1 / 36

Hedging risk with Derivatives

Hedging risk with Derivatives. Review of equity options Review of financial futures Using options and futures to hedge portfolio risk Introduction to Hedge Funds. Options -- Contract. Calls and Puts Underlying Security (Number of Units) Exercise or Strike Price Expiration date

skyla
Download Presentation

Hedging risk with Derivatives

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Hedging risk with Derivatives • Review of equity options • Review of financial futures • Using options and futures to hedge portfolio risk • Introduction to Hedge Funds

  2. Options -- Contract • Calls and Puts • Underlying Security (Number of Units) • Exercise or Strike Price • Expiration date • Option Premium • American, European, Asian, etc.

  3. Options -- Markets • 1 Buyer + 1 Seller (writer) = 1 Contract • Examples of Price Quotations • Premium = Intrinsic Value + Time Prem • Options available on • Equities • Indicies • Foreign Currencies • Futures

  4. Options -- Basic Strategies • Buy Call • Sell (write) Call • Buy Put • Sell (write) Put

  5. Options -- Advanced Strategies • Straddle • Strips and Straps • Vertical Spreads • Bullish • Bearish

  6. Options - Determinants of Value • Value of Underlying Asset • Exercise Price • Time to Expiration • VOLATILITY • Interest Rates • Dividends

  7. Options -- Black Scholes Option Pricing Model • C = SN(d1) - Xe-rTN(d2) ln(S/X) +(r+s2/2)T d1 = ---------------------------sT1/2d2 = d1 - sT1/2 • Put-Call Parity: P = C + Xe-rT - S

  8. Futures Contract • Agreement to make (sell) or take (buy) delivery of a prespecified quantity of an asset at an agreed upon price at a specific future date. • ex. S&P 500 Index Futures: • Price: 1126.10; Delilvery month: June • Buyer agrees to purchase a portfolio representing the S&P 500 (or its cash equivalent) for $1126.10 x 250 = $281,525 on Thursday prior to 3rd Friday in June. (Buyer is locking in the purchase price for the portfolio.) • Seller agrees to deliver the portfolio described above. • Note: since this is a cash settled contract, if the price was 1116.10 on the delivery date, the buyer would pay the seller $2,500 (= 10 x 250). If the price was 1136.10, the seller would pay the buyer $2,500

  9. Futures Contract: Marking to Market • Marking to market: • Price of Futures contract is reset every day • Gains/Losses versus previous day are posted to buyer and seller margin accounts • Futures = a bundle of consecutive 1-day forward contracts • If futures held to expiration, effective delivery price is same as when contract initiated

  10. Futures Contract: Marking to Market example (C$ contract)

  11. April 4 June 17 1. Contract to sell S&P @ 1126.1 ($281,525) on June 17. 2. Buy S&P @ 1106.1 ($276,525) on spot market and deliver @ 1126.1 3. Profit = $5,000. Index Futures Market • Speculators often sell index futures when they expect the underlying index to depreciate, and vice versa.

  12. April 4 June 17 1.Contract to sell S&P @ 1126.1 ($281,525) on June 17. 2. Market falls to 1106.1.Gain =$5000 3. Gain offsets (approx.) loss of $5000 on securities held Index Futures Market • Index futures may be sold by investors to hedge risk associated with securities held.

  13. Index Futures Market • Most index futures contracts are closed out before their settlement dates (99%). • Brokers who fulfill orders to buy or sell futures contracts earn a transaction or brokerage fee in the form of the bid/ask spread.

  14. Hedging with Derivatives • Basic option strategies • Covered call • Protective put • Synthetic short • Basic futures strategies • Using interest rate futures to reduce risk

  15. Covered Call • Sell call on stock you own. (Long stock, short call) • Good: • As value of stock falls, loss is partially offset by premium received on calls sold. • Essentially costless since hedge generates a cash inflow • Bad: • Maximum inflow from call = premium; Hedge is less effective for large drop in stock price • If stock price rises, call will be exercised; Investor transfers gains on stock to holder of call.

