1. Hedging and speculative strategies using index futures Finance 30233 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)

2. Hedging with Stock Index futures Example: Portfolio manager has well-diversified $40 million stock portfolio, with a beta of 1.20 1 % 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

3. 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

4. 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 2/2/02 855 $37,600,000 futures drop 45 points -45 -$2,400,000 gain = (174)(45)(250) = $1,957,500

5. 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 =  {

6. 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)

7. 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 2/2/02 855 $37,600,000 futures drop 45 points -45 -$2,400,000 gain = (208)(45)(250) = $2,340,000

8. 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

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

10. 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 (.50 - 1.20) V (920) ($250)   New  PF  = P F = - 122 contracts

11. 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 2/2/02 855 $37,600,000 futures drop 45 points -45 -$2,400,000 gain = (122)(45)(250) = $1,372,500

12. 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)

13. "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

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

15. 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 (0 - 1.30) V (920) ($250)   NEW  SF  = P F = - 56 contracts The desired beta is zero, and the number of contracts to buy (sell) is:

16. 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 2/2/02 855 $9,550,000 futures drop 45 points -45 - $450,000 gain = (56)(45)(250) = $630,000

17. 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 2/2/02 945 $10,850,000 futures rise 45 points 45 $850,000 loss = (56)(45)(250) = $630,000