Fall-01 FIBI Zvi Wiener Fixed Income Instruments 3

Zvi WienerFIFIBI - 3 slide 2 Government-Sponsored Enterprises Fannie Mae “benchmark” and Freddie Mac “reference” notes and bond. Can be electronically transferred through clearing houses as Euroclear and Cedel and NBES. Outstanding amount $150B with 2-30 years to maturity.

Zvi WienerFIFIBI - 3 slide 3 Government-Sponsored Enterprises GNMA - Government National Mortgage Association FHLBS - Federal Home Loan Bank System Sallie Mar - Student Loan Marketing Association

Zvi WienerFIFIBI - 3 slide 4 Corporate Debt Instruments corporate bonds medium-term notes CP = commercial papers ABS = asset backed securities They have priority over common stocks in the case of bankruptcy.

Zvi WienerFIFIBI - 3 slide 5 Corporate Bonds Main types of issuers utilities transportation industrial banks and financial companies

Zvi WienerFIFIBI - 3 slide 6 Bond Indentures trustee term bonds, serial bonds collateral debenture bond - not secured guaranteed bonds

Zvi WienerFIFIBI - 3 slide 7 Bond Provisions Call and refund provisions - the issuer has the right to redeem the entire amount before maturity. Sometimes there is a premium to be paid in such a case (redemption schedule). Special redemption prices for debt redeemed through the sinking fund Refunding means replacing by another debt.

Zvi WienerFIFIBI - 3 slide 8 Bond Provisions Sinking fund provision sometimes the issuer is required to retire a portion of an issue each year. – either by cash payment to bondholders (lottery) – or by buyback bonds

Zvi WienerFIFIBI - 3 slide 9 Bond Rating Duff and Phelps Credit Rating Co. Fitch Investors Service Moody’s Investors Service Standard & Poor’s Corporation

Zvi WienerFIFIBI - 3 slide 10 Rating Moody’sS&PFitchD&P AaaAAAAAAAAA Aa1AA+AA+AA+ Aa2AAAAAA Aa3AA-AA-AA- A1A+A+A+ A2AAA A3A-A-A-

Zvi WienerFIFIBI - 3 slide 11 Rating BBB- or better = investment grade BB+ and below - speculative grade D to DDD default transition matrix

Zvi WienerFIFIBI - 3 slide 12 One year transition matrix AaaAaABaaBaBC&D Aaa Aa A Baa

Zvi WienerFIFIBI - 3 slide 13 High Yield Bonds LBO, downgrading, refinancing fallen angels deferred interest bonds Step-up bonds pay initially low interest which increases with time

Zvi WienerFIFIBI - 3 slide 14 SEC rule 144A Allows to trade private placements among qualified institutions.

Zvi WienerFIFIBI - 3 slide 15 Medium Term Notes (MTN) Notes are registered with the SEC under Rule 415 (the shelf registration) and are offered continuously to investors by an agent of the issuer. Maturities vary from 9 months to 30 years. Can be either fixed or floating. Very flexible way to raise debt!

Zvi WienerFIFIBI - 3 slide 16 Primary Market (MTN) Issuer posts spreads over Treasuries for a variety of maturities. Then an agent tries to find an investor. Minimal size is between $1M and $25M. The schedule can be changed at any time! Often structured MTNs are used (caps, floors, etc.) = structured notes.

Zvi WienerFIFIBI - 3 slide 17 Structured Notes Many institutional investors can use swaps and structured notes to participate in markets that were prohibited. Another use of structured notes is in risk management. Financial Engineering is used to create securities satisfying the needs of investors.

Zvi WienerFIFIBI - 3 slide 18 Commercial Papers Short term unsecured promissory note An alternative to short term bank borrowing A typical round-lot transaction is $100,000 In the USA maturity is up to 270 days Requires less paperwork Those with maturity up to 90 days can be used as collateral for FED discount window.

