Document Sample

Advanced Financial Economics Introduction Econ 426 Discussion Outline Course Mechanics - Learning Objectives - Course Outline - Expectations: How to do well? Why Advanced Financial Economics: Derivatives & Structured Products? - Trends and historical growth - Controversial—The Bad Rep! Finance Essentials - No Arbitrage Principle - Standard Present Value Methodology - Compounding, Interest rates/LIBOR, Term structure, yields & forward rates - Day count conventions - Duration 2 Davis 2008 Who Am I? Education B.A., Economics & Mathematics--University of Washington (Int’l Certificate) Ph.D., Economics--MIT Career Experience Wall Street, New York: Lehman Brothers, Goldman Sachs Main Street, Seattle: Bulge bracket to boutique independent wealth advisory UW Lecturer (Econ 422, Econ 423, Econ 399/499/497) Consultant: Financial services firms, primarily hedge funds Research Interests* Finance: Behavioral Finance; Practical Applications of Finance Theory; Hedge Funds; Derivative Securities & Structured Finance. *Primary research is for non-public use. 3 Davis 2008 Course Mechanics Course website Course Description Economics 426 provides an introduction to the study of complex financial securities, with particular emphasis on financial derivatives and structured products. The course begins with an in depth study of futures and options, including economic theory, market and institutional considerations, valuation methods, trading strategies, and hedging. More complex derivative securities will be discussed, including exotics, index options, options on futures, callable and convertible bonds, swaps, credit derivatives, and credit default swaps. The process of securitization will be introduced as the basis for understanding structured financial products such as asset backed securities and collateralized debt obligations. Real world applications, recent events and ongoing developments in the economy and financial markets— domestic and global--will be heavily emphasized throughout the course, in particular, discussion of the subprime credit crisis, role of hedge funds, and real option analysis as an investment decision making protocol for firms. 4 Davis 2008 Learning Objectives Be able to understand, analyze, and value a variety of simple (‘plain vanilla’) to complex securities from derivatives to structured products in the global economy. - Lectures - Course reading material: Required Hull text and supplementary course reading packet - Regular problem sets (group work encouraged!) Recognize and understand real world economic applications of such financial securities—for good or for bad?! - In class discussions - Case studies: Required Marthinsen and supplementary course readings Be conversant in current topics in the financial markets and the interplay in the global economy. - Supplementary course reading packet - Regular reading of financial sources - In class discussions 5 Davis 2008 General Course Outline May be fluid, ultimate moving target = subprime/financial crisis discussion Part I: (2/3) Both broader and more in depth coverage of derivative securities than that in Econ 422 - Math/Stat 492: presents stochastic calculus—the foundations for Black-Scholes--This course is not meant as a substitute but as a complement to augment Math 492 with the focus on application of derivatives in real world financial situations. - Other great course complements: 464 Financial Crises 424 Computational Finance Part II: (1/3) With advanced coverage of derivatives securities the course will provide exposure and basic understanding of ‘Structured Finance’ providing the framework within which specific complex securities involved in the subprime/current financial crisis can be discussed. Specific Outline: See Syllabus 6 Davis 2008 Structured Finance: Structured Credit Meets Derivatives Structured Credit Credit Derivatives ABS RMBS CDS Swaps MBS CDOs Options CMBS Forwards/ Futures DERIVATIVES Source: IMF Global Stability Report, October 2008. 7 Davis 2008 Course Mechanics Announcements - website & email alias Google group? – opt in (volunteer to establish?) Office hours - Immediately following class 10:30 – 11:30 (noon) - Condon 401E (in the Department office) - By appointment, email larinad@u.washington.edu Prerequisites - Econ 422 (Prereqs: Econ 300; Calculus (Math 124); Statistics (Stat 311 or 390; Qmeth 201)) Required readings - Hull’s Fundamentals of Futures and Options Markets (6th edition) (Available at U Bookstore or e-book) - Lecture notes (Available for download from course website—password protected) - Supplementary course packet of readings available at Ave Copy Center: 4141 University Way - Marthinsen’s Risk Takers: Uses and Abuses of Financial Derivatives (Available at U Bookstore) 8 Davis 2008 Course Mechanics Should I go out and buy a financial calculator? Grading - Midterm (30%) - Final (30%) - Homework: Problem Sets & Case Studies (40%) No late work accepted. All assignments to be handed in at the beginning of class. No emailed homework accepted unless pre-approved. Zero tolerance for cheating or lack of academic integrity. University Policies strictly adhered to. 9 Davis 2008 How to do well? Invest time and effort: - Come to class…lecture notes are ‘mad libs’ style! - Read required readings/lecture notes - Seek help (office hours or by appointment) if you do not understand lectures Connect to the material - Work in a group - Engage in class discussion - Take an interest in and keep current on developments in the financial markets & industry - The Wall Street Journal, Barron’s, The Economist: Finance & Economics section 10 Davis 2008 Why study derivatives and structured products? 