Facts and Fallacies of Dynamic Hedging Strategies August 21, 2014 In Joon Kim

I. Dynamic Hedging Strategies (1/7)  Trading strategies The Black-Scholes model is derived from the idea that the options can be synthesized from dynamic hedging strategies Adjusting hedge ratios continuously as the underlying asset’s price moves (delta neutral strategies) The key is to determine how many shares should be purchased/sold based on delta Assumption: the stochastic process of an underlying asset’s price is not affected by dynamic hedging strategies 2

I. Dynamic Hedging Strategies (2/7)  To hedge short positions in calls and puts Purchase asset if the price of underlying asset goes up –Additional purchase as the price goes up Sell asset if the price of underlying asset goes down –Additional sale as the price goes down Dynamic hedging strategies are trend enforcing If the underlying asset is an index portfolio, the entire stock market would be affected 3

I. Dynamic Hedging Strategies (3/7) The index option market and the stock market are separated in the absence of dynamic hedging strategies 4 Stock Market Participants Short Positions in Index Puts Long Positions in Index Puts  General equilibrium implications

I. Dynamic Hedging Strategies (4/7)  General equilibrium implications Dynamic hedging strategies can affect the stochastic process of an underlying asset’s price Dynamic hedging strategies transfer risk from the option investors implementing dynamic hedging strategies to investors in the underlying asset’s market When the short positions in puts are hedged with dynamic hedging strategies, the stock market participants become counter-parties to the long puts. Stock market participants thus are forced to bear more downside risk than before. Stock market participants are not aware of risk transferred to themselves 5

I. Dynamic Hedging Strategies (5/7) Long Positions in Index Puts Short Positions in Index Puts Stock Market Participants 6  General equilibrium implications

I. Dynamic Hedging Strategies (6/7)  General equilibrium implications The problem arises if the trading volume needed to implement dynamic hedging strategies is a large portion of the total trading volume of the underlying asset. Dynamic hedging strategies to hedge short positions in calls and puts would affect the underlying asset market in such a way as to increase the volatility of the underlying asset 7

I. Dynamic Hedging Strategies (7/7)  Economic Impacts Dynamic hedging strategies are effective only when few investors implement them. If a large number of investors join the bandwagon, dynamic hedging strategies are not effective means to reduce risk (Fallacy of composition) It might be an illusion that risk can be eliminated with dynamic hedging strategies Overconfidence in dynamic hedging strategies to reduce risk can lead to underestimation of risk Volatility increased excessively, markets destabilized and crashed in extreme situations 88

II. Failure of Dynamic Hedging Strategies 1.Black Monday in Failure of LTCM 3.Recent Global Financial Crisis 9

1. Black Monday in 1987 (1/4)  On Monday, October 19, 1987, the Dow Jones Index fell 508 points, dropping 22.6% in a day.  The stock market crash gave rise to a worldwide recession  The Brady Committee and General Accounting Office tried to investigate what caused the market crash  It was widely believed that large amounts of sell orders for portfolio insurance were the main cause Great Depression

1. Black Monday in 1987 (2/4)  Portfolio Insurance Upside potential with limited downside risk Long position in stock index and index put option (or portfolio with the same payoff as index put option) Buy stock index put option Buy stock index Portfolio Insurance Strike PriceStock Index Payoff 11

1. Black Monday in 1987 (3/4)  Situation A large number of institutional investors employed portfolio insurance programs The Brady Report blamed the portfolio insurance programs as the culprit for the market crash The Brady Report indicated that vicious cycles occurred, “index falls → sell index futures for portfolio insurance → index futures drops → sell index for index arbitrage ” leading to the market crash Why didn’t vicious cycles occur on other days in which the stock market started lower than the previous day? 12

1. Black Monday in 1987 (4/4)  Fundamental reasons for the crash Dynamic hedging strategies for portfolio insurance programs are trend enforcing so that bubbles were accumulated in the period of economic recovery during the1980s The number of investors participating in portfolio insurance programs increased such that the market could not absorb the adverse effects of dynamic hedging strategies Dynamic hedging strategies for portfolio insurance were destined to fail as more investors participated in portfolio insurance programs (Fallacy of composition) 13