Zvi WienerFIFIBI - 3 slide 19 Commercial Papers Typically rolled over Rollover risk is backed by an unused bank credit line In order to issue CP one need either a high rating or good collateral Sometimes credit enhancement is used (LOC) CP issued in the USA by foreigners are called Yankee CP

Zvi WienerFIFIBI - 3 slide 20 Commercial Papers Between 71 an 89 there was one default on CP. 3 defaults occurred in 89 and 4 in 90 Direct paper is sold without an agent Secondary market is thin There is a special rating for CP, P-1,3, A-1,3 discount instruments, used by money market

Zvi WienerFIFIBI - 3 slide 21 Bankruptcy and Credit Rights liquidation - all assets will be distributed reorganization - a new corporate entity will result a company that files for protection becomes a debtor in possession and continues to operate under the supervision of the court

Zvi WienerFIFIBI - 3 slide 22 Bankruptcy and Credit Rights Absolute priority rule - senior creditors are paid in full before junior creditors are paid anything. Works in liquidation but often does not work in reorganization.

Zvi WienerFIFIBI - 3 slide 23 Municipal Securities Exemption of interest income from federal taxation. Issued by states, counties, special districts, cities, towns, school districts.

Zvi WienerFIFIBI - 3 slide 24 Municipal Securities Exemption of interest income from federal taxation. General obligation bonds - backed by tax power Limited tax general obligation bonds Revenue bonds - based on specific projects

Zvi WienerFIFIBI - 3 slide 25 Municipal Securities Airport Revenue Bonds College and University Revenue Bonds Hospital Revenue Bonds Industrial Revenue Bonds Single-Family Revenue Bonds (mortgages) Multifamily Revenue Bonds (housing projects) Water Revenue Bonds

Zvi WienerFIFIBI - 3 slide 26 Hybrid and Special Bond Securities Insured bonds - typically by an insurance firm Bank-backed municipal bonds (letter of credit) Refunded Bonds - a portfolio of safe securities is placed in trust and they will cover the payments. Troubled city bailout bonds

Zvi WienerFIFIBI - 3 slide 27 Municipal Money Market Products TAN = tax anticipation notes RAN = revenue anticipation notes GAN = grant anticipation notes BAN = bond anticipation notes Tax exempt commercial paper

Zvi WienerFIFIBI - 3 slide 28 Municipal Derivatives floaters = floating rate + spread inverse floaters = interest - floating rate strips partial strip = are zeros till a call date and then become coupon type

Zvi WienerFIFIBI - 3 slide 29 Yield on Municipal Bonds tax-exempt yield equivalent taxable yield = 1-marginal tax rate for example bond offers 6.5% and marginal tax rate 40%: =

Zvi WienerFIFIBI - 3 slide 30 Non-US Bonds national bond markets – domestic market – Foreign market  Yankee USA  Samurai Japan  bulldog UK  Rembrandt Holland  matador Spain

Zvi WienerFIFIBI - 3 slide 31 International bond market Eurobond and Euroyen markets Global bond - simultaneous offering Typically registered in Luxembourg, London or Zurich, but traded OTC. Supranationals - IBRD, World Bank, etc.

Zvi WienerFIFIBI - 3 slide 32 Eurobond market Dual currency bonds (coupon in one currency, principal in another). Option currency bond one side can choose the currency. Convertible bonds with warrants - can be converted into another asset. Equity, debt, gold or currency warrant.