1. Together they represent largest and fastest growing segment of the global financial markets. - By the early 1980s, the volume of derivatives trading had grown so rapidly that the number of shares underlying the option contracts traded daily exceeded the daily volume of shares traded on the NYSE. - BIS Quarterly Review statistics 2. Derivatives can be useful for hedging, speculating, and arbitrage. 3. Structured products typically involve derivatives to provide customized, versatile solutions. Source: Bank for International Settlements, 2008. 11 Davis 2008 Growth of Derivatives-Notional Terms Notional amount: the Face Value or underlying value upon which a contract is written, on which basis payments are calculated. Source: Bank for International Settlements, 2008. For historical data see: www.bis.org/statistics/derstats.htm 12 Davis 2008 Derivative Contract Volumes Source: The Options Clearing Corporation, 2008. 13 Davis 2008 Structured Finance Sources: IMF Global Stability Report, Inside MBS & ABS, JP Morgan Chase & Co.; European Securitization Forum. IMF Global Stability Report has bi-annual release: April and October. Next update will be April 2009. 14 Davis 2008 CFA Study Guide Derivative Markets & Instruments, #11: The most likely reason derivative markets have flourished is that: A. Derivatives are easy to understand. B. Derivatives have relatively low transaction costs. C. The pricing of derivatives is relatively straightforward. D. Strong regulation ensures that transacting parties are protected from fraud. 15 Davis 2008 Reason 4. Controversial— Is The Bad Rep Warranted? Examples in the media: Gerald Corrigan of Goldman Sachs: “Derivatives, like NFL quarterbacks, probably get more credit and more blame than they deserve.” Warren Buffet, Berkshire Hathaway Annual Report, 2002: I view derivatives as time bombs, both for the parties that deal in them and the economic system . . . Many people argue that derivatives reduce systemic problems, in that participants who can’t bear certain risks are able to transfer them to stronger hands. These people believe that derivatives act to stabilize the economy, facilitate trade, and eliminate bumps for individual participants. On a micro level, what they say is often true. I believe, however, that the macro picture is dangerous and getting more so. Large amounts of risk, particularly credit risk, have become concentrated in the hands of relatively few derivatives dealers, who in addition trade extensively with one another. The troubles of one could quickly infect the others . . . In my view, derivatives are financial weapons of mass destruction, carrying dangers that while now latent, are potentially lethal. [emphasis mine] “Structured Products Lose Their Appeal,” The Financial News, March 25, 2008: “It was clear that this product was all about the firm’s investment bank shoveling c*** down its private banking distribution channel. And the disclosure was appalling.” Andrew Merricks, financial advisor at Skerritts Consultants, quoted by Telegraph.co.uk (6/19/08) “ . . .structured products put a straitjacket around your investment decisions . . .” 16 Davis 2008 Why the Bad Rep: Derivatives and Structured Products highly controversial: 1. High level of complexity. 2. Lack of transparency. 3. Derivatives often used improperly can lead to large losses. - Derivatives can reduce many risks, except the human kind!* - In particular: when things go awry, derivatives themselves take the blame, rather than the users of derivatives. In many cases, the critics of derivatives do not understand them well. Scapegoats for crises. Is it deserved? How to know? Current financial crisis: structured products and derivatives (CMOs, MBSs, CDSs, TRSs, etc.) to blame (???) for tipping an otherwise recessionary decline in the housing market into a full fledged systemic crisis of global proportions. Due to controversial nature, lack of transparency, and association/involvement in the financial crises, much congressional and regulatory focus going forward will be on these markets. If they fail colossally does this mean they are not useful, if better understood?? *See “Financial WMD” The Economist, January 22, 2004. 