Trading the Yield Curve. Copyright Investment Analytics
|
|
|
- Brett Holt
- 8 years ago
- Views:
Transcription
1 Trading the Yield Curve Copyright Investment Analytics 1
2 Trading the Yield Curve Repos Riding the Curve Yield Spread Trades Coupon Rolls Yield Curve Steepeners & Flatteners Butterfly Trading Copyright Investment Analytics Trading the Yield Curve Slide: 2
3 Repos Firm A Firm A Repurchase of Security Today Sale of T 1 Security Firm B Firm A funds itself by doing a repo Pays interest to the buyer at the repo rate Firm B lends money by doing a reverse repo Regarded as a collateralized loan Firm B Copyright Investment Analytics Trading the Yield Curve Slide: 3
4 Repo Trades Repo Master Agreement Term Mainly short term: overnight (70%) to 1 week (20%) Long term up to one year ( Term repos ) Repo Rate Can be paid as interest or by setting repurchase price above sale price Simple add-on interest, 360 day year: (1 + r x n/360) Overnight repo rate typically spread below Fed Funds Copyright Investment Analytics Trading the Yield Curve Slide: 4
5 Repo Trades Securities ( Collateral ) Mainly Treasuries & Agency securities, but also CD s BA s, CP, MBS Credit risk: applies to both parties Margin ( Haircut ) Good faith deposit paid by borrower to lender Sells securities worth $100, borrows $98 Right of substitution Borrow may pay extra 2-3 bp for right to offer lender other collateral Copyright Investment Analytics Trading the Yield Curve Slide: 5
6 Repo Markets Borrowers of collateral (reverses) Mainly dealers wanting to short specific issues The specials market Lenders of collateral (repos) Banks, S&L s Munis Brokers Garvin, Prebon, Tullet Copyright Investment Analytics Trading the Yield Curve Slide: 6
7 Trading Applications Customer Arbs Reverses to maturity Tails Copyright Investment Analytics Trading the Yield Curve Slide: 7
8 Customer Arbs Reverses to maturity Yields have risen, customer portfolios are underwater Portfolio managers can t take a loss Carrying securities at book value, rather than current lower market value Choice: Sell securities, book loss, & reinvest proceeds at higher yields Hang onto underwater securities, avoid booking a loss, earn a lower yield Copyright Investment Analytics Trading the Yield Curve Slide: 8
9 Reverses to Maturity Dealer offers to reverse in underwater securities for remaining term Sells securities in market Invests proceeds in securities of equal maturity at yield spread above break-even reverse rate Customer gets funds at repo rate, re-invests in higher yield securities at e.g. X% + 50bp At maturity dealer offsets amount lent to customer (plus interest) against face value of securities he has reversed in (plus final coupon) Copyright Investment Analytics Trading the Yield Curve Slide: 9
10 Reverse to Maturity Customer Underwater securities, Loan at x% Dealer Sell underwater securities Invest proceeds at x% + 50bp Invest proceeds at > x% + 50bp Copyright Investment Analytics Trading the Yield Curve Slide: 10
11 Tails Purchase 90-day bill 0 Discount rate 5.95% 90 Finance purchase with 30-day term repo 0 Repo rate 5.75% day forward bill 30 Effective discount rate?? (current 60-day bill yield is 5.80%) 90 Copyright Investment Analytics Trading the Yield Curve Slide: 11
12 Lab: Figuring the Tail Current 90-day bill yield is 5.95% 30-day term repo rate is 5.75% Earn 20bp carry by repo-ing the 90-day bill Effectively creates a 60-day bill in 30-days time What is the effective discount rate on this forward bill? Current 60-day bill yield is 5.80% Copyright Investment Analytics Trading the Yield Curve Slide: 12
13 Figuring the Tail Effective yield on future security = Yield on cash security purchased + (Carry x Days carried / Days left to maturity) Yield = 5.95% + (0.20% x 30 / 60) = 6.09% Profit = 6.09% % = 0.29% Will do trade if Fed doesn t tighten or spreads don t change unfavorably Copyright Investment Analytics Trading the Yield Curve Slide: 13
14 Cash and Carry Trade Create the tail as before Buy cash bill Finance with term repo Sell the tail forward using bill futures Break-even repo rate is called the implied repo rate Trade is profitable when current repo rate is less than the implied repo rate. Copyright Investment Analytics Trading the Yield Curve Slide: 14
15 Cash & Carry Trade - Example March 98 T-Bill 147 days to maturity Discount rate is 4.93% Dec 97 T-Bill futures contract Expiry in 56 days Futures price What is the implied repo rate? If the 56-day repo rate is 4.83%, calculate the $ profit per $1MM on the cash and carry trade Copyright Investment Analytics Trading the Yield Curve Slide: 15
16 Cash & Carry Trade - Solution Purchase 147-day bill at $979,869 Sell Dec futures contract at $987,589 Implied repo rate: (979, ,589) x 360/56 = 5.06% Profit on C&C Trade: (5.06% %) x $1MM x 56/360 = $357 Copyright Investment Analytics Trading the Yield Curve Slide: 16
17 Riding the Yield Curve A strategy to increase return Works for positively sloped yield curves Assumes stable yield curve Copyright Investment Analytics Trading the Yield Curve Slide: 17
18 Riding Yield Curve Method Buy security out on shoulder of curve As it progresses to maturity, yield decreases Buy Sell Yield Copyright Investment Analytics Trading the Yield Curve Slide: 18
19 Example: Riding Yield Curve 6m (180 day) T-Bill Trading at m (90 day) T-Bill Trading at 6.50 Alternatives: Buy 3m T-Bill and mature it Buy 6m T-Bill and sell after 3 months Perform break-even analysis Copyright Investment Analytics Trading the Yield Curve Slide: 19
