introduction to financial markets

FRMhttp://pluto.mscc.huji.ac.il/

~mswiener/zvi.html

Zvi Wiener02-588-3049

[email protected]

Introduction to Financial Markets

Zvi WienerIntroduction to Financial

Marketsslide 2

Call Option

European Call

X Underlying

premium


Marketsslide 3

Put Option

European Put

X Underlying

premium

X


Marketsslide 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?


Marketsslide 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.


Marketsslide 6

Collar payoff

payoff

90 100 K stock

90

K


Marketsslide 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!


Marketsslide 8

Inverse Floater

Today

1 yr

2 yr

3 yr

4 yr

5 yr

A

-100

L

L

L

L

L+100

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


Marketsslide 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!).


Marketsslide 10

Yield Enhancement

USD

1.07

1.045

Payoff at the year end

Sell some amount of USD Put options,the money received invest in SHEKELaccount!


Marketsslide 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


~mswiener/zvi.html

Zvi Wiener02-588-3049

[email protected]

Example of Risk Management


Marketsslide 13

Investment Decision

$1000M bonds

capital capital

$900M bonds

$100M stocks5%13%


Marketsslide 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.


Marketsslide 15

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


Marketsslide 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.


Marketsslide 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.


Marketsslide 18

Tax in Financial Sector

%299.45%)361(17.1

17.0%36


Marketsslide 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?


Marketsslide 20

Long term options

payoff

k K stock

50

K

Sell a call

Your option

Result


Marketsslide 21

ExampleYou 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!


Marketsslide 22

Example

payoff

10 15 26

50

K

Your option

Result

60

exercise


~mswiener/zvi.html

Bond Market Bootcamp:Handouts

Session One


~mswiener/zvi.html

Bond Market Bootcamp

2001 FRM Certification Review

Session One


Marketsslide 25

Fixed Income Securities

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


Marketsslide 26

Overview of Bond Markets

•Bond

•Note

•Money Market Securities

•Sovereign, Agency,Corporate Debentures

•Handout A-1 & A-2, Street Software Inc


Marketsslide 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


Marketsslide 28

Types of Fixed Income Securities

•Corporate bonds

•Foreign bonds

•Eurobonds

•Mortgage Backed Securities (pass throughs)

•ABS

•Brady Bonds


Marketsslide 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


Marketsslide 30


Marketsslide 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)


Marketsslide 32

Brady Bonds

Argentina, Brazil, Costa Rica, Dominican Republic, Ecuador, Mexico, Uruguay, Venezuela, Bulgaria, Jordan, Nigeria, Philippines, Poland.

Partially collateralized by US government securities


Marketsslide 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


Marketsslide 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


Marketsslide 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


Marketsslide 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


Marketsslide 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


Marketsslide 38

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)


Marketsslide 39

Fixed Income Universe

•Perpetual notes (consols in UK)

•Structured notes

•Inverse floaters

•Callable bonds

•Puttable bonds

•Convertible notes


Marketsslide 40

Characteristics of a Bond

• Issuer

• Time to maturity

• Coupon rate, type and frequency

• Linkage

• Embedded options

• Indentures

• Guarantees or collateral


Marketsslide 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


Marketsslide 42

Applications

• Active Bond Portfolio Management

• Indexation

• Liability Funding Strategies

• Bond Performance Measurements (AIMR)

• Interest Rate Futures & Options

• Interest Rate Swaps, Caps, Floors


Marketsslide 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


Marketsslide 44

Analytic Tools to be Reviewed (cont’d)

•Price volatility for option free bonds

•Duration

•Convexity

•Embedded options & their applications


Marketsslide 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


Marketsslide 46

Basic NomenclatureCoupon 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.


