Transcript No Slide Title

Fixed Income 5
Zvi Wiener
02-588-3049
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Fixed Income
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COSS
Cash of Share Security
• Underlying asset
• Time to maturity
• Sold at discount, notional
• Minimal amount
• Listing
• Yield
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CHKP
3M
$1
50,000
Luxemburg
43%
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Payoff Graph
1
0.85
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CHKP
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COSS
COSS 1TBill 3 M
1

Put 3 M , $0.85
0.85
Static Replication
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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.
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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[ bsPutFX[104.813, 1.5/12, 90, sg, 0.07,0]==8.25,{sg, 0.2, 2}]
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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.
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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
upward move
Current TS
Downward move
T
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Twist
r
flattening
T
steepening
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r
Butterfly
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
B
C
8.5%
9.5%
9.25%
5
20
10
8.5 4.005
9.5 8.882
9.25 6.434
19.81
124.17
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 =
0.502*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?
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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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r
Flattener
Current TS
Sell, Buy
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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(1+r2M/6)
(1+r3Y)3
x(1+r5Y)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
Fixed Income
Financial Losses
• Barings
• Bank Negara, Malaysia 92
• Banesto, Spain
• Credit Lyonnais
• S&L, U.S.A.
• Japan
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$1.3B
$3B
$4.7B
$10B
$150B
$500B
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What is the current Risk?
• Bonds
• Stocks
• Options
• Credit
• Forex
• Total
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duration, convexity
volatility
delta, gamma, vega
rating
target zone
?
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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
Current position
Market data
Risk Mapping
Valuation
Value-at-Risk
Reporting and Risk Management
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Value
8.25
8
7.75
7.5
7.25
10
4.3
4.25
4.2
11
4.15
12
13
Interest Rate
14
4.1
dollar
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 P&L (profit-loss).
• Find the lowest quantile.
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Returns
year
1% of worst cases
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VaR
1
0.8
0.6
0.4
VaR1%
1%
0.2
Profit/Loss
-3
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-2
-1
1
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2
3
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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 VaR1%  V  2.33 V
1%
2.33
-2.33
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Monte Carlo
1
0.5
-1
0.5
-0.5
1
-0.5
-1
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Monte Carlo
• Distribution of market factors
• Simulation of a large number of events
• P&L for each scenario
• Order the results
• VaR = lowest quantile
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Monte Carlo Simulation
15
10
5
10
20
30
40
-5
-10
-15
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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 model’s forecast VaR with
the actual outcome - P&L.
Exception occurs when actual loss exceeds
VaR.
After exception - explanation and action.
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Backtesting
Green zone - up to 4 exceptions
OK
Yellow zone - 5-9 exceptions
increasing k
Red zone - 10 exceptions or more
intervention
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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
bank’s 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
Fixed Income
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.
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10,000 NIS
Risk
2,000 NIS
Client’s
8,000 NIS
Agent
3,000 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
Fixed Income
Value of an Option at Expiration
E. Call
X
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Underlying
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Call Value before Expiration
E. Call
X
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Underlying
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Call Value before Expiration
E. Call
premium
X
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Underlying
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Put Value at Expiration
E. Put
X
X
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Underlying
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Put Value before Expiration
E. Put
X
premium
X
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Underlying
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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
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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
Your option
K
Result
50
k
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Sell a call
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
Result
Your option
60
50
exercise
10
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