Zvi Wiener

1
Introduction to Financial Markets

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

2
Call Option
European Call
X Underlying
3
Put Option
European Put
X
X Underlying
4
Collar

• Firm B has shares of firm C of value 100
• They do not want to sell the shares, but need
  money.
• Moreover they would like to decrease the
  exposure to financial risk.
• How to get it done?

5
Collar

• 1. Buy a protective Put option (3y to maturity,
  strike 90 of spot).
• 2. Sell an out-the-money Call option (3y to
  maturity, strike above spot).
• 3. Take a cheap loan at 90 of the current
  value.

6
Collar payoff
payoff
K
90
90 100 K stock
7
Inverse Floater

• Today -100
• 1 yr 7.5
• 2 yr 9 - LIBOR
• 3 yr 10 - LIBOR
• 4 yr 11 - LIBOR
• 5 yr 12 - LIBOR 100
• Callable!

8
Inverse Floater

• Today
• 1 yr
• 2 yr
• 3 yr
• 4 yr
• 5 yr

A -100 L L L L L100
B -100 5 5 5 5 105
C -100 5 4 5 6 105
D -call option 0 0 0 0 2
B C D - A
9
Yield Enhancement

• Today you have 100 NIS invested in shekels for 1
  year and 100 NIS invested in dollars for one
  year.
• Yields are 4.5 NIS, 2 USD.
• You can create a deposit that offers 7 NIS or
  4.5 USD (the linkage is chosen by the bank!).

10
Yield Enhancement
Payoff at the year end
Sell some amount of USD Put options, the money
received invest in SHEKEL account!
USD
11
Combined CPI deal

• You are underexposed to CPI
• You have TA25 exposure
• One can sell an out-of-the-money call on TA25
• Buy a Call on CPI

12
Example of Risk Management

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

13
Investment Decision
1000M bonds
900M bonds
5 13
100M stocks
14
Investment Decision

• You manage 1B (OPM) and consider a decision to
  transfer 100M to a more risky investment
  (stocks).
• Your trader claims that on average he can earn
  13 on the risky portfolio instead of 5 that you
  have now.

15
Investment Decision

• Your stockholders have required rate of return on
  capital 15.
• 1. Calculate VaR before the transaction VaRo15.
• 2. Calculate VaR after the transaction VaR124.
• 3. The difference is an additional capital that
  will be used to back this transaction
• additional capital (VaR1- VaR0)3 27M

16
Investment Decision

• required additional net profit is
• Additional Capital Required rate of return
• 27M 15 4.05M
• required additional profit before tax is
• 4.05M/(1-tax) 7.4M
• this profit should be earned by an extra return
  on the risky investment.

17
Investment Decision

• Thus the required return on the stock portfolio
  is
• 7.4M (x-5)100M
• x 12.4
• You should accept the proposed transaction.

18
Tax in Financial Sector
19
Options in Hi Tech

• Many firms give options as a part of
  compensation.
• There is a vesting period and then there is a
  longer time to expiration.
• Most employees exercise the options at vesting
  with same-day-sale (because of tax).
• How this can be improved?

20
Long term options
payoff
K
50
k K stock
21
Example

• You have 10,000 vested options for 10 years with
  strike 5, while the stock is traded at 10.
• An immediate exercise will give you 50,000
  before tax.
• Selling a (covered) call with strike 15 will
  give you 60,000 now (assuming interest rate 6
  and 50 volatility) and additional profit at the
  end of the period!

22
Example
payoff
K
60
50
10 15 26
23
Bond Market BootcampHandouts

• Session One

24
Bond Market Bootcamp

• 2001 FRM Certification Review
• Session One

25
Fixed Income Securities

• Definition has evolved to include any security
  that obligates specific payments at specified
  dates.

26
Overview of Bond Markets

• Bond
• Note
• Money Market Securities
• Sovereign, Agency,Corporate Debentures
• Handout A-1 A-2, Street Software Inc

27
Fixed Income Securities

• Overview of major bond markets
• Types of instruments day counts
• Repo and Securities Lending
• Basic tools of analysis
• Mortgage Backed Securities
• Forward Rate Pricing

28
Types of Fixed Income Securities

• Corporate bonds
• Foreign bonds
• Eurobonds
• Mortgage Backed Securities (pass throughs)
• ABS
• Brady Bonds

29
World Bond Markets

• Particular focus on differences in nomenclature
  and conventions expanded section of FRM in
  recognition of significant increase in candidates
  from emerging markets

30
(No Transcript)
31
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)

32
Brady Bonds

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

33
Types of Securities MBS ABS

• Mortgage Loans
• Mortgage Pass-Through Securities
• CMO and Stripped MBS
• ABS
• Bonds with Embedded Options
• Analysis of MBS
• Analysis of Convertible Bonds

34
Arbitrage Motivations of ABS

• Direct descendant of zero coupon bonds, replacing
  rate risk with credit risk
• Necessity for investors to comprehend motivation
  of arb desk maintaining syndication book of
  primary issue

35
Fixed income Analysis

• Pricing of Bonds
• Yield Conventions
• Bond Price Volatility
• Factors Affecting Yields and the Term Structure
  of IR
• Treasury and Agency Securities Markets
• Corporates Municipals

36
Types of Fixed Income Securities

• Government securities (sovereign)
• Bills (discount)
• Notes
• Bonds (including new index linked)
• Government agency and guaranteed securities
• GNMA, SLMA, FNMA
• Municipal Securities
• State and local obligations

37
Securities Sectors

• Treasury sector bills, notes, bonds
• Agency sector debentures (no collateral)
• Municipal sector tax exempt
• Corporate sector US and Yankee issues
• bonds, notes, structured notes, CP
• investment grade and non-investment grade
• Asset-backed securities sector
• MBS sector

38
Fixed Income Universe

• Fixed coupon securities
• 6.75 UST 3/05
• Floating Rate notes
• WB 3/05 T15
• Zero Coupon Bonds
• 0 USP 3/05 (or USC)

39
Fixed Income Universe

• Perpetual notes (consols in UK)
• Structured notes
• Inverse floaters
• Callable bonds
• Puttable bonds
• Convertible notes

40
Characteristics of a Bond

• Issuer
• Time to maturity
• Coupon rate, type and frequency
• Linkage
• Embedded options
• Indentures
• Guarantees or collateral