  16. Protective Put • Buy put on stock you own. (Long stock, long put) • Good: • As value of stock falls, loss is partially offset by gain in value of put. Gain from put continues to grow as stock price falls. • If stock price rises, maximum loss on put = premium; Investor keeps all stock gains less fixed put premium. • Bad: • More expensive to hedge with put

  17. Synthetic Short • Sell call and buy put on stock you own. (Long stock, short call, long put) • Good: • As value of stock falls, loss is offset by gain in value of put. Gain from put continues to grow as stock price falls. • If stock price rises, gain is offset by loss on call. Loss from call continues to grow as stock price rises. • Very effective hedging device • Can be self-financing (premium received on put sold offsets premium paid on call purchased) • Bad: • Often more expensive than simply shorting the stock itself.

  18. Delta Hedging with Options • Call Delta = DC= dC/dS • From Black-Scholes model, DC = N(d1) Ex.: If S=74.49, X=75, r=1.67%, s =38.4%, t=0.1589 yrs. Then, C = 4.40 and N(d1) = 0.5197 If S increases by $1, C increases by $0.5197 Hedge Ratio = H = 1/DC = 1/0.5197 = 1.924 Sell 1.924 calls per share of stock held to hedge!

  19. Example of Call Hedge – Held to Expiration, 1000 share stock position

  20. Delta Hedging - Puts • Put Delta = DP= dP/dS • From Black-Scholes model and Put-Call Parity, DP= DC – 1 =N(d1) - 1 Ex.: If S=74.49, X=75, r=1.67%, s =38.4%, t=0.1589 yrs. Then, C = 4.40, P = 4.71, N(d1) = 0.5197, and N(d1) -1 = -0.4803 If S increases by $1, P decreases by $0.4803 Hedge Ratio = H = 1/D = 1/0.4803 = 2.082 Buy 2.082 puts per share of stock held to hedge!

  21. Example of Put Hedge – Held to Expiration, 1000 share stock position

  22. Delta Hedging with Options • Delta changes over time! • S changes • Time declines • Other factors (r, s) may change

  23. True Delta Hedging – Adjust hedge when S changes • Scenarios 1 & 2: • IBM stock drops by $1 to $73.49 ==> Loss of $1000 • Call options also drop by $0.5197 ==> Gain of $1037.97 ==>Net change $37.97 • IBM stock rises by $1 to $75.49 ==> Gain of $1000 • Call options also rise by $0.5193 ==> Loss of $1037.97 ==> Net change ($37.97)

  24. True Delta Hedging – Adjust hedge when t changes • Scenario 3: • One week passes, IBM stock at $71.49 ==> Loss of $3000 • Call options now worth $2.73 ==> Gain of $3173 ==>Net change $173 • New call delta = 0.4029 • New hedge ratio = 1/0.4029 = 2.482 ==> Sell 5 more contracts! • Scenario 4: • One week passes, IBM stock at $77.49 ==> Gain of $3000 • Call options now worth $5.82 ==> Loss of $2698 ==> Net change ($302) • New call delta = 0.6238 • New hedge ratio = 1/0.6238 = 1.603 ==> Buy 3 contracts!

  25. True Delta Hedging – Adjust hedge when S changes • Scenarios 1 & 2: • IBM stock drops by $1 to $73.49 ==> Loss of $1000 • Put options also rise by $0.4803 ==> Gain of $1008.63 ==>Net change $8.63 • IBM stock rises by $1 to $75.49 ==> Gain of $1000 • Put options also fall by $0.4803 ==> Loss of $1008.63 ==> Net change ($8.63)

  26. True Delta Hedging – Adjust hedge when t changes • Scenario 3: • One week passes, IBM stock at $71.49 ==> Loss of $3000 • Put options now worth $6.06 ==> Gain of $2835 ==>Net change ($165) • New put delta = 0.4028 – 1 = -0.5972 • New hedge ratio = 1/0.5972 = 1.674 ==> Sell 4 contracts! • Scenario 4: • One week passes, IBM stock at $77.49 ==> Gain of $3000 • Put options now worth $3.15 ==> Loss of $3276 ==> Net change ($276) • New put delta = 0.6238 – 1 = -0.3762 • New hedge ratio = 1/0.3762 = 2.658 ==> Buy 5 more contracts!

