Transcript No Slide Title

Introduction to Financial Markets
Zvi Wiener
02-588-3049
[email protected]
FRM
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Call Option
European Call
premium
X
Zvi Wiener
Introduction to Financial Markets
Underlying
slide 2
Put Option
European Put
X
premium
X
Zvi Wiener
Introduction to Financial Markets
Underlying
slide 3
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?
Zvi Wiener
Introduction to Financial Markets
slide 4
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.
Zvi Wiener
Introduction to Financial Markets
slide 5
Collar payoff
payoff
K
90
90
Zvi Wiener
100
K
Introduction to Financial Markets
stock
slide 6
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!
Zvi Wiener
Introduction to Financial Markets
slide 7
Inverse Floater
A
B
C
D
Today
-100
-100
-100
-call option
1 yr
L
5
5
0
2 yr
L
5
4
0
3 yr
L
5
5
0
4 yr
L
5
6
0
5 yr
L+100
105
105
2
B+C+D-A
Zvi Wiener
Introduction to Financial Markets
slide 8
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!).
Zvi Wiener
Introduction to Financial Markets
slide 9
Yield Enhancement
Payoff at the year end
1.07
Sell some amount of USD Put options,
the money received invest in SHEKEL
account!
1.045
USD
Zvi Wiener
Introduction to Financial Markets
slide 10
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
Zvi Wiener
Introduction to Financial Markets
slide 11
Example of Risk Management
Zvi Wiener
02-588-3049
[email protected]
FRM
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Investment Decision
$1000M bonds
capital
Zvi Wiener
$900M bonds 5%
$100M stocks 13%
capital
Introduction to Financial Markets
slide 13
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.
Zvi Wiener
Introduction to Financial Markets
slide 14
Investment Decision
Your stockholders have required rate of return on
capital 15%.
1. Calculate VaR before the transaction VaRo=15.
2. Calculate VaR after the transaction VaR1=24.
3. The difference is an additional capital that will
be used to back this transaction:
additional capital = (VaR1- VaR0)*3 = 27M
Zvi Wiener
Introduction to Financial Markets
slide 15
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.
Zvi Wiener
Introduction to Financial Markets
slide 16
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.
Zvi Wiener
Introduction to Financial Markets
slide 17
Tax in Financial Sector
0.17
36% 
 (1  36%)  45.299 %
1.17
Zvi Wiener
Introduction to Financial Markets
slide 18
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?
Zvi Wiener
Introduction to Financial Markets
slide 19
Long term options
payoff
Your option
K
Result
50
k
Zvi Wiener
K
Sell a call
Introduction to Financial Markets
stock
slide 20
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!
Zvi Wiener
Introduction to Financial Markets
slide 21
Example
payoff
K
Result
Your option
60
50
exercise
10
Zvi Wiener
15
Introduction to Financial Markets
26
slide 22
Bond Market Bootcamp:
Handouts
Session One
FRM
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Bond Market Bootcamp
2001 FRM Certification Review
Session One
FRM
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Fixed Income Securities
•Definition has evolved to include any
security that obligates specific payments at
specified dates.
Zvi Wiener
Introduction to Financial Markets
slide 25
Overview of Bond Markets
•Bond
•Note
•Money Market Securities
•Sovereign, Agency,Corporate Debentures
•Handout A-1 & A-2, Street Software Inc
Zvi Wiener
Introduction to Financial Markets
slide 26
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
Zvi Wiener
Introduction to Financial Markets
slide 27
Types of Fixed Income
Securities
•Corporate bonds
•Foreign bonds
•Eurobonds
•Mortgage Backed Securities (pass
throughs)
•ABS
•Brady Bonds
Zvi Wiener
Introduction to Financial Markets
slide 28
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
Zvi Wiener
Introduction to Financial Markets
slide 29
Zvi Wiener
Introduction to Financial Markets
slide 30
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 Wiener
Introduction to Financial Markets
slide 31
Brady Bonds
Argentina, Brazil, Costa Rica, Dominican
Republic, Ecuador, Mexico, Uruguay,
Venezuela, Bulgaria, Jordan, Nigeria,
Philippines, Poland.
Partially collateralized by US government
securities
Zvi Wiener
Introduction to Financial Markets
slide 32
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
Zvi Wiener
Introduction to Financial Markets
slide 33
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
Zvi Wiener
Introduction to Financial Markets
slide 34
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
Zvi Wiener
Introduction to Financial Markets
slide 35
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
Zvi Wiener
Introduction to Financial Markets
slide 36
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
Zvi Wiener
Introduction to Financial Markets
slide 37
Fixed Income Universe
•Fixed coupon securities
–6.75% UST 3/05
•Floating Rate notes
–WB 3/05 T+15
•Zero Coupon Bonds
–0% USP 3/05 (or USC)
Zvi Wiener
Introduction to Financial Markets
slide 38
Fixed Income Universe
•Perpetual notes (consols in UK)
•Structured notes
•Inverse floaters
•Callable bonds
•Puttable bonds
•Convertible notes
Zvi Wiener
Introduction to Financial Markets
slide 39
Characteristics of a Bond
• Issuer
• Time to maturity
• Coupon rate, type and frequency
• Linkage
• Embedded options
• Indentures
• Guarantees or collateral
Zvi Wiener
Introduction to Financial Markets
slide 40
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
Zvi Wiener
Introduction to Financial Markets
slide 41
Applications
• Active Bond Portfolio Management
• Indexation
• Liability Funding Strategies
• Bond Performance Measurements (AIMR)
• Interest Rate Futures & Options
• Interest Rate Swaps, Caps, Floors
Zvi Wiener
Introduction to Financial Markets
slide 42
Analytic Tools to be Reviewed
•Time Value of $
•Yield Conventions
•Pricing Factors for Specific Securities
•Converting Yield Measurements
•Yield Curve Analysis
•Day Counts
•Repo
Zvi Wiener
Introduction to Financial Markets
slide 43
Analytic Tools to be Reviewed
(cont’d)
•Price volatility for option free bonds
•Duration
•Convexity
•Embedded options & their applications
Zvi Wiener
Introduction to Financial Markets
slide 44
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
Zvi Wiener
Introduction to Financial Markets
slide 45
Basic Nomenclature
Coupon securities are quoted in terms of price
expressed in dollars.
Clean price excludes accrued interest.
Accrued interest =
next coupon*fraction 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.
Zvi Wiener
Introduction to Financial Markets
slide 46
UST Nomenclature
•Clean v. Dirty Pricing
•6.25% UST 5/30 104-12
•Actual/Actual Day Count
•AI=Coupon x actual days since last coupon
actual days in current coupon period
Price 20mm bonds for settlement April 12
Zvi Wiener
Introduction to Financial Markets
slide 47
Zvi Wiener
Introduction to Financial Markets
slide 48
UST Pricing Example 1
•8.75 UST 11/08
•Security was purchased 06 Jun @ 110-31
•Security was sold 06 Sep @ 109-27+
•Calculate the loss
Zvi Wiener
Introduction to Financial Markets
slide 49
UST Pricing Example 1
•Bought at 110-31
•Sold at
109-27
•Net “loss” is a profit of
11,151,562,50
11,257,812.50
$106,350.00
•See Handouts 1-1 and 1-2
Zvi Wiener
Introduction to Financial Markets
slide 50
UST Pricing Example 2
•$3.125 (semi-annual coupon)
•$3.125 x 163 = 2.798763
•($20mm/100) x [(104 + 12/32) + 2.798763 =
$21,434,753]
Zvi Wiener
Introduction to Financial Markets
slide 51
Discount Nomenclature
(T Bills)
•DR = (Face-Price)/Face x(360/t)
•$P = Face x [1-DR x (t/360)]
•$P = $100 x [1-5.19% x (91/360) =
$98.6881
•YTM = F/P = (1+y x t/365), or 5.33% for
the above 5.19%
Zvi Wiener
Introduction to Financial Markets
slide 52
Price quotes for T-Bills
Yd Ft
D
360
 Yd t 
price  F  D  F 1 

