1192001 Lecture Money and Bond Markets Copyright K

11/9/2001 Lecture Money and Bond Markets Copyright K. Cuthbertson and D. Nitzsche 1

TOPICS INSTRUMENTS WHO PLAYS IN THE MONEY MARKETS YIELD OR ‘ADD ON’ INSTRUMENTS (LOANS , CDs) DISCOUNT INSTRUMENTS (T-BILLS, COMMERCIAL BILLS) Copyright K. Cuthbertson and D. Nitzsche 2

Instruments and Who Plays in the Money Markets Copyright K. Cuthbertson and D. Nitzsche 4

Money Market Instruments For Short -term Borrowing and Lending Discount Instruments T- Bills ~ e. g. Buy T-bill = lend to the government) Commercial Bills ~ lend to companies (for financing inventories) Bankers’ Acceptances - bank lends to company, based on its future sales receipts Yield Instruments Bank deposits, interbank borrowing (LIBOR / LIBID) Certificates of Deposit (CDs), Euro-currencies. Copyright K. Cuthbertson and D. Nitzsche 5

Who Plays in the Money Markets ? Interbank loans Bank charges LIBOR to another bank (or quality corporate customer) who borrows from it. Banks pays LIBID for deposits placed with it. LIBOR > LIBID LIBOR is cost of funds to the bank for “on-lending” Also PIBOR, NYBOR, SIBOR, EURIBOR Key reference rate (eg. for Swaps, FRN’s, FRA’s) Copyright K. Cuthbertson and D. Nitzsche 6

Who plays in the Money Markets ? u u u u FOREX Speculators Will place “hot money” in money market assets Corporate Treasurers Raise large amounts of “cash” in the commercial paper market in US Surplus funds invested in money market assets Central Banks To implement monetary policy via “open market operations” using repos Copyright K. Cuthbertson and D. Nitzsche 7

Yield or ‘Add on’ Instruments and Discount Instruments Copyright K. Cuthbertson and D. Nitzsche 8

Conventions in the Money Market u Assets are quoted on a discount or yield basis. u Simple annual rates are quoted u The day count convention for “grossing up” to annual rates differs between markets and types of asset. (UK : “actual / 365 “ , US “actual/ 360” ) u What is ultimately important is “what you paid”, “what you got at the end” and the intervening time period. Then you can work out your “Return” in a manner that is “reasonable” (eg. Using simple or compound “interest” ). Copyright K. Cuthbertson and D. Nitzsche 9

YIELD (“ADD-ON”) INSTRUMENTS: Example : Certificate of deposit (CD) u u u (CD or Inter-bank Deposit) quoted yield = y =12. 5% p. a. CD Pays m-days maturity of m-days £ 100 deposited £ 100 [ 1 + (m / 365 ) ( y/100) ] after 100[1+(m /365) (y/100) ] 100 0 m/365 Copyright K. Cuthbertson and D. Nitzsche 1 Time in years 10

DISCOUNT INSTRUMENTS Example: 1 -YR T-BILL u u u 1 -yr T-Bill with Par (face or maturity) value FV = 100 Trading at a quoted discount rate d=10%, has a current market price of P: FV= 100 D = FV (d / 100) =£ 10 P D = (sterling or dollar)discount 0 P = FV - D = 100 - 10 =£ 90 1 Copyright K. Cuthbertson and D. Nitzsche Time 11

Discount Instrument: Price of US T-Bill FV = $1000, 90 days to maturity, 1 -year = 360 days quoted discount rate d = 8% p. a. , FV=$1000 What is the market price and the yield ? u u Dollar discount D : D = $1000 (8/100) (90/360) = $20 = FV [ (d / 100) ( m / a) ] Invoice price, P. P = FV-D = $980 Yield y = [(1000 - 980) /980 ] x 360/90 x 100% = 8. 163% Copyright K. Cuthbertson and D. Nitzsche 12

