PORTFOLIO “INSURANCE”Presented By: JOHN O’BRIEN Director, Master in Financial Engineering (MFE) and Adjunct Professor University of California, Haas School of Business [email protected] University of California, Haas School of Business www.haas.berkeley.edu China, 4 - 16 November 2001 PI - 1 Portfolio “Insurance” • Traditional insurance is based on the principles of diversification and actuarial science. • Portfolio “insurance” is based only on the principal of risk transfer. One person’s protection is another person’s liability. • For the market for portfolio “insurance” to clear: money protected must equal money at risk. • The cost of portfolio “insurance” is the mechanism to equilibrate its demand with supply. University of California, Haas School of Business www.haas.berkeley.edu China, 4 - 16 November 2001 PI - 2 3 .16 November 2001 PI .Supply/Demand Curve for Portfolio “Insurance” University of California.edu China.haas. Haas School of Business www.berkeley. 4 . • Alternatively. Haas School of Business www.edu China. University of California.berkeley.16 November 2001 PI .haas. the investor could buy a Put Option at a cost of “p”. and invest the remainder.4 . (100 – p). bearing all the risk and reaping all the reward.Basic Portfolio “Insurance” – Stock plus Put Option • An investor with 100 to invest could invest it all in a portfolio of stock. 4 . Basic Portfolio “Insurance” – Stock plus Put Option (2) • The protected investor will gain only a fraction. of future stock gains. but would be protected from loss beyond the protection level provided by the Put Option (see graph on next slide). 4 . from where does the 25 come? University of California. Haas School of Business www. (100 – p)/100.berkeley.edu China. • Question: If the stock declines such that the protected investor should receive 25.haas.5 .16 November 2001 PI . edu China. 4 .berkeley.Graph Illustrating Portfolio “Insurance” University of California.haas. Haas School of Business www.16 November 2001 PI .6 . 4 . • All option and future’s markets are zero sum. • Fundamental identity in every Option and Future’s market: buyers gain (loss) equals seller’s loss (gain). Haas School of Business www. University of California.16 November 2001 PI .7 .edu China. “p”) • Our example makes clear that every gain is exactly offset by a corresponding loss.berkeley.haas.Option’s Markets are “Zero Sum” • The protected investor in our example received 25 from his Put Option – the option seller lost 25 (but kept his premium. Haas School of Business www.haas.8 . • The seller must carry out this short-stock management program without losing more than the premium he received. p. University of California.16 November 2001 PI .edu China. the seller must take a short position in the stock. in order to make a profit equal to his payout if the stock closes below the protected level.berkeley. To hedge this exposure. 4 .Hedging a Put Option • The seller of a Put Option is at risk when the stock declines. and adjust that short position. 16 November 2001 PI .edu China.Hedging a Put Option (2) • Properly interpreted. Haas School of Business www.haas.berkeley. University of California. 4 . and within the bounds of its assumptions.9 . the Black/Scholes/Merton option pricing formulae prescribes exactly how to carry out the necessary short-stock management. is derived from the Black/Scholes/Merton formulae. 4 .10 .edu China. The fraction of stock in the stock plus cash position is known as the “delta” of the position. and the appropriate subsequent delta adjustments.16 November 2001 PI . The appropriate initial delta. University of California.haas. Haas School of Business www. • Dynamic hedging requires taking positions only in the stock in question and cash.berkeley.Leland O’Brien Rubinstein’s (LOR) Dynamic Hedging • In 1980 LOR introduced the strategy of dynamic hedging to replicate the payoff from any position in stock plus option. 4 . University of California.16 November 2001 PI .haas.berkeley.edu China.11 . Haas School of Business www.Leland O’Brien Rubinstein’s (LOR) Dynamic Hedging (2) • The implication of dynamic hedging is that investors can think of options and dynamic stock strategies interchangeably. the price (or cost) of an option replicating strategy is the fair price (or premium) of the option being replicated.berkeley. University of California.12 .edu China. Haas School of Business www.The Economic Law of “One Price” • Defined: All assets offering the same payout in all states of the world will sell at the same price. • Implication: Any option and its replicating strategy must have the same price. • Said another way.haas.16 November 2001 PI . 4 . 4 .edu China. This distinction is often overlooked – an often costly mistake.13 .haas.berkeley. Haas School of Business www. the cost of a replicating strategy indicates the cost of an option in the real world. University of California.16 November 2001 PI .The Economic Law of “One Price” (2) • Black/Scholes/Merton indicates the fair price of an option in an idealized world. constant-volatility market. 4 . – The actual. Haas School of Business www. 0.14 .16 November 2001 PI . selling low).berkeley.5) to the delta at expiration (either 0 or 1). cost of moving from the initial strategy delta (say. University of California.haas.Determinants of the Cost of a Replicating Strategy • Pure Cost – Cost in a continuous. plus – The “reversal” costs resulting from volatility-driven reversals in the strategy delta (buying high. frictionless.edu China. or opportunity. haas.Determinants of the Cost of a Replicating Strategy (2) PLUS • Real World Costs – Costs resulting from price discontinuities.15 . trading frictions. 