20 Lab: Riding Yield Curve Worksheet: Riding Yield Curve Use Bond Tutor: Treasury Calculator Work out Returns: Strategy I (buy 90 day bill) Strategy II (buy 180 days bill & sell after 90 days) What is the extra profit from the yield curve play? What is the Break-Even Discount Rate? Rate at which 180-day bill is sold, after 90 days Rate at which return from Strategy II = return from Strategy Use Goal Seek to find rate Copyright Investment Analytics Trading the Yield Curve Slide: 20
21 Break Even Analysis Copyright Investment Analytics Trading the Yield Curve Slide: 21
22 Riding Yield Curve: Risk/Reward B/e yield is 7.3% Yield on 3m bill will be 6.5%, if yields are unchanged So, strategy has 80bp protection How likely is Fed to tighten 80bp in next 3 months? Exposure of riding yield curve strategies:- Upward shift across yield curve Yield curve might invert at short end Copyright Investment Analytics Trading the Yield Curve Slide: 22
23 Yield Spread Trades Short End T-Bills vs. Short-dated Bonds Treasury coupons vs. Eurodollar Strips Long End Curve Steepeners & Flatteners Bond Basis Trading Copyright Investment Analytics Trading the Yield Curve Slide: 23
24 Trading T-Bills vs. Coupon Issues Yield on Treasury Notes vs. T-Bills Yield on Notes > Bills (usually): Bills have greater liquidity Bills have greater convexity Coupon issues have reinvestment risk, Bills do not Copyright Investment Analytics Trading the Yield Curve Slide: 24
25 Coupons-Bills Spread - Typical Coupon vs. Bills Yield (%) Days to Maturity Notes Bills Copyright Investment Analytics Trading the Yield Curve Slide: 25
26 Coupons-Bills Spread - Nov 94 Coupons vs. Bills Yield (%) Days to Maturity Notes Bills Copyright Investment Analytics Trading the Yield Curve Slide: 26
27 Coupons-Bills Spread Shape of curves not atypical But spread has narrowed by 30 bp or so. Betting on spread widening would have been very profitable Sell Notes, buy Bills NB must take rolldown effects into consideration Copyright Investment Analytics Trading the Yield Curve Slide: 27
28 TED Spread Spread of LIBOR over Treasury spot curve Compare: Eurodollar futures yields Yields on Treasury coupons Typical spread bp, historically Spreads widen: Financial crises Weakness in banking sector NB can trade with basis swaps Copyright Investment Analytics Trading the Yield Curve Slide: 28
29 Coupon Rolls Simultaneous purchase & sale E.g. Buy current 5-year Sell new 5-year (WI) Spread between securities yields is what dealer gives to do the roll Used by customers to roll investment from the outstanding note to the new note Enables customer to lock in yield on new issue No risk of being shut out of auction and having to pay more for bonds later Copyright Investment Analytics Trading the Yield Curve Slide: 29
30 Economic Significance of Coupon Rolls Used to position dealers for Treasury auctions Dealer usually shorts outstanding issue prior to announcement of new issue In anticipation of market decline By doing the roll, the dealer: Closes out short position in outstanding issue Eliminates cost of borrowing bond to cover short Creates a short position in new security So he will be an active bidder in the auction i.e. coupon rolls assist distribution process Copyright Investment Analytics Trading the Yield Curve Slide: 30
31 Pricing a Coupon Roll 4 Factors Maturity Investor usually gains yield pickup by extending maturity Coupon rates May be some yield pickup from rolling into the new issue, if the coupon is higher Return on funds between settlement dates E.g. investor sells outstanding note, settlement Apr 3, purchases new note, settlement Apr 15 Invests funds at 12-day term repo rate Scarcity of outstanding issue Dealers may give more to cover short position Copyright Investment Analytics Trading the Yield Curve Slide: 31
32 Pricing a Coupon Roll - Example Coupon roll on 10-year note Existing Note Settlement April 3rd Maturity November 15, 2007 Trading at /32 Coupon 5 3/4% Treasury announces auction Reopens existing 5 3/4% of Nov 15, 2007 Auction April 8, settlement April 15th Price the 10-year coupon roll Copyright Investment Analytics Trading the Yield Curve Slide: 32
33 Pricing a Coupon Roll - Steps Compute dirty price of note for regular settlement Accrued interest since November Calculate financing cost Dirty price of note financed for 12 days Cost = P x (1 + r x 12/360) This must be equivalent to dirty price of forward note Calculate clean price of forward note Subtract accrued interest from dirty price Compute fair price of coupon role Difference in yields on cash vs. forward note Copyright Investment Analytics Trading the Yield Curve Slide: 33
34 Pricing a Coupon Roll - Solution Outstanding 10-Year New 10-Year Settlement Date 3-Feb-98 Settlement Date 15-Feb-98 Quoted Price /32 Value for Settlement 103 7/32 Accrued Interest Accrued Interest Dirty Price Derived Price Quote Financing Break-even Roll Term (days) 12 Repo Rate 5.00% Yield on New Issue 5.637% Funds Borrowed Yield on Outstanding Issue 5.634% Funds Owed Break-even Roll 0.003% Copyright Investment Analytics Trading the Yield Curve Slide: 34
35 Yield Curve Plays STEEPENERS Bet that the yield curve will steepen Buy the short end, Sell the long end FLATTENERS Bet that the yield curve will flatten Sell the short end, Buy the long end Duration-Weigh the trade to hedge parallelshifts in the curve Popular choices: Two s-bonds NoB Spread (10y Notes over Bonds) Copyright Investment Analytics Trading the Yield Curve Slide: 35
36 Example: 2 s-bonds Trade Upcoming numbers: Expect good news on inflation Question 1: what trade should you put on? Steepener of flattener? Question 2: Assume you want to hedge against parallel moves in the yield curve What hedging action do you need to take? Copyright Investment Analytics Trading the Yield Curve Slide: 36