“Yield” on a Discount Instrument u Quoted discount rate is not a correct measure of the “return” (even if held to maturity) u u Correct measure is the “yield (to maturity)” and is defined with respect to the purchase price. . Note if you sell prior to maturity you do not earn the yield to maturity- and the (holding period) return is risky u Quoted yield is: y= Copyright K. Cuthbertson and D. Nitzsche 13

Summary : Money Markets u Short term borrowing and lending - used by Banks, FX-traders, Corporate Treasurer’s and C. Banks u Quote conventions differ between markets and instruments - LIBOR is a key reference rate u T-Bill, CD’s and Commercial Paper (in US) are highly liquid markets up to 3 -6 months Copyright K. Cuthbertson and D. Nitzsche 14

BOND MARKETS Copyright K. Cuthbertson and D. Nitzsche 15

TOPICS: Bonds TREASURIES (T-Bonds/notes) u u Zero Coupon Bond -Spot rate Coupon Bonds - Yield to Maturity - pricing using spot yields CORPORATE BONDS Bonds and Duration SELF STUDY u Holding Period Return u Organisation of the UK Gilts Market u Accrued Interest Plain Vanilla/Straight Foreign = Yankee/Samurai/Bulldog/ Matadors Convertible and Callable Eurobonds Copyright K. Cuthbertson and D. Nitzsche 16

READING: BOND MARKETS Investments: Spot and Derivative Markets K. Cuthbertson and D. Nitzsche Chapter 7 Section 7. 1: Prices, Yields and Return Section 7. 3: Corporate Bonds Chapter 9 Section 9. 1: Duration and Convexity Copyright K. Cuthbertson and D. Nitzsche 17

Zero Coupon Bonds: Spot rates Coupon Bonds: Yield to Maturity Pricing using spot yields Copyright K. Cuthbertson and D. Nitzsche 18

Zero Coupon / Pure Discount Bond M=100 Discount P n 0 years • A ‘zero’ offers a single (or ‘spot’) payment of $M in the future • n = time to maturity of bond • M =100 = redemption /par/ maturity value of the bond • What is the fair price P for this ‘zero’ Copyright K. Cuthbertson and D. Nitzsche 19

ZERO’s u u u Suppose the current quoted market yield on ‘nyear money’ is r =10% (at a compound rate) r is known as a ‘spot rate’ of interest Then the ‘fair price’ for the zero is: u P = M / (1+r) n e. g. u P = 100 / (1. 1)2 = 82. 64 Note that if you know P =82. 64 then you can (if you wish) calculate r = 10% using: (1+r ) = ( M / P ) 1/n Copyright K. Cuthbertson and D. Nitzsche 20

Plain Vanilla: Coupon Paying Bond 100 P C C 1 2 3 0 • n = time to maturity of bond n • 100 = redemption/principal/par value • P = market price C = $ coupon on bond Copyright K. Cuthbertson and D. Nitzsche 21

If you know the price, what is the YTM on a Bond ? u P= u We require a single(%) figure to ‘represent’ the “return”, if bond is held to maturity y is the IRR of the bond and is known as YTM. u u Given P, C, M and n the FT calculates the YTM. (M=£ 100 in UK and M=$1000 in US) u Note: P and y are inversely related u YTM is ‘made up’ of coupons+interest on coupons + capital gain to maturity. Copyright K. Cuthbertson and D. Nitzsche 22

If you know the price, what is the YTM on a Bond ? u P= u In F. T. y = “Gross Redemption yield” “Flat”, “interest” or “coupon” yield= C/P u In FT “Treasury 10% ‘ 04” u Also called “Exchequer” , “Consols” Yield Int Red 8. 97 5. 90 Copyright K. Cuthbertson and D. Nitzsche Price 113. 79 23

Price and YTM are inversely related (“convex”) Price B 106 A 100 C 98 8 9 10 Copyright K. Cuthbertson and D. Nitzsche Yield 24

