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Skipped• Tailing the hedge means rounding the number of contracts needed to
hedge.
LO31‐35
Interest Rates and Swap Valuation
LO36
Interest Rates• Treasury rates correspond to government borrowing in its own currency. Often considered to be “risk free” although derivative traders generally view these rates as being too low to be considered a useful “risk free” benchmark.
• London Interbank Offered Rate (LIBOR) is the rate at which large international banks fund their activities. Traders often use LIBOR as the short term benchmark for risk free rates even though contain some credit risk because it better reflects their opportunity cost of capital
• “Repo” rate or repurchase agreement rate is the implied rate on a repurchase agreement.
LO36
Compounding• Future value of an investment A that
earns annual rate R compounded m times a year for n years
• As m approaches infinity the formula approaches the that for continuous compounding
• To find the discretely compounded rate that provides the same FV as a continuously compounded rate set rates equal
• and solve for R
LO36
Spot Rates for Bond pricing• Spot rates (i.e. zero rates) are zero‐coupon bond yields and are therefore
the appropriate discount rates for a single future cash flow.– Not typically observed and thus need to be “bootstrapped”– Typically provided as “annualized”.
• Thus, a bond paying coupon (c) over N periods with currently observed spot rates zj has PV (assuming continuous compounding).
• Bootstrapping spot rates requires observing bond prices with a range of maturities (ex. 6m, 1y, 1.5y, …). The 6m bond pays its last coupon with the face‐value so the spot rate is implied by the yield (example below for PV = 102.3, c = 6.125).
Use z1 (6m spot rate) to calculate z2 (1yr spot rate) using bond
maturing in 1yr.
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Forward Rates• Forward rates are interest rates implied by spot rates for a specified future
period (time interval). The 1‐year forward rate, one year from now equals
R0,1 R1,2 R2,3 R3,4
S1
R1,2
S2S3
S4
TT0 T1 T2 T3 T4
S2T2−S1T1 T2−T1
If supplied spot rates are continuously compounded then so will the computed forward rate
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Forward Rate Agreement• An FRA obligates two parties to agree that a certain interest rate will apply
to a principal amount, L, during a specified future time. The T2 cash flow of an FRA that promises the receipt of payment of Rk is:
• The payout of the FRA is at the end of the contract. Thus, to get the PV of the cash flow, multiply by which discounts CF by continuously compounded rate S2 over the period T2.
•
where
LO36
Duration• Duration of a bond is the average time until cash flows on
the bond are received. This is accomplished in two steps:1. Calculate the weight, w, which equals the % of
discounted CF, C, that arrive in each period, t. The formula below assumes discounting is performed using a discrete rate, y.
2. Duration, D, equals the sum of these weights multiplied by the period
• The usefulness of duration is that the approximate change in Bond’s price, P, for a parallel change in the yield curve, ∆ , is
∆∆
LO36
Duration• Duration is only useful in predicting the change in price for small
changes in interest rates (i.e. yield curve). For this reason, larger changes in interest rates should also incorporate convexity
LO36
Convexity• The relationship between bond price and yield is not linear (as assumed
by duration) but convex. For this reason, bond price changes for larger changes in the yield curve should incorporate convexity as follows:
• Notice that convexity always increases the price movement of a bond regardless of the direction of the change in yield curve
∆ ∆ .5 ∆
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Theories of Term Structure
• Expectations Theory suggests that forward rates correspond to expected future spot rates. In reality, theory fails to explain all future spot rate expectations.
• Market Segmentation Theory states that the market is segmented into different maturity sectors and that supply and demand for bonds in each maturity range dictate rates in that maturity range
• Liquidity Preference Theory suggests that most depositors prefer short‐term liquid deposits
LO36
Forward and Future PricesLO37
• Investment Asset – Held for the purpose of investing (ex. stocks & bonds)
• Consumption Asset – Held for the purpose of consumption (ex. oil, natural gas)
• Short‐Sales are orders to sell securities that the seller does not own. To do this the seller:– Simultaneously borrows and sells securities through a broker– Must return securities at the request of the lender or when the short
sale is closed– Must keep a portion of the proceeds of the short sale on deposit with
the broker• Forward vs Future:
– Both are obligations to transact an asset on some future date– Forwards do not trade on an exchange, are not standardized, and do
not normally close our prior to expiration– Futures contracts are marketed to market
Forward and Future Prices – Key TermsLO37
Forward & Futures Prices• Forward price of the underlying, F0, is calculated
from the current price of the underlying, S0, using a continuously compounded rate of return, r. Return, r, is expressed as an annual rate modified by T.
• Cost‐of‐Carry: If the underlying pays a known PV amount, I, subtract from the S0 because the owner of the contract does not yet own the underlying.
• Dividend: If the underlying pays a continuous dividend yield, q, this is subtracted from return, r. Yield, q, is annualized, but modified by T.
• Note that F0 and, S0, are not the contract prices, but rather the prices of the underlying referenced asset
LO37
Valuing a Forward Contract• The present value of a forward contract, V, equals zero at inception. The
value is non‐zero when the obligated delivery price on the referenced asset at inception, K, diverges from the current price, S0. The value on the long side with
• No Cash Flows: V = S0 – Ke‐rT– We no longer discount the current price because we are calculating PV– Instead we discount the obligated delivery price, K
• Single Cash Flow: V = S0 – I – Ke‐rT– The known cash flow, I, is assumed to already equal the present value in this formula– The cash flow is paid to the owner of the referenced asset which the long doesn’t own
• Dividend Yield: V = S0e‐qT – Ke‐rt– The dividend yield, paid over T, reduces the present value of the forward contract
Currency Futures• Interest Rate Parity states that the forward exchange rate, F (measured in
domestic per unit of foreign currency), must be related to the spot exchange rate, S, and to the interest rate differential between domestic and the foreign country, r – rf
• This equation is similar to that used to value forwards and futures. The difference is that now F and S are exchange rates instead of prices.