4 . Haas School of Business www.edu China. and volatile volatility University of California.16 November 2001 PI .berkeley. haas.edu China.Real World Replicating Strategy Costs • Stock Price Jump – Prevents maintaining the appropriate delta as the stock price moves from one level to another.16 November 2001 PI .16 . but continuous trading – Causes the number of actual reversals of stock price to differ from the anticipated number. University of California. Haas School of Business www.berkeley. • Changing volatility. 4 . 17 .Real World Replicating strategy Costs (2) • Transaction friction (cost) – Causes more value loss per reversal than anticipated (similar impact as higher than anticipated volatility). 4 .16 November 2001 PI . Haas School of Business www. University of California.edu China. • Cost of capital and profit.haas.berkeley. the payoff is certain. and. • When you replicate an option either the cost or the payout is uncertain.haas. University of California.16 November 2001 PI . and who sells options and hedges his position (mostly broker / dealers / investment bankers). except for default risk.18 . 4 .berkeley. Haas School of Business www.edu China.Real World difference between Buying and Replicating an Option • When you buy an option the cost is certain. • This difference tends to define who buys options (mostly end-users). • Replicating strategies are not transparent to the market.Macro-market Implications of Portfolio “Insurance” • Option’s markets provide transparency for prices. Therefore. This uncertainty prevents a proper equilibration of demand and supply.edu China. Haas School of Business www. or any option’s strategy.19 . Portfolio “Insurance”) is not clearly known.haas. and allow price to equilibrate the demand and supply of Portfolio “Insurance”. the cost of any strategy (say. 4 . University of California.berkeley. Stock transactions initiated for differing reasons are confounded in the market.16 November 2001 PI . Bad things can result. October 1987 in the U.S.16 November 2001 PI .20 . market was generally seen to be “overvalued”.haas. • The amount of Portfolio “Insurance” in force was not well understood by market participants. University of California.edu China. • The Portfolio “Insurance” replicating strategy was not well understood by market participants. 4 . • The Index option’s market had just developed. It did not provide sufficient position limits. for broad institutional use. or liquidity.berkeley. Haas School of Business www.S. Market • The U. the above factors caused natural “value” buyers to step aside.16 November 2001 PI . • Taken together.October 1987 in the U.haas. • Fear of broker and market-maker insolvency caused stock bids and trading capital to be reduced by market participants.21 . University of California.edu China. 4 . Haas School of Business www. Market (2) • Stock-index stocks/stock-index futures arbitrage was in early development and not well understood by market participants. or to demand large price discounts.berkeley.S. 22 . say 500. an asset allocation shift using Index Futures would be seen as a “no-information” trade with respect to the individual stocks in the index.Cash-Index/Index Futures Arbitrage • Sale (purchase) of an Index Future is more efficient than the sale (purchase) of a list of.edu China. University of California. hence less disruptive to individual stock prices. • Properly implemented.haas. Long stock plus short futures contract equals cash. 4 .16 November 2001 PI . Haas School of Business www. stocks to affect an asset allocation shift.berkeley. 23 . 4 .edu China. Haas School of Business www.berkeley.haas. an Index Futures trade involves much less stock-transfer activity (and cost) than trading a large list of stocks.Cash-Index/Index Futures Arbitrage (2) • Operationally. University of California.16 November 2001 PI . edu China. Haas School of Business www. • Appreciation of the economic benefit of Portfolio “Insurance”. 4 .16 November 2001 PI .berkeley. • A well developed cash-index/index futures arbitrage market.24 . University of California.Requirements for an Orderly Portfolio “Insurance” Market • Transparency in the price and amount of Portfolio “Insurance”.haas. one would expect them to develop and for Portfolio “Insurance” to become part of any robust capital market. University of California.edu China.berkeley.haas.16 November 2001 PI .25 . Haas School of Business www. 4 .Requirements for an Orderly Portfolio “Insurance” Market (2) • Since the above outcomes would benefit all market participants. edu/MFE • Financial Investment Technology (F.16 November 2001 PI .edu China. Certificate.I. 2002 – One-month intensive course in quantitative financial economics leading to an F.berkeley. 4 .edu/BPF University of California.haas. – www.haas.C. – www. Berkeley.) – 7 January – 1 February.Interested in a Deeper Understanding of Finance? • Master’s in Financial Engineering Program (MFE) – 12 Month program leading to a Master of Financial Engineering degree from U.26 .berkeley.T.berkeley. – www.T.haas. Haas School of Business www. two-day seminar in contemporary issues in finance.I.haas.berkeley.edu/finance/FIT • Berkeley Program in Finance (BPF) – Twice yearly.