Zvi WienerFIFIBI - 3 slide 33 Eurobond market Floating Rate Notes = FRN based on LIBOR or LIBID many are collared some are perpetual

Zvi WienerFIFIBI - 3 slide 34 Comparing Yields bond equivalent yield of Eurodollar bond =2[(1+yield to maturity) ] for example: A Eurodollar bond with 10% yield has the bond equivalent yield of 2[ ] = 9.762%

Zvi WienerFIFIBI - 3 slide 35 Japanese Government Bonds JGB short term Treasury bills medium term bonds long term bonds super long term bonds (20 years)

Zvi WienerFIFIBI - 3 slide 36 German Government Bonds U-Schatze discount paper up to 2 years Kassens = federal government notes (2-6 y.) OBLEs = 5 year federal government notes Bunds = federal government bonds (6-30 y.) all coupon payments are annual

Zvi WienerFIFIBI - 3 slide 37 UK Government Bonds Gilts straights = bullet bonds (some callable) convertibles (option to holder to convert to longer gilts) index linked low coupon 2-2.5% irredeemable (perpetual)

Zvi WienerFIFIBI - 3 slide 38 Brady Bonds Argentina, Brazil, Costa Rica, Dominican Republic, Ecuador, Mexico, Uruguay, Venezuela, Bulgaria, Jordan, Nigeria, Philippines, Poland. Partially collateralized by US government securities

Zvi WienerFIFIBI - 3 slide 39 Internet sites

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Fall-01 FIBI Hedging Linear Risk Following Jorion 2001, Chapter 14 Financial Risk Manager Handbook

Zvi WienerFIFIBI - 3 slide 44 Hedging Taking positions that lower the risk profile of the portfolio. Static hedging Dynamic hedging

Zvi WienerFIFIBI - 3 slide 45 Unit Hedging with Currencies A US exporter will receive Y125M in 7 months. The perfect hedge is to enter a 7-months forward contract. Such a contract is OTC and illiquid. Instead one can use traded futures. CME lists yen contract with face value Y12.5M and 9 months to maturity. Sell 10 contracts and revert in 7 months.

Zvi WienerFIFIBI - 3 slide 46 Market data07mP&L time to maturity92 US interest rate6%6% Yen interest rate5%2% Spot Y/$ Futures Y/$

Zvi WienerFIFIBI - 3 slide 47 Stacked hedge - to use a longer horizon and to revert the position at maturity. Strip hedge - rolling over short hedge.

Zvi WienerFIFIBI - 3 slide 48 Basis Risk Basis risk arises when the characteristics of the futures contract differ from those of the underlying. For example quality of agricultural product, types of oil, Cheapest to Deliver bond, etc. Basis = Spot - Future

Zvi WienerFIFIBI - 3 slide 49 Cross hedging Hedging with a correlated (but different) asset. In order to hedge an exposure to Norwegian Krone one can use Euro futures. Hedging a portfolio of stocks with index future.

Zvi WienerFIFIBI - 3 slide 50 FRM-00, Question 78 What feature of cash and futures prices tend to make hedging possible? A. They always move together in the same direction and by the same amount. B. They move in opposite direction by the same amount. C. They tend to move together generally in the same direction and by the same amount. D. They move in the same direction by different amount.

Zvi WienerFIFIBI - 3 slide 51 FRM-00, Question 78 What feature of cash and futures prices tend to make hedging possible? A. They always move together in the same direction and by the same amount. B. They move in opposite direction by the same amount. C. They tend to move together generally in the same direction and by the same amount. D. They move in the same direction by different amount.

Zvi WienerFIFIBI - 3 slide 52 FRM-00, Question 79 Under which scenario is basis risk likely to exist? A. A hedge (which was initially matched to the maturity of the underlying) is lifted before expiration. B. The correlation of the underlying and the hedge vehicle is less than one and their volatilities are unequal. C. The underlying instrument and the hedge vehicle are dissimilar. D. All of the above.

Zvi WienerFIFIBI - 3 slide 53 FRM-00, Question 79 Under which scenario is basis risk likely to exist? A. A hedge (which was initially matched to the maturity of the underlying) is lifted before expiration. B. The correlation of the underlying and the hedge vehicle is less than one and their volatilities are unequal. C. The underlying instrument and the hedge vehicle are dissimilar. D. All of the above.