17 Davis 2008 Finance Essentials Review of concepts (primarily from 422) that will be important later on in the course. As a contrast: Traditional presented discounted cash flow analysis generally does not apply to the derivative securities we will be considering; however, if the derivative security payoff mimics that of a bond, we can use our PV framework. What we will use heavily: No-arbitrage principle Interest rates and the term structure And not so heavily, but occasionally: Bond Duration 18 Davis 2008 No-Arbitrage Principle An arbitrage is any trading strategy which requires no cash input that has some probability of making profits with potentially risk of loss: - Pure arbitrage is risk-less and rare. - Near arbitrage is risky and more relevant. No-Arbitrage Principle; In an efficiently functioning financial market, arbitrage opportunities cannot persist as individuals take advantage of arbitrage profits, reducing them in the process to zero. →Implies: 19 Davis 2008 Present Value Methodology Recall (422) we used present value methodology for both simple stock and bond valuations. The idea is that you value the security for its future expected cash flows such that what you are willing to pay today for these cash flows is precisely the sum of the discounted value of these today. For these simplest stock and bond cases we considered, the biggest challenge is determining the appropriate discount rate(s). We established the idea that the discount rate should mirror the risk of the cash flows, i.e., use a risk-less rate (Treasury yields, a.k.a our term structure) to discount risk-less cash flows and use a risk-adjusted discount rate (CAPM based as one example) to discount risky cash flows. Investment valuation: Bond valuation: Dividend discount model: 20 Davis 2008 Interest rates Interest rates are a factor in the valuation of virtually all derivatives. Financial Accounting An interest rate is the amount of money that a borrower promises Standard No. 138, allows for the to pay a lender; includes: mortgage rates, deposit rates, prime, etc. LIBOR/swap rate to be used as one of only two Treasury rates are the rates an individual earns on Treasury bills, market interest-rate Notes, and bonds. Treasuries are the instruments used by a benchmarks in hedge government to borrow in its own currency. Treasury securities are accounting. The other deemed the least risky securities under the presumption that a allowable market interest rate government would not default on an obligation denominated in its benchmark is the U.S. own currency.* Treasury curve. LIBOR is increasingly LIBOR (London Interbank Borrowing Offered Rate) rates are typically important in pricing used for defining OTC derivatives payoffs such that LIBOR is the commercial credit and more common benchmark among derivative traders. LIBOR is the even more important in rate at which a bank is willing to offer on a large deposit pricing derivatives. with other banks. *Examples of defaults: Russia, Argentina…’never say never!’ **LIBID (London Interbank Bid Rate) is the rate at which a bank is willing to accept deposits. See article “The LIBOR versus 14, 2007. Treasury rates, “ PBS Nightly Business Report, SeptemberDavis 2008 21 Day Count The day count determines the way in which interest accrues over time. Typically we need to calculate the interest over a period of time different than the reference period (i.e., the accrued interest on a bond owed when purchased in the secondary market sometime in between coupon payments) Accrued Interest = Three day count conventions commonly used in the United States: Quoted prices 1. Actual/Actual (‘clean prices’) do 2. 30/360 not include 3. Actual/360 accrued interest Cash or ‘dirty’ price = quoted price + accrued interest 22 Davis 2008 Day Count Matters! Between February 28, 2009 and March 1, 2009 you have your choice between owning a corporate bond paying 10% or a US Treasury bond paying 10%. Which do you choose, based on interest payments alone? 23 Hull/Davis 2008 Compounding Suppose an amount A is invested for n years, compounded m times per year, at an annual interest rate r per year. If the rate is compounded once per annum (m = 1), then the future value of the investment is: (1) If the rate is compounded m times per year, then the future value of the investment is: (2) As m approaches infinity (continuous compounding), the future value of the investment grows to: (3) To convert a rate with a compounding frequency of m times per year (rm) to a continuously compounded rate (rc): (4) and (5) 24 Davis 2008 PV with Continuous Compounding When interest rates are continuously compounded: Investment Valuation: Bond Valuation: Dividend discount model: 25 Davis 2008 In Class Problem #1 A bank quotes you an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with: a. continuous compounding? b. annual compounding? 26 Hull/Davis 2008 In Class Problem #2 Suppose the following continuously compounded zero rates: Maturity Rates (months) 6 4% 12 4.2% 18 4.4% 24 4.6% 30 4.8% What is the price of a bond with a FV of $1,000 that will mature in 30 months and pays a coupon of 4% semi-annually? 