1Lec 3 Hedging Strategies Using Futures Lec 3: Hedging Strategies Using Futures (Hull, Ch. 3) Important Ideas: 1. Short Hedges, Long Hedges 2. Basis Risk 3. Hedge Ratios for Equity Risk Management 4. Use SP Futures to Change a Portfolio Beta 1. Short Hedges, Long Hedges Remember: If you are Long the Spot (A/R FC ) ➟ go Short Futures (Short Hedge) Short the Spot (A/P FC ) ➟ Long Futures (Long Hedge)

2Lec 3 Hedging Strategies Using Futures 2. Basis Risk. By Def’n: Basis risk is variability in SpotPrice t - FuturesPrice t Example. ▸ At t = 0 (now), UTC has an A/R from a company in Turkey for ₤ 50 M (50M Liras) ▸ Suppose S 0 = 0.75 $/₤ ➟ $ Value of A/R 0 $ = ₤ 50M(0.75 $/₤) = $ 37.5M, 1 $/₤ ➟ A/R 1 $ = ₤ 50 M(1 $/₤) = $ 50 M ➟ GREAT 0.75 $/₤ 0.50 $/₤ ➟ A/R 1 $ = ₤ 50M(0.5 $/₤) = $ 25M ☹ Not so Great | –––––––––––––| 0 THow to hedge this risk (risk of ₤ ↓)?

3Lec 3 Hedging Strategies Using Futures Problem It is difficult to hedge this currency so UTC will cross-hedge with the Euro. To cross-hedge: Sell Futures contracts on the Euro. UTC expects the spot rate to be S T = 0.78 $/₤ (this is just a guess) ➟ UTC expects an A/R T $ = ₤ 50 M(0.78 $/₤) = $ 39 M At time 0 (now), Suppose ▸ Suppose the Euro Futures rate is F 0 = 0.78 $/€, ▸ Size of 1 Futures = € Z = € 125,000 ▸ Sell N F such that € 125,000 (0.78 $/€) (N F contracts) = $ 39 M, ➟ N F = 400 contracts (short)

4Lec 3 Hedging Strategies Using Futures At time T, Suppose spot rates are: S T = 0.72$/₤, ➀ Receive ₤ 50 M from A/R, sell it in the spot market = ₤ 50 M(0.72 $/₤) = $ 36 M, ➁ Close Futures position. Suppose F T = 0.725$/€ CF from Futures = - [ 0.725$/€ $/€ ] € 125,000(400) = + $ 2.75 M, And ➂ Total $ CF from the A/R T $ = $ 36M + $ 2.75M = $ M As of t=0: Expected A/R T $ = $ 39 M, As of t=1: Ex-post actual A/R T $ = $ M. The difference is due to Basis Risk.

5Lec 3 Hedging Strategies Using Futures 3. How to Use Stock Index Futures to Hedge Equity Risk Example 1: ▸ Suppose SMF is long 18 stocks. Portfolio Value = $5.05 M, β SMF = 1.50 ➟ SMF is 50% more volatile than SP500 Index We are in a Bear market, if market ↓ by 20%, then SMF Portfolio ↓ by 30%. what to do? ▸ Sell all stocks, and invest in Cash securities. Is this feasible? Another solution, ▸ Keep portfolio intact and Short SP Futures (Job of Portfolio Risk Manager). ▸ Key decisions: 1) How much Beta risk to Hedge?, and 2) How Many Contracts?

6Lec 3 Hedging Strategies Using Futures We need to short Futures. Sell N F such that Δ Portfolio Value + Δ Futures = 0 Assumptions: ▸ NO Basis Risk (i.e., F 1 = S 1 ) ➀ SMF Portfolio Value 0 = $5.05 M, β SMF = 1.50 ➁ Div Yield = 0 both for the fund and the SP500 Index, and Rf = 0.0/yr ▸ Use CAPM to connect SMF portfolio with SP Index: ROR SMF = Rf + β(ROR I - Rf) ➟ ROR SMF = β(ROR I ) ▸ SP500 Futures Index is at F 0 = $ 1,000. $ Notional Value of 1 SP500 Futures = = 250*F 0 = 250* $ 1000 = $ 250,000