Zvi WienerFIFIBI - 3 slide 54 The Optimal Hedge Ratio  S - change in $ value of the inventory  F - change in $ value of the one futures N - number of futures you buy/sell

Zvi WienerFIFIBI - 3 slide 55 The Optimal Hedge Ratio Minimum variance hedge ratio

Zvi WienerFIFIBI - 3 slide 56 Hedge Ratio as Regression Coefficient The optimal amount can also be derived as the slope coefficient of a regression  s/s on  f/f:

Zvi WienerFIFIBI - 3 slide 57 Optimal Hedge One can measure the quality of the optimal hedge ratio in terms of the amount by which we have decreased the variance of the original portfolio. If R is low the hedge is not effective!

Zvi WienerFIFIBI - 3 slide 58 Optimal Hedge At the optimum the variance is

Zvi WienerFIFIBI - 3 slide 59 Example Airline company needs to purchase 10,000 tons of jet fuel in 3 months. One can use heating oil futures traded on NYMEX. Notional for each contract is 42,000 gallons. We need to check whether this hedge can be efficient.

Zvi WienerFIFIBI - 3 slide 60 Example Spot price of jet fuel $277/ton. Futures price of heating oil $0.6903/gallon. The standard deviation of jet fuel price rate of changes over 3 months is 21.17%, that of futures 18.59%, and the correlation is

Zvi WienerFIFIBI - 3 slide 61 Compute The notional and standard deviation f the unhedged fuel cost in $. The optimal number of futures contracts to buy/sell, rounded to the closest integer. The standard deviation of the hedged fuel cost in dollars.

Zvi WienerFIFIBI - 3 slide 62 Solution The notional is Qs=$2,770,000, the SD in $ is  (  s/s)sQ s =  $277  10,000 = $586,409 the SD of one futures contract is  (  f/f)fQ f =  $  42,000 = $5,390 with a futures notional fQ f = $  42,000 = $28,993.

Zvi WienerFIFIBI - 3 slide 63 Solution The cash position corresponds to a liability (payment), hence we have to buy futures as a protection.  sf =  / =  sf =   = The optimal hedge ratio is N* =  sf Q s  s/Q f  f = 89.7, or 90 contracts.

Zvi WienerFIFIBI - 3 slide 64 Solution  2 unhedged = ($586,409) 2 = 343,875,515,281 -  2 SF /  2 F = -(2,605,268,452/5,390) 2  hedged = $331,997 The hedge has reduced the SD from $586,409 to $331,997. R 2 = 67.95%(= )

Zvi WienerFIFIBI - 3 slide 65 Duration Hedging Dollar duration

Zvi WienerFIFIBI - 3 slide 66 Duration Hedging If we have a target duration D V * we can get it by using

Zvi WienerFIFIBI - 3 slide 67 Example 1 A portfolio manager has a bond portfolio worth $10M with a modified duration of 6.8 years, to be hedged for 3 months. The current futures prices is 93-02, with a notional of $100,000. We assume that the duration can be measured by CTD, which is 9.2 years. Compute: a. The notional of the futures contract b.The number of contracts to by/sell for optimal protection.

Zvi WienerFIFIBI - 3 slide 68 Example 1 The notional is: (93+2/32)/100  $100,000 =$93,062.5 The optimal number to sell is: Note that DVBP of the futures is 9.2  $93,062  0.01%=$85

Zvi WienerFIFIBI - 3 slide 69 Example 2 On February 2, a corporate treasurer wants to hedge a July 17 issue of $5M of CP with a maturity of 180 days, leading to anticipated proceeds of $4.52M. The September Eurodollar futures trades at 92, and has a notional amount of $1M. Compute a. The current dollar value of the futures contract. b. The number of futures to buy/sell for optimal hedge.

Zvi WienerFIFIBI - 3 slide 70 Example 2 The current dollar value is given by $10,000  ( (100-92)) = $980,000 Note that duration of futures is 3 months, since this contract refers to 3-month LIBOR.