41
Basic security structures

• Coupon, discount and premium bonds
• Zero coupon bonds
• Floating rate bonds
• Inverse floaters
• Perpetual notes
• Convertible bonds
• Interest Only, Principal Only notes
• ABS Structured Products

42
Applications

• Active Bond Portfolio Management
• Indexation
• Liability Funding Strategies
• Bond Performance Measurements (AIMR)
• Interest Rate Futures Options
• Interest Rate Swaps, Caps, Floors

43
Analytic Tools to be Reviewed

• Time Value of
• Yield Conventions
• Pricing Factors for Specific Securities
• Converting Yield Measurements
• Yield Curve Analysis
• Day Counts
• Repo

44
Analytic Tools to be Reviewed (contd)

• Price volatility for option free bonds
• Duration
• Convexity
• Embedded options their applications

45
FRM Cheat Sheet

• The answers are (virtually always)
• Negative convexity
• Effective duration
• SMM
• Double the BEY big figure when quoting Europeans
• Know your current duration ratios by heart

46
Basic Nomenclature

• Coupon securities are quoted in terms of price
  expressed in dollars.
• Clean price excludes accrued interest.
• Accrued interest
• next couponfraction of time that passed.
• Bills are quoted in terms of discount rate as
  of face value. Assuming 360 days in a year, i.e.
  multiplied by 360 and divided by the actual
  number of days remaining to maturity.

47
UST Nomenclature

• Clean v. Dirty Pricing
• 6.25 UST 5/30 104-12
• Actual/Actual Day Count
• AICoupon x actual days since last coupon
• actual days in current coupon period
• Price 20mm bonds for settlement April 12

48
(No Transcript)
49
UST Pricing Example 1

• 8.75 UST 11/08
• Security was purchased 06 Jun _at_ 110-31
• Security was sold 06 Sep _at_ 109-27
• Calculate the loss

50
UST Pricing Example 1

• Bought at 110-31 11,151,562,50
• Sold at 109-27 11,257,812.50
• Net loss is a profit of 106,350.00
• See Handouts 1-1 and 1-2

51
UST Pricing Example 2

• 3.125 (semi-annual coupon)
• 3.125 x 163 2.798763
• (20mm/100) x (104 12/32) 2.798763
  21,434,753

52
Discount Nomenclature (T Bills)

• DR (Face-Price)/Face x(360/t)
• P Face x 1-DR x (t/360)
• P 100 x 1-5.19 x (91/360) 98.6881
• YTM F/P (1y x t/365), or 5.33 for the above
  5.19

53
Price quotes for T-Bills
54
Price quotes for T-Bills
100 days to maturity price 97,569 will be
quoted at 8.75
55
FRM 9813T Bill Calculation

• 100,000 USB 100 days out, 97.569 should be
  quoted on a bank discount basis at
• A) 8.75
• B) 8.87
• C) 8.97
• D) 9.09

56
FRM 9813

• A US T-Bill selling for 97,569 with 100 days to
  maturity and a face value of 100,000 should be
  quoted on a bank discount basis at
• A) 8.75
• B) 8.87
• C) 8.97
• D) 9.09

57
FRM 9813Bank Discount Rate Question

• DR (Face-Price)/Face x (360/t)
• (100,000-97,569)/100,000 x (360/100)
• 8.75
• VERY IMPORTANT NOTE THAT THE YIELD IS 9.09,
  WHICH IS HIGHER

58
Price quotes for T-Bills
The quoted yield is based on the face value and
not on the actual amount invested. The yield is
annualized on 360 days basis. Bond equivalent
yield CD equivalent yield
59
TIPS

• Index linked government securities
• Pricing key is the compression factor, which
  relates its spread to normal government
  securities of comparable maturity

60
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
• Eurobond equivalent yield is always greater than
  UST

61
Annualizing Yield

• Effective annual yield (1periodic rate)m-1
  examples
• Effective annual yield 1.042-18.16
• Effective annual yield 1.024-18.24

62
The Yield to Maturity

• The yield to maturity of a fixed coupon bond y is
  given by

63
Embedded Options

• Calls, Puts
• Repricing Features (Inverse Floaters)
• Prepayment Features
• Credit Features

64
Callable bond

• The buyer of a callable bond has written an
  option to the issuer to call the bond back.
• Rationally this should be done when
• Interest rate fall and the debt issuer can
  refinance at a lower rate.

65
Callable Bond

• Long callable bond long bond (call)
• Therefore, px of callable bond need be the price
  of the straight bond straight call option px
  (adjusted for credit spread where applicable)

66
Puttable bond

• The buyer of a such a bond can request the loan
  to be returned.
• The rational strategy is to exercise this option
  when interest rates are high enough to provide an
  interesting alternative.

67
Putable Bond

• Long Bond Put
• PX Straight Bond Put Option (adjusted for
  credit spread as appropriate)

68
FRM 0009Callable Bonds

• An investment in a callable bond can be
  decomposed into a
• A) long position in a non-callable bond and
  short a put
• B) short position in a non-callable bond and
  long a call
• C) long position in a non-callable bond and long
  a call
• D) long position in a non-calable bond and short
  a call

69
FRM 0074Derivatives v. Cash Bonds

• In a market crash, the following are usually
  true
• I) fixed income portfolios hedged with short UST
  and futures lose less than those hedged with
  interest rate swaps given equivalent durations
• II) bid offer spreads widen due to less liquidity
• III) spread between off the runs and benchmarks
  widen
• A) all of the above B)
  II III
• C) I III D) None of the
  above

70
Repo Market

• Repurachase agreement - a sale of a security with
  a commitment to buy the security back at a
  specified price at a specified date.
• Overnight repo (1 day) , term repo (longer).

71
Repurchase Agreements

• Borrowing and lending using Treasuries and other
  debt as collateral.
• Repo (loan). You sell a security to counterparty
  and agree to repurchase the same security at a
  specified price at a later date (often next day).
• Reverse Repo - you agree to purchase a security
  and sell it back at a specified price later.

72
Repurchase Agreements

• Most repos are general-collateral repo rate.
• Some securities are special (for example
  on-the-run).
• Specialness peaks around next auction, then
  declines sharply.
• NY FED operates a securities lending for primary
  dealers using FEDs portfolio while posting other
  Treasury security as collateral.