37 Lab: 2 s-bonds Trade Use Bond Tutor Subject: Bond Values & Yield Curve Bond & Yield Curve details Yield curve: Flat at 7% out to 30 years 30 year Bond 7% coupon 2 year Notes, 7% coupon Work out Hedge Ratio Based on duration Assume 1 bp parallel shift up or down Work out change in value of both bond & note Compute hedge ratio Copyright Investment Analytics Trading the Yield Curve Slide: 37
38 Lab: 2 s-bond Trade Assume you put on a duration-weighted trade Start with yield curve flat at 7% What is your P/L if: Curve flattens or steepens by 10 bp? There is a parallel shift of 10 bp? A parallel shift of 50bp? A flattening (2 yr down 10bp, 30 yr down 20bp)? Repeat, but now with curve flat at 14% Conclusions: How effective is duration-hedge? What difference does level of yield curve make? Copyright Investment Analytics Trading the Yield Curve Slide: 38
39 Solution: 2 s-bond Flattener Yield Sell 7% 2Y Notes (Duration = 1.84) Buy 7% Bonds (Duration=12.47) Hedge Ratio = 12.47/1.84 = 6.79 Short $6.79MM 2Y for each $1MM Long Bond Maturity Copyright Investment Analytics Trading the Yield Curve Slide: 39
40 Solution: Flattener Trade P&L Yield Bond 2-Yr Position Curve Move P/L P/L P/L 30yr down 10bp yr up 10bp Parallel up 10bp Parallel down 10bp Parallel up 50bp Parallel down 50bp Flattening Copyright Investment Analytics Trading the Yield Curve Slide: 40
41 Questions on the Lab 1. Why isn t the P/L exactly zero for a 10 bp parallel move? 2. Why is the gain on a 10bp steepening not exactly equal to the loss on a 10bp flattening? 3. Why is there such a large P/L for a 50bp parallel move? 4. Why is there a gain from a parallel move up or down? 5. Can you guess what the P/L characteristics of an equivalent steepener trade would be? Copyright Investment Analytics Trading the Yield Curve Slide: 41
42 Flattener P&L as F n of Yield P&L (Points) Duration weighted positions At 7%: Long 1 30Y, short Y At 14%: Long 1 30Y, short Y Yield = 7% Yield = 14% Change in Yield Spread: 2y less 30y (bp) Copyright Investment Analytics Trading the Yield Curve Slide: 42
43 Risks of Curve Plays Convexity Spread Volatility Systematic effects in yield-curve motion Copyright Investment Analytics Trading the Yield Curve Slide: 43
44 Convexity 0.3 Duration weighted position, long 1 30y, short DW 2y Even Yield Movement: 2y yield change = 30y yield change 0.2 P&L (Points) 0.1 Yield = 7% Change in 30y Yield (bp) Yield = 14% Copyright Investment Analytics Trading the Yield Curve Slide: 44
45 Volatility Sd. of daily changes in bond yield: - 10bp Sd. of daily changes in 2-30 spread: - 8bp Not much gain from diversification Can easily lose extra ticks legging into & out of trade Copyright Investment Analytics Trading the Yield Curve Slide: 45
46 2Y Yield Change vs. 30Y Yield Change Change in 2-Year Yield (bp) Even-Yield Movement Best Fit: Y = X Change in Yield for 30-Year (bp) Copyright Investment Analytics Trading the Yield Curve Slide: 46
47 Bias in Curve Trade Standard Duration Weighting produces: Bullish bias to steepeners Bearish bias to flatteners Need to adjust hedge ratio by Yield Change Multiplier Example (2Y v Bonds): Adjusted Hedge Ratio = 6.79 / = 5.35 Sell $5.35MM 2 Year Notes vs Buy S1MM 30 Year Bond Copyright Investment Analytics Trading the Yield Curve Slide: 47
48 Bond Swaps Yield Enhancement Swap Quality Enhancement Swap Liquidity Enhancement Swap Convexity Enhancement Swap Interest Rate Anticipation Swap Copyright Investment Analytics Trading the Yield Curve Slide: 48
49 Convexity Enhancement Swaps: Barbell-Bullet Trades Barbell: Combination of short and long tenor bonds Bullet Single bond of intermediate maturity Barbell-Bullet trade: Arbitrage spread trade Long one position, short the other Equal duration risk and market values Copyright Investment Analytics Trading the Yield Curve Slide: 49
50 Barbell-Bullet Example Woksheet: Barbell Clean Acrrued Dirty Modified Maturity Coupon Price Interest Price YTM Duration A 15-Feb / / % B 15-Feb / / % C 15-Feb / / % Barbell: purchase bonds A&B Bullet: sell bond C What weights to assign to bonds A&B? Copyright Investment Analytics Trading the Yield Curve Slide: 50
51 Barbell-Bullet Trade Analysis Yield gain is 0.06% A B C Modified Weight Market Dollar YTM Duration Qty (%) Value Duration % % Dollar Convexity % % % % % Yield Gain Use Solver to find these weights W A and W B Net Duration = 0 Copyright Investment Analytics Trading the Yield Curve Slide: 51
52 Cash-Flow Yield Previous analysis is very approximate Estimate s Barbell s YTM as weighted average of YTM of each bond Approximate because bonds A and B have different maturities Better method: Calculate Barbell YTM from actual cash flows Copyright Investment Analytics Trading the Yield Curve Slide: 52
53 Calculating Barbell YTM Set out Barbell cash flows w A Fc A + w B Fc B Don t forget face value on maturity of bond A Compute discount factors PV = ( Periods 1+ [1 + 2] Refinement: adjust for weekends Use Solver to find y so that: y / AccrualDays ) ActualDaysin Periods Cash flow NPV = Market Value ( %) Copyright Investment Analytics Trading the Yield Curve Slide: 53 1
54 Barbell-Bullet Solution Cash Flow YTM Barbell % Bullet % Yield pick-up % Copyright Investment Analytics Trading the Yield Curve Slide: 54
55 Duration-Weighted Yield Approximate the cash flow yield using dollar-duration weighted average yield: Y* = Y A D A + Y B D B D A + D B Y* = % x % x Y* = % (actual %) Copyright Investment Analytics Trading the Yield Curve Slide: 55
56 Barbell-Bullet Risk Analysis Barbell gains 21bp yield over bullet Is there any explanation for this? Is the Barbell position more risky than the bullet? Risk Duration risk of two positions is the same Convexity? Convexity formula: Convexity = [1 + y / 2] tpv ( t)[1 n 1 + t= 1 2 Dirty Pr ice t] Copyright Investment Analytics Trading the Yield Curve Slide: 56