27 Davis 2008 In Class Problem #3 An investor receives $1,100 in one year in return for an investment of $1,000 now. Calculate the percentage return per annum with: a. annual compounding b. semi-annual compounding c. monthly compounding d. continuous compounding 28 Hull/Davis 2008 Yield to Maturity A bond’s yield to maturity (YTM or yield) is the discount rate that equates the discounted value of the bond’s promised cash flow to its market price. r = Yield to Maturity: Example: Suppose a Treasury zero bond that matures in three months is selling for $97.50. Face value is $1,000. What is the bond’s yield to maturity? Suppose we want to express the interest rate with continuous compounding. Using equation 5 from the ‘compounding’ slide: 29 Davis 2008 For current term structure: http://www.ustreas.gov/offices/domestic- Term Structure finnace/debt-management/interest-rate/yield.html Yield curves can have various shapes. Increasing rates are most common---upward sloping yield curve, but the plot can show a decrease, hump or flat region. The benchmark yield curve plots the going ‘spot’ rates for various constant maturity Government securities—T-bills, T-Notes and T-Bonds that have been stripped of coupons (Zeros). These yields and their respective maturities are referred to as the Term Structure. ‘Normal’ yield curve (Associated with ‘loose’ monetary r0,30 policy, i.e., short term money is ‘easy’ r0,30 Inverted yield curve or cheap.) (Associated with ‘tight’ monetary policy, i.e., r0,10 r0,10 shortage/high cost of short-term money.) r0,5 r0,5 r0,1 r0,1 t1 t5 t10 t30 t1 t5 t10 t30 30 R.W. Parks/Davis 2008 Relationship Between Rates Along Yield Curve In a world with certainty, in order for there to be no arbitrage, the return on holding a 2 year Treasury investment must be the same as investing in a one year Treasury today then rolling this forward into another one year Treasury in one year: You can solve for r0,2: A similar relationship will hold for the period T interest rate: 31 R.W. Parks/Davis 2008 Forward Interest Rates In reality, we live in a world of uncertainty, such that in our previous example, r1,2 is unknown. In reality, we do not know with certainty any future interest rates, i.e., rt-1,t for t >1. We can use today’s term structure, combined with our No Arbitrage condition; however, to infer something about future rates. Future rates from today are referred to as forward interest rates. 32 R.W. Parks/Davis 2008 Forward Rates and Term Structure Recall our No Arbitrage Condition under certainty: We can infer what the market thinks r1,2 will be in the future. This is the implied forward rate f1,2 the one period ahead rate implied by our no arbitrage condition: The implied forward rate is Note: This forward rate is entirely described by current term structure! 33 R.W. Parks/Davis 2008 Forward Rates and Term Structure The following general formula allows us to determine the forward rate for any future period between periods t-1 and t: Interpretation: 34 R.W. Parks/Davis 2008 In Class Problem #4 The term structure of interest rates is upward sloping. Put the following in order of magnitude: a. 5 year zero rate b. yield on a 5 year coupon bearing bond c. forward rate corresponding between 4.75 and 5 years 35 Hull/Davis 2008 Calculating Forward Rates Forward interest rates are the rates of interest implied by the current zero rates for periods of time in the future. Suppose the following represent zero rates, continuously compounded: Year (n) Zero rate for n-year investment 1 3.0 2 4.0 3 4.6 4 5.0 5 5.3 To determine the forward rate for year two, consider the future value of a two year investment of $100: If instead you invested one year at 3% then rolled the investment forward at f12, by our no arbitrage condition, the value of this investment must equal $108.33: 36 Hull/Davis 2008 Calculating Forward Rates Similarly, we can solve for the forward rates for n =3-5 as shown below: Year (n) Zero rate for n-year investment fn 1 3.0 2 4.0 5.0 3 4.6 5.8 4 5.0 6.2 5 5.3 6.5 In general, if R1 and R2 are the zero rates for maturities T1 and T2, respectively, and RF is the forward interest rate for the period of time between T1 and T2: RF = (R2T2-R1T1)/T2-T1 or equivalently: RF = R2 + (R2 –R1)*[T1/(T2-T1)] 37 Hull/Davis 2008 Duration Duration is an important concept in the use of interest rate futures for hedging. The duration of a financial asset measures the sensitivity of the asset's price to movements in the interest rate as expressed as a number of years, i.e. dV/dr . Suggested by Frederick Macaulay in 1938. Bond Duration The duration of a bond is a measure of how long on average the holder of the bond must wait before receiving cash flows. (Also referred to as effective maturity.) A zero coupon bond that matures in n years has a duration of n years. Coupon bearing bonds with maturity of n years will have a duration less than n years because some of the cash payments (coupons) are received prior to year n. Example: A bond with a higher coupon rate (10% or $100/year) will return a higher percentage of the bond’s current market value over a given number of years when compared to a bond of similar maturity but with a lower coupon rate say 8%. 