Zvi Wiener

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Fixed Income 5

• Zvi Wiener
• 02-588-3049
• http//www.tfii.org

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COSSCash of Share Security

• Underlying asset CHKP
• Time to maturity 3M
• Sold at discount, notional 1
• Minimal amount 50,000
• Listing Luxemburg
• Yield 43

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Payoff Graph
1
0.85 CHKP
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COSS

• Static Replication

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Valuation

• Price of 3M Treasury Bill 1/(10.25r3M)
• 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.

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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 bsPutFX104.813, 1.5/12, 90, sg,
0.07,08.25,sg, 0.2, 2
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Valuation
fairpriceCOSS 1/(10.070.25)-bsPutFX1, 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.

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Fixed Income 5

• Mortgage loans
• Pass-through securities
• Prepayments
• Agencies
• MBS
• CMO
• ABS

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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.

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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

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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

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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

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Parallel shift
r
T
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Twist
?r
T
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Butterfly
?r
T
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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.

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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
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• Dollar duration of barbell portfolio
• 0.5024.005 0.4988.882 6.434
• it has the same duration as bullet portfolio.
• Dollar convexity of barbell portfolio
• 0.50219.81 0.498124.17 71.78
• the convexity here is higher!
• Is this an arbitrage?

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• The yield of the bullet portfolio is 9.25
• The yield of the barbell portfolio is 8.998
• This is the cost of convexity!

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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!

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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).

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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.

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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.

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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.

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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?

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Indexing

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

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Flattener
r
T
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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.

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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?

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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.

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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.

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Use of futures to take position
0 2M 3Y 5Y
-x(1r2M/6) (1r3Y)3 x(1r5Y)5

• One should chose x such that the resulting
  duration will be 3.5 years.

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Risk Management

• Zvi Wiener
• 02-588-3049
• http//pluto.mscc.huji.ac.il/mswiener/zvi.html

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Financial Losses

• Barings 1.3B
• Bank Negara, Malaysia 92 3B
• Banesto, Spain 4.7B
• Credit Lyonnais 10B
• SL, U.S.A. 150B
• Japan 500B

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What is the current Risk?

• duration, convexity
• volatility
• delta, gamma, vega
• rating
• target zone

• Bonds
• Stocks
• Options
• Credit
• Forex

• Total ?

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Standard Approach
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Modern Approach
Financial Institution
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Risk Management

• Risk measurement
• Reporting to board
• Limits monitoring
• Diversification, reinsurance
• Vetting
• Reporting to regulators
• Decision making based on risk

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Risk Management Structure
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Value
dollar
Interest Rate
interest rates and dollar are NOT independent
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Risk Measuring Software

• CATS, CARMA
• Algorithmics, Risk Watch
• Infinity
• J.P. Morgan, FourFifteen
• FEA, Outlook
• Reuters, Sailfish
• Kamacura
• Bankers Trust, RAROC
• INSSINC, Orchestra

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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

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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

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Types of Assets and Risks

• Real projects - cashflow versus financing
• Fixed Income
• Optionality
• Credit exposure
• Legal, operational, authorities

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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

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How to measure VaR

• Historical Simulations
• Variance-Covariance
• Monte Carlo
• Analytical Methods

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Historical Simulations

• Fix current portfolio.
• Pretend that market changes are similar to those
  observed in the past.
• Calculate PL (profit-loss).
• Find the lowest quantile.

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Returns
year
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VaR
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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.

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Variance Covariance

• Means and covariances of market factors
• Mean and standard deviation of the portfolio
• Delta or Delta-Gamma approximation
• VaR1 ?P 2.33 ?P
• Based on the normality assumption!

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Variance-Covariance
?-2.33?
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Monte Carlo
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Monte Carlo

• Distribution of market factors
• Simulation of a large number of events
• PL for each scenario
• Order the results
• VaR lowest quantile

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Monte Carlo Simulation
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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?

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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.

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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.

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Airline company

• fuel - oil prices and
• purchasing airplanes - and Euro
• salaries - NIS, some
• tickets
• marketing - different currencies
• payments to airports for services

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Airline company

• loans
• equity
• callable bonds

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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.

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Reporting

• Division of VaR by business units, areas of
  activity, counterparty, currency.
• Performance measurement - RAROC (Risk Adjusted
  Return On Capital).

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How VaR is used

• Internal Risk Management
• Reporting
• Regulators

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Backtesting

• Verification of Risk Management models.
• Comparison if the models forecast VaR with the
  actual outcome - PL.
• Exception occurs when actual loss exceeds VaR.
• After exception - explanation and action.

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Backtesting
OK increasing k intervention

• Green zone - up to 4 exceptions
• Yellow zone - 5-9 exceptions
• Red zone - 10 exceptions or more

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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?

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Unifying Approach

• One number
• Based on Statistics
• Portfolio Theory
• Verification
• Widely Accepted
• Easy Comparison

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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
  banks strategy and risk limits.

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pluto.mscc.huji.ac.il/mswiener/
Risk Management resources

• Useful Internet sites
• Regulators
• Insurance Companies
• Risk Management in SEC reports

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DAC

• Zvi Wiener
• 02-588-3049
• http//pluto.mscc.huji.ac.il/mswiener/zvi.html

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Life Insurance

• yearly contribution 10,000 NIS
• yearly risk premium 2,000 NIS
• first year agents 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.

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10,000 NIS

• insufficient funds if the client leaves
• insufficient profits

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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

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Obligations

• The most important question is what are the
  obligations?
• The Ministry of Finance should decide
• Transparent to a client
• Accounted as a loan

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Introduction to Options

• Zvi Wiener
• 02-588-3049
• http//pluto.mscc.huji.ac.il/mswiener/zvi.html

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Value of an Option at Expiration
E. Call
X Underlying
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Call Value before Expiration
E. Call
X Underlying
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Call Value before Expiration
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Put Value at Expiration
E. Put
X
X Underlying
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Put Value before Expiration
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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?

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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.

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Collar payoff
payoff
K
90
90 100 K stock
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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?

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Long term options
payoff
K
50
k K stock
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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!

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Example
payoff
K
60
50
10 15 26