57 Solution: Barbell-Bullet Risk Analysis Yield gain: +21bp Convexity gain: Something doesn t add up! Modified Weight Market Dollar YTM Duration Qty (%) Value Duration % % Dollar Convexity % % % % % Yield Gain Convexity Gain Copyright Investment Analytics Trading the Yield Curve Slide: 57
58 Horizon Value and Volatility Consider following example: Assume yield curve is flat at 10% Horizon yield is 10% over 5 years Assume rates move, then hold for 5 years How does Barbell perform relative to bullet? Worksheet: Barbell convexity Weighted Weighted BOND Maturity Coupon Price Weight YTM Duration Convexity Duration Value A 5/15/ % % 10.00% B 5/15/ % % 10.00% C 5/15/ % % 10.00% Net Position Copyright Investment Analytics Trading the Yield Curve Slide: 58
59 Barbell vs. Bullet Analysis Barbell apparently enjoys convexity advantage But, assumptions are unrealistic: Rates do not move instantaneously and then hold for 5 years Takes no account of how likely rates are to move by given amount Need an interest rate model E.g Binomial short-rate tree Takes account of interest rate volatility Generate distribution function of like horizon values Copyright Investment Analytics Trading the Yield Curve Slide: 59
60 Barbell vs. Bullet Interest Rate Model Short Rate Probability Bullet FV Dumbell FV Difference 4.81% 0.1% % 1.0% % 4.4% % 11.7% % 20.5% % 24.6% % 20.5% % 11.7% % 4.4% % 1.0% % 0.1% Source: Active Total Return Management of Fixed Income Portfolios, Dattatreya and Fabozzi, Probus Publishing, 1989 Copyright Investment Analytics Trading the Yield Curve Slide: 60
61 Barbell vs. Bullet Interest Rate Model $3.50 Difference in Return per $100 $3.00 $2.50 $2.00 $1.50 $1.00 $0.50 $- 0.00% $(0.50) 5.00% 10.00% 15.00% 20.00% 25.00% $(1.00) Short Rate Copyright Investment Analytics Trading the Yield Curve Slide: 61
62 Summary: Trading the Yield Curve Repo Trades Figuring the tail Cash & carry trades Riding the curve Yield spread trades Coupon rolls Steepeners & flatteners Butterfly trades Copyright Investment Analytics Trading the Yield Curve Slide: 62
Fixed Income Portfolio Management. Interest rate sensitivity, duration, and convexity
Fixed Income ortfolio Management Interest rate sensitivity, duration, and convexity assive bond portfolio management Active bond portfolio management Interest rate swaps 1 Interest rate sensitivity, duration,
FIN 684 Fixed-Income Analysis From Repos to Monetary Policy. Funding Positions
FIN 684 Fixed-Income Analysis From Repos to Monetary Policy Professor Robert B.H. Hauswald Kogod School of Business, AU Funding Positions Short-term funding: repos and money markets funding trading positions
Fixed Income: Practice Problems with Solutions
Fixed Income: Practice Problems with Solutions Directions: Unless otherwise stated, assume semi-annual payment on bonds.. A 6.0 percent bond matures in exactly 8 years and has a par value of 000 dollars.
FIN 472 Fixed-Income Securities Forward Rates
FIN 472 Fixed-Income Securities Forward Rates Professor Robert B.H. Hauswald Kogod School of Business, AU Interest-Rate Forwards Review of yield curve analysis Forwards yet another use of yield curve forward
Pricing and Strategy for Muni BMA Swaps
J.P. Morgan Management Municipal Strategy Note BMA Basis Swaps: Can be used to trade the relative value of Libor against short maturity tax exempt bonds. Imply future tax rates and can be used to take
550.444 Introduction to Financial Derivatives
550.444 Introduction to Financial Derivatives Week of October 7, 2013 Interest Rate Futures Where we are Last week: Forward & Futures Prices/Value (Chapter 5, OFOD) This week: Interest Rate Futures (Chapter
Eurodollar Futures, and Forwards
5 Eurodollar Futures, and Forwards In this chapter we will learn about Eurodollar Deposits Eurodollar Futures Contracts, Hedging strategies using ED Futures, Forward Rate Agreements, Pricing FRAs. Hedging
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER : THE TERM STRUCTURE OF INTEREST RATES CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS
1 CHAPTER 11 INTRODUCTION TO SECURITY VALUATION TRUE/FALSE QUESTIONS (f) 1 The three step valuation process consists of 1) analysis of alternative economies and markets, 2) analysis of alternative industries
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
Chapter - The Term Structure of Interest Rates CHAPTER : THE TERM STRUCTURE OF INTEREST RATES PROBLEM SETS.. In general, the forward rate can be viewed as the sum of the market s expectation of the future
Interest Rate Futures. Chapter 6
Interest Rate Futures Chapter 6 1 Day Count Convention The day count convention defines: The period of time to which the interest rate applies. The period of time used to calculate accrued interest (relevant
FNCE 301, Financial Management H Guy Williams, 2006
REVIEW We ve used the DCF method to find present value. We also know shortcut methods to solve these problems such as perpetuity present value = C/r. These tools allow us to value any cash flow including
Hedging with Futures and Options: Supplementary Material. Global Financial Management
Hedging with Futures and Options: Supplementary Material Global Financial Management Fuqua School of Business Duke University 1 Hedging Stock Market Risk: S&P500 Futures Contract A futures contract on
Understanding Futures on the DTCC GCF Repo Index
Understanding Futures on the DTCC GCF Repo Index White Paper June 2014 This material may not be reproduced or redistributed in whole or in part without the express, prior written consent of Intercontinental
In this chapter we will learn about. Treasury Notes and Bonds, Treasury Inflation Protected Securities,
2 Treasury Securities In this chapter we will learn about Treasury Bills, Treasury Notes and Bonds, Strips, Treasury Inflation Protected Securities, and a few other products including Eurodollar deposits.