 360
Zvi Wiener
Introduction to Financial Markets
slide 53
Price quotes for T-Bills
100 days to maturity
price = $97,569 will be quoted at 8.75%
100  97.569 360
Yd 
 8.75%
100
100
 0.0875100
$97,569  $100,0001 

360


Zvi Wiener
Introduction to Financial Markets
slide 54
FRM 98:13
T 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%
Zvi Wiener
Introduction to Financial Markets
slide 55
FRM 98:13
• A US T-Bill selling for $97,569 with 100
•
•
•
•
Zvi Wiener
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%
Introduction to Financial Markets
slide 56
FRM 98:13
Bank 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
Zvi Wiener
Introduction to Financial Markets
slide 57
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
360Yd
CD equiv. yiel 
360 t  Yd
360  8.75%
CD equiv . yiel 
 8.97%
360  100  8.75%
Zvi Wiener
Introduction to Financial Markets
slide 58
TIPS
•Index linked government securities
•Pricing key is the “compression factor”,
which relates its spread to normal government
securities of comparable maturity
Zvi Wiener
Introduction to Financial Markets
slide 59
Comparing Yields
bond equivalent yield of Eurodollar bond
= 2[(1+yield to maturity)0.5-1]
for example: A Eurodollar bond with 10% yield has
the bond equivalent yield of
2[1.100.5-1] = 9.762%
Eurobond equivalent yield is always greater than
UST
Zvi Wiener
Introduction to Financial Markets
slide 60
Annualizing Yield
Effective annual yield = (1+periodic rate)m-1
examples
Effective annual yield = 1.042-1=8.16%
Effective annual yield = 1.024-1=8.24%
annualcouponrate
current yield 
price
Zvi Wiener
Introduction to Financial Markets
slide 61
The Yield to Maturity
The yield to maturity of a fixed coupon
bond y is given by
n
p(t )   ci e
(Ti t ) y
i 1
Zvi Wiener
Introduction to Financial Markets
slide 62
Embedded Options
•Calls, Puts
•Repricing Features (Inverse Floaters)
•Prepayment Features
•Credit Features
Zvi Wiener
Introduction to Financial Markets
slide 63
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.
Zvi Wiener
Introduction to Financial Markets
slide 64
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)
Zvi Wiener
Introduction to Financial Markets
slide 65
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.
Zvi Wiener
Introduction to Financial Markets
slide 66
Putable Bond
Long Bond + Put
PX = Straight Bond + Put Option (adjusted
for credit spread as appropriate)
Zvi Wiener
Introduction to Financial Markets
slide 67
FRM 00:09
Callable Bonds
• An investment in a callable bond can be
•
•
•
•
Zvi Wiener
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
Introduction to Financial Markets
slide 68
FRM 00:74
Derivatives 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
Zvi Wiener
Introduction to Financial Markets
slide 69
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).
Zvi Wiener
Introduction to Financial Markets
slide 70
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.
Zvi Wiener
Introduction to Financial Markets
slide 71
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 FED’s portfolio while posting other
Treasury security as collateral.
Zvi Wiener
Introduction to Financial Markets
slide 72
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.
Zvi Wiener
Introduction to Financial Markets
slide 73
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.
Zvi Wiener
Introduction to Financial Markets
slide 74
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.
Zvi Wiener
Introduction to Financial Markets
slide 75
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?
Zvi Wiener
Introduction to Financial Markets
slide 76
Yield Curve Analysis
•Normal Curve
•Inverted Curve
•Twister
Zvi Wiener
Introduction to Financial Markets
slide 77
Yield Curve Analysis
•Par curve
weighted avg of spot rates
•Spot Curve
currently priced zero curve
Forward Curve
commence at future date
Zvi Wiener
Introduction to Financial Markets
slide 78
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
Zvi Wiener
Introduction to Financial Markets
slide 79
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).
(1+r2)=(1+r1)(1+f12)
Zvi Wiener
Introduction to Financial Markets
slide 80
Forward Rates
(1+r3)=(1+r1)(1+f13)= (1+r1)(1+f12)(1+f13)
Term structure of instantaneous forward rates.
Zvi Wiener
Introduction to Financial Markets
slide 81
Time Value of Money
•Future Value
•Discounted Present Value (DPV)
•Internal Rate of Return
•Implications of curve structure on pricing
•Conventional Yield Measurements
Zvi Wiener
Introduction to Financial Markets
slide 82
Time Value of Money
• present value PV = CFt/(1+r)t
• Future value FV = CFt(1+r)t
• Net present value NPV = sum of all PV
105
5
5
5
5
-PV
4
5
105
PV  