38 Davis 2008 Bond Duration Bond Value = V = ΣCFt/(1+i)t t = 1 to T CFt = cash flow per period t = coupon payment for t = 1 to T-1 and coupon plus face for t = T i = r/m = current annual market yield (r )adjusted by the compounding frequency m t = time in compounding periods = mY where Y = number of years To measure the sensitivity of the value (V) of the bond in response to changes in i: dV/di = dV/di = Noting that 1/(1+i) is substantially ≈ 1, then: dV/di ≈ dV/di ≈ Duration = the total weighted average time for recovery of the payments and principal in relation to the current market price of the bond: Duration = Duration varies inversely with yields! 39 Davis 2008 Duration Calculation-continuous compounding Current time is 0 Bond provides holder with payments ci at time ti for (1< i <T) r represents the continuously compounded yield Price of the bond, B The duration, D, of the bond is defined as: From this second notation we see that the duration is a weighted average of the times when cash flows are received with the weights representing the proportion of the bond’s total present value provided by the cash flow at time ti. 40 Davis 2008 Duration Calculation-continuous compounding Three year, 6% coupon Treasury (semi-annual coupon!) with a FV of $1000. Assume a yield of 4% continuously compounded. -ti (yrs) Cash Flow Present Value Weight t * Weight (CF) =CFe-r/2*t = CFt/B -0.5 -1.0 -1.5 -2.0 -2.5 -3.0 Bond Value Duration Note: Duration will be negative. However, you may not always see it being referred to with a negative sign! 41 Davis 2008 Relationship of Duration and % changes in Bond prices What is the impact on the bond price of a change in yields? Given: B = Σcie-rti for i = 1 to n Want to know: ∂B/∂r = ? Using our definition of duration, we can write this as: Meaning: the percentage change in a bond’s price is equal to its duration (this will be negative!) multiplied by the size of the parallel shift in the yield curve. → Approximate relationship between percentage changes in a bond’s yield and bond price. 42 Davis 2008 Duration With reference to the previous example: ∆B = BD∆r ∆B = 1,054.85 * -2.796*∆r ∆B = -2,949.36*∆r If ∆r = 0.001 (so that r increases to 0.041), we expect ∆B to be -2.95, i.e., we expect the price of the bond to decrease: $1,054.85 – $2.95 = $1,051.90. 43 Davis 2008 In Class Problem #5 A five year bond with a yield of 11% continuously compounded pays an 8% coupon at the end of each year. a. What is the bond’s price? b. What is the bond’s duration? c. Use the duration to calculate the effect on the bond’s price of a 0.2% decrease in its yield. d. Recalculate the bond’s price on the basis of a 10.8% per annum yield and verify it is in agreement with part c. above. 44 Hull/Davis 2008 Bond Portfolio Duration The duration of a bond portfolio is a weighted average of the duration of the individual bonds in the portfolio where the weights are proportionate to the value of the respective bond in the portfolio. When duration is used for bond portfolios there is an implicit assumption that the yields of all bonds will change by the same amount (i.e., a parallel shift of the yield curve). - Note: this calculation relies on a specific type of change in the yield curve which if not realized can lead to ‘slippage,’ i.e., losses from a hedge, etc. (More on this to come!) 45 Davis 2008 Importance of duration Match duration of assets with duration of liabilities Examples: Insurance firm issuing life insurance: - Insurance firms will frequently invest in bonds with durations matched to the duration of future projected death benefits. Leasing company - Will issue debt to purchase assets to lease. The lease payments and the debt each have a duration. - Leasing companies will typically structure debt financing so the duration of the debt (liability) matches the duration of the leases (asset). Pension funds* - Pension funds have obligations to retirees. These obligations have a duration. - The pension fund can invest assets into fixed income securities. - Pension fund managers commonly select pension assets with given duration that match the pension fund liability duration. - * Readings: “Company Pensions: Time for a Reality Check” and “Actuaries and the Pensions Crunch: When the Spinning Stops,” The Economist, January 26, 2006; “ 46 Davis 2008

DOCUMENT INFO

Shared By:

Categories:

Tags:

Stats:

views: | 3 |

posted: | 9/21/2011 |

language: | English |

pages: | 23 |

OTHER DOCS BY liaoqinmei

How are you planning on using Docstoc?
BUSINESS
PERSONAL

Feel free to Contact Us with any questions you might have.