Fixed Income Arbitrage
Risk & Return Fixed Income Arbitrage: Nickels in Front of a Steamroller by Jefferson Duarte Francis A. Longstaff Fan Yu Fixed Income Arbitrage Broad set of market-neutral strategies intended to exploit
Assumptions: No transaction cost, same rate for borrowing/lending, no default/counterparty risk
Derivatives Why? Allow easier methods to short sell a stock without a broker lending it. Facilitates hedging easily Allows the ability to take long/short position on less available commodities (Rice, Cotton,
Lecture 15: Final Topics on CAPM
Lecture 15: Final Topics on CAPM Final topics on estimating and using beta: the market risk premium putting it all together Final topics on CAPM: Examples of firm and market risk Shorting Stocks and other
Treasury Floating Rate Notes
Global Banking and Markets Treasury Floating Rate Notes DATE: April 2012 Recommendation summary The USD 7trn money market should support significant FRN issuance from the Treasury. This would diversify
CHAPTER 5. Interest Rates. Chapter Synopsis
CHAPTER 5 Interest Rates Chapter Synopsis 5.1 Interest Rate Quotes and Adjustments Interest rates can compound more than once per year, such as monthly or semiannually. An annual percentage rate (APR)
Money Market and Debt Instruments
Prof. Alex Shapiro Lecture Notes 3 Money Market and Debt Instruments I. Readings and Suggested Practice Problems II. Bid and Ask III. Money Market IV. Long Term Credit Markets V. Additional Readings Buzz
Answers to Review Questions
Answers to Review Questions 1. The real rate of interest is the rate that creates an equilibrium between the supply of savings and demand for investment funds. The nominal rate of interest is the actual
Lecture 12. Options Strategies
Lecture 12. Options Strategies Introduction to Options Strategies Options, Futures, Derivatives 10/15/07 back to start 1 Solutions Problem 6:23: Assume that a bank can borrow or lend money at the same
CHAPTER 22: FUTURES MARKETS
CHAPTER 22: FUTURES MARKETS PROBLEM SETS 1. There is little hedging or speculative demand for cement futures, since cement prices are fairly stable and predictable. The trading activity necessary to support
Université d Evry Séance 6
Université d Evry Séance 6 Strategies de courbe à base de swaptions & Straddles et strangles de swaptions Philippe PRIAULET Overview An alternative to conventional bond/swap curve positions How to build
Learning Curve Forward Rate Agreements Anuk Teasdale
Learning Curve Forward Rate Agreements Anuk Teasdale YieldCurve.com 2004 Page 1 In this article we review the forward rate agreement. Money market derivatives are priced on the basis of the forward rate,
BOND FUTURES. 1. Terminology... 2 2. Application... 11. FINANCE TRAINER International Bond Futures / Page 1 of 12
BOND FUTURES 1. Terminology... 2 2. Application... 11 FINANCE TRAINER International Bond Futures / Page 1 of 12 1. Terminology A future is a contract to either sell or buy a certain underlying on a specified
The Repo Market. Outline Repurchase Agreements (Repos) The Repo Market Uses of Repos in Practice
The Repo Market Outline and Readings Outline Repurchase Agreements (Repos) The Repo Market Uses of Repos in Practice Buzzwords Repo, Reverse repo, Repo rates, Collateral, Margin, Haircut, Matched book,
Introduction to Fixed Income (IFI) Course Syllabus
Introduction to Fixed Income (IFI) Course Syllabus 1. Fixed income markets 1.1 Understand the function of fixed income markets 1.2 Know the main fixed income market products: Loans Bonds Money market instruments
ASSET LIABILITY MANAGEMENT Significance and Basic Methods. Dr Philip Symes. Philip Symes, 2006
1 ASSET LIABILITY MANAGEMENT Significance and Basic Methods Dr Philip Symes Introduction 2 Asset liability management (ALM) is the management of financial assets by a company to make returns. ALM is necessary
Lecture 09: Multi-period Model Fixed Income, Futures, Swaps
Lecture 09: Multi-period Model Fixed Income, Futures, Swaps Prof. Markus K. Brunnermeier Slide 09-1 Overview 1. Bond basics 2. Duration 3. Term structure of the real interest rate 4. Forwards and futures
Finance 350: Problem Set 6 Alternative Solutions
Finance 350: Problem Set 6 Alternative Solutions Note: Where appropriate, the final answer for each problem is given in bold italics for those not interested in the discussion of the solution. I. Formulas
The Short Dated Interest Rate Market Trading JIBAR Futures
JOHANNESBURG STOCK EXCHANGE Interest Rates The Short Dated Interest Rate Market Trading JIBAR Futures JIBAR Futures are Short Term Interest Rate (STIR) Futures based on the 3-month JIBAR (Johannesburg
i T-bill (dy) = $10,000 - $9,765 360 = 6.768% $10,000 125
Answers to Chapter 5 Questions 1. First, money market instruments are generally sold in large denominations (often in units of $1 million to $10 million). Most money market participants want or need to
Chapter 12. Page 1. Bonds: Analysis and Strategy. Learning Objectives. INVESTMENTS: Analysis and Management Second Canadian Edition
INVESTMENTS: Analysis and Management Second Canadian Edition W. Sean Cleary Charles P. Jones Chapter 12 Bonds: Analysis and Strategy Learning Objectives Explain why investors buy bonds. Discuss major considerations
American Options and Callable Bonds
American Options and Callable Bonds American Options Valuing an American Call on a Coupon Bond Valuing a Callable Bond Concepts and Buzzwords Interest Rate Sensitivity of a Callable Bond exercise policy