73
Repo Example

• You are a dealer and you need 10M to purchase
  some security.
• Your customer has 10M in his account with no
  use. You can offer your customer to buy the
  security for you and you will repurchase the
  security from him tomorrow. Repo rate 6.5
• Then your customer will pay 9,998,195 for the
  security and you will return him 10M tomorrow.

74
Repo Example

• 9,998,195 0.065/360 1,805
• This is the profit of your customer for offering
  the loan.
• Note that there is almost no risk in the loan
  since you get a safe security in exchange.

75
Reverse Repo

• You can buy a security with an attached agreement
  to sell them back after some time at a fixed
  price.
• Repo margin - an additional collateral.
• The repo rate varies among transactions and may
  be high for some hot (special) securities.

76
Example

• You manage 1M of your client. You wish to buy
  for her account an adjustable rate passthrough
  security backed by Fannie Mae. The coupon rate is
  reset every month according to LIBOR1M 80 bp
  with a cap 9.
• A repo rate is LIBOR 10 bp and 5 margin is
  required. Then you can essentially borrow 19M
  and get 70 bp 19M.
• Is this risky?

77
Yield Curve Analysis

• Normal Curve
• Inverted Curve
• Twister

78
Yield Curve Analysis

• Par curve
• weighted avg of spot rates
• Spot Curve
• currently priced zero curve
• Forward Curve
• commence at future date

79
Handouts 2 3

• Illustrations of current swap yield curves for
  US, UK, Germany and Japan as of 06 Sep 01
• Note inversion
• Note normality
• Note twister
• All three types exhibited in Big Four

80
Forward Rates

• Buy a two years bond
• Buy a one year bond and then use the money to buy
  another bond (the price can be fixed today).

(1r2)(1r1)(1f12)
81
Forward Rates

• (1r3)(1r1)(1f13) (1r1)(1f12)(1f13)
• Term structure of instantaneous forward rates.

82
Time Value of Money

• Future Value
• Discounted Present Value (DPV)
• Internal Rate of Return
• Implications of curve structure on pricing
• Conventional Yield Measurements

83
Time Value of Money

• present value PV CFt/(1r)t
• Future value FV CFt(1r)t
• Net present value NPV sum of all PV

84
Determinants of the Term Structure

• Expectation theory
• Market segmentation theory
• Liquidity theory
• Mathematical models Ho-Lee, Vasichek,
  Hull-White, HJM, etc.

85
Term structure of interest rates
Yield IRR
How do we know that there is a solution?
86
Parallel shift
r
T
87
Twist
?r
T
88
Butterfly
?r
T
89
Do not use yield curve to price bonds

• Period A B
• 1-9 6 1
• 10 106 101
• They can not be priced by discounting cashflow
  with the same yield because of different
  structure of CF.
• Use spot rates (yield on zero-coupon Treasuries)
  instead!

90
Hedge Ratios for On the Run Treasuries

• See Handout 4
• Note discrepancies between employing hedge ratios
  and risk factors -- convexity rearing its ugly
  head

91
Position Duration Management

• See Handouts 5-1 through 5-3
• Hedging the current UST 30 with UST10 The NOB
  Spread
• Why is this trade a perfect arbitrage in any
  direction of interest rates?
• Why did I note employ the Bond future contract
  cheapest to deliver?

92
FRM 0095Curve Risk

• Which statement about historic UST yield curve
  changes is TRUE?
• A) changes in long term yields tend to be larger
  than short term yields
• B) changes in long term yields tend to
  approximate those of short term yields
• C) the same size yield change in both long term
  and short term rates tends to produce a larger
  price change in short term instruments when
  securities are trading near par
• The largest part of total return variability of
  spot rates is due to parallel changes with a
  smaller portion due to slope changes and the
  residual due to curvature changes.

93
FRM 9839Yield Curve Analysis

• Which of the following statements about yield
  curve arbitrage are true?
• A) no arb conditions require that the zero curve
  is either upward sloping or downward sloping
• B) it is a violation of the no-arb condition if
  the USB 1 yr rate is 10 or more, higher than the
  UST 10.
• C) as long as all discounted factors are less
  than one but greater than zero, the curve is arb
  free
• D) the no-arb condition requires all forward
  rates to be non-negative.

94
FRM 9839

• D) discount factors need be below one, as
  interest rates need be positive (JGBs ???), but
  in addition forward rates also need be positive.

95
FRM 971Yield Curve Arbitrage

• Suppose a risk manager made the mistake of
  valuing a zero coupon bond using a swap (par)
  curve rather than a zero curve. Assume the par
  curve is normal. The risk manager is therefore
• A) indiffernt to the rate used
• B) over-estimating the value of the security
• C) under-estimating the value of the security
• D) does not have enough information

96
FRM 971

• B) In a normal interest rate environment, the par
  curve need always be below the spot curve. As a
  result, the selected par curve is too law,
  over-estimating the value of the security.

97
FRM 991Yield Curve Analysis

• Assume a normal yield curve. Which statement is
  TRUE?
• A) the forward rate curve is above the zero
  curve, which is above the coupon-bearing bond
  curve
• B) the forward rate curve is above the par curve,
  which is above the zero coupon yield curve
• C) the coupon bearing curve is above the zero
  coupon curve, which is above the forward rate
  curve
• D) coupon bearing curve is above the forward
  curve, which is above the zero curve.

98
FRM 991

• A) In a normal (upwardly sloping) yield curve,
  the coupon curve (which is the avg of the spot or
  zero curve) lies below the zero curve. The
  forward curve can be interpolated as the spot
  curve plus the slope of the spot curve, so must
  be above the spot curve.

99
Bond Market Bootcamp

• 2001 FRM Certification Review
• Session Two

100
YTM and Reinvestment Risk

• YTM assumes that all coupon (and amortizing)
  payments will be invested at the same yield.

101
YTM and Reinvestment Risk

• An investor has a 5 years horizon
• Bond Coupon Maturity YTM
• A 5 3 9.0
• B 6 20 8.6
• C 11 15 9.2
• D 8 5 8.0
• What is the best choice?

