Fixed Income Zvi Wiener 02-588-3049 Fixed Income 5.

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

http://www.tfii.org FI - 5 slide 2

http://www.tfii.org FI - 5 slide 6 COSS Cash of Share Security Underlying assetCHKP Time to maturity 3M Sold at discount, notional$1 Minimal amount50,000 ListingLuxemburg Yield43%

http://www.tfii.org FI - 5 slide 7 Payoff Graph 0.85CHKP 1

http://www.tfii.org FI - 5 slide 8 COSS Static Replication

http://www.tfii.org FI - 5 slide 9 Valuation Price of 3M Treasury Bill = 1/(1+0.25r 3M ) 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.

http://www.tfii.org FI - 5 slide 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}]

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

http://www.tfii.org FI - 5 slide 12 Fixed Income 5 Mortgage loans Pass-through securities Prepayments Agencies MBS CMO ABS

http://www.tfii.org FI - 5 slide 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.

http://www.tfii.org FI - 5 slide 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

http://www.tfii.org FI - 5 slide 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

http://www.tfii.org FI - 5 slide 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

http://www.tfii.org FI - 5 slide 17 Parallel shift T r Current TS Downward move upward move

http://www.tfii.org FI - 5 slide 18 Twist T rr steepening flattening

http://www.tfii.org FI - 5 slide 19 Butterfly T rr

http://www.tfii.org FI - 5 slide 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.

http://www.tfii.org FI - 5 slide 21 Example bondcouponmaturityyielddurationconvex. A8.5%58.54.00519.81 B9.5%209.58.882124.17 C9.25%109.256.43455.45 Bullet portfolio: 100% bond C Barbell portfolio: 50.2% bond A, 49.8% bond B

http://www.tfii.org FI - 5 slide 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?

http://www.tfii.org FI - 5 slide 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!

http://www.tfii.org FI - 5 slide 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!

http://www.tfii.org FI - 5 slide 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).

http://www.tfii.org FI - 5 slide 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.

http://www.tfii.org FI - 5 slide 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.

http://www.tfii.org FI - 5 slide 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.

http://www.tfii.org FI - 5 slide 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?

http://www.tfii.org FI - 5 slide 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

http://www.tfii.org FI - 5 slide 31 Flattener T r Current TS Sell, Buy

http://www.tfii.org FI - 5 slide 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.

http://www.tfii.org FI - 5 slide 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?

http://www.tfii.org FI - 5 slide 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.

http://www.tfii.org FI - 5 slide 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.

http://www.tfii.org FI - 5 slide 36 Use of futures to take position One should chose x such that the resulting duration will be 3.5 years. 02M3Y5Y -x(1+r 2M /6) (1+r 3Y ) 3 x(1+r 5Y ) 5

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

http://www.tfii.org FI - 5 slide 38 Barings$1.3B Bank Negara, Malaysia 92$3B Banesto, Spain$4.7B Credit Lyonnais$10B S&L, U.S.A.$150B Japan$500B Financial Losses

http://www.tfii.org FI - 5 slide 39 What is the current Risk? duration, convexity volatility delta, gamma, vega rating target zone Bonds Stocks Options Credit Forex Total?

http://www.tfii.org FI - 5 slide 40 Standard Approach

http://www.tfii.org FI - 5 slide 41 Modern Approach Financial Institution

http://www.tfii.org FI - 5 slide 42 Risk Management Risk measurement Reporting to board Limits monitoring Diversification, reinsurance Vetting Reporting to regulators Decision making based on risk

http://www.tfii.org FI - 5 slide 43 Risk Management Structure Market data Current position Risk Mapping Valuation Value-at-Risk Reporting and Risk Management

http://www.tfii.org FI - 5 slide 44 interest rates and dollar are NOT independent Value Interest Rate dollar

http://www.tfii.org FI - 5 slide 45 Risk Measuring Software CATS, CARMA Algorithmics, Risk Watch Infinity J.P. Morgan, FourFifteen FEA, Outlook Reuters, Sailfish Kamacura Bankers Trust, RAROC INSSINC, Orchestra

http://www.tfii.org FI - 5 slide 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

http://www.tfii.org FI - 5 slide 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

http://www.tfii.org FI - 5 slide 48 Types of Assets and Risks Real projects - cashflow versus financing Fixed Income Optionality Credit exposure Legal, operational, authorities

http://www.tfii.org FI - 5 slide 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

http://www.tfii.org FI - 5 slide 50 How to measure VaR Historical Simulations Variance-Covariance Monte Carlo Analytical Methods

http://www.tfii.org FI - 5 slide 51 Historical Simulations Fix current portfolio. Pretend that market changes are similar to those observed in the past. Calculate P&L (profit-loss). Find the lowest quantile.

http://www.tfii.org FI - 5 slide 52 Returns year 1% of worst cases

http://www.tfii.org FI - 5 slide 53 Profit/Loss VaR 1% VaR 1%

http://www.tfii.org FI - 5 slide 56 Weights Since old observations can be less relevant, there is a technique that assigns decreasing weights to older observations. Typically the decrease is exponential. See RiskMetrics Technical Document for details.

http://www.tfii.org FI - 5 slide 57 Variance Covariance Means and covariances of market factors Mean and standard deviation of the portfolio Delta or Delta-Gamma approximation VaR 1% =  P – 2.33  P Based on the normality assumption!