7Lec 3 Hedging Strategies Using Futures From APT: Δ Futures Value = $ 250,000 x (%ΔSP500) From CAPM: Δ Portfolio Value = ROR SMF V 0 = [β x ROR I ] V 0 Goal is to find N F such that ΔP + N F ΔF = 0 ➟ N F ( $ 250,000) x (%ΔSP500) + β (ROR I ) V 0 = 0 solve for N F ➟ N F = - 1.5(5.05M)/0.25M = (Short 30 SP Futures)

8Lec 3 Hedging Strategies Using Futures Cash Flow Analysis. Possible scenarios at time T: What is the beta of the Hedged Portfolio = ? SP500 Index T %ΔSP Index Ror SMF Unhedged SMF Value T SP Futures Price, F T CF from {-F} -30.3(F T - F 0 ) Hedged Value T $ 900 ➀ -10%-15%$4.2925M $ 900$ M$5.05M $ 950 ➁ -5%-7.5%$4.671M $ 950$ M$5.05M $1,000 ➂ 0% $5.05 M$1,000$0$5.05M 1,050 ➃ +5%+7.5%$5.429M$1,050-$ M$5.05M 1,100 ➄ +10%+15%$5.808M$1,100-$ M$5.05M

9Lec 3 Hedging Strategies Using Futures Use SP Futures to change the Beta of a Portfolio Example 2: ▸ Suppose SMF is long 18 stocks. Portfolio Value = $5.05 M, β SMF = 1.50 ➟ SMF is 50% more volatile than SP500 Index We are in a Bull market and we want to increase the Portfolio Beta to 2. How? ▸ Sell all stocks, and buy much riskier ones. Is this feasible? ▸ Keep portfolio intact and Buy futures on the SP500. ➟ Q: How Many Contracts?

10Lec 3 Hedging Strategies Using Futures Assumptions: ▸ NO Basis Risk (i.e., F 1 = S 1 ) ➀ SMF Portfolio Value 0 = $5.05 M, β SMF = 1.50 ➁ Div Yield = 0 both for the fund and the SP500 Index, and Rf = 0.0/yr ▸ Use CAPM to connect SMF portfolio with SP Index: ROR SMF = Rf + β(ROR I - Rf) ➟ ROR SMF = β(ROR I ) ▸ SP500 Futures Index is at F 0 = 1,000. ▸ $ N 0 = Notional $ Value of 1 SP500 Futures contract = 250*F 0 = 250*1000 = $ 250,000 From CAPM: Expected Δ in Portfolio Value = β OLD (ROR I ) V 0 Desired Δ in Portfolio Value = β NEW (ROR I ) V 0 From APT: Expected Δ Futures Value = N F ( $ 250,000) x (%ΔSP500)

11Lec 3 Hedging Strategies Using Futures Set β OLD (ROR I ) V 0 + N F ( $ 250,000) x (%ΔSP500) = β NEW (ROR I ) V 0 ➟ β OLD V 0 + N F ( $ 250,000) = β NEW V 0 and solve for N F ➟ N F = ( ) (5.05M)/0.25M = (Long 10 SP Futures)

12Lec 3 Hedging Strategies Using Futures Cash Flow Analysis. Possible scenarios at time T (1-year later): What is the beta of the Hedged Portfolio = ? SP500 Index T %ΔSP Index Ror SMF Unhedged SMF Value T SP Futures Price, F T CF from {-F} +10.1(F T - F 0 ) Hedged Value T $ 900 ➀ -10%-15%$4.2925M $ ,500$4.04M $ 950 ➁ -5%-7.5%$4.671M $ ,250$4.545M 1,000 ➂ 0% $5.05 M$1,000$0$5.05M 1,050 ➃ +5%+7.5%$5.429M$1, ,250$5.55M 1,100 ➄ +10%+15%$5.808M$1, ,500$6.06M

13Lec 3 Hedging Strategies Using Futures Thank You! (A favara)