Marketsslide 47

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


Marketsslide 48


Marketsslide 49

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


Marketsslide 50


•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


Marketsslide 51


•$3.125 (semi-annual coupon)

•$3.125 x 163 = 2.798763

•($20mm/100) x [(104 + 12/32) + 2.798763 = $21,434,753]


Marketsslide 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 = (1+y x t/365), or 5.33% for the above 5.19%


Marketsslide 53

Price quotes for T-Bills

360

FtYD d

3601

tYFDFprice d


Marketsslide 54


%75.8100

360

100

569.97100

dY

100 days to maturityprice = $97,569 will be quoted at 8.75%

360

1000875.01000,100$569,97$


Marketsslide 55

FRM 98:13T 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%


Marketsslide 56

FRM 98:13

• 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%


Marketsslide 57

FRM 98:13Bank 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


Marketsslide 58


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

d

d

Yt

YyielequivCD

360

360.

%97.8%75.8100360

%75.8360.

yielequivCD


Marketsslide 59

TIPS

•Index linked government securities

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


Marketsslide 60

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


Marketsslide 61

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%

price

ratecouponannualyieldcurrent


Marketsslide 62

The Yield to Maturity

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

n

i

ytTi

iectp1

)()(


Marketsslide 63

Embedded Options

•Calls, Puts

•Repricing Features (Inverse Floaters)

•Prepayment Features

•Credit Features


Marketsslide 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.


Marketsslide 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)


Marketsslide 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.


Marketsslide 67

Putable Bond

Long Bond + Put

PX = Straight Bond + Put Option (adjusted for credit spread as appropriate)


Marketsslide 68

FRM 00:09Callable 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


Marketsslide 69

FRM 00:74Derivatives 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


Marketsslide 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).


Marketsslide 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.


Marketsslide 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 FED’s portfolio while posting other Treasury security as collateral.


Marketsslide 73

Repo ExampleYou 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.


Marketsslide 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.


Marketsslide 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.


Marketsslide 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?


Marketsslide 77

Yield Curve Analysis

•Normal Curve

•Inverted Curve

•Twister


Marketsslide 78

Yield Curve Analysis

•Par curve

weighted avg of spot ratesweighted avg of spot rates

•Spot Curve

currently priced zero curveurrently priced zero curve

Forward Curve

commence at future datecommence at future date


Marketsslide 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


Marketsslide 80

Forward RatesBuy 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(


Marketsslide 81

Forward Rates

(1+r3)=(1+r1)(1+f13)= (1+r1)(1+f12)(1+f13)

Term structure of instantaneous forward rates.


Marketsslide 82

Time Value of Money

•Future Value

•Discounted Present Value (DPV)

•Internal Rate of Return

•Implications of curve structure on pricing

•Conventional Yield Measurements


Marketsslide 83

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-PV5555105

5

4

1 )1(

105

)1(

5

rrPV

tt


Marketsslide 84

Determinants of the Term Structure

Expectation theory

Market segmentation theory

Liquidity theory

Mathematical models: Ho-Lee, Vasichek,

Hull-White, HJM, etc.


Marketsslide 85

TT

T

tt

t

r

C

r

CPV

)1()1(1

Term structure of interest rates

TT

TT

tt

t

t

r

C

r

CPV

)1()1(1

Yield = IRR

TT

T

tt

t

y

C

y

Cice

)1()1(Pr

1

How do we know that there is a solution?


Marketsslide 86

Parallel shift

T

r

Current UST

Downward move

upward move


Marketsslide 87

Twist

T

r

steepening

flattening


Marketsslide 88

Butterfly

T

r


Marketsslide 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!


Marketsslide 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


Marketsslide 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?


Marketsslide 92

FRM 00:95Curve 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.


Marketsslide 93

FRM 98:39Yield 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.


Marketsslide 94

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.


Marketsslide 95

FRM 97:1Yield 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


Marketsslide 96

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.


Marketsslide 97

FRM 99:1Yield 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.


Marketsslide 98

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.


~mswiener/zvi.html



Session Two


Marketsslide 100

YTM and Reinvestment Risk

• YTM assumes that all coupon (and

amortizing) payments will be invested at the

same yield.


Marketsslide 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?


Marketsslide 102

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.