102

• Bond selling at Relationship
• Par Coupon ratecurrent yieldYTM
• Discount Coupon rateltcurrent yieldltYTM
• Premium Coupon rategtcurrent yieldgtYTM
• Yield to call uses the first call as cashflow.
• Yield of a portfolio is calculated with the total
  cashflow.

103
FRM 006Dollar value of an 01

• A Eurodollar futures contract has a constant PVBP
  of 25.00 per million. The bank bill contract in
  Sydney trades on a discount basis and the PVBP is
  therefore different at each yield level. Assuming
  positive yields, the PVBP for the Sydney
  contract will be
• A) always less than the Eurodollar contract
• B) always greater than the Eurodollar contract
• C) dependent upon market yield
• D) A27.00 per million

104
FRM 9953Dollar Value of an 01

• Consider a 9 annual coupon 20 year bond trading
  at 6 with a price of 134.41.When rates rise
  10bp, price reduces to 132.99, and when rates
  drop 10bp, price rises to 135.85.
• What is the modified duration?
• A) 11.25
• B) 10.63
• C) 10.50
• D) 10.73

105
FRM 9953Dollar Value of an 01

• (135.85-132.99)/134.41/0.0012 10.63

106
Volatility and Bond Valuation

• Volatility plays a critical role in theoretical
  value of bonds with embedded options. Not readily
  comprehended, this is the concept behind OAS

107
Inverse Floater

• Is usually created from a fixed rate security.
• Floater coupon LIBOR 1
• Inverse Floater coupon 10 - LIBOR
• Note that the sum is a fixed rate security.
• If LIBORgt10 there is typically a floor.

108
FRM 983The price of an inverse floater

• A) increases as interest rates increase
• B) decreases as rates increase
• C) remains constant as rates change
• D) behaves like none of the above

109
FRM 983Inverse Floater Question

• (B) decreases as rates increase
• As rates increase, the coupon decreases.
  Additionally, the discount factor increases.
  Hence the value of the note need decrease even
  more than a regular fixed income security.

110
FRM 98 3

• Answer is DR 8.75
• Yield is 9.09

111
Duration and IR sensitivity
112
Understanding of Duration/Convexity

• What happens with duration when a coupon is paid?
• How does convexity of a callable bond depend on
  interest rate?
• How does convexity of a puttable bond depend on
  interest rate?

113
FRM 9831Duration

• A 10 year zero coupon bond is callable annually
  at par, commencing at the beginning of year six.
  Asssume a flat yield curve of 10. What is the
  bonds duration?
• A) 5 years
• B) 7.5 years
• C) 10 years
• D) cannot be determined from given data

114
FRM 9831Zero Coupon Question

• Trick Question (both Zvi and I got it wrong on
  first read thru)
• Its a zero, the bond will never be called
  because it will never trade above par prior to
  maturity
• C) regular 10 year duration for a zero

115
Duration
116
Duration
117
Meaning of Duration
118
Macaulay Duration

• Definition of duration, assuming t0.

119
Macaulay Duration
A weighted sum of times to maturities of each
coupon.

• What is the duration of a zero coupon bond?

120

• KEY MISCONCEPTION
  OF DURATION
• Do not think of duration as a measure of time!

121
FRM 9832IOs and POs

• A 10 yr reverse floater pays seminannual coupon
  of 8 less 6 month LIBOR.Assume the yield curve
  is 8 flat, the current UST 10 yr has a duration
  of 7 yrs, and interest on the note was reset
  today. What is the notes duration?
• A) 6 mos B) shorter than 7
  yrs
• C) longer than 7 yrs D) 7
  years

122
FRM 0073Duration

• What assumptions does a duration-based hedging
  scheme make about interest rate movement?
• A) all interest rates change by the same amount
• B) a small parallel shift in the yield curve
• C) parallel shift in the term structure
• D) rate movements are highly correlated

123
Example

• Portfolio consists of 1M of a bond with duration
  of 1 year and 1M worth of a bond with duration
  of 20 years.
• What is the duration of the portfolio?

124
Rough calculation

• Duration of the first bond is 1 year, of the
  second bond is 20 years.
• This means that when IR go 1 up we will lose 1
  of the first bond and 20 of the second.
• All together we will lose 10.5 of the portfolio.
• The duration is (roughly) 10.5 years.

125
FRM 9749FRN Duration

• A money markets desk holds a floating rate note
  with an 8 year maturity. The interest rate is
  floating at 3 mo LIBOR, reset quarterly. The next
  reset is in one week. What is the securitys
  duration?
• A) 8 yrs
• B) 4 yrs
• C) 3 months
• D) 1 week

126
FRM 9749Floating Rate Note Question

• (d) duration is not related to maturity when
  coupons are not fixed for the life of the
  security. The duration or price risk is only
  related to the time to the next reset, which is
  one week.

127
Duration
128
Convexity
129
Convexity

• For a simple bond portfolio it does not help
  much!
• It is much more important to consider 2 risk
  factors!

130
Value
value
Parallel shift
131
FRM 9940Effective Duration Convexity

• Which attribute of a bond is NOT a reason for
  using effective duration rather than modified
  duration?
• A) its life may be uncertain
• B) its cash flow may be uncertain
• C) its price volatility tends to decline as
  maturity approaches
• D) it may include changes in adjustable rate
  coupons with caps or floors

132
FRM 9940

• C) all attributes are reasons for using effective
  convexity, except that the price risk decreases
  as maturity approaches since this would hold for
  a regular security as well.

133
Negative Convexity and Duration

• MBS and particularly I/Os have negative
  convexity, the result of contraction risk and
  extension risk
• Accordingly, effective duration and effective
  convexity need always be computed

134
Negative Convexity

• Negative convexity means that the PX appreciation
  will be less than the price depreciation for a
  large change in yields
• BP C -C
• 100 more than x less than Y
• -100 x Y

135
Negative Convexity

• Also address topic of price compression, lack of
  linearity in PX
• Limited appreciation as yields decline, which is
  why probability on straight bonds skews towards
  par in options trading allusion to necessity to
  employ yield volatility rather than price
  volatility (session four)

136
Bond Market Bootcamp

• 2001 FRM Certification Review
• Session Four

137
Bootcamp Warmups

• Closing outstanding value of contracts, in US
  trillions, of OTC contracts as measured by BIS
  last year 65, 16, 2
• Which is FX
• Which is equity
• Which is interest rate

138
Bootcamp Warmups

• Which exchanges merged to form Euronext?