Investments Analysis
Investments Analysis Last 2 Lectures: Fixed Income Securities Bond Prices and Yields Term Structure of Interest Rates This Lecture (#7): Fixed Income Securities Term Structure of Interest Rates Interest
Interest Rate Options
Interest Rate Options A discussion of how investors can help control interest rate exposure and make the most of the interest rate market. The Chicago Board Options Exchange (CBOE) is the world s largest
YIELD CURVE GENERATION
1 YIELD CURVE GENERATION Dr Philip Symes Agenda 2 I. INTRODUCTION II. YIELD CURVES III. TYPES OF YIELD CURVES IV. USES OF YIELD CURVES V. YIELD TO MATURITY VI. BOND PRICING & VALUATION Introduction 3 A
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES
CHAPTER 15: THE TERM STRUCTURE OF INTEREST RATES 1. Expectations hypothesis. The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is
FIN 683 Financial Institutions Management Interest-Rate Risk
FIN 683 Financial Institutions Management Interest-Rate Risk Professor Robert B.H. Hauswald Kogod School of Business, AU Interest Rate Risk FIs (financial institutions or intermediaries) face two core
Learning Curve Interest Rate Futures Contracts Moorad Choudhry
Learning Curve Interest Rate Futures Contracts Moorad Choudhry YieldCurve.com 2004 Page 1 The market in short-term interest rate derivatives is a large and liquid one, and the instruments involved are
The Term Structure of Interest Rates CHAPTER 13
The Term Structure of Interest Rates CHAPTER 13 Chapter Summary Objective: To explore the pattern of interest rates for different-term assets. The term structure under certainty Forward rates Theories
Chapter 1 - Introduction
Chapter 1 - Introduction Derivative securities Futures contracts Forward contracts Futures and forward markets Comparison of futures and forward contracts Options contracts Options markets Comparison of
Simple Interest. and Simple Discount
CHAPTER 1 Simple Interest and Simple Discount Learning Objectives Money is invested or borrowed in thousands of transactions every day. When an investment is cashed in or when borrowed money is repaid,
Floating-Rate Securities
Floating-Rate Securities A floating-rate security, or floater, is a debt security whose coupon rate is reset at designated dates and is based on the value of a designated reference rate. - Handbook of
2. Determine the appropriate discount rate based on the risk of the security
Fixed Income Instruments III Intro to the Valuation of Debt Securities LOS 64.a Explain the steps in the bond valuation process 1. Estimate the cash flows coupons and return of principal 2. Determine the
MONEY MARKET FUTURES. FINANCE TRAINER International Money Market Futures / Page 1 of 22
MONEY MARKET FUTURES 1. Conventions and Contract Specifications... 3 2. Main Markets of Money Market Futures... 7 3. Exchange and Clearing House... 8 4. The Margin System... 9 5. Comparison: Money Market
Zero-Coupon Bonds (Pure Discount Bonds)
Zero-Coupon Bonds (Pure Discount Bonds) The price of a zero-coupon bond that pays F dollars in n periods is F/(1 + r) n, where r is the interest rate per period. Can meet future obligations without reinvestment
Chapter 3 Fixed Income Securities
Chapter 3 Fixed Income Securities Road Map Part A Introduction to finance. Part B Valuation of assets, given discount rates. Fixed-income securities. Stocks. Real assets (capital budgeting). Part C Determination
19. Interest Rate Swaps
19. Interest Rate Swaps Reading: Stigum 19 on Swaps. See also Hull who builds from the idea (mentioned in Stigum) that swaps are like a portfolio of forward contracts. Daily Financial Times includes bid-ask
Yield Curve September 2004
Yield Curve Basics The yield curve, a graph that depicts the relationship between bond yields and maturities, is an important tool in fixed-income investing. Investors use the yield curve as a reference
Exam 1 Morning Session
91. A high yield bond fund states that through active management, the fund s return has outperformed an index of Treasury securities by 4% on average over the past five years. As a performance benchmark
MANAGING INTEREST RATE RISK IN A FIXED INCOME PORTFOLIO
CALIFORNIA DEBT & INVESTMENT ADVISORY COMMISSION MANAGING INTEREST RATE RISK IN A FIXED INCOME PORTFOLIO SEPTEMBER 2008 CDIAC #08-11 INTRODUCTION California statute requires the governing body of local
How To Invest In Stocks And Bonds
Review for Exam 1 Instructions: Please read carefully The exam will have 21 multiple choice questions and 5 work problems. Questions in the multiple choice section will be either concept or calculation
How To Understand A Rates Transaction
International Swaps and Derivatives Association, Inc. Disclosure Annex for Interest Rate Transactions This Annex supplements and should be read in conjunction with the General Disclosure Statement. NOTHING
Forward Contracts and Forward Rates
Forward Contracts and Forward Rates Outline and Readings Outline Forward Contracts Forward Prices Forward Rates Information in Forward Rates Reading Veronesi, Chapters 5 and 7 Tuckman, Chapters 2 and 16
Risk and Investment Conference 2013. Brighton, 17 19 June
Risk and Investment Conference 03 Brighton, 7 9 June 0 June 03 Acquiring fixed income assets on a forward basis Dick Rae, HSBC and Neil Snyman, Aviva Investors 8 June 0 Structure of Presentation Introduction
BEAR: A person who believes that the price of a particular security or the market as a whole will go lower.
