Hedging and speculative strategies using index futures Finance S. Mann, Fall 2001 Short hedge: Sell Index futures - offset market losses on portfolio by generating gains on futures Market Spot Position (Portfolio) Short Hedge (Sell Index Futures)

Hedging with Stock Index futures Example: Portfolio manager has well-diversified $40 million stock portfolio, with a beta of % movement in S&P 500 Index expected to induce 1.20% change in value of portfolio. Scenario: Manager anticipates "bear" market (fall in value), and wishes to hedge against possibility. One Solution: Liquidate some or all of portfolio. (Sell securities and place in short-term debt instruments until "prospects brighten") n Broker Fees n Market Transaction costs (Bid/Ask Spread) n Lose Tax Timing Options (Forced to realize gains and/or losses) n Market Impact Costs n If portfolio large, liquidation will impact prices

Naive Short hedge: dollar for dollar Assume you hedge using the June 02 S&P 500 contract, currently priced at 920. The contract multiplier is $250 per point. Dollar for dollar hedge: find number of contracts: V $40,000,000 = 174 contracts V (920) ($250) = P F where: V = value of portfolio V = value of one futures contract P F

But: portfolio has higher volatility than S&P 500 Index ( portfolio beta=1.20) hedge initiated November 15, 2001, with Index at 900. If S&P drops 5% by 2/2/02 to 855, predicted portfolio change is 1.20 (-5%) = -6.0%, a loss of $2.4 million Net loss = $ 442,500 Assumes: 1) portfolio moves exactly as predicted by beta 2) futures moves exactly with spot Date IndexSpot position (equity) futures position 11/15/01 900$40,000,000 short 174 contracts 2/2/ $37,600,000 futures drop 45 points -45 -$2,400,000 gain = (174)(45)(250) = $1,957,500

Estimating Minimum Variance Hedge ratio Estimate Following regression: spot return t =  SF  Futures ‘return’ t +  t Portfolio Return Futures ‘return’ (% change ) x x x x xxx x x x x x xx x x x x x xx x x x xx x line of best fit (slope =  SF ) intercept =  {

Calculating number of contracts for minimum variance hedging Hedge using June 02 S&P 500 contract, currently priced at 920 [ 920  900 ( 1 + r - d) t ] Minimum variance hedge number of contracts: V P $40,000,000 = 208 contracts V F (920) ($250)  PF  where: V P = value of portfolio V = value of one futures contract F  PF = beta of portfolio against futures (1.20)

Minimum variance hedging results hedge initiated November 15, 2001, with Index at 900. If S&P drops 5% by 2/2/02 to 855, predicted portfolio change is 1.20 (-5%) = -6.0%, a loss of $2.4 million Net loss = $ 60,000 Assumes: 1) portfolio moves exactly as predicted by beta 2) futures moves exactly with spot ( note: futures actually moves more than spot : F = S (1+c) ) Date IndexSpot position (equity) futures position 11/15/01 900$40,000,000 short 208 contracts 2/2/ $37,600,000 futures drop 45 points -45 -$2,400,000 gain = (208)(45)(250) = $2,340,000

Altering the beta of a portfolio where: V F = value of one futures contract V P = value of portfolio Define  PF as portfolio beta (against futures) Change market exposure of portfiolio to  new by buying (selling):  new -  PF  contracts VPVP VFVF

Impact of synthetic beta adjustment Return on Portfolio Return on Market Original Expected exposure Expected exposure from increasing beta Expected exposure from reducing beta

Changing Market Exposure: Example Begin with $40,000,000 portfolio:  PF  = 1.20 Prefer a portfolio with 50% of market risk (  New =.50) Hedge using June 02 S&P 500 contract, currently priced at 920. V $40,000,000 ( ) V (920) ($250)   New  PF  = P F = contracts

Reducing market exposure: results hedge initiated November 15, 2001, with Index at 900. If S&P drops 5% by 2/2/02 to 855, predicted portfolio change is 1.20 (-5%) = -6.0%, a loss of $2.4 million. predicted loss for  P =0.5 is (-2.5% of $40 m) = $1 million Net loss = $ 1,027,500 Assumes: 1) portfolio moves exactly as predicted by beta 2) futures moves exactly with spot ( note: futures actually moves more than spot : F = S (1+c) Date IndexSpot position (equity) futures position 11/15/01 900$40,000,000 short 122 contracts 2/2/ $37,600,000 futures drop 45 points -45 -$2,400,000 gain = (122)(45)(250) = $1,372,500

Sector "alpha capture" strategies Portfolio Return Futures ‘return’ (% change) x x x x xxx x x x x x xx x x x x x xx x x x xx x line of best fit (slope =  ) intercept =  { Portfolio manager expects sector to outperform rest of market (  > 0)

"Alpha Capture" Return on Sector Portfolio Return on Market Expected exposure with "hot" market sector portfolio }  > 0 Slope =  SF = beta of sector portfolio against futures 0

"Alpha Capture" Return on Asset Return on Market Expected exposure with "hot" market sector Expected return on short hedge } expected gain on alpha 0

Alpha Capture example Assume $10 m sector fund portfolio with  = 1.30 You expect Auto sector to outperform market by 2% Eliminate market risk with minimum variance short hedge. ( using the June 02 S&P 500 contract, currently priced at 920) V $10,000,000 ( ) V (920) ($250)   NEW  SF  = P F = - 56 contracts The desired beta is zero, and the number of contracts to buy (sell) is:

Alpha capture: market down 5% hedge initiated November 15, 2001, with Index at 900. If S&P drops 5% by 2/2/02 to 855, predicted portfolio change is 1.30(-5%) + 2% = -4.5%, a loss of $450,000. Net GAIN = $ 180,000 Assumes: 1) portfolio moves exactly as predicted by beta 2) futures moves exactly with spot ( note: futures actually moves more than spot : F = S (1+c)) Date IndexSpot position (equity) futures position 11/15/01 900$10,000,000 short 56 contracts 2/2/ $9,550,000 futures drop 45 points $450,000 gain = (56)(45)(250) = $630,000

Alpha capture: market up 5% hedge initiated November 15, 2001, with Index at 900. If S&P rises 5% by 2/2/02 to 945, predicted portfolio change is 1.30( 5%) + 2% = 8.5%, a gain of $850,000. Net GAIN = $ 220,000 Assumes: 1) portfolio moves exactly as predicted by beta 2) futures moves exactly with spot ( note: futures actually moves more than spot : F = S (1+c)) Date IndexSpot position (equity) futures position 11/15/01 900$10,000,000 short 56 contracts 2/2/ $10,850,000 futures rise 45 points 45 $850,000 loss = (56)(45)(250) = $630,000