Marketsslide 103

FRM 00:6Dollar 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) A$27.00 per million


Marketsslide 104

FRM 99:53Dollar 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


Marketsslide 105

FRM 99:53Dollar Value of an 01

•(135.85-132.99)/134.41/[0.001*2] = 10.63


Marketsslide 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


Marketsslide 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 LIBOR>10% there is typically a floor.


Marketsslide 108

FRM 98:3The 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


Marketsslide 109

FRM 98:3Inverse 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.


Marketsslide 110

FRM 98: 3

•Answer is DR = 8.75%

•Yield is 9.09%


Marketsslide 111

Duration and IR sensitivity


Marketsslide 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?


Marketsslide 113

FRM 98:31Duration

• 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 bond’s duration?

• A) 5 years

• B) 7.5 years

• C) 10 years

• D) cannot be determined from given data


Marketsslide 114

FRM 98:31Zero 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


Marketsslide 115

Duration

nn y

M

y

C

y

C

y

CP

)1()1()1()1( 2

nn y

nM

y

nC

y

C

y

C

P

DurationMacaulay

)1()1()1(

2

)1(

112


Marketsslide 116

Duration

y

DurationMacaulayDurationModified

1

DurationModifiedPdy

dP 1


Marketsslide 117

Meaning of Duration

Dpecdy

d

dy

dp n

i

yTi

i

1


Marketsslide 118

Macaulay Duration

Definition of duration, assuming t=0.

p

ecTD

n

i

yTii

i

1


Marketsslide 119

Macaulay Duration

T

tt

tT

tt y

CFt

iceBondwtD

11 )1(Pr

1

A weighted sum of times to maturities of each coupon.

What is the duration of a zero coupon bond?


Marketsslide 120

KEY MISCONCEPTION OF DURATION

Do not think of duration as a measure of time!


Marketsslide 121

FRM 98:32IO’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


Marketsslide 122

FRM 00:73Duration

• 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


Marketsslide 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?


Marketsslide 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.


Marketsslide 125

FRM 97:49FRN 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


Marketsslide 126

FRM 97:49Floating 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.


Marketsslide 127

Duration

8212.907.1

20

05.1

1

2

1

8212.9

1

07.1

1

05.1

2

1

0

2020

20

1

xxrxrdx

d

dr

dA

ADA

1

BA

BD

BA

ADD BA

BA


Marketsslide 128

Convexity


Marketsslide 129

Convexity

368

1

07.1

1

05.1

0

2020

20

12

2

x

xrxrdx

d

2

2

dr

AdCA

For a simple bond portfolio it does not help much!

It is much more important to consider 2 risk factors!


Marketsslide 130

-0.03 -0.02 -0.01 0.01 0.02 0.03

1.6

1.8

2.2

2.4

2.6

2.8

Value

2

07.01

07.1

05.01

05.1

1

07.1

1

05.120

20

2020

20

1

rr

Parallel shift

value


Marketsslide 131

FRM 99:40Effective 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


Marketsslide 132

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.


Marketsslide 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


Marketsslide 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%

•-100x% Y%


Marketsslide 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)


~mswiener/zvi.html



Session Four


Marketsslide 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


Marketsslide 138

Bootcamp Warmups

•Which exchanges merged to form Euronext?


Marketsslide 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


Marketsslide 140

Bootcamp Warmups

•Which market is mean-reverting?

•California energy futures

•TA-25 index

•HM T-Bills

•Notes/Bond spread


Marketsslide 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


Marketsslide 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


Marketsslide 143

Bonds 102

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


Marketsslide 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


Marketsslide 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)


Marketsslide 146

KEY MISCONCEPTION OF DURATION

Do not think of duration as a measure of time!


Marketsslide 147

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)


Marketsslide 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


~mswiener/zvi.html



Session Five


Marketsslide 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


Marketsslide 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?