Contango and Backwardation• Contango refers to a situation where futures prices are
above spot prices. This is more typical because of the time value of money
• Backwardation refers to the opposite situation which only occurs if there is a significant benefit to holding the asset.
Delivery Options in the Futures Market
• Some futures contracts grant delivery options to the short which can provide significant value
• Some Treasury bond contracts give the short a choice of several bonds that are acceptable to deliver and options as to when to deliver during the expiration month
• Physical assets may offer a choice of delivery locations to the short
Interest Rate Futures• Accrued Interest is the amount the buyer of a bond must pay the owner for any
interest from coupon, c, earned through the settlement date.
• Day Count Conventions: The number of days used in the above formula depend on three conventions in the US:1. Treasury Bonds: Actual/Actual2. US Corporate and Municipal Bonds: 30/3603. Treasury Bills and other money market instruments (<1‐year maturity): Actual/360
• Clean and Dirty Prices:– Full Price (i.e. dirty price) is the actual price that the seller of the bond should be paid– Flat Price (i.e. clean price) is the full price minus accrued interest
LO38
Treasury Bond Futures
• Some Treasury bond contracts give the short a choice of several bonds that are acceptable to deliver and options as to when to deliver during the expiration month
• Conversion Factors (CF) are used to calculate the price received by the short position of a T‐Bond futures contract
• Price received by short = Ps = (QFP x CF) + AI– QFP = Quoted futures price (i.e. recent settlement price)– Conversion Factor = (PV of bond – accrued interest) / Face Value– AI = Accrued Interest
• Cost to purchase bond = PF = quoted bond price + AI = “Full (i.e. Dirty) Price”• The Cheapest to Deliver (CTD) Bond is that which minimizes the cost (to the short) of
delivering the bond.• CTD = Min(Cost of delivery) = Min(PF ‐ Ps) = Min(quoted bond price ‐ (QFP x CF))
• The CF system allows for the value of a bond to diverge from the cash transacted• Ex: Which Bond is CTD?
Settlement Price = $95
Both terms contain AI which drops
Value of bond ignoring AI
Cash received ignoring AI
LO38
Bond QFP CF
A 100 1.02
B 112 1.15
Eurodollar Futures Contract
• The 3‐month EFC is the most popular interest rate futures in the US and traded on CME. Based on USD deposits outside US (less regulated) reflecting anticipated LIBOR rates. (Nothing to do with Euro currency)
• Settles in cash and the minimum price change is 1 “tick” (i.e. 1 bp) or $25 per $1Million contract. For a quoted price, Z, the contract price =
• Ex: On Sept 1, the Dec EFC price = $96, implying an interest rate of 4.0%, and that at the expiry in Dec the final closing price is $95, reflecting a higher interest rate of 5.0%. If the company had sold 8 December Eurodollar contracts at $96.00 in September, it would have profited by 100 basis points (100 x $25 = $2,500) on 8 contracts, equaling $20,000 ($2,500 x 8) when it covered the short position.
• Long dated EFC typically have implied rates higher than actual. This difference can be reduce by using convexity adjustment.
LO38
Duration Based Hedging
• The 3‐month EFC is the most popular interest rate futures contract in the US and traded on CME. Based on USD deposits outside US reflecting anticipated LIBOR rates. (Nothing to do with Euro currency)
• Example: Find the number of hedging contracts needed to hedge a portfolio, P, of $1Million with duration, DP, of 8. To do this, use futures contracts with size $100,000 quoted at $103 (F=$103,000), with duration DF of 12:
LO38
Plain Vanilla SwapLO39
Plain Vanilla Swap ‐ ExampleLO39
Currency SwapLO39
Currency SwapLO39
Other Swaps
• Equity Swap: The return on a stock, a portfolio, or a stock index is paid each period by one party in return for a fixed‐rate or floating‐rate payment
• Swaption: An option which gives the holder the risk to enter into an interest rate swap
• Commodity Swap: Pay a fixed rate for the multi‐period delivery of a commodity and receive a corresponding floating rate based on the average commodity spot rates at the time of delivery.
• Volatility Swap: Exchange of volatility based on a notional principal with one side paying a pre‐specified volatility.
LO39
Mechanics of Option Markets
• Skipped
Factors that Affect Option PricesLO41
Put‐Call ParityLO41
Nondividend Paying StockLO41
Trading Strategies Involving OptionsLO42
• Long Straddle• Strangle• Protective Put• Bull Call• Bear Call• Butterfly Spread• Strip & Strap• Covered Call• Collar• Calendar and Diagonal Spreads• Box Spread
Trading Strategies Involving OptionsLO42
Call Options Put Options
Trading Strategies Involving OptionsLO42
Trading Strategies Involving OptionsLO42
Bull Call Spread
Bear Put Spread
Trading Strategies Involving OptionsLO42
Trading Strategies Involving OptionsLO42
Butterfly Spread
Trading Strategies Involving OptionsLO42
Long Straddle
Trading Strategies Involving OptionsLO42
Trading Strategies Involving OptionsLO42
Collar
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