  27. Delta Hedging with options • Delta represents response of call (or put) price with change in the stock price • Delta changes as stock price, time to expiration, interest rates, volatility change • It is too expensive to hedge individual stock positions with matching options. It is more common to hedge a portfolio with index options (cross hedging) • Most managers monitor delta itself to decide when to rebalance.

  28. A True Protective Put • Puts can be used to build a floor under the value of a long position • Buy 1 put per long share • Ex.: Long 1000 shares of IBM at $74.49 • Buy 1000 puts at $4.71 • Puts guarantee a value of $75 per share • This is insurance, not a hedge!

  29. A True Protective Put

  30. Hedging with Futures (example from May 2001) • There are futures on the S&P500. Suppose I have a portfolio that is currently worth $1,117,672. The portfolio has a beta of 1.3. • June S&P500 futures are at 1430.70 • ==> contract is worth 500 x 1430.70 = $715,350 • Hedge ratio = • (Value of portfolio / Value of Futures contract)(Portfolio Beta) • = (1,117,672/715,350)(1.3) = 2.031 ==> Sell 2 Contracts !

  31. Hedging with Futures (example from May 2001)

  32. Adjusting Systematic Risk with Futures • PM may choose to adjust systematic exposure up or down to reflect • investor desires • expectations of market movements • About index futures: • Represents contract to make/take delivery of a portfolio represented by the index • Since index itself may be non-investable, most index futures contracts are cash-settled • example: • S&P500 futures CME contract value = 250 x index • Initial margin: $6K for spec, $2.5K for hedgers.

  33. Adjusting Systematic Risk with Futures • I have an $11 million stock portfolio with b=1.05. I want to increase b to 1.2. • Value of Futures = 1314.50 x 250 = $328,625 • bf = 1.0. • Target b = contribution from portfolio + contribution from futures • 1.2 = (1.0)(1.05) + [(F x 328,625)/$11,000,000](1.0) • F = (bT - Wsbs)(Vs/VF) • F = 5.02 => buy 5 contracts • What have we done? • Used futures contracts to leverage holdings and increase exposure to market risk

  34. Adjusting Systematic Risk with Futures • Suppose target b = .90 • 0.90 = (1.0)(1.05) + [(F x 328,625)/$11,000,000](1.0) • F = (.90 - 1.05)(33.4728)(1.0) = -5.02 contracts (sell) • We have shorted futures to reduce systematic exposure.

  35. Hedging with Interest Rate Futures • How do you reduce duration for a bond portfolio? • Sell high D, buy low D • Sell bonds, buy Tbills • Sell interest rate futures • Interest rate futures: agreement to make/take delivery of a fixed income asset on a particular date for an agreed upon price • ex: Sept Tbond futures contract • $100K FV US Treas bonds with 15-years to maturity and 8% coupon (what if they don't exist?) • Price: 99-27 = 99 27/32 % of $100,000 = $998,437.50 • (Tick = $31.25) D = 8.64 years

  36. Hedging with Interest Rate Futures • I own an $11,000,000 face value portfolio of high grade US corporate bonds with an aggregate value of 101-08 (or $11,137,500) and a duration of 7.7 years. • I expect rates to rise. How can I immunize my portfolio? • Target D = contribution of bond port + contribution of fut. • 0 = (1.0)(7.7) + [(F x 998,437.50)/11,137,500](8.64) • F = (0.0 - (1.0)(7.7))(11,137,500/998,437.50)/8.64 • F = -9.94 contracts => short 10 Tbond futures contracts • This is the weighted average duration approach

More Related