Marketsslide 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)


Marketsslide 153

Modified Duration

•3/ (1+.043/2) =

•3/1.0215 =

•2.9368


Marketsslide 154

Duration Warmups

•5% UST 9/03

•Purchased today @ YTM 4.33%

•Calculate the duration


Marketsslide 155

Duration Review: Gilts

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


Marketsslide 156

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=


Marketsslide 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


Marketsslide 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


Marketsslide 159

FRM 98:50Leverage 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?


Marketsslide 160

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%.


Marketsslide 161

BONDS WITH EMBEDDED OPTIONS

•Convertibles

•Mortgage Backeds (first generation)

•I/Os and P/Os


Marketsslide 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


Marketsslide 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


Marketsslide 164

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


Marketsslide 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


Marketsslide 166

Convertible Hedge

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


Marketsslide 167

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


Marketsslide 168

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.


Marketsslide 169

FRM 97:52Convertible 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


Marketsslide 170

Convertible RiskFRM 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.


Marketsslide 171

FRM 98:9Equity 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


Marketsslide 172

Equity IndecesFRM 98:9

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


Marketsslide 173

IO/PO Key Concepts

•I/O+ P/O must equal the MBS

•IO’s are bullish securities with negative duration.


Marketsslide 174

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


Marketsslide 175

FRM 99:79IO’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


Marketsslide 176

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.


Marketsslide 177

Mortgage Backed Securities: Conceptual Review


Marketsslide 178

Fixed Rate Mortgage

A series of equal payments with PV=loan.

Example: 100,000 for 20 years with 6% and equal monthly payments.

20*12

1

1206.0

1

000,100i

i

x


Marketsslide 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.


Marketsslide 180

Balloon Mortgage

One payment at the end.

Sometimes they have renegotiation points.


Marketsslide 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.


Marketsslide 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


Marketsslide 183

PSA prepayment benchmarkThe 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.


Marketsslide 184

PSA standard default assumptions

0 30 60 120Age in months

Annual default rate (SDA) in%

0.3

0.6Month 1 - 0.02%

increases by 0.02% till 30mstable at 0.6% 30-60m

declines by 0.01% 61-120mremains at 0.03% after 120m

0.02


Marketsslide 185

100 PSA

030Age in months

Annual CPR in%

0.2

6


Marketsslide 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.


Marketsslide 187

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.


Marketsslide 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


Marketsslide 189

FRM 99:44Prepayment 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


Marketsslide 190

FRM 99:44MBS Prepayments

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


Marketsslide 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.


Marketsslide 192

FRM 99:51CPR 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%


Marketsslide 193

FRM 99:51Convert CPR to SMM

•(A) 0.51%

•(1-6%)=(1-SMM) 12

•SMM = 0.51%


Marketsslide 194

MBS Bond Equivalent YieldBond 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.


~mswiener/zvi.html



Session Six


Marketsslide 196

Options 102

•Review of Basic Concepts & Their Applications


Marketsslide 197

Options 101

•Never forget the fact that lognormal distributions are positively skewed


Marketsslide 198

Options 101

•Delta

•Gamma

•Vega

•Theta


Marketsslide 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.


Marketsslide 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


Marketsslide 201

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 longer-term options

• B) buying short-dated options & selling longer-term options

• C) selling both periods D) buying both periods


Marketsslide 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


Marketsslide 203

Options 102

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


Marketsslide 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


Marketsslide 205

Options 102

•European v. American

•Model implications


Marketsslide 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.


Marketsslide 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.


Marketsslide 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


Marketsslide 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


Marketsslide 210

FRM 99:35Put 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.


Marketsslide 211

FRM 99:35Put 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.


Marketsslide 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.


Marketsslide 213

Equity Options

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


Marketsslide 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.


Marketsslide 215

Options 102:Nomenclature Question

•Buy 1 43P @ $6

•Sell 2 37P @ $4

•Buy 1 32P @ $1

•Stock expires at $19

•Calculate P/L


Marketsslide 216

Options 102: Nomenclature

•(43-19) + (2 *-37+19)+(32-19) + (-6+4+4-1) =

•2 per share


Marketsslide 217

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


Marketsslide 218

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


Marketsslide 219

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


Marketsslide 220

Options 102:“Myron, you still deserve that

damned Nobel”

•prices embedded options very simply and accurately


Marketsslide 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)


Marketsslide 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


Marketsslide 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


Marketsslide 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.