139
Bootcamp Warmups

• What risks would a Euro denominated fund take
  when investing in the Euronext index?
• Interest rate
• Foreign exchange
• Equity price
• Dividend risk

140
Bootcamp Warmups

• Which market is mean-reverting?
• California energy futures
• TA-25 index
• HM T-Bills
• Notes/Bond spread

141
Emerging Markets Risk Warmups

• Majority of EM is Latin (over 40 of total EM
  market)
• Mexican IPC Brazilian BOVESPA are most
  important
• Argentine MERVAL is most volatile, and the tail
  that wags the dog from BOVESPA to Chilean IPSA.
• Now major, liquid contracts in local mkts

142
Emerging Markets Warmup EVT

• Extreme Value Theory adds two magnitudes of risk
  not otherwise calculated in major markets (until
  WTC/Pentagon)
• Magnitude of an X year return (the norm in
  Buenos Aires) and
• Excess loss given Value-at-Risk
• It is NOT a scenario analysis per se in the
  manner of VAR

143
Bonds 102

• A quick return and review (Promises, Promises) to
  duration, convexity and yield curve analysis

144
Basis

• Any expression of negative convexity in the
  relationship of two securities
• Cash/futures (most common, but not exclusive)
• On-the-run/off-the-run
• Deliverables v. Cheapest-to-Deliver

145
Duration Revisited

• Influences on duration, in order of importance
• Coupon
• Frequency of coupon payment
• YTM
• Life at issue (what is the difference in duration
  between a 20/30 and a 30/40? This is a key
  concept)

146

• KEY MISCONCEPTION
  OF DURATION
• Do not think of duration as a measure of time!

147
Duration Reconsidered

• Duration is NOT an approximation, it is a
  first-order derivative
• Its APPLICATION is an approximation
• This makes it a particularly seductive error
• Duration can reagularly exceed remaining life of
  a security (inverse floaters, I/Os)

148
Duration Reconsidered

• At low yields, prices rise at an increasing rate
  as yields fall
• At high yields, prices rise at a decreasing rate
  as yields rise
• Why?? Coupon effect takes over in importance

149
Bond Market Bootcamp

• 2001 FRM Certification Review
• Session Five

150
NPV Warmups

• Arb Desk buys DM 100,000 of new issue John
  Fairfax HY 9/30/16 step-up note, priced at par,
  coupons are 2 (annual 30/360).
• Internally assigned cost of capital for HY
  Eurobonds, 7-15 yrs is 6.
• Calculate the NPV

151
NPV Warmups

• Arb Desk buys 1mm 10 World Bank 10/16 at par
• Internal cost of capital discount rate is 4
  ANNUAL for supranationals from 7-15 yrs.
• What is the DPV?

152
Duration Warmups

• USC of the 9.375 UST 10/04
• YTM 4.30
• Calculate the modified duration
• (trick question, there will be one or two of
  these on each exam testing nomenclature)

153
Modified Duration

• 3/ (1.043/2)
• 3/1.0215
• 2.9368

154
Duration Warmups

• 5 UST 9/03
• Purchased today _at_ YTM 4.33
• Calculate the duration

155
Duration Review Gilts

• Calculate the modified duration of a UKT with a
  McCauley duration of 7.865 years. Assume rates
  are 4.75

156
Duration on Gilts

• Dont panic, the US used to be a colony even if
  Ben Franklin insisted we switch traffic flows to
  the French side of the road in 1776 as a sign of
  independence.
• 7.865/1.0475/2

157
Convexity Reconsidered

• Most critical (potentially flawed) assumption
  when calculating convexity is its reliance on YTM
  and therefore a flat yield curve
• Tattoo this onto the top of your Bloomberg before
  performing quick-and-dirty hedges

158
Implications for Yield Curve Analysis

• Forward rate curve requires that all yield curve
  interpolation be done in a steps manner rather
  than simple linear curve smoothing

159
FRM 9850Leverage Factors

• Hedge fund invests 100mm by a factor of 3 in HY
  bonds yielding 14 at an average borrowing cost
  of 8. What is its yearend return on capital?

160
FRM 9850

• Fund borrows 200mm and invests 300m.
• 300 x 0.14 42mm
• 200 x 0.08 16mm
• Net profits are 26mm on 100mm, or 26.

161
BONDS WITH EMBEDDED OPTIONS

• Convertibles
• Mortgage Backeds (first generation)
• I/Os and P/Os

162
Convertibles

• Q in class last week why are there calls?
• A forces conversion, as convertibles are
  generally highly advantageously priced for the
  issuing entity, not the option holder

163
Convertibles

• Bond is convertible at 40, redemption call at 106
• Bond trades at 115, stock is at 45
• A) sell the bond
• B) convert sell equity
• C) await the call at 106
• D) do nothing and earn the coupon

164
Convertibles

• 1000 (face value is always 1000)/40 25 shares
• 25 shares _at_451,125
• Bond may be sold at higher price than convertible
  value

165
Convertibles

• ABS issue we locate a convertible priced very
  attractively post WTC/Pentagon, but cannot
  maintain the credit name on a term basis
• Hedge the risk

166
Convertible Hedge

• Requires an asset swap to maintain investment
  structure yet modify underlying credit to an
  acceptable name and tenure.

167
FRM 9834

• A 3 yr convertible paying 4 p.a. priced at par,
  right to conversion ratio of 10 _at_ 75, forced
  conversion at maturity. Convexity relative to
  underlying equity is
• a) zero b) always positive
• c) always negative d) none of the above

168
FRM 9834

• B) as the convertible includes a warrant ( a call
  option on the underlying stock) its convexity
  must trade positive relative to the underlying
  equity. This is what the purchaser paid premium
  to receive.

169
FRM 9752Convertible Risk

• Trader purchases convertible with call provision.
  Assuming a 50 conversion risk, which combination
  of stock price and interest rates would
  constitute a perfect storm?
• a) lower rates, lower equity prices
• b) lower rates, higher equity prices
• c) higher rates, lower equity prices
• d) higher rates, higher equity prices

170
Convertible RiskFRM 9752

• C) value of the fixed rate bond will fall as
  rates increase, value of the embedded warrant
  will fall as equity prices decline.