t
5
(1  r )
t 1 (1  r )
Zvi Wiener
Introduction to Financial Markets
slide 83
Determinants of the Term Structure
Expectation theory
Market segmentation theory
Liquidity theory
Mathematical models: Ho-Lee, Vasichek,
Hull-White, HJM, etc.
Zvi Wiener
Introduction to Financial Markets
slide 84
T
Ct
CT
PV  

t
T
(1  r )
t 1 (1  r )
Term structure of interest rates
T
Ct
CT
PV  

t
T
(
1

r
)
(
1

r
)
t 1
t
T
Yield = IRR
T
Ct
CT
Price  

t
T
(
1

y
)
(
1

y
)
t 1
How do we know that there is a solution?
Zvi Wiener
Introduction to Financial Markets
slide 85
r
Parallel shift
upward move
Current UST
Downward move
T
Zvi Wiener
Introduction to Financial Markets
slide 86
r
Twist
flattening
T
steepening
Zvi Wiener
Introduction to Financial Markets
slide 87
r
Butterfly
T
Zvi Wiener
Introduction to Financial Markets
slide 88
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!
Zvi Wiener
Introduction to Financial Markets
slide 89
Hedge Ratios for On the Run
Treasuries
•See Handout 4
•Note discrepancies between employing
hedge ratios and risk factors -- convexity
rearing its ugly head
Zvi Wiener
Introduction to Financial Markets
slide 90
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?
Zvi Wiener
Introduction to Financial Markets
slide 91
FRM 00:95
Curve 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
residualtodue
to curvature
changes.
slide 92
Zvi Wienerchanges and theIntroduction
Financial
Markets
FRM 98:39
Yield Curve Analysis
• Which of the following statements about yield curve
•
•
•
•
Zvi Wiener
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.
Introduction to Financial Markets
slide 93
FRM 98:39
•D) discount factors need be below one, as
interest rates need be positive (JGB’s ???),
but in addition forward rates also need be
positive.
Zvi Wiener
Introduction to Financial Markets
slide 94
FRM 97:1
Yield 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
Zvi Wiener
Introduction to Financial Markets
slide 95
FRM 97:1
•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.
Zvi Wiener
Introduction to Financial Markets
slide 96
FRM 99:1
Yield Curve Analysis
• Assume a normal yield curve. Which statement is
•
•
•
•
Zvi Wiener
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.
Introduction to Financial Markets
slide 97
FRM 99:1
•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.
Zvi Wiener
Introduction to Financial Markets
slide 98
Bond Market Bootcamp
2001 FRM Certification Review
Session Two
FRM
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
YTM and Reinvestment Risk
• YTM assumes that all coupon (and
amortizing) payments will be invested at the
same yield.
Zvi Wiener
Introduction to Financial Markets
slide 100
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?
Zvi Wiener
Introduction to Financial Markets
slide 101
Bond selling at
Relationship
Par
Coupon rate=current yield=YTM
Discount
Coupon rate<current yield<YTM
Premium
Coupon rate>current yield>YTM
Yield to call uses the first call as cashflow.
Yield of a portfolio is calculated with the total
cashflow.
Zvi Wiener
Introduction to Financial Markets
slide 102
FRM 00:6
Dollar value of an 01
• A Eurodollar futures contract has a constant
•
•
•
•
Zvi Wiener
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) A$27.00 per million
Introduction to Financial Markets
slide 103
FRM 99:53
Dollar Value of an 01
• Consider a 9% annual coupon 20 year bond
•
•
•
•
•
Zvi Wiener
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
Introduction to Financial Markets
slide 104
FRM 99:53
Dollar Value of an 01
•(135.85-132.99)/134.41/[0.001*2] = 10.63
Zvi Wiener
Introduction to Financial Markets
slide 105
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
Zvi Wiener
Introduction to Financial Markets
slide 106
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 LIBOR>10% there is typically a floor.
Zvi Wiener
Introduction to Financial Markets
slide 107
FRM 98:3
The 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
Zvi Wiener
Introduction to Financial Markets
slide 108
FRM 98:3
Inverse 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.
Zvi Wiener
Introduction to Financial Markets
slide 109
FRM 98: 3
•Answer is DR = 8.75%
•Yield is 9.09%
Zvi Wiener
Introduction to Financial Markets
slide 110
Duration and IR sensitivity
Zvi Wiener
Introduction to Financial Markets
slide 111
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?
Zvi Wiener
Introduction to Financial Markets
slide 112
FRM 98:31
Duration
• A 10 year zero coupon bond is callable
•
•
•
•
Zvi Wiener
annually at par, commencing at the
beginning of year six. Asssume a flat yield
curve of 10%. What is the bond’s duration?
A) 5 years
B) 7.5 years
C) 10 years
D) cannot be determined from given data
Introduction to Financial Markets
slide 113
FRM 98:31
Zero Coupon Question
•Trick Question (both Zvi and I got it wrong
on first read thru)
•It’s 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
Zvi Wiener
Introduction to Financial Markets
slide 114
Duration
C
C
C
M
P



