FIBI

1
Fixed Income Instruments 3

• Zvi Wiener
• 02-588-3049
• mswiener_at_mscc.huji.ac.il

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.

3
Government-Sponsored Enterprises

• GNMA - Government National Mortgage Association
• FHLBS - Federal Home Loan Bank System
• Sallie Mar - Student Loan Marketing Association

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.

5
Corporate Bonds

• Main types of issuers
• utilities
• transportation
• industrial
• banks and financial companies

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Bond Indentures

• trustee
• term bonds, serial bonds
• collateral
• debenture bond - not secured
• guaranteed bonds

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.

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

9
Bond Rating

• Duff and Phelps Credit Rating Co.
• Fitch Investors Service
• Moodys Investors Service
• Standard Poors Corporation

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Rating

• Moodys SP Fitch DP
• Aaa AAA AAA AAA
• Aa1 AA AA AA
• Aa2 AA AA AA
• Aa3 AA- AA- AA-
• A1 A A A
• A2 A A A
• A3 A- A- A-

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Rating

• BBB- or better investment grade
• BB and below - speculative grade
• D to DDD default
• transition matrix

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One year transition matrix

• Aaa Aa A Baa Ba B CD
• Aaa 91.9 7.38 0.72 0 0 0 0
• Aa 1.1 91.3 7.1 0.3 0.2 0 0
• A 0.1 2.6 91.2 5.3 0.6 0.2 0
• Baa 0 0.2 5.4 87.9 5.5 0.8 0.2

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High Yield Bonds

• LBO, downgrading, refinancing
• fallen angels
• deferred interest bonds
• Step-up bonds pay initially low interest which
  increases with time

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SEC rule 144A

• Allows to trade private placements among
  qualified institutions.

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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!

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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.

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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.

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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.

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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

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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

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

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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.

23
Municipal Securities

• Exemption of interest income from federal
  taxation.
• Issued by states, counties, special districts,
  cities, towns, school districts.

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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

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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

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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

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Municipal Money Market Products

• TAN tax anticipation notes
• RAN revenue anticipation notes
• GAN grant anticipation notes
• BAN bond anticipation notes
• Tax exempt commercial paper

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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

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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
• 0.065
• 0.1083
• 1-0.40

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Non-US Bonds

• national bond markets
• domestic market
• Foreign market
• Yankee USA
• Samurai Japan
• bulldog UK
• Rembrandt Holland
• matador Spain

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.

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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.

33
Eurobond market

• Floating Rate Notes FRN based on LIBOR or
  LIBID
• many are collared
• some are perpetual

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Comparing Yields

• bond equivalent yield of Eurodollar bond
• 2(1yield to maturity)0.5-1
• for example A Eurodollar bond with 10 yield has
  the bond equivalent yield of
• 21.100.5-1 9.762

35
Japanese Government Bonds JGB

• short term Treasury bills
• medium term bonds
• long term bonds
• super long term bonds (20 years)

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

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)

38
Brady Bonds

• Argentina, Brazil, Costa Rica, Dominican
  Republic, Ecuador, Mexico, Uruguay, Venezuela,
  Bulgaria, Jordan, Nigeria, Philippines, Poland.
• Partially collateralized by US government
  securities

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Internet sites

• www.federalreserve.gov/releases
• www.tradeweb.com
• www.bondclick.com
• www.fxall.com
• www.atriax.com
• www.convertbond.com
• www.bondsonline.com
• www.bba.org.uk
• www.streetsoftware.com/data/mpage.htm
• www.bondmarkets.com

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Hedging Linear Risk

• Following Jorion 2001, Chapter 14
• Financial Risk Manager Handbook

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Hedging

• Taking positions that lower the risk profile of
  the portfolio.
• Static hedging
• Dynamic hedging

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.

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• Market data 0 7m PL
• time to maturity 9 2
• US interest rate 6 6
• Yen interest rate 5 2
• Spot Y/ 125.00 150.00
• Futures Y/ 124.07 149.00

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• Stacked hedge - to use a longer horizon and to
  revert the position at maturity.
• Strip hedge - rolling over short hedge.

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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

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.

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.

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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.

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.

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.

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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

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The Optimal Hedge Ratio
Minimum variance hedge ratio
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Hedge Ratio as Regression Coefficient

• The optimal amount can also be derived as the
  slope coefficient of a regression ?s/s on ?f/f

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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!
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Optimal Hedge

• At the optimum the variance is

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.

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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 0.8243.

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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.

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Solution

• The notional is Qs2,770,000, the SD in is
• ?(?s/s)sQs0.2117?277 ?10,000 586,409
• the SD of one futures contract is
• ?(?f/f)fQf0.1859?0.6903?42,000 5,390
• with a futures notional
• fQf 0.6903?42,000 28,993.

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Solution

• The cash position corresponds to a liability
  (payment), hence we have to buy futures as a
  protection.
• ?sf 0.8243 ? 0.2117/0.1859 0.9387
• ?sf 0.8243 ? 0.2117 ? 0.1859 0.03244
• The optimal hedge ratio is
• N ?sf Qs?s/Qf?f 89.7, or 90 contracts.

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Solution

• ?2unhedged (586,409)2 343,875,515,281
• - ?2SF/ ?2F -(2,605,268,452/5,390)2
• ?hedged 331,997
• The hedge has reduced the SD from 586,409 to
  331,997.
• R2 67.95 ( 0.82432)

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Duration Hedging
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Duration Hedging
If we have a target duration DV we can get it by
using
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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.

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Example 1

• The notional is
• (932/32)/100?100,000 93,062.5
• The optimal number to sell is

Note that DVBP of the futures is
9.2?93,062?0.0185
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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.

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Example 2

• The current dollar value is given by
• 10,000?(100-0.25(100-92)) 980,000
• Note that duration of futures is 3 months, since
  this contract refers to 3-month LIBOR.

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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?0.0125
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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

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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

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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

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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

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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

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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?0.0186,000.
• 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

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Beta Hedging

• ? represents the systematic risk, ? - the
  intercept (not a source of risk) and ? - residual.

A stock index futures contract
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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.
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Example

• A portfolio manager holds a stock portfolio worth
  10M, with a beta of 1.5 relative to SP500. The
  current SP 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.

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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.
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• A typical US stock has correlation of 50 with
  SP.
• Using the regression effectiveness we find that
  the volatility of the hedged portfolio is still
  about
• (1-0.52)0.5 87 of the unhedged volatility for
  a typical stock.
• If we wish to hedge an industry index with SP
  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.

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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 0.623
  and a value of 0.5M. How many options contracts
  are needed to hedge the portfolio?
• A. 169
• B. 289
• C. 306
• D. 321

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FRM-00, Question 93

• The optimal hedge ratio is
• N -1.8?50,000,000/(0.623?500,000)289