fixed income zvi wiener 02-588-3049 fixed income 5

Fixed Income

Zvi Wiener

02-588-3049http://www.tfii.org

Fixed Income 5

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


COSSCash 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

0.85 CHKP

1


COSS

85.0$,33 85.0

11 MM PutTBillCOSS

Static Replication


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.


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}]


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


Fixed Income 5

• Mortgage loans

• Pass-through securities

• Prepayments

• Agencies

• MBS

• CMO

• ABS


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.


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


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


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


Parallel shift

T

r

Current TS

Downward move

upward move


Twist

T

r

steepening

flattening


Butterfly

T

r


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.


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


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?


The yield of the bullet portfolio is 9.25%

The yield of the barbell portfolio is 8.998%

This is the cost of convexity!


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!


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).


Repo ExampleYou 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.


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.


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.


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?


Indexing

The idea of a benchmark (liabilities, actuarial or artificial).

Cellular approach, immunization, dynamic approach

Tracking error

Performance measurement, and attribution

Optimization

Risk measurement


Flattener

T

r

Current TS

Sell, Buy


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.


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?



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.



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.



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

0 2M 3Y 5Y

-x(1+r2M/6) (1+r3Y)3 x(1+r5Y)5

Fixed Income

Zvi Wiener

02-588-3049http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

Risk Management


• 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


What is the current Risk?

duration, convexity

volatility

delta, gamma, vega

rating

target zone

• Bonds

• Stocks

• Options

• Credit

• Forex• Total ?


Standard Approach


Modern Approach

Financial Institution


Risk Management

• Risk measurement

• Reporting to board

• Limits monitoring

• Diversification, reinsurance

• Vetting

• Reporting to regulators

• Decision making based on risk


Risk Management Structure

Market data Current position

Risk Mapping

Valuation

Value-at-Risk

Reporting and Risk Management


1011

1213

14 4.1

4.15

4.2

4.25

4.3

7.257.5

7.758

8.25

1011

1213

14

interest rates and dollar areNOT independent

Value

Interest Ratedollar


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


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


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


Types of Assets and Risks

• Real projects - cashflow versus financing

• Fixed Income

• Optionality

• Credit exposure

• Legal, operational, authorities


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


How to measure VaR

• Historical Simulations

• Variance-Covariance

• Monte Carlo

• Analytical Methods


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.


Returns

year

1% of worst cases


-3 -2 -1 1 2 3

0.2

0.4

0.6

0.8

1

Profit/Loss

VaR

1% VaR1%


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.


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!


Variance-Covariance VVVaR 33.2%1

2.33

-2.33

1%


Monte Carlo

-1 -0.5 0.5 1

-1

-0.5

0.5

1


Monte Carlo

• Distribution of market factors

• Simulation of a large number of events

• P&L for each scenario

• Order the results

• VaR = lowest quantile


Monte Carlo Simulation

10 20 30 40

-15

-10

-5

5

10

15


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?


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.


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.


Airline company

• fuel - oil prices and $

• purchasing airplanes - $ and Euro

• salaries - NIS, some $

• tickets $

• marketing - different currencies

• payments to airports for services


Airline company

• loans

• equity

• callable bonds


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.


Reporting

Division of VaR by business units, areas of

activity, counterparty, currency.

Performance measurement - RAROC (Risk

Adjusted Return On Capital).


How VaR is used

• Internal Risk Management

• Reporting

• Regulators


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.


Backtesting

Green zone - up to 4 exceptions

Yellow zone - 5-9 exceptions

Red zone - 10 exceptions or more

OK

increasing k

intervention


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?


Unifying Approach

• One number

• Based on Statistics

• Portfolio Theory

• Verification

• Widely Accepted

• Easy Comparison


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.


pluto.mscc.huji.ac.il/~mswiener/

• Useful Internet sites

• Regulators

• Insurance Companies

• Risk Management in SEC reports

Risk Management resources

Fixed Income

Zvi Wiener


DAC


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.


10,000 NIS

Risk2,000 NIS

Client’s8,000 NIS

Agent3,000 NIS

• insufficient funds if the client leaves

• insufficient profits


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


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


Introduction to Options


Value of an Option at Expiration

E. Call

X Underlying


Call Value before Expiration

E. Call

X Underlying


Call Value before Expiration

E. Call

X Underlying

premium


Put Value at Expiration

E. Put

X Underlying

X


Put Value before Expiration

E. Put

X Underlying

premium

X


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?


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.


Collar payoff

payoff

90 100 K stock

90

K


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?


Long term options

payoff

k K stock

50

K

Sell a call

Your option

Result


ExampleYou 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!


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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