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Fixed Income 5

Fixed Income 5. Zvi Wiener 02-588-3049 http://www.tfii.org. COSS Cash of Share Security. Underlying asset CHKP Time to maturity 3M Sold at discount, notional $1 Minimal amount 50,000 Listing Luxemburg Yield 43%. Payoff Graph. 1. 0.85 CHKP. COSS. Static Replication.

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Fixed Income 5

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  1. Fixed Income 5 Zvi Wiener 02-588-3049 http://www.tfii.org Fixed Income

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  6. COSSCash of Share Security • Underlying asset CHKP • Time to maturity 3M • Sold at discount, notional $1 • Minimal amount 50,000 • Listing Luxemburg • Yield 43% FI - 5

  7. Payoff Graph 1 0.85 CHKP FI - 5

  8. COSS Static Replication FI - 5

  9. Valuation Price of 3M Treasury Bill = 1/(1+0.25r3M) Price of a Put option is defined by volatility. We can derive the implied volatility from similar traded contracts. For example, we can use January 01 Put option which was traded at bid $8.25, ask $9.125, strike $90. FI - 5

  10. Valuation For example we can use January 01 Put option which was traded at bid $8.25, ask $9.125. Time to maturity of this option (to be exercised on the third Tuesday of January 2001) is 1.5M Then the implied volatility is between 109% and 115%. FindRoot[ bsPutFX[104.813, 1.5/12, 90, sg, 0.07,0]==8.25,{sg, 0.2, 2}] FI - 5

  11. Valuation fairpriceCOSS= 1/(1+0.07*0.25)-bsPutFX[1, 0.25, strike, 1.1, 0.07,0]/strike The fair price of the COSS is about $0.84. Merrill Lynch offered this at $0.9015. FI - 5

  12. Fixed Income 5 • Mortgage loans • Pass-through securities • Prepayments • Agencies • MBS • CMO • ABS FI - 5

  13. Bonds with Embedded Options (14) Traditional yield analysis compares yields of bonds with yield of on-the-run similar Treasuries. The static spread is a measure of the spread that should be added to the zero curve (Treasuries) to get the market value of a bond. FI - 5

  14. Active Bond Portfolio Management(17) Basic steps of investment management Active versus passive strategies Market consensus Different types of active strategies Bullet, barbell and ladder strategies Limitations of duration and convexity How to use leveraging and repo market FI - 5

  15. Investment Management • Setting goals, idea of ALM or benchmark • GAAP, FAS 133, AIMR - reporting standards • passive or active strategy - views, not transactions • available indexes • mixed strategies FI - 5

  16. Major risk factors • level of interest rates • shape of the yield curve • changes in spreads • changes in OAS • performance of a specific sector/asset • currency/linkage FI - 5

  17. upward move Current TS Downward move Parallel shift r T FI - 5

  18. flattening steepening Twist r T FI - 5

  19. Butterfly r T FI - 5

  20. Yield curve strategies Bullet strategy: Maturities of securities are concentrated at some point on the yield curve. Barbel strategy: Maturities of securities are concentrated at two extreme maturities. Ladder strategy: Maturities of securities are distributed uniformly on the yield curve. FI - 5

  21. Example bond coupon maturity yield duration convex. A 8.5% 5 8.5 4.005 19.81 B 9.5% 20 9.5 8.882 124.17 C 9.25% 10 9.25 6.434 55.45 Bullet portfolio: 100% bond C Barbell portfolio: 50.2% bond A, 49.8% bond B FI - 5

  22. Dollar duration of barbell portfolio = 0.502*4.005 + 0.498*8.882 = 6.434 it has the same duration as bullet portfolio. Dollar convexity of barbell portfolio = 0.502*19.81 + 0.498*124.17 = 71.78 the convexity here is higher! Is this an arbitrage? FI - 5

  23. The yield of the bullet portfolio is 9.25% The yield of the barbell portfolio is 8.998% This is the cost of convexity! FI - 5

  24. Leverage Risk is not proportional to investment! This can be achieved in many ways: futures, options, repos (loans), etc. Duration of a levered portfolio is different form the average time of cashflow! Use of dollar duration! FI - 5