Trading Terms ARBITRAGE: The simultaneous purchase and sale of identical or equivalent financial instruments in order to benefit from a discrepancy in their price relationship. More generally, it refers
Obligatory transactions on a specified date at a predetermined price
Obligatory transactions on a specified date at a predetermined price DERIVATIVE MARKET Bond Derivatives Bond Futures www.jse.co.za Johannesburg Stock Exchange A bond future is a contractual obligation
MONEY MARKET FUND GLOSSARY
MONEY MARKET FUND GLOSSARY 1-day SEC yield: The calculation is similar to the 7-day Yield, only covering a one day time frame. To calculate the 1-day yield, take the net interest income earned by the fund
Analytical Research Series
EUROPEAN FIXED INCOME RESEARCH Analytical Research Series INTRODUCTION TO ASSET SWAPS Dominic O Kane January 2000 Lehman Brothers International (Europe) Pub Code 403 Summary An asset swap is a synthetic
Weekly Relative Value
Back to Basics Identifying Value in Fixed Income Markets As managers of fixed income portfolios, one of our key responsibilities is to identify cheap sectors and securities for purchase while avoiding
DERIVATIVES Presented by Sade Odunaiya Partner, Risk Management Alliance Consulting DERIVATIVES Introduction Forward Rate Agreements FRA Swaps Futures Options Summary INTRODUCTION Financial Market Participants
VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below
VALUATION OF DEBT CONTRACTS AND THEIR PRICE VOLATILITY CHARACTERISTICS QUESTIONS See answers below 1. Determine the value of the following risk-free debt instrument, which promises to make the respective
Chapter. Interest Rates. McGraw-Hill/Irwin. Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved.
Chapter Interest Rates McGraw-Hill/Irwin Copyright 2008 by The McGraw-Hill Companies, Inc. All rights reserved. Interest Rates Our goal in this chapter is to discuss the many different interest rates that
FIXED-INCOME SECURITIES. Chapter 10. Swaps
FIXED-INCOME SECURITIES Chapter 10 Swaps Outline Terminology Convention Quotation Uses of Swaps Pricing of Swaps Non Plain Vanilla Swaps Terminology Definition Agreement between two parties They exchange
Problems and Solutions
Problems and Solutions CHAPTER Problems. Problems on onds Exercise. On /04/0, consider a fixed-coupon bond whose features are the following: face value: $,000 coupon rate: 8% coupon frequency: semiannual
New York University Courant Institute of Mathematical Sciences. Syllabus
New York University Courant Institute of Mathematical Sciences Syllabus Mathematical Finance Seminar Course: A Practical Approach to Risk Assessment of Mortgage-Backed Securities September 8, 2010 December
FINANCIAL MATHEMATICS MONEY MARKET
FINANCIAL MATHEMATICS MONEY MARKET 1. Methods of Interest Calculation, Yield Curve and Quotation... 2 1.1 Methods to Calculate Interest... 2 1.2 The Yield Curve... 6 1.3 Interpolation... 8 1.4 Quotation...
CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING
CHAPTER 7: FIXED-INCOME SECURITIES: PRICING AND TRADING Topic One: Bond Pricing Principles 1. Present Value. A. The present-value calculation is used to estimate how much an investor should pay for a bond;
Lecture 12/13 Bond Pricing and the Term Structure of Interest Rates
1 Lecture 1/13 Bond Pricing and the Term Structure of Interest Rates Alexander K. Koch Department of Economics, Royal Holloway, University of London January 14 and 1, 008 In addition to learning the material
Problems and Solutions
1 CHAPTER 1 Problems 1.1 Problems on Bonds Exercise 1.1 On 12/04/01, consider a fixed-coupon bond whose features are the following: face value: $1,000 coupon rate: 8% coupon frequency: semiannual maturity:
Futures Spreads For Interactive Brokers, LLC January 18, 2007
Risk Disclosure Futures Spreads For Interactive Brokers, LLC January 18, 2007 Presented by: Kevin Baldwin The risk of loss in trading commodities can be substantial. You should therefore carefully consider
U.S. Treasury Securities
U.S. Treasury Securities U.S. Treasury Securities 4.6 Nonmarketable To help finance its operations, the U.S. government from time to time borrows money by selling investors a variety of debt securities
THE STOCK MARKET GAME GLOSSARY
THE STOCK MARKET GAME GLOSSARY Accounting: A method of recording a company s financial activity and arranging the information in reports that make the information understandable. Accounts payable: The
Learning Curve Using Bond Futures Contracts for Trading and Hedging Moorad Choudhry
Learning Curve Using Bond Futures Contracts for Trading and Hedging Moorad Choudhry YieldCurve.com 2004 Page 1 A widely used risk management instrument in the debt capital markets is the government bond
Financial-Institutions Management. Solutions 1. 6. A financial institution has the following market value balance sheet structure:
FIN 683 Professor Robert Hauswald Financial-Institutions Management Kogod School of Business, AU Solutions 1 Chapter 7: Bank Risks - Interest Rate Risks 6. A financial institution has the following market
Introduction to Interest Rate Trading. Andrew Wilkinson
Introduction to Interest Rate Trading Andrew Wilkinson Risk Disclosure Futures are not suitable for all investors. The amount you may lose may be greater than your initial investment. Before trading futures,
Equity-index-linked swaps
Equity-index-linked swaps Equivalent to portfolios of forward contracts calling for the exchange of cash flows based on two different investment rates: a variable debt rate (e.g. 3-month LIBOR) and the
Derivatives Interest Rate Futures. Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles
Derivatives Interest Rate Futures Professor André Farber Solvay Brussels School of Economics and Management Université Libre de Bruxelles Interest Rate Derivatives Forward rate agreement (FRA): OTC contract
You just paid $350,000 for a policy that will pay you and your heirs $12,000 a year forever. What rate of return are you earning on this policy?