http://www.tfii.org FI - 5 slide 58  Variance-Covariance 2.33   -2.33  1%

http://www.tfii.org FI - 5 slide 59 Monte Carlo

http://www.tfii.org FI - 5 slide 60 Monte Carlo Distribution of market factors Simulation of a large number of events P&L for each scenario Order the results VaR = lowest quantile

http://www.tfii.org FI - 5 slide 61 Monte Carlo Simulation

http://www.tfii.org FI - 5 slide 62 Example Your portfolio consists of two positions. The first one is a zero coupon bond maturing in 1 year with current market value of $10M. The second one is a zero coupon bond maturing in 10 years with market value of $1M. Which position contributes more to the risk of the portfolio?

http://www.tfii.org FI - 5 slide 63 Real Projects Most daily returns are invisible. Proper financing should be based on risk exposure of each specific project. Note that accounting standards not always reflect financial risk properly.

http://www.tfii.org FI - 5 slide 64 Example You are going to invest in Japan. Take a loan in Yen. Financial statements will reflect your investment according to the exchange rate at the day of investment and your liability will be linked to yen. Actually there is no currency risk.

http://www.tfii.org FI - 5 slide 65 Airline company fuel - oil prices and $ purchasing airplanes - $ and Euro salaries - NIS, some $ tickets $ marketing - different currencies payments to airports for services

http://www.tfii.org FI - 5 slide 66 Airline company loans equity callable bonds

http://www.tfii.org FI - 5 slide 67 Airline company Base currency - by major stockholder. Time horizon - by time of possible price change. Earnings at risk, not value at risk, since there is too much optionality in setting prices. One can create a one year cashflow forecast and measure its sensitivity to different market events.

http://www.tfii.org FI - 5 slide 68 Reporting Division of VaR by business units, areas of activity, counterparty, currency. Performance measurement - RAROC (Risk Adjusted Return On Capital).

http://www.tfii.org FI - 5 slide 69 How VaR is used Internal Risk Management Reporting Regulators

http://www.tfii.org FI - 5 slide 70 Backtesting Verification of Risk Management models. Comparison if the model’s forecast VaR with the actual outcome - P&L. Exception occurs when actual loss exceeds VaR. After exception - explanation and action.

http://www.tfii.org FI - 5 slide 71 Backtesting Green zone - up to 4 exceptions Yellow zone - 5-9 exceptions Red zone - 10 exceptions or more OK increasing k intervention

http://www.tfii.org FI - 5 slide 72 Stress Designed to estimate potential losses in abnormal markets. Extreme events Fat tails Central questions: How much we can lose in a certain scenario? What event could cause a big loss?

http://www.tfii.org FI - 5 slide 73 Unifying Approach One number Based on Statistics Portfolio Theory Verification Widely Accepted Easy Comparison

http://www.tfii.org FI - 5 slide 74 Board of Directors (Basle, September 1998) periodic discussions with management concerning the effectiveness of the internal control system a timely review of evaluations of internal controls made by management, internal and external auditors periodic efforts to ensure that management has promptly followed up on recommendations and concerns expressed by auditors and supervisory authorities on internal control weaknesses a periodic review of the appropriateness of the bank’s strategy and risk limits.

http://www.tfii.org FI - 5 slide 75 pluto.mscc.huji.ac.il/~mswiener/ Useful Internet sites Regulators Insurance Companies Risk Management in SEC reports Risk Management resources

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

http://www.tfii.org FI - 5 slide 77 Life Insurance yearly contribution 10,000 NIS yearly risk premium 2,000 NIS first year agent’s commission 3,000 NIS promised accumulation rate 8,000 NIS/yr After the first payment there is a problem of insufficient funds. 8,000 NIS are promised (with all profits) and only 5,000 NIS arrived.

http://www.tfii.org FI - 5 slide 78 10,000 NIS Risk 2,000 NIS Client’s 8,000 NIS Agent 3,000 NIS insufficient funds if the client leaves insufficient profits

http://www.tfii.org FI - 5 slide 79 Risk measurement The reason to enter this transaction is because of the expected future profits. Assume that the program is for 15 years and the probability of leaving such a program is . Fees are – 0.6% of the portfolio value each year – 15% real profit participation

http://www.tfii.org FI - 5 slide 80 Obligations The most important question is what are the obligations? The Ministry of Finance should decide Transparent to a client Accounted as a loan

Fixed Income Zvi Wiener 02-588-3049 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html Introduction to Options

http://www.tfii.org FI - 5 slide 82 Value of an Option at Expiration E. Call XUnderlying

http://www.tfii.org FI - 5 slide 83 Call Value before Expiration E. Call XUnderlying

http://www.tfii.org FI - 5 slide 84 Call Value before Expiration E. Call XUnderlying premium

http://www.tfii.org FI - 5 slide 85 Put Value at Expiration E. Put XUnderlying X

http://www.tfii.org FI - 5 slide 86 Put Value before Expiration E. Put XUnderlying premium X

http://www.tfii.org FI - 5 slide 87 Collar Firm B has shares of firm C of value $200M 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?

http://www.tfii.org FI - 5 slide 88 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.

http://www.tfii.org FI - 5 slide 89 Collar payoff payoff 90 100Kstock 90 K

http://www.tfii.org FI - 5 slide 90 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?

http://www.tfii.org FI - 5 slide 91 Long term options payoff k K stock 50 K Sell a call Your option Result

http://www.tfii.org FI - 5 slide 92 Example You have 10,000 vested options for 10 years with strike $5, while the stock is traded at $10. An immediate exercise will give you $50,000 before tax. Selling a (covered) call with strike $15 will give you $60,000 now (assuming interest rate 6% and 50% volatility) and additional profit at the end of the period!

http://www.tfii.org FI - 5 slide 93 Example payoff 10 15 26 50 K Your option Result 60 exercise

Fixed Income Zvi Wiener 02-588-3049 Fixed Income 5.

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Fixed Income Zvi Wiener 02-588-3049 Fixed Income 5.

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