2
n
n
(1  y) (1  y)
(1  y ) (1  y)
Macaulay Duration 
1  1C
2C
nC
nM 







2
n
n 
P  (1  y) (1  y)
(1  y) (1  y) 
Zvi Wiener
Introduction to Financial Markets
slide 115
Duration
Macaulay Duration
Modified Duration 
1 y
dP
1
  Modified Duration
dy
P
Zvi Wiener
Introduction to Financial Markets
slide 116
Meaning of Duration
dp d  n
Ti y 
  ci e    Dp
dy dy  i 1

Zvi Wiener
Introduction to Financial Markets
slide 117
Macaulay Duration
Definition of duration, assuming t=0.
n
D
Zvi Wiener
T c e
i 1
Ti y
i i
p
Introduction to Financial Markets
slide 118
Macaulay Duration
T
T
CFt
1
D   t wt 
t

t
Bond Price t 1 (1  y)
t 1
A weighted sum of times to maturities of each coupon.
What is the duration of a zero coupon bond?
Zvi Wiener
Introduction to Financial Markets
slide 119
KEY MISCONCEPTION
OF DURATION
Do not think of duration as a measure of time!
Zvi Wiener
Introduction to Financial Markets
slide 120
FRM 98:32
IO’s and PO’s
• 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 note’s duration?
• A) 6 mos
B) shorter than 7 yrs
• C) longer than 7 yrs
D) 7 years
Zvi Wiener
Introduction to Financial Markets
slide 121
FRM 00:73
Duration
• 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
Zvi Wiener
Introduction to Financial Markets
slide 122
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?
Zvi Wiener
Introduction to Financial Markets
slide 123
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.
Zvi Wiener
Introduction to Financial Markets
slide 124
FRM 97:49
FRN 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 security’s
duration?
• A) 8 yrs
• B) 4 yrs
• C) 3 months
• D) 1 week
Zvi Wiener
Introduction to Financial Markets
slide 125
FRM 97:49
Floating 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.
Zvi Wiener
Introduction to Financial Markets
slide 126
Duration
1 1
20 


  9.8212
2  1.05 1.07 
1 dA
DA  
A dr
D A B
AD A
BD B


A B A B

1 d  1.05
1.0720




20 

2 dx  1  r1  x 1  r20  x  
Zvi Wiener
Introduction to Financial Markets
 9.8212
x 0
slide 127
Convexity
Zvi Wiener
Introduction to Financial Markets
slide 128
Convexity
2
d A
CA  2
dr
20


d
1.05
1.07




368
20
2 
dx  1  r1  x 1  r20  x  
x 0
2
For a simple bond portfolio it does not
help much!
It is much more important to consider
2 risk factors!
Zvi Wiener
Introduction to Financial Markets
slide 129
Value
20
20
1.05 1.07
1.05
1.07



