© 2004 South-Western Publishing1

Chapter 16

Financial Engineering and Risk Management

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Outline

Introduction and background Financial engineering Risk management

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Introduction and Background

Financial engineering:– Is a relatively new derivatives endeavor– Has led directly to improvements in the process

of risk management

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Introduction and Background (cont’d)

Risk management awareness is associated with various phrases:– Asian flu– Global contagion– Orange County

“We take the risks because of the potential reward”

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Financial Engineering

Synthetic put Engineering an option Gamma risk

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Synthetic Put

Financial engineering is the popular name for constructing asset portfolios that have precise technical characteristics

In the early days of the CBOE there were no puts; only calls traded– Can construct a put by combining a short

position in the underlying asset with a long call – Synthetic puts were the first widespread use of

financial engineering

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Synthetic Put (cont’d)

+ =

short stock +long call = long put

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Engineering an Option

There are a variety of tactics by which wealth can be protected without disturbing the underlying portfolio– Shorting futures provides downside protection

but precludes gains from price appreciation– Writing a call provides only limited downside

protection– Buying a put may be the best alternative

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Engineering an Option (cont’d)

Strategy Advantages Disadvantages

Short futures Low trading fees;

Easy to do

Lose upside potential;

Possible tracking error

Write calls Generate income Lose most upside potential;

Inconvenience if exercised;

Limited protection

Buy puts Reliable protection

Premium must be paid;

Hedge may require periodic adjustment

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Engineering an Option (cont’d)

Extensive purchase of individual equity puts is inefficient in a large portfolio– Portfolio may contain dozens of stocks,

resulting in numerous trading fees, managerial time, and high premium cost

– Index options or futures options are best suited

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Engineering an Option (cont’d)

Financial Engineering Example

Assume that T-bills yield 8% and market volatility is 15%. Black’s options pricing model predicts the theoretical variables for a 2-year XPS futures put option with a 325.00 striking price as follows:

Striking price = 325.00Index level = 326.00Option premium = $23.15Delta = -0.388Theta = -0.011Gamma = 0.016Vega = 1.566

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Engineering an Option (cont’d)

Financial Engineering Example

Linear programming models can be utilized to obtain the desired theoretical values from existing call and put options. The greater the range of striking prices and expirations from which to choose, the easier the task.

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Engineering an Option (cont’d)

Financial Engineering Example

Available XPS

Options

Linear

Programming

Synthetic Put

With Desired

Theoretical Values

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Engineering an Option (cont’d)

The tough part of engineering an option is dealing with the dynamic nature of the product– To keep the engineered put behaving like a

“real” one, it is necessary to adjust the option positions that comprise it (dynamic hedging)

– How frequently you should reconstruct the portfolio to fine-tune delta depends on the rest of your market positions and the magnitude of the trading fees you pay

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Engineering an Option (cont’d)

Primes and Scores

PRIME is the acronym for “Prescribed Right to Income and Maximum Equity”

SCORE stands for “Special Claim on Residual Equity”

PRIMEs and SCOREs were arguable the first of the engineered hybrid securities

Securities provided investors a means of separating a stock’s income and capital appreciation potential

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Engineering an Option (cont’d)

Primes and Scores (cont’d)

Americus Trust

UnitPRIME SCORE Common

Stock

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Gamma Risk

There are several ways to engineer derivatives products that differ with regard to their cost and their robustness

Gamma risk measures:– How sensitive the position is to changes in the

underlying asset price– The consequences of a big price change

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Gamma Risk (cont’d)

An options portfolio with a gamma far from zero will rattle apart when the market experiences stormy weather

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Gamma Risk (cont’d)

Gamma Risk Example

Suppose we hold 10,000 shares of a $60 stock and want to temporarily move to a position delta of zero.

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Gamma Risk (cont’d)

Gamma Risk Example (cont’d)Options Data

Calls Puts

Strike Premium Delta Gamma Premium Delta Gamma

50 $11.24 0.880 0.019 $0.63 -0.121 0.019

60 $4.51 0.565 0.037 $3.84 -0.445 0.038

70 $1.31 0.244 0.029 $10.71 -0.787 0.033

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Gamma Risk (cont’d)

Gamma Risk Example (cont’d)Alternative Solution A

Position Quantity Delta Gamma Premium

Stock +10,000 +10,000 - -

60 Call -100 -5,650 -370 +$45,100

60 Put +98 -4,361 +372 -$37,632

-11 +2 +$7,468

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Gamma Risk (cont’d)

Gamma Risk Example (cont’d)Alternative Solution B

Position Quantity Delta Gamma Premium

Stock +10,000 +10,000 - -

50 Call -114 -10,032 -217 +$128,136

-32 -217 +$128,136

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Gamma Risk (cont’d)

Gamma Risk Example (cont’d)

Both solutions have an initial position delta close to zero Solution B has the attraction of bringing in a great deal more

than Solution A Solution B’s negative gamma may be hurt by a fast market

Assume the underlying stock price rises by 5% to $63

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Gamma Risk (cont’d)

Gamma Risk Example (cont’d)Options Data

Calls Puts

Strike Premium Delta Gamma Premium Delta Gamma

50 $13.96 0.927 0.012 $0.36 -0.074 0.013

60 $6.38 0.668 0.032 $2.68 -0.339 0.033

70 $2.14 0.336 0.033 $8.47 -0.687 0.035

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Gamma Risk (cont’d)

Gamma Risk Example (cont’d)Alternative Solution A: 5% Increase in Stock Price

Position Quantity New Delta Change in Option Value

Gain or Loss

Stock +10,000 +10,000 - +$30,000

60 Call -100 -6,680 +$1.87 -$18,700

60 Put +98 -3,322 -$1.16 -$11,368

-2 +$68

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Gamma Risk (cont’d)

Gamma Risk Example (cont’d)Alternative Solution B: 5% Increase in Stock Price

Position Quantity New Delta Change in Option Value

Gain or Loss

Stock +10,000 +10,000 - +$30,000

60 Call -114 -10,568 +$2.72 -$31,008

-568 -$1,008

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Gamma Risk (cont’d)

Gamma Risk Example (cont’d)

Solution A is preferable because: Its position delta remains near the target figure of zero Its value changed by only $68, while the other portfolio declined

by over $1,000

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Risk Management

Managing company risk Managing market risk

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Managing Company Risk

Many modern portfolio managers actively practice some form of delta management– Delta management refers to any investment

practice that monitors position delta and seeks to maintain it within a certain range

– Delta is a direct measure of the “degree of bullishness” represented in a particular security position or portfolio

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Managing Company Risk (cont’d)

Bullish

Out of the Fully

Market 0% + + 100% Invested

- -

Bearish

Position Delta

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Managing Market Risk

Most institutional use of SPX futures is to reduce risk rather than eliminate it– If you completely eliminate risk, returns should

be modest

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Managing Market Risk (cont’d)

Delta management of market risk involves futures puts and calls– A long futures contract has a delta of 1.0– Call options have deltas near 1.0 if they are

deep-in-the-money and near zero if they are far out-of-the-money

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Managing Market Risk (cont’d)

Delta management of market risk involves futures puts and calls (cont’d)– Puts have deltas near –1.0 when deep-in-the-

money and near zero if far out-of-the-money– When the striking price is near the price of the

underlying asset, the option delta will be near 0.5 (for calls) or –0.5 (for puts)