© 2004 south-western publishing 1 chapter 16 financial engineering and risk management
TRANSCRIPT
© 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)