171
FRM 989Equity Indeces

• To prevent arbitrage, the theoretical price of a
  stock index need be fully determined via
• I) cash price II) financing cost
• III) inflation IV) dividend yield
• a) I II b) II III
• c) I, II IV d) all of the above

172
Equity IndecesFRM 989

• While embedded in the underlying nominal interest
  rate of the futures, inflationis not a direct
  calculation of any futures index.

173
IO/PO Key Concepts

• I/O P/O must equal the MBS
• IOs are bullish securities with negative
  duration.

174
Duration and I/Os P/Os

• Five year note dollar duration is
• 50m x DF 50m x D1F 100m x D
• Duration of inverse floater must be
• D1F (100m/50m) x D 2 x D
• Or twice that of the original note

175
FRM 9979IOs and POs

• Suppose the coupon and modified duration of a 10
  yr note priced to par is 6 and 7.5,
  respectively. What is the approximate modified
  duration of a 10 yr inverse floater priced to par
  with a coupon of (18-2x 1m LIBOR)?
• A) 7.5 B) 15.0
• C) 22.5 D) 0.0

176
FRM 9979

• C) following the same reasoning, we must divide
  the fixed rate bonds into 2/3 FRN and 1/3 inverse
  floater. This will ensure that the inverse
  floater payment is related to twice LIBOR. As a
  result, the duration of the inverse floater must
  be 3x the bond.

177
Mortgage Backed Securities Conceptual Review
178
Fixed Rate Mortgage

• A series of equal payments with PVloan.
• Example 100,000 for 20 years with 6 and equal
  monthly payments.

179
Adjustable-Rate Mortgage (ARM)

• The contract rate is reset periodically, based on
  a short term interest rate.
• Adjustment from one month to several years.
• Spread is fixed, some have caps or floors.
• Market based rates.
• Rates based on cost of funds for thrifts.
• Initially low rate is often offered teaser rate.

180
Balloon Mortgage

• One payment at the end.
• Sometimes they have renegotiation points.

181
Prepayments

• Prevailing mortgage rate relative to original.
• Path of mortgage rates.
• Level of mortgage rates.
• Seasonal factors (home buying is high in spring
  summer and low in fall, winter).
• General economic activity.

182
Prepayments

• Prepayment speed, conditional prepayment rate CPR
  (prepayment rate assumed for a pool).
• Single-Monthly mortality rate SMM.
• SMM 1 - (1-CPR)1/12

183
PSA prepayment benchmark

• The Public Securities Association benchmark is
  expressed as monthly series of annual prepayment
  rates.
• Low prepayment rates of new loans and higher for
  old ones.
• Assumes CPR increasing 0.2 to 6 with life of a
  loan.
• Actual rate is expressed as of PSA.

184
PSA standard default assumptions
Annual default rate (SDA) in
0.6
Month 1 - 0.02 increases by 0.02 till
30m stable at 0.6 30-60m declines by 0.01
61-120m remains at 0.03 after 120m
0.3
0.02
0 30 60 120 Age in months
185
100 PSA
Annual CPR in
6
0.2
0 30 Age in months
186
Prepayments

• A general model should be based on a dynamic
  transition matrix, very similar to credit
  migration.
• But note the difference of a pool of not
  completely rational customers and a single firm.

187
Example of prepayments

• Example let CPR6, then
• SMM 1-(1-0.06)1/12 0.005143.
• An SMM of 0.5143 means that approximately 0.5
  of the mortgage balance will be prepaid this
  month.

188
Example of prepayments

• If the balance at the beginning of a month is
  290M, SMM 0.5143 and the scheduled principal
  payment is 3M, then the estimated repayment for
  this month is
• 0.005143 (290,000,000-3,000,000)1,476,041

189
FRM 9944Prepayment Risk

• The following are reasons why a prepayment model
  will not accurately predict future mortgage
  prepayments. Which of these will have the
  greatest effect on convexity of mortgage pass
  throughs?
• A) refinancing incentive
• B) seasoning
• C) refinancing burnout
• D) seasonality

190
FRM 9944MBS Prepayments

• A) the factor influencing most the decision to
  repay early (the embedded option) is, from this
  list, refinancing incentives

191
Prepayment Risk and Convexity

• Negative convexity - if interest rates go up the
  price of a pass through security will decline
  more than a government bond due to lower
  prepayment rate.

192
FRM 9951CPR to SMM Conversion

• Suppose the annual prepayment rate CPR for a
  mortgage backed security is 6. What is its
  corresponding single-monthly mortality (SMM)
  rate?
• A) 0.514
• B) 0.334
• C) 0.5
• D) 1.355

193
FRM 9951Convert CPR to SMM

• (A) 0.51
• (1-6)(1-SMM) 12
• SMM 0.51

194
MBS Bond Equivalent Yield

• Bond equivalent yield 2 (1yM)6 - 1
• Yield is based on prepayment assumptions and must
  be checked!
• PSA benchmark Public Securities Association.
  Assumes low prepayment rates for new mortgages,
  and higher rates for seasoned loans.

195
Bond Market Bootcamp

• 2001 FRM Certification Review
• Session Six

196
Options 102

• Review of Basic Concepts Their Applications

197
Options 101

• Never forget the fact that lognormal
  distributions are positively skewed

198
Options 101

• Delta
• Gamma
• Vega
• Theta

199
Compound Option Risks

• Option risk compounds with each layer of
  additional risk embedded in position. Therefore,
  while all recognize the risk of a short gamma
  position, for example, consider the additional
  incremental risk involved in whether this was
  established at a delta neutral or short/long
  delta price. The delta risk can easily exceed the
  originally accepted embedded (and priced) gamma
  risk if not properly hedged.