2
20
20
1  r1 1  r20 
1  0.05 1  0.07
2.8
value
2.6
2.4
2.2
Parallel shift
-0.03
-0.02
-0.01
0.01
0.02
0.03
1.8
1.6
Zvi Wiener
Introduction to Financial Markets
slide 130
FRM 99:40
Effective Duration & Convexity
• Which attribute of a bond is NOT a reason for
•
•
•
•
Zvi Wiener
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
Introduction to Financial Markets
slide 131
FRM 99:40
•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.
Zvi Wiener
Introduction to Financial Markets
slide 132
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
Zvi Wiener
Introduction to Financial Markets
slide 133
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%
•-100x%
Y%
Zvi Wiener
Introduction to Financial Markets
slide 134
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)
Zvi Wiener
Introduction to Financial Markets
slide 135
Bond Market Bootcamp
2001 FRM Certification Review
Session Four
FRM
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
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
Zvi Wiener
Introduction to Financial Markets
slide 137
Bootcamp Warmups
•Which exchanges merged to form Euronext?
Zvi Wiener
Introduction to Financial Markets
slide 138
Bootcamp Warmups
•What risks would a Euro denominated fund
take when investing in the Euronext index?
•Interest rate
•Foreign exchange
•Equity price
•Dividend risk
Zvi Wiener
Introduction to Financial Markets
slide 139
Bootcamp Warmups
•Which market is mean-reverting?
•California energy futures
•TA-25 index
•HM T-Bills
•Notes/Bond spread
Zvi Wiener
Introduction to Financial Markets
slide 140
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
Zvi Wiener
Introduction to Financial Markets
slide 141
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
Zvi Wiener
Introduction to Financial Markets
slide 142
Bonds 102
•A quick return and review (Promises,
Promises) to duration, convexity and yield
curve analysis
Zvi Wiener
Introduction to Financial Markets
slide 143
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
Zvi Wiener
Introduction to Financial Markets
slide 144
Duration Revisited
• Influences on duration, in order of
•
•
•
•
Zvi Wiener
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)
Introduction to Financial Markets
slide 145
KEY MISCONCEPTION
OF DURATION
Do not think of duration as a measure of time!
Zvi Wiener
Introduction to Financial Markets
slide 146
Duration Reconsidered
•Duration is NOT an approximation, it is a
first-order derivative
•It’s APPLICATION is an approximation
•This makes it a particularly seductive error
•Duration can reagularly exceed remaining
life of a security (inverse floaters, I/Os)
Zvi Wiener
Introduction to Financial Markets
slide 147
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
Zvi Wiener
Introduction to Financial Markets
slide 148
Bond Market Bootcamp
2001 FRM Certification Review
Session Five
FRM
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
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
Zvi Wiener
Introduction to Financial Markets
slide 150
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?
Zvi Wiener
Introduction to Financial Markets
slide 151
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)
Zvi Wiener
Introduction to Financial Markets
slide 152
Modified Duration
•3/ (1+.043/2) =
•3/1.0215 =
•2.9368
Zvi Wiener
Introduction to Financial Markets
slide 153
Duration Warmups
•5% UST 9/03
•Purchased today @ YTM 4.33%
•Calculate the duration
Zvi Wiener
Introduction to Financial Markets
slide 154
Duration Review: Gilts
•Calculate the modified duration of a UKT
with a McCauley duration of 7.865 years.
Assume rates are 4.75%
Zvi Wiener
Introduction to Financial Markets
slide 155
Duration on Gilts
•Don’t 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=
Zvi Wiener
Introduction to Financial Markets
slide 156
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
Zvi Wiener
Introduction to Financial Markets
slide 157
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
Zvi Wiener
Introduction to Financial Markets
slide 158
FRM 98:50
Leverage 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?
Zvi Wiener
Introduction to Financial Markets
slide 159
FRM 98:50
•Fund borrows 200mm and invests 300m.
•300 x 0.14 = $42mm
•200 x 0.08 = $16mm
•Net profits are $26mm on $100mm, or 26%.
Zvi Wiener
Introduction to Financial Markets
slide 160
BONDS WITH EMBEDDED
OPTIONS
•Convertibles
•Mortgage Backeds (first generation)
•I/Os and P/Os
Zvi Wiener
Introduction to Financial Markets
slide 161
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
Zvi Wiener
Introduction to Financial Markets
slide 162
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
Zvi Wiener
Introduction to Financial Markets
slide 163
Convertibles
•$1000 (face value is always $1000)/40= 25
shares
•25 shares @45=$1,125
•Bond may be sold at higher price than
convertible value
Zvi Wiener
Introduction to Financial Markets
slide 164
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
Zvi Wiener
Introduction to Financial Markets
slide 165
Convertible Hedge
•Requires an asset swap to maintain
investment structure yet modify underlying
credit to an acceptable name and tenure.
Zvi Wiener
Introduction to Financial Markets
slide 166
FRM 98:34
•A 3 yr convertible paying 4% p.a. priced at
par, right to conversion ratio of 10 @ $75,
forced conversion at maturity. Convexity
relative to underlying equity is:
•a) zero
b) always positive
•c) always negative d) none of the above
Zvi Wiener
Introduction to Financial Markets
slide 167
FRM 98:34
•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.
Zvi Wiener
Introduction to Financial Markets
slide 168
FRM 97:52
Convertible 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
Zvi Wiener
Introduction to Financial Markets
slide 169
Convertible Risk
FRM 97:52
•C) value of the fixed rate bond will fall as
rates increase, value of the embedded warrant
will fall as equity prices decline.
Zvi Wiener
Introduction to Financial Markets
slide 170
FRM 98:9
Equity Indeces
•To prevent arbitrage, the theoretical price of
a stock index need be fully determined via:
•I) cash price
•III) inflation
•
•a) I & II
•c) I, II & IV
Zvi Wiener
II) financing cost
IV) dividend yield
b) II & III
d) all of the above
Introduction to Financial Markets
slide 171
Equity Indeces
FRM 98:9
•While embedded in the underlying nominal
interest rate of the futures, inflationis not a
direct calculation of any futures index.
Zvi Wiener
Introduction to Financial Markets
slide 172
IO/PO Key Concepts
•I/O+ P/O must equal the MBS
•IO’s are bullish securities with negative
duration.
Zvi Wiener
Introduction to Financial Markets
slide 173
Duration and I/O’s P/O’s
•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
Zvi Wiener
Introduction to Financial Markets
slide 174
FRM 99:79
IO’s and PO’s
• 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
Zvi Wiener
Introduction to Financial Markets
slide 175
FRM 99:79
•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.
Zvi Wiener
Introduction to Financial Markets
slide 176
Mortgage Backed Securities:
Conceptual Review
Zvi Wiener
Introduction to Financial Markets
slide 177
Fixed Rate Mortgage
A series of equal payments with PV=loan.
Example: 100,000 for 20 years with 6% and
equal monthly payments.
100,000 
12*20