PRICE - YIELD: Simplified Equation • Use Annuity formula (you do not have to memorise this !) - useful in Excel: • P = ANNUITY + 100 / (1+y)n • where “ANNUITY” = ( C / y ) [ 1 - 1 / (1+y) n ] • For “Perpetuity” / “Consol” / “Undated stocks” then P=C/y Copyright K. Cuthbertson and D. Nitzsche 25

Pricing of Coupon Bonds using Spot Rates Copyright K. Cuthbertson and D. Nitzsche 26

Pricing Using Spot Rates Above we calculated the YTM, from the observed market price P. But how do we calculate this ‘fair’ (no arbitrage) price P for the bond ? The correct method of pricing a bond is to discount using spot yields, r 1, r 2 etc. This is because the coupons can be “stripped” and sold separately, which could lead to riskless arbitrage profits, unless is P is determined as: Copyright K. Cuthbertson and D. Nitzsche 27

Pricing Using Spot Rates Suppose interbank rates for 1 -year and 2 -year deposits (ie. Spot yields) are r 1 = 5% r 2 = 6%. Suppose there is a 2 -year, 10% coupon bond in the market (par = 100). What is the “fair price of this bond ? C 1 = $10 C 2 + M = $110 Copyright K. Cuthbertson and D. Nitzsche 28

PRICING and STRIPS 1 st coupon sells for 2 nd year cash sells for If market price of the COUPON PAYING BOND P( 2 -yr bond) = 106, then you could buy it for 106 and immediately sell off the coupons today, separately for 9. 52+97. 9 = 107. 42. This is a risk free arbitrage opportunity, giving a profit of 1. 42. So the 2 -yr coupon bond must sell for P = 107. 42 ( = “correct”, “fair”, no-arbitrage price) Copyright K. Cuthbertson and D. Nitzsche 29

PRICES AND YIELD: LOGICAL SEQUENCE u Knowing all the spot rates r, (from the yield curve) you can calculate the “correct ( or ‘fair’ or “no arbitrage”) price of the bond P. u Knowing P, the F. T. then calculates the YTM using our previous IRR formula for y. Copyright K. Cuthbertson and D. Nitzsche 30

Corporate Bonds Copyright K. Cuthbertson and D. Nitzsche 31

Corporate Bonds 1) Floating Rate Notes, FRN Future Coupons payable vary with LIBOR and are therefore uncertain 2)Convertibles Can be converted by the holder (if she wishes) for a known number of shares/equity at specific times in the future Known as “equity kickers” - useful way of raising finance for ‘new’ firms. Yield is lower than on ‘plain vanilla’ Copyright K. Cuthbertson and D. Nitzsche 32

Corporate Bonds 3) Callable Can be redeemed (bought back) by the issuer at par value, after a certain date in future (e. g. after 5 years, on a 10 year bond) - if interest rates (yields) fall in the future then P > par value and the bond will be called and company may re-issue bonds at the new lower rates Callable bonds have higher yields (when issued) than straights. Copyright K. Cuthbertson and D. Nitzsche 33

Corporate Bonds 4) Foreign Bonds Yankee/Samurai/Bulldog/Matador e. g. Yankee bond - Sony issues USD denominated bond in N. York - via a placement and subject to US listing requirements (and it will probably be listed on NYSE to trade in secondary market, as well as an OTC secondary market between banks and securities houses) Copyright K. Cuthbertson and D. Nitzsche 34

Corporate Bonds 5) Eurobonds Issued in ‘ 3 rd country’, usually by private placement (via banks) e. g. Sony issues USD bonds in London - lax regulation, , bearer bonds, tax paid gross - much innovation: floaters, convertibles warrants attached (and detachable) for option to purchase equity, more bonds, commodities (copper, oil) in the future, at a known price fixed today. - issued by corporations, governments and international orgs (W. Bank) Copyright K. Cuthbertson and D. Nitzsche 35