200
Compound Option Example

• Arb desk owns 1mm shares of GE at 50
• Writes 3mm ATM calls exp 12/01 at 40 volatility
  post-WTC/Pentagon madness to capitalize on spike
  in volatility
• Calculate the delta hedge

201
FRM 9749

• An option strategy exhibits unfavorable
  sensitivity to increases in implied volatility
  while experiencing significant daily time decay.
  The portfolio may be hedged by
• A) selling short-dated options buying
  longer-term options
• B) buying short-dated options selling
  longer-term options
• C) selling both periods D) buying both
  periods

202
Options 102

• Continuously rebalancing an options portfolio to
  small change in delta is called dynamic hedging
• Because of its transaction costs, it is virtually
  never profitable long term from the short side

203
Options 102

• Butterfly strategies are employed in very stable
  markets precisely as means of capitalizing on
  dynamic hedging from the long side

204
Options 102

• From the short side, a condor would accomplish a
  similar objective, except it would be expressed
  as vega positive while remaining delta neutral

205
Options 102

• European v. American
• Model implications

206
American Options

• May be exercised at any time to maturity
• Accordingly, on equity options, early exercise of
  an American option on a non-dividend paying stock
  can never be optimal strategy.

207
Core Concept Options

• An American call option on a non-dividend paying
  stock (or asset with no income) should never be
  exercised early. If the asset pays income, there
  is a possibility of early exercise, which
  increases with the size of the income payments.

208
Options 102

• Discrete time models will make a stochastic path
  into steps, thereby eliminating intraperiod
  volatility this will ALWAYS make them value
  volatility (and therefore options) cheaper than
  continuous time models

209
Put Call Parity (and other myths of mathematics)

• Highly problematic when applied to american
  options
• Very problematic when applied to volatility
  smiles (let alone emerging market smirks)
• Even in European options not necessarily valid

210
FRM 9935Put Call Parity

• According to put call parity, writing a put is
  equivalent to
• a) buying a call,buying stovk and lending on repo
• b) writing a call, buying stock and borrowing
• c) writing a call, buying stock and lending
• d) writing a call, selling stock and borrowing.

211
FRM 9935Put Call Parity Theory

• B) a short put position is equivalent to a long
  asset position plus a short call. To finance the
  purchase, we need borrow, as the value of the
  options is minute relative to the value of the
  underlying asset.

212
Convexity Adjustment

• Because interest rate futures are more highly
  correlated with the underlying reinvestment rate,
  profits would be reinvested at a different rate
  than calculated in a static forward price. To
  offset this advantage, futures are priced above
  the forward price. This becomes increasingly
  significant in longer maturity contracts.

213
Equity Options

• Key concept focus upon whether option model
  requires inclusion or exclusion on dividend

214
Dividend Paying Stocks

• In EUROPEAN options, the stock price need be
  recalculated in pricing the option by first
  deducting the discounted dividend. The fact that
  the dividend comes later need be accounted for in
  the option price. This is a critical and frequent
  error in calculation.

215
Options 102Nomenclature Question

• Buy 1 43P _at_ 6
• Sell 2 37P _at_ 4
• Buy 1 32P _at_ 1
• Stock expires at 19
• Calculate P/L

216
Options 102 Nomenclature

• (43-19) (2 -3719)(32-19) (-644-1)
• 2 per share

217
Options 102

• 180 day Call option, strike price _at_ 50
• Current price 55, option price 5
• What underlying instrument are we pricing?
• A) Eurodollar futures
• B) DAX equity index
• C) JGBs
• D) KOSPI 200 Index

218
Options 102Bonds

• When related to fixed income, a model must
  accommodate mean-reversion in calculating
  stochastic behavior, a concept rarely considered
  in equity options
• This is the BS model demise in fixed income
• Recall the warmup question

219
Options 102Myron, the Damned Model Doesnt
Work

• BS does not account for transaction costs,
  occassionally the most significant factor in
  emerging markets, less liquid markets, or three
  standard deviation events like WTC/Pentagon
• At an extreme, the BS assumes the option is a
  tradable instrument (how does FIBI price 83 of
  open interest in index options, in but only one
  EM examplecost TF Bank the ranch in identical
  trade in 1998, and Ulusal/Demir this year

220
Options 102Myron, you still deserve that
damned Nobel

• prices embedded options very simply and
  accurately

221
BS Assumptions

• Price of the underlying asset moves in a
  continuous fashion
• interest rates are known and constant
• variance of returns is constant
• perfect liquidity and transaction capabilities
  (not simply liquidity, also short sales, taxes,
  etc)

222
Stupid Dog Tricks You Need Comprehend but Not
Calculate

• Martingales are the quant soup-du-jour solution,
  as they represent a zer-drift stochastic process
• Beware bespeckled thirtysomethings bearing
  Martingale solutions

223
Backwardation/Negative Price Options

• Any option on an underlying instrument that can
  go/regularly goes negative in price (long terms
  WTI Crude, JGBs, waste and environment) MUST
  employ an arithmetic Brownian motion

224
Options on Index Securities

• Options relate to the INDEX, not the underlying
  intent think of Israeli mortgages or TIPS. The
  options need relate to the INDEX, not the true
  inflation rate.
• Difference is but another example of basis, and
  the risk would be another example of negative
  convexity.

225
Options 102

• Rank delta, gamma, vega, theta, rho as risks for
  the following options
• Deep ITM 5 days to expiration
• ATM 180 days to expiration
• Slightly OTM LEAPs

226
Options 102

• We own a swaption on 10 year Yen LIBOR to 3
  annual swap
• Trader hedged by shorting JGB 83s (couldnt
  resist a JGB example in Tel Aviv as payback for
  the Shachars and Gilboas)
• What risks are hedged, what risks remain?

227
Options 102

• Volatility risk remains as primary risk
• Basis risk remains, and has added another
  demension
• Interest rate reduced, but not curve risk

228
Options 102Bermuda Triangles

• Any option with a discontinuous payoff function
  necessitates an exceedingly high gamma near the
  strike price

229
Options 102

• Therefore, any such option Asiatic, Bermudan
  will require a specific model loosely based upon
  but VERY different than a traditional BS

230
FRM 9934

• What is the lower pricing bound for an ITM
  European call option, strike at 80, current price
  90, expiration one year? GB 12m is 5.
• A) 14.61 B) 13.90
• C) 10.00 D) 5.90

231
FRM 9934

• 90-80 (-0.05 x 1) 90-76.1013.90
• pricing a simple European option, and likely one
  American to comprehend the difference, is a
  guaranteed set of questions on any FRM exam. Like
  reading a bond quote, one cannot walk around with
  3 letters after their name without this
  capability mastered.