i 1
Zvi Wiener
x
 0.06 
1 

12 

Introduction to Financial Markets
i
slide 178
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.
Zvi Wiener
Introduction to Financial Markets
slide 179
Balloon Mortgage
One payment at the end.
Sometimes they have renegotiation points.
Zvi Wiener
Introduction to Financial Markets
slide 180
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.
Zvi Wiener
Introduction to Financial Markets
slide 181
Prepayments
Prepayment speed, conditional prepayment rate
CPR (prepayment rate assumed for a pool).
Single-Monthly mortality rate SMM.
SMM = 1 - (1-CPR)1/12
Zvi Wiener
Introduction to Financial Markets
slide 182
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.
Zvi Wiener
Introduction to Financial Markets
slide 183
PSA standard default assumptions
Annual default rate (SDA) in %
0.6
0.3
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
0.02
Age in months
Zvi Wiener
120
Introduction to Financial Markets
60 0
30
slide 184
100 PSA
Annual CPR in %
6
0.2
Age in months
Zvi Wiener
30
Introduction to Financial Markets
0
slide 185
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.
Zvi Wiener
Introduction to Financial Markets
slide 186
Example of prepayments
Example: let CPR=6%, 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.
Zvi Wiener
Introduction to Financial Markets
slide 187
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
Zvi Wiener
Introduction to Financial Markets
slide 188
FRM 99:44
Prepayment Risk
• The following are reasons why a prepayment
•
•
•
•
Zvi Wiener
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
Introduction to Financial Markets
slide 189
FRM 99:44
MBS Prepayments
•A) the factor influencing most the decision to
repay early (the embedded option) is, from
this list, refinancing incentives
Zvi Wiener
Introduction to Financial Markets
slide 190
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.
Zvi Wiener
Introduction to Financial Markets
slide 191
FRM 99:51
CPR to SMM Conversion
• Suppose the annual prepayment rate CPR
•
•
•
•
Zvi Wiener
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%
Introduction to Financial Markets
slide 192
FRM 99:51
Convert CPR to SMM
•(A) 0.51%
•(1-6%)=(1-SMM) 12
•SMM = 0.51%
Zvi Wiener
Introduction to Financial Markets
slide 193
MBS Bond Equivalent Yield
Bond equivalent yield = 2[ (1+yM)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.
Zvi Wiener
Introduction to Financial Markets
slide 194
Bond Market Bootcamp
2001 FRM Certification Review
Session Six
FRM
http://pluto.mscc.huji.ac.il/~mswiener/zvi.html
Options 102
•Review of Basic Concepts & Their
Applications
Zvi Wiener
Introduction to Financial Markets
slide 196
Options 101
•Never forget the fact that lognormal
distributions are positively skewed
Zvi Wiener
Introduction to Financial Markets
slide 197
Options 101
•Delta
•Gamma
•Vega
•Theta
Zvi Wiener
Introduction to Financial Markets
slide 198
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.
Zvi Wiener
Introduction to Financial Markets
slide 199
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
Zvi Wiener
Introduction to Financial Markets
slide 200
FRM 97:49
• 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 longerterm options
• B) buying short-dated options & selling longerterm options
• C) selling both periods D) buying both periods
Zvi Wiener
Introduction to Financial Markets
slide 201
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
Zvi Wiener
Introduction to Financial Markets
slide 202
Options 102
•Butterfly strategies are employed in very
stable markets precisely as means of
capitalizing on dynamic hedging from the
long side
Zvi Wiener
Introduction to Financial Markets
slide 203
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
Zvi Wiener
Introduction to Financial Markets
slide 204
Options 102
•European v. American
•Model implications
Zvi Wiener
Introduction to Financial Markets
slide 205
American Options
•May be exercised at any time to maturity
•Accordingly, on equity options, early
exercise of an American option on a nondividend paying stock can never be optimal
strategy.
Zvi Wiener
Introduction to Financial Markets
slide 206
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.
Zvi Wiener
Introduction to Financial Markets
slide 207
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
Zvi Wiener
Introduction to Financial Markets
slide 208
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
Zvi Wiener
Introduction to Financial Markets
slide 209
FRM 99:35
Put Call Parity
• According to put call parity, writing a put is
equivalent to:
•
•
•
•
Zvi Wiener
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.
Introduction to Financial Markets
slide 210
FRM 99:35
Put 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.
Zvi Wiener
Introduction to Financial Markets
slide 211
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.
Zvi Wiener
Introduction to Financial Markets
slide 212
Equity Options
•Key concept: focus upon whether option
model requires inclusion or exclusion on
dividend
Zvi Wiener
Introduction to Financial Markets
slide 213
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.
Zvi Wiener
Introduction to Financial Markets
slide 214
Options 102:Nomenclature
Question
•Buy 1 43P @ $6
•Sell 2 37P @ $4
•Buy 1 32P @ $1
•Stock expires at $19
•Calculate P/L
Zvi Wiener
Introduction to Financial Markets
slide 215
Options 102: Nomenclature
•(43-19) + (2 *-37+19)+(32-19) + (-6+4+4-1)
=
•2 per share
Zvi Wiener
Introduction to Financial Markets
slide 216
Options 102
•180 day Call option, strike price @ 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
Zvi Wiener
Introduction to Financial Markets
slide 217
Options 102:
Bonds
•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
Zvi Wiener
Introduction to Financial Markets
slide 218
Options 102:
“Myron, the Damned Model