Marketsslide 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


Marketsslide 226

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?


Marketsslide 227

Options 102

•Volatility risk remains as primary risk

•Basis risk remains, and has added another demension

•Interest rate reduced, but not curve risk


Marketsslide 228

Options 102:Bermuda Triangles

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


Marketsslide 229

Options 102

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


Marketsslide 230

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 B) 13.90

•C) 10.00 D) 5.90


Marketsslide 231

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.


Marketsslide 232

FRM 99:52American 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.


Marketsslide 233

FRM 99:52

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


Marketsslide 234

FRM 98:58Options 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


Marketsslide 235

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.


Marketsslide 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


Marketsslide 237

Options ExoticaFRM 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


Marketsslide 238

FRM 98:4

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


Marketsslide 239

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


Marketsslide 240

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.


Marketsslide 241

Swaps, FX, Caps & Collars

•Review of Nomenclature and Core Concepts


Marketsslide 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.


Marketsslide 243

FRM 99:42Swaps

•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


Marketsslide 244

FRM 99:42Swaps

•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?


Marketsslide 245

FRM 99:59Swap 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


Marketsslide 246

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.


Marketsslide 247

FRA & Forward Pricing

•6x9 FRA $10mm 4.25% LIBOR 30/360

•settles at 4.85%

•calculate P/L


Marketsslide 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


Marketsslide 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


Marketsslide 250

FRA Pricing Example Two

•6x9 FRA 4.25% LIBOR, 30/360 daycount

•settles at 3.95% on $10mm

•calculate the P/L


Marketsslide 251

FRA Pricing Example Two

•$10mm @ 4.25 * .25= $106,250

•$10mm @ 3.95 * .25= $ 98,750

•$7500/ 1.009875 = $7,426.66


Marketsslide 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


Marketsslide 253

US $ cash flows

•25mm 4% each coupon is 1mm

•6m DPV@3% = 985,000

•[email protected]%= 965,000

•18mDPV@4%= 940,000


Marketsslide 254

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


Marketsslide 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


Marketsslide 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


Marketsslide 257

•0.9100 ( -.01/2) = -0.00455

•forward FX rate of 0.90545


Marketsslide 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.


Marketsslide 259

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


Marketsslide 260

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


Marketsslide 261

FRM 99:60Cap 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 the caplets is also dependent upon the volatility term structure.


Marketsslide 262

SwaptionsFRM 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)


Marketsslide 263

FRM 97:18Swaptions

•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.


Marketsslide 264

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.


Marketsslide 265

FX 101Core 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


Marketsslide 266

FX 101

•$:JPY 120

•12 month Libor is 6%

•12 month Yen rates are 1%

•Calculate the forward


Marketsslide 267

FX Options 102

•Therefore, in FX options the BS model need be ammended to include consideration of the all-important foreign interest rate


Marketsslide 268

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.


Marketsslide 269

Physical & Precious Commodities

•Beans in the Teens, or why there are still no Nice Jewish Boys in the Pork Bellies pit


Marketsslide 270

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.


Marketsslide 271

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


Marketsslide 272

“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)


Marketsslide 273

Metals

•Base metals: aluminum, copper, nickel, zinc

•Precious: gold, silver, platinum


Marketsslide 274

Convenience Yield in Physicals

•Forward prices are only at a discount v. spot prices in backwardation markets.


Marketsslide 275

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


Marketsslide 276

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


Marketsslide 277

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


Marketsslide 278

Energy Products

•Natural gas, heating oil, WTI unleaded gasoline, crude oil

•electricity (California/Oregon Border)

•Weather & Waste


Marketsslide 279

FRM 98:27Metallgesellscaft 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


Marketsslide 280

FRM 98:27MG 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).

introduction to financial markets

Documents