Zvi WienerFIFIBI - 3 slide 71 Example 2 If Rates increase, the cost of borrowing will be higher. We need to offset this by a gain, or a short position in the futures. The optimal number of contracts is: Note that DVBP of the futures is 0.25  $1,000,000  0.01%=$25

Zvi WienerFIFIBI - 3 slide 72 FRM-00, Question 73 What assumptions does a duration-based hedging scheme make about the way in which interest rates move? A. All interest rates change by the same amount B. A small parallel shift in the yield curve C. Any parallel shift in the term structure D. Interest rates movements are highly correlated

Zvi WienerFIFIBI - 3 slide 73 FRM-00, Question 73 What assumptions does a duration-based hedging scheme make about the way in which interest rates move? A. All interest rates change by the same amount B. A small parallel shift in the yield curve C. Any parallel shift in the term structure D. Interest rates movements are highly correlated

Zvi WienerFIFIBI - 3 slide 74 FRM-99, Question 61 If all spot interest rates are increased by one basis point, a value of a portfolio of swaps will increase by $1,100. How many Eurodollar futures contracts are needed to hedge the portfolio? A. 44 B. 22 C. 11 D. 1100

Zvi WienerFIFIBI - 3 slide 75 FRM-99, Question 61 The DVBP of the portfolio is $1,100. The DVBP of the futures is $25. Hence the ratio is 1100/25 = 44

Zvi WienerFIFIBI - 3 slide 76 FRM-99, Question 109 Roughly how many 3-month LIBOR Eurodollar futures contracts are needed to hedge a position in a $200M, 5 year, receive fixed swap? A. Short 250 B. Short 3,200 C. Short 40,000 D. Long 250

Zvi WienerFIFIBI - 3 slide 77 FRM-99, Question 109 The dollar duration of a 5-year 6% par bond is about 4.3 years. Hence the DVBP of the fixed leg is about $200M  4.3  0.01%=$86,000. The floating leg has short duration - small impact decreasing the DVBP of the fixed leg. DVBP of futures is $25. Hence the ratio is 86,000/25 = 3,440. Answer A

Zvi WienerFIFIBI - 3 slide 78 Beta Hedging  represents the systematic risk,  - the intercept (not a source of risk) and  - residual. A stock index futures contract

Zvi WienerFIFIBI - 3 slide 79 Beta Hedging The optimal N is The optimal hedge with a stock index futures is given by beta of the cash position times its value divided by the notional of the futures contract.

Zvi WienerFIFIBI - 3 slide 80 Example A portfolio manager holds a stock portfolio worth $10M, with a beta of 1.5 relative to S&P500. The current S&P index futures price is 1400, with a multiplier of $250. Compute: a. The notional of the futures contract b. The optimal number of contracts for hedge.

Zvi WienerFIFIBI - 3 slide 81 Example The notional of the futures contract is $250  1,400 = $350,000 The optimal number of contracts for hedge is The quality of the hedge will depend on the size of the residual risk in the portfolio.

Zvi WienerFIFIBI - 3 slide 82 A typical US stock has correlation of 50% with S&P. Using the regression effectiveness we find that the volatility of the hedged portfolio is still about ( ) 0.5 = 87% of the unhedged volatility for a typical stock. If we wish to hedge an industry index with S&P futures, the correlation is about 75% and the unhedged volatility is 66% of its original level. The lower number shows that stock market hedging is more effective for diversified portfolios.

Zvi WienerFIFIBI - 3 slide 83 FRM-00, Question 93 A fund manages an equity portfolio worth $50M with a beta of 1.8. Assume that there exists an index call option contract with a delta of and a value of $0.5M. How many options contracts are needed to hedge the portfolio? A. 169 B. 289 C. 306 D. 321

Zvi WienerFIFIBI - 3 slide 84 FRM-00, Question 93 The optimal hedge ratio is N = -1.8  $50,000,000/(0.623  $500,000)=289