232
FRM 9952American option pricing question

• Price of an American equity call option equals an
  otherwise equivalent European option at time t
  when
• I) stock pays continuous dividends from t to
  option expiration T.
• II) interest rates are mean reverting from t to
  T.
• III) stock pays no dividends from t to T.
• IV) interest rates are non-stochastic between t
  and T.

233
FRM 9952

• B) an American call option will not be exercised
  early when there is no income payment on the
  underlying asset.

234
FRM 9858Options on Futures

• Which statement is true regarding options on
  futures?
• A) an American call equals a European call
• B) an American put equals a European put
• C) put/call parity holds for both European
  American options
• D) none of the above

235
FRM 9858

• D) futures have an implied income stream equal to
  the risk free rate. As a result, both sets of
  calls may be exercised early as distinct from
  normal American call options. Similarly,
  American puts would certainly be likely exercised
  early, dismissing laws of put/call parity.

236
Options Exotica

• Binary digital options
• Barriers (knock-in, knock-out)
• Down Out, Down In, Up Out, Up In
• Asian options, or average rate options

237
Options ExoticaFRM 984

• A knock-in barrier option is harder to hedge when
  it is
• a) ITM
• b) OTM
• c) at the barrier and near maturity
• d) at the barrier and at trade inception

238
FRM 984

• Discontinuous are harder to price at barrier with
  little time remaining.

239
FRM 9710

• Knock out options are often employed rather than
  regular options because
• a) they have lower volatility
• b) they have lower premium
• c) they have a shorter average maturity
• d) they have a smaller gamma

240
FRM 9710

• Knockouts are no different from regular options
  in terms of maturity or underlying volatility,
  but are much cheaper than equivalent European
  options since they involve a much lower
  probability of exercise.

241
Swaps, FX, Caps Collars

• Review of Nomenclature and Core Concepts

242
Core Concepts Swaps

• A position receiving a fixed rate swap is
  eqivalent to a long position in bond with
  similar coupon and maturity characteristics
  offset by a short position in an FRN. Its
  duration is equivalent to the fixed rate note,
  adjusted for the near coupon of the floater.

243
FRM 9942Swaps

• Client may either issue a fixed rate bond or an
  FRN with an interest rate swap. To achieve this,
  client should
• a) issue FRN of same maturity and enter IRS
  paying fixed/receiving float
• b) issue FRN and enter IRS paying float/receiving
  fixed

244
FRM 9942Swaps

• A) receiving float on the swap will offset
  payments on the FRN and leave a net fixed income
  obligation, presumably at a lower cost to issuer.
• Why would this make sense for Israeli issuers in
  general?

245
FRM 9959Swap Convexity

• If an interest rate swap is priced off the
  Eurodollar futures strip curve without correcting
  the rates for convexity, the resulting arbitrage
  may be exploited by an
• a) receive fixed swap short ED position
• b) pay fixed short ED position
• c) receive fixed long ED position
• d) pay fixed long ED position

246
FRM 9959

• A) futures rate need be corrected downward to
  forward rate otherwise too high a fixed rate is
  implied. The arb would be closed by shorting ED
  futures and rolling the thunder until futures
  and forwards price consistently closer to
  maturity.

247
FRA Forward Pricing

• 6x9 FRA 10mm 4.25 LIBOR 30/360
• settles at 4.85
• calculate P/L

248
FRA Pricing Example One

• (1mm x 0.425) 42,500 x 90/360 10,625
• (1mm x 0.485) 48,500 x .25 12,125
• 12,125-10,625 1,527.00

249
FRA Pricing Example One

• 1,527 was, of course, wrong
• We neglected to discount for the forward rate
• 1527/1(.0485 .25) 1,508.71

250
FRA Pricing Example Two

• 6x9 FRA 4.25 LIBOR, 30/360 daycount
• settles at 3.95 on 10mm
• calculate the P/L

251
FRA Pricing Example Two

• 10mm _at_ 4.25 .25 106,250
• 10mm _at_ 3.95 .25 98,750
• 7500/ 1.009875 7,426.66

252
FX Swaps

• 25mm 4 fixed for GBP 17mm 5 fixed
• 18 months tenor
• 1 GBP 1.4775
• present rates are US LIBOR 3 for 180, 3.5 for
  365 days
• present rates are UK LIBOR 4.0 for 180, 4.5 for
  365 days
• Calculate the swap

253
US cash flows

• 25mm 4 each coupon is 1mm
• 6m DPV_at_3 985,000
• 12mDPV_at_3.5 965,000
• 18mDPV_at_4 940,000

254
GBP cash flows

• GBP17mm 5 coupon GBP 850,000
• 6m DPV _at_ 4 828,750
• 12mDPV_at_4.5 811,750
• 18mDPV_at_5 786,250
• convert cumulative GBP cash flows _at_ 1.4775

255
FX Swaps Example

• 6m cash flow 985,000-951,197.81 33,802.19
• 12m c/f 965,000-931,686.86 33,313.14
• 18m c/f 940,000-902,418.43 37,581.57
• total p/l adjustment 104,696.90

256
FX Swaps Example Two

• Estimate the forward rate for 6 month Eur/.
• US LIBOR is 3, Eur is 4.
• Eur/ is 0.9100 spot

257

• 0.9100 ( -.01/2) -0.00455
• forward FX rate of 0.90545

258
Caps Floors

• Caps are simply call options on interest rates,
  usually written to FRN issuers to provide a
  maximum cost of borrowing
• Floors are simply put options on rates.
• Collars are a combination of caps/floors locking
  in a predefined range of potential interest rates.

259
FRM 9954

• Cap/Floor parity can be stated as
• a) short cap long floor fixed rate bond
• b) long cap short floor fixed swap
• c) long cap short floor FRN
• d) short cap short floor collar

260
FRM 9954

• A) with same strike price, a short cap/long floor
  loses money if rates increase which is equivalent
  to a fixed rate bond position

261
FRM 9960Cap Risk

• For a 5 yr ATM cap on LIBOR, what can be said
  about the individual caplets in a downward
  sloping term structure?
• A) short mturity caplets are ITM,longer are OTM
• b) longer maturities are ITM, longer are OTM
• c) all are ATM
• d) The moneyness of t