1. Black Monday in 1987 (4/4)  Risk Transfer 14 Stock Market Participants PI

2. Failure of LTCM (1/3)  Outline Founded in March 1994 by John Meriwether, a bond trader at Salomon Brothers, with Robert Merton and Myron Scholes, who won the 1997 Nobel Memorial Prize in Economic Sciences LTCM began its operation with $1.2 billion in February 1994 Bailed out in September 1998 and dissolved in early 2000  Investment strategies Market-neutral investing : employed dynamic hedging strategies Strategies that neutralize market risk by maintaining delta neutral with respect to movements of market. High leverage in order to enhance returns 15

2. Failure of LTCM (2/3)  An example High risk investment speculating on credit spreads Prediction that spreads would be narrow –Buying junk bonds (Russian government bonds) and selling Treasury bonds –High returns would have been realized if the prediction were right  Results Incurred losses as credit spreads widened due to the possibility of Russia defaulting Yield of Treasury Bond Yield of Junk Bond Spread Prediction 16

2. Failure of LTCM (3/3)  Problems pointed out by news media Wrong valuation models for derivatives and liquidity dried up BusinessWeek, September 21, 1998 –“Can you devise the surefire way to beat the markets? The rocket scientists thought they could. Boy, were they ever wrong?” –“When computer models slip on runway”  Fundamental reasons for failure Failure of dynamic hedging strategies that were prepared in case credit spreads moved against its prediction Liquidity dried up in the process of LTCM trying to implement dynamic hedging strategies 17

3. Recent Global Financial Crisis (1/3)  Global Financial Crisis was in part a result of failure to spread risk  Complex financial derivatives (structured products, CDO, CDS etc.) and overconfidence in financial engineering techniques to reduce risk  Underestimation of financial risk by financial companies (CB, IB, Hedge Funds, PEF etc.)  High risk investment strategies encouraged  High risk investment strategies caused distortion in risk allocation 18

3. Recent Global Financial Crisis (2/3)  Bubbles created by high risk investment strategies and magnified by dynamic hedging strategies  Effective risk management of derivatives with financial engineering techniques might be an illusion  Bursting of bubbles led to insolvency of financial companies  When bubbles burst, misused derivatives exacerbated financial crisis with destructive power  Lack of understanding of the general equilibrium implications of risk management techniques by market participants contributed to financial crisis 19

3. Recent Global Financial Crisis (3/3)  CDS (Credit Default Swaps) and Risk Management CDS are designed to provide protection for default risk A large part of default risk is systematic risk which cannot be diversified in a portfolio of CDS Risk of CDS portfolios was significantly underestimated A financial company with a large number of short positions in CDS would have incentive to increase its short positions if the CDS spreads do not reflect the increased default risk CDS spreads should have depended on the size of short positions of a protection seller –CDS protection would be useless if the protection seller is likely to default when the bonds underlying CDS default 20

III. Related Issues (1/2)  Failure of risk management models based on historical statistical data “Black Swan” by Nassim Nicholas Taleb “We are seeing things that are 25 standard deviation moves, several days in a row.” by David Viniar, CFO of Goldman Sachs, FT August 13, 2007  The stock market crash on Black Monday in 1987, LTCM failure and the Global Financial Crisis could be labeled as “Black Swan” events 21

III. Related Issues (2/2)  Those extremely rare events were endogenous events resulted from the blind execution of dynamic hedging strategies by a large number of investors  Those extremely rare events can be prevented by inducing rational decisions in market participants if they understand the general equilibrium implications of dynamic hedging strategies 22

IV. Conclusions (1/2)  Derivatives valuation models are partial equilibrium models The models are valid if the underlying asset market is not affected If a large number of investors employ dynamic hedging strategies, the price dynamics of the underlying asset can be altered General equilibrium implications for risk allocation  Risk transfer vs. risk elimination What happens if every investor tries to transfer systematic downside risk to someone else? Systematic risk (market risk) cannot be eliminated from an economy 23

IV. Conclusions (2/2)  Fallacy of composition Systematic risk can be eliminated (transferred to other investors) from the view point of an individual investor If all investors try to eliminate (transfer) systematic risk, no one can  Fundamental functions of derivatives Emphasis on risk allocation (risk spreading) Risk allocation role of dynamic hedging strategies  How to measure risk? Risk of derivative securities hedged with dynamic hedging strategies “Black Swan” events 24

Fallacy of Composition

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