‘Simple’ Pricing of (Plain Vanilla)Corporate Bonds Same as pricing Treasuries except (fixed) coupon payments are discounted using the (spot) yields on corporate bonds of a particular credit rating (eg. BBB) Yield on BBB-rated bond: y = r + credit/default spread for BBB(eg. 250 bp) The credit spread reflects the fact that bonds are more likely to default in recessions than in booms (- this ‘market risk’ cannot be diversified away - see later lectures on CAPM and asset ‘betas’. Copyright K. Cuthbertson and D. Nitzsche 36

DEFAULT SPREADS ON BONDS 7. 0 7. 3 7. 7 8. 0 12+ 6. 5 T-Bond. Increasing Risk AAA AA A BBB Junk Bonds (“Crap. Corp”? ) e. g. In 1996 Russia made its first Eurobond issue since 1917, of $1 bn - at 345 bp over US Treasuries ~ Junk Bonds (ie. below investment grade of BBB) Copyright K. Cuthbertson and D. Nitzsche 37

‘Simple’ Pricing of (Plain Vanilla)Corporate Bonds We could also replace the promised coupons with the expected coupons E(Coupon) = (1 -p) C + p ( z x C) p= prob of default (can be extracted from observed credit spreads or from mortality rates of sample of BBB rated corporate bonds eg. For BBB prob. default after 1, 5, and 10 years is 3%, 1. 6% and 2. 8% Copyright K. Cuthbertson and D. Nitzsche 38

‘Value of Debt and Equity of the Firm The value of marketable debt: V(debt) = NB x PBBB We can then calculate the equity value of the firm as V(equity) = ‘Enterprise DCF - V(debt) Copyright K. Cuthbertson and D. Nitzsche 39

Bonds and Duration Copyright K. Cuthbertson and D. Nitzsche 40

Bonds and Duration measures the ‘riskiness’ of a bond or more accurately the bond’s price response to a 1% change in the yield (to maturity) Crudely: High duration (e. g. D =10) implies ‘high risk’ If yield falls by 1% (in a week) then bond price will rise by 10% (over the week) The larger is “duration” the larger is the price response (‘up’ or ‘down’) after a change in yield. Copyright K. Cuthbertson and D. Nitzsche 41

Bonds and Duration D = 10 “summarises” the relationship between the (absolute) change in the yield and the percentage change in the price of the bond. Speculation and Duration: If you expect yields to fall then switch into “high duration” bonds High duration bonds (I. e. large D) are bonds with : a) “long maturities” or, b) “low” coupon rates (payments) Copyright K. Cuthbertson and D. Nitzsche 42

DURATION ( D = 5 say) Measures (approximate) price response to change in yield ‘Percentage change in price’ yield) = - D x (absolute change in e. g If D=5 then 1% fall in y from say 5% to 4% over the next day, will lead to a rise in the price of the bond by 5% (in a day) If y is given as a percentage e. g. 5%, then Correct expression, here y is a decimal e. g. 0. 05 Copyright K. Cuthbertson and D. Nitzsche 43

‘Convexity’ is ‘Good’ ‘Negative Convexity’ is ‘bad’ ‘greater convexity’ = more curvature Price actual price rise Z-B, exceeds that given by duration, Z-A B actual price fall is less than that given by duration A Z 8 9 D C 10 Copyright K. Cuthbertson and D. Nitzsche Yield 44

Calculate DURATION ( D) Duration of 5 -year bond = 4. 2 years u u Messy, not intuitive ! - do in EXCEL D = [1. PV(C 1) + 2. PV(C 2)+. . . + n PV(Cn+M)] / P where PV(Ci ) = Ci / (1+y) i Limitations of Duration It provides an approximation to the price change Strictly it is only valid for parallel shifts in Yield Curve Duration falls as the bond approaches maturity, so you need to “rebalance” your bond portfolio if you want to maintain a given duration. Copyright K. Cuthbertson and D. Nitzsche 45