Doesn’t 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
example…cost TF Bank the ranch in identical
trade in 1998, and Ulusal/Demir this year
Zvi Wiener
Introduction to Financial Markets
slide 219
Options 102:
“Myron, you still deserve that
damned Nobel”
•prices embedded options very simply and
accurately
Zvi Wiener
Introduction to Financial Markets
slide 220
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)
Zvi Wiener
Introduction to Financial Markets
slide 221
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
Zvi Wiener
Introduction to Financial Markets
slide 222
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
Zvi Wiener
Introduction to Financial Markets
slide 223
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.
Zvi Wiener
Introduction to Financial Markets
slide 224
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
Zvi Wiener
Introduction to Financial Markets
slide 225
Options 102
•We own a swaption on 10 year Yen LIBOR
to 3% annual swap
•Trader hedged by shorting JGB 83s (couldn’t
resist a JGB example in Tel Aviv as payback
for the Shachars and Gilboas)
•What risks are hedged, what risks remain?
Zvi Wiener
Introduction to Financial Markets
slide 226
Options 102
•Volatility risk remains as primary risk
•Basis risk remains, and has added another
demension
•Interest rate reduced, but not curve risk
Zvi Wiener
Introduction to Financial Markets
slide 227
Options 102:
Bermuda Triangles
•Any option with a discontinuous payoff
function necessitates an exceedingly high
gamma near the strike price
Zvi Wiener
Introduction to Financial Markets
slide 228
Options 102
•Therefore, any such option: Asiatic,
Bermudan will require a specific model
loosely based upon but VERY different than a
traditional BS
Zvi Wiener
Introduction to Financial Markets
slide 229
FRM 99:34
•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
•C) 10.00
Zvi Wiener
B) 13.90
D) 5.90
Introduction to Financial Markets
slide 230
FRM 99:34
•$90-[$80 (-0.05 x 1)] = 90-76.10=$13.90
•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.
Zvi Wiener
Introduction to Financial Markets
slide 231
FRM 99:52
American option pricing question
• Price of an American equity call option equals an
•
•
•
•
Zvi Wiener
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.
Introduction to Financial Markets
slide 232
FRM 99:52
•B) an American call option will not be
exercised early when there is no income
payment on the underlying asset.
Zvi Wiener
Introduction to Financial Markets
slide 233
FRM 98:58
Options 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
Zvi Wiener
Introduction to Financial Markets
slide 234
FRM 98:58
•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.
Zvi Wiener
Introduction to Financial Markets
slide 235
Options Exotica
•Binary & digital options
•Barriers (knock-in, knock-out)
•Down & Out, Down & In, Up & Out, Up &
In
•Asian options, or average rate options
Zvi Wiener
Introduction to Financial Markets
slide 236
Options Exotica
FRM 98:4
•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
Zvi Wiener
Introduction to Financial Markets
slide 237
FRM 98:4
•Discontinuous are harder to price at barrier
with little time remaining.
Zvi Wiener
Introduction to Financial Markets
slide 238
FRM 97:10
•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
Zvi Wiener
Introduction to Financial Markets
slide 239
FRM 97:10
•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.
Zvi Wiener
Introduction to Financial Markets
slide 240
Swaps, FX, Caps & Collars
•Review of Nomenclature and Core Concepts
Zvi Wiener
Introduction to Financial Markets
slide 241
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.
Zvi Wiener
Introduction to Financial Markets
slide 242
FRM 99:42
Swaps
•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
Zvi Wiener
Introduction to Financial Markets
slide 243
FRM 99:42
Swaps
•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?
Zvi Wiener
Introduction to Financial Markets
slide 244
FRM 99:59
Swap 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
Zvi Wiener
Introduction to Financial Markets
slide 245
FRM 99:59
•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.
Zvi Wiener
Introduction to Financial Markets
slide 246
FRA & Forward Pricing
•6x9 FRA $10mm 4.25% LIBOR 30/360
•settles at 4.85%
•calculate P/L
Zvi Wiener
Introduction to Financial Markets
slide 247
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
Zvi Wiener
Introduction to Financial Markets
slide 248
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
Zvi Wiener
Introduction to Financial Markets
slide 249
FRA Pricing Example Two
•6x9 FRA 4.25% LIBOR, 30/360 daycount
•settles at 3.95% on $10mm
•calculate the P/L
Zvi Wiener
Introduction to Financial Markets
slide 250
FRA Pricing Example Two
•$10mm @ 4.25 * .25= $106,250
•$10mm @ 3.95 * .25= $ 98,750
•$7500/ 1.009875 = $7,426.66
Zvi Wiener
Introduction to Financial Markets
slide 251
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
Zvi Wiener
Introduction to Financial Markets
slide 252
US $ cash flows
•25mm 4% each coupon is 1mm
•6m DPV@3% = 985,000
•[email protected]%= 965,000
•18mDPV@4%= 940,000
Zvi Wiener
Introduction to Financial Markets
slide 253
GBP cash flows
•GBP17mm 5% coupon = GBP 850,000
•6m DPV @ 4% = 828,750
•[email protected]% = 811,750
•18mDPV@5% = 786,250
•convert cumulative GBP cash flows @
1.4775
Zvi Wiener
Introduction to Financial Markets
slide 254
FX Swaps Example
•6m cash flow: $985,000-951,197.81
=$33,802.19
•12m c/f:
=$33,313.14
•18m c/f:
=37,581.57
$965,000-931,686.86
$940,000-902,418.43
•total p/l adjustment = $ 104,696.90
Zvi Wiener
Introduction to Financial Markets
slide 255
FX Swaps Example Two
•Estimate the forward rate for 6 month Eur/$.
•US$ LIBOR is 3%, Eur is 4%.
•Eur/$ is 0.9100 spot
Zvi Wiener
Introduction to Financial Markets
slide 256
•0.9100 ( -.01/2) = -0.00455