1 You estimate that you will have $24,500 in student loans by the time you graduate. The interest rate is 6.5%. If you want to have this debt paid in full within five years, how much must you pay each
Investment insight. Fixed income the what, when, where, why and how TABLE 1: DIFFERENT TYPES OF FIXED INCOME SECURITIES. What is fixed income?
Fixed income investments make up a large proportion of the investment universe and can form a significant part of a diversified portfolio but investors are often much less familiar with how fixed income
Asset Valuation Debt Investments: Analysis and Valuation
Asset Valuation Debt Investments: Analysis and Valuation Joel M. Shulman, Ph.D, CFA Study Session # 15 Level I CFA CANDIDATE READINGS: Fixed Income Analysis for the Chartered Financial Analyst Program:
1.2 Structured notes
1.2 Structured notes Structured notes are financial products that appear to be fixed income instruments, but contain embedded options and do not necessarily reflect the risk of the issuing credit. Used
Solutions 2. 1. For the benchmark maturity sectors in the United States Treasury bill markets,
FIN 472 Professor Robert Hauswald Fixed-Income Securities Kogod School of Business, AU Solutions 2 1. For the benchmark maturity sectors in the United States Treasury bill markets, Bloomberg reported the
CHAPTER 6 ASSET-LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPS
CHAPTER 6 ASSET-LIABILITY MANAGEMENT: DETERMINING AND MEASURING INTEREST RATES AND CONTROLLING INTEREST-SENSITIVE AND DURATION GAPS Goals of This Chapter: The purpose of this chapter is to explore the
Treasury Bond Futures
Treasury Bond Futures Concepts and Buzzwords Basic Futures Contract Futures vs. Forward Delivery Options Reading Veronesi, Chapters 6 and 11 Tuckman, Chapter 14 Underlying asset, marking-to-market, convergence
Swap Rate Curve Strategies with Deliverable Interest Rate Swap Futures
Swap Rate Curve Strategies with Deliverable Interest Rate Swap By James Boudreault, CFA Research & Product Development Table of Contents I. Introduction II. Swap Curve: Level, Slope, and Shape III. Trading
The TED spread trade: illustration of the analytics using Bloomberg
The TED spread trade: illustration of the analytics using Bloomberg Aaron Nematnejad January 2003 1 The views, thoughts and opinions expressed in this article represent those of the author in his individual
Introduction to swaps
Introduction to swaps Steven C. Mann M.J. Neeley School of Business Texas Christian University incorporating ideas from Teaching interest rate and currency swaps" by Keith C. Brown (Texas-Austin) and Donald
EURODOLLAR FUTURES PRICING. Robert T. Daigler. Florida International University. and. Visiting Scholar. Graduate School of Business
EURODOLLAR FUTURES PRICING Robert T. Daigler Florida International University and Visiting Scholar Graduate School of Business Stanford University 1990-91 Jumiaty Nurawan Jakarta, Indonesia The Financial
Advanced forms of currency swaps
Advanced forms of currency swaps Basis swaps Basis swaps involve swapping one floating index rate for another. Banks may need to use basis swaps to arrange a currency swap for the customers. Example A
Financial Markets And Financial Instruments - Part I
Financial Markets And Financial Instruments - Part I Financial Assets Real assets are things such as land, buildings, machinery, and knowledge that are used to produce goods and services. Financial assets
Canadian Life Insurance Company Asset/Liability Management Summary Report as at: 31-Jan-08 interest rates as of: 29-Feb-08 Run: 2-Apr-08 20:07 Book
Canadian Life Insurance Company Asset/Liability Management Summary Report as at: 31Jan08 interest rates as of: 29Feb08 Run: 2Apr08 20:07 Book Book Present Modified Effective Projected change in net present
INTEREST RATE FUTURES. "Safeguard your interest in the future. Page 1
INTEREST RATE FUTURES "Safeguard your interest in the future Page 1 Contents NSE An Overview......03 Interest Rate Futures A Global Perspective 04 New prospects with Interest Rate Futures...05 Interest
Chapter 5 Option Strategies
Chapter 5 Option Strategies Chapter 4 was concerned with the basic terminology and properties of options. This chapter discusses categorizing and analyzing investment positions constructed by meshing puts
This act of setting a price today for a transaction in the future, hedging. hedge currency exposure, short long long hedge short hedge Hedgers
Section 7.3 and Section 4.5 Oct. 7, 2002 William Pugh 7.3 Example of a forward contract: In May, a crude oil producer gets together with a refiner to agree on a price for crude oil. This price is for crude
Short Sale. Dr. Patrick Toche
Short Sale Dr. Patrick Toche References : Zvi Bodie, Alex Kane, Alan J. Marcus. Essentials of Investment. McGraw- Hill Irwin. Chapter 3 of the Bodie-Kane-Marcus textbook will be followed closely. Other
Bond Price Arithmetic
1 Bond Price Arithmetic The purpose of this chapter is: To review the basics of the time value of money. This involves reviewing discounting guaranteed future cash flows at annual, semiannual and continuously