Uses of Portfolio Duration Portfolio duration Dp Dp = wi D i where wi = proportions held in each bond-i 1) speculation: If you expect interest rates (yields) to fall tomorrow then sell your “low duration” bonds and use the funds to move into “high duration” bonds. Hence you increase the overall duration of your portfolio of bonds. Copyright K. Cuthbertson and D. Nitzsche 46

Uses of Portfolio Duration 2) Hedging (“Immunisation”) Pension fund has payment of $10 m in 5 years time (with PV of 9 m). To be certain of meeting this $10 m payment, even if interest rates rise or fall over the next five years, the pension fund should: Buy $9 m bonds in such combinations that (portfolio) duration Dp = 5. This is a statement not an “explanation” ! This allows the pension fund to earn coupon payments while hedging its future pension payment at t+5 and hence being able to meet this payout of $10 m at t+5 Copyright K. Cuthbertson and D. Nitzsche 47

LECTURE ENDS HERE SELF STUDY SLIDES FOLLOW Copyright K. Cuthbertson and D. Nitzsche 48

INSTITUTIONAL DETAILS Copyright K. Cuthbertson and D. Nitzsche 49

Copyright K. Cuthbertson and D. Nitzsche 50

UK Gilts : Price Quotes and “Liquidity” Price quotes are good for up to £ 10 m u Spreads on price quotes are about 1/32% (= 0. 0312 of 1%) for shorts (< 5 yrs maturity) and up to 1/8% (=0. 125 of 1%)for longer maturities u Prices are now quoted in decimals (eg. £ 102. 17) u Gilts can now be used as collateral in repos u New issues : mainly via auction Copyright K. Cuthbertson and D. Nitzsche 51

DEFAULT RISK ON CORPORATE BONDS u Reflected in quoted yields on bonds (e. g. lower credit rating implies higher yield) u US corporate bonds rated by agencies (Moody’s, Standard and Poor’s) according to financial strength of company (over the complete economic cycle) u Sovereign debt is also rated (eg. Mexico, Russia) and so are Municipal bonds. Copyright K. Cuthbertson and D. Nitzsche 52

Clean Price and Dirty Price “Clean price” (as in the FT/WSJ) excludes accrued interest AI or rebate interest RI. In F. T. “xd”= ‘ex-dividend, implies purchaser will not receive next coupon payment P = clean price = f ( all future C’s) - ie clean price ‘includes’ all future coupons Copyright K. Cuthbertson and D. Nitzsche 53

Clean Price and Dirty Price A B C 0 P 182 Z C 1 C 2 Cum Div: Implies that at B the purchaser will receive C 1, Hence the seller must be compensated for the loss of AI over the period A-B , hence Dirty (invoice) price = Pclean + AI where AI = (C 1 /2)x( no. of days A-B /182) “xd”: Purchaser will not receive next coupon payment C 1, Hence buyer must be compensated for this, since clean price P=f(C 1, C 2 , . . ) “includes” the next coupon payment. Hence: Dirty(invoice) Price = Pclean - Rebate Interest where RI = (C/2) x (no. of days B-Z/182) Copyright K. Cuthbertson and D. Nitzsche 54

Self-Assessment: Price -YTM Relationship Given the coupon and market price, can you explain the qualitative “pattern’ of the YTM’s in the final column? (Note: Par = M = 100 ) Copyright K. Cuthbertson and D. Nitzsche 55

Holding Period Return (Yield) • Note that if you intend to sell the bond before maturity (eg after 3 years) • then the “expected return” on the bond is known as • the “holding period yield” HPY where: HPY= C P 0 C C C interest on interest P 4 Copyright K. Cuthbertson and D. Nitzsche 56

SLIDES END HERE Copyright K. Cuthbertson and D. Nitzsche 57