•forward FX rate of 0.90545
Zvi Wiener
Introduction to Financial Markets
slide 257
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.
Zvi Wiener
Introduction to Financial Markets
slide 258
FRM 99:54
•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
Zvi Wiener
Introduction to Financial Markets
slide 259
FRM 99:54
•A) with same strike price, a short cap/long
floor loses money if rates increase which is
equivalent to a fixed rate bond position
Zvi Wiener
Introduction to Financial Markets
slide 260
FRM 99:60
Cap Risk
• For a 5 yr ATM cap on LIBOR, what can be said
about the individual caplets in a downward
sloping term structure?
•
•
•
•
Zvi Wiener
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 the caplets is also dependent
upon the volatility term structure.
Introduction to Financial Markets
slide 261
Swaptions
FRM 97:18
•The price of an option to receive fixed on a
swap will decrease as:
•a) time to expiry of the option increases
•b) time to expiry of the swap increases
•c) swap rate rises
•d) volatility increases
•(think, this is a bit of a trick question)
Zvi Wiener
Introduction to Financial Markets
slide 262
FRM 97:18
Swaptions
•C) value of the call increases with the
maturity of the call and underlying asset
value. In contrast, the value of the right to
receive an asset at K decreases as K increases.
Zvi Wiener
Introduction to Financial Markets
slide 263
FRM 99:60
•A) in an inverted interest rate environment,
forwards are higher for short rates. As caplets
involve the right to buy a series of FRN
options stuck at the same fixed strike price,
short dates will be ITM and longer dates OTM
for an ATM cap.
Zvi Wiener
Introduction to Financial Markets
slide 264
FX 101
Core Concept
• receiving an FX swap is equivalent to a long
position in a foreign pay bond and a short
position in a dollar pay bond
Zvi Wiener
Introduction to Financial Markets
slide 265
FX 101
•$:JPY 120
•12 month Libor is 6%
•12 month Yen rates are 1%
•Calculate the forward
Zvi Wiener
Introduction to Financial Markets
slide 266
FX Options 102
•Therefore, in FX options the BS model need
be ammended to include consideration of the
all-important foreign interest rate
Zvi Wiener
Introduction to Financial Markets
slide 267
Garman Kohlhagen Model
•Applied BS to FX, employing the foreign
interest rate as the yield in the original BS
model. In short, any income payment is
automatically reinvested in the asset.
Zvi Wiener
Introduction to Financial Markets
slide 268
Physical & Precious
Commodities
•Beans in the Teens, or why there are still no
Nice Jewish Boys in the Pork Bellies pit
Zvi Wiener
Introduction to Financial Markets
slide 269
Commodities
•If a commodity is more expensive for
immediate delivery than for future delivery,
the commodity curve is said to be in
backwardation. As distinct from interest rate
curves where interest accrues with the normal
passage of time, backwardation is the
“normal” term structure for almost all
physical storage and delivery commodities.
Zvi Wiener
Introduction to Financial Markets
slide 270
Backwardation Aspect
•GSCI is useful in that it provides an accurate
market value of the major commodity indeces
adjusted for their storage costs at present
market conditions
Zvi Wiener
Introduction to Financial Markets
slide 271
“Beans in the Teens”
•agricultural futures: grains (corns, wheat,
soybeans) and food & fiber
(cocoa,coffee,sugar, OJ…think Eddie
Murphy)
•livestock: cattle, hogs, pork bellies
•trade with inflation rather than against
inflation (such as financial assets)
Zvi Wiener
Introduction to Financial Markets
slide 272
Metals
•Base metals: aluminum, copper, nickel, zinc
•Precious: gold, silver, platinum
Zvi Wiener
Introduction to Financial Markets
slide 273
Convenience Yield in Physicals
•Forward prices are only at a discount v. spot
prices in backwardation markets.
Zvi Wiener
Introduction to Financial Markets
slide 274
FRM 99:32
•Spot April Corn is 207/bushel. CNU1 is
241.50. What statement is true about the
expected spot price in September?
•A) higher than 207 B) lower than 207
•C) higher than 241.50 D) lower than 241.50
Zvi Wiener
Introduction to Financial Markets
slide 275
Gold Pricing
•Spot gold $288/ounce
•12m LIBOR (continuou compounded) is
5.73%
•storage costs are $2/ounce p.a.
•Price the one year forward
Zvi Wiener
Introduction to Financial Markets
slide 276
Gold Pricing
•290 (1.0573) = 307.10
•price rose rather than dropped, as forward
purchaser need not incur the storage costs for
the year
•a reverse dividend, conceptually
Zvi Wiener
Introduction to Financial Markets
slide 277
Energy Products
•Natural gas, heating oil, WTI unleaded
gasoline, crude oil
•electricity (California/Oregon Border)
•Weather & Waste
Zvi Wiener
Introduction to Financial Markets
slide 278
FRM 98:27
Metallgesellscaft AG
• MG Trading’s losses were the direct result
of employing an interest rate type strategy
of “stack-and-roll”. This hedge involved:
• a) buying short dates futures to hedge long term exposures,
expecting long term oil to rise
• b) buying short dated futures to hedge long term exposure,
expecting long term oil prices to decline
• c) selling short dates futures, expecting short term prices to
rise
• d) selling short term futures, expecting short term prices to
decline
Zvi Wiener
Introduction to Financial Markets
slide 279
FRM 98:27
MG Trading AG
• A) MG hedged sales of oil forward by
buying short term oil contracts on a
“duration ratio basis”. In theory, price
declines in one should have offset the other.
Compound Hedging Error: They got convexity
wrong as well. In futures markets, however, losses
were realized immediately, which led to significant
liquidity problems even if the long term price of oil
had remained constant (which, of course, it did
not).
Zvi Wiener
Introduction to Financial Markets
slide 280