frm - level 1 part 3 - financial markets and products

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

LO30

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

LO30

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.

LO36

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

LO36

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 ∆

LO36

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

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


Call Options Put Options


Bull Call Spread

Bear Put Spread


Butterfly Spread


Long Straddle


Collar

Skipped 43 ‐ 48

frm - level 1 part 3 - financial markets and products

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