  25. 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). FI - 5

  26. Repo Example You are a dealer and you need $10M to purchase some security. Your customer has $10M in his account with no use. You can offer your customer to buy the security for you and you will repurchase the security from him tomorrow. Repo rate 6.5% Then your customer will pay $9,998,195 for the security and you will return him $10M tomorrow. FI - 5

  27. 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. FI - 5

  28. 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. FI - 5

  29. 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? FI - 5

  30. Indexing The idea of a benchmark (liabilities, actuarial or artificial). Cellular approach, immunization, dynamic approach Tracking error Performance measurement, and attribution Optimization Risk measurement FI - 5

  31. Current TS Sell, Buy Flattener r T FI - 5

  32. Example of a flattener • sell short, say 1 year • buy long, say 5 years • what amounts? In order to be duration neutral you have to buy 20% of the amount sold and invest the proceedings into money market. • Sell 5M, buy 1M and invest 4M into MM. FI - 5

  33. Use of futures to take position Assume that you would like to be longer then your benchmark. This means that you expect that interest rates in the future will move down more than predicted by the forward rates. One possible way of doing this is by taking a future position. How to do this? FI - 5

  34. Use of futures to take position Your benchmark is 3 years, your current portfolio has duration of 3 years as well and value of $1M. You would like to have duration of 3.5 years since your expectation regarding 3 year interest rates for the next 2 months are different from the market. Each future contract will allow you to buy 5 years T-notes in 2 months for a fixed price. FI - 5

  35. Use of futures to take position Each future contract will allow you to buy 5 years T-notes in 2 months for a fixed price. If you are right and the IR will go down (relative to forward rates) then the value of the bonds that you will receive will be higher then the price that you will have to pay and your portfolio will earn more than the benchmark. FI - 5

  36. Use of futures to take position 0 2M 3Y 5Y One should chose x such that the resulting duration will be 3.5 years. -x(1+r2M/6) (1+r3Y)3 x(1+r5Y)5 FI - 5

  37. Risk Management Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Fixed Income

  38. Financial Losses • Barings $1.3B • Bank Negara, Malaysia 92 $3B • Banesto, Spain $4.7B • Credit Lyonnais $10B • S&L, U.S.A. $150B • Japan $500B FI - 5

  39. duration, convexity volatility delta, gamma, vega rating target zone What is the current Risk? • Bonds • Stocks • Options • Credit • Forex • Total ? FI - 5

  40. Standard Approach FI - 5

  41. Modern Approach Financial Institution FI - 5

  42. Risk Management • Risk measurement • Reporting to board • Limits monitoring • Diversification, reinsurance • Vetting • Reporting to regulators • Decision making based on risk FI - 5

  43. Current position Market data Risk Mapping Valuation Value-at-Risk Reporting and Risk Management Risk Management Structure FI - 5

  44. Value dollar Interest Rate interest rates and dollar are NOT independent FI - 5

  45. Risk Measuring Software • CATS, CARMA • Algorithmics, Risk Watch • Infinity • J.P. Morgan, FourFifteen • FEA, Outlook • Reuters, Sailfish • Kamacura • Bankers Trust, RAROC • INSSINC, Orchestra FI - 5

  46. Qualitative Requirements • An independent risk management unit • Board of directors involvement • Internal model as an integral part • Internal controller and risk model • Backtesting • Stress test FI - 5

  47. Quantitative Requirements • 99% confidence interval • 10 business days horizon • At least one year of historic data • Data base revised at least every quarter • All types of risk exposure • Derivatives FI - 5

  48. Types of Assets and Risks • Real projects - cashflow versus financing • Fixed Income • Optionality • Credit exposure • Legal, operational, authorities FI - 5

  49. Risk Factors There are many bonds, stocks and currencies. The idea is to choose a small set of relevant economic factors and to map everything on these factors. • Exchange rates • Interest rates (for each maturity and indexation) • Spreads • Stock indices FI - 5

  50. How to measure VaR • Historical Simulations • Variance-Covariance • Monte Carlo • Analytical Methods FI - 5

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