Lec 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 Remember: If you are Long the Spot (A/RFC ) ➟ go Short Futures (Short Hedge) Short the Spot (A/PFC ) ➟ Long Futures (Long Hedge) Lec 3 Hedging Strategies Using Futures dfdf

Lec 3 Hedging Strategies Using Futures 2. Basis Risk. By Def’n: Basis risk is variability in SpotPricet - FuturesPricet Example. ▸ At t = 0 (now), UTC has an A/R from a company in Turkey for ₤50 M (50M Liras) ▸ Suppose S0 = 0.75 $/₤ ➟ $ Value of A/R0$ = ₤50M(0.75 $/₤) =$37.5M, 1 $/₤ ➟ A/R1$ = ₤50 M(1 $/₤) = $50 M ➟GREAT 0.75 $/₤ 0.50 $/₤ ➟ A/R1$=₤50M(0.5 $/₤) = $25M ☹ Not so Great | –––––––––––––| 0 T How to hedge this risk (risk of ₤ ↓)? Lec 3 Hedging Strategies Using Futures dfdf

Lec 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 ST = 0.78 $/₤ (this is just a guess) ➟ UTC expects an A/RT$ = ₤50 M(0.78 $/₤) = $39 M At time 0 (now), ▸Suppose the Euro Futures rate is F0 = 0.78 $/€, ▸ Size of 1 Futures = €Z = €125,000 ▸ Sell NF such that €125,000 (0.78 $/€) (NF contracts) = $39 M, ➟ NF = 400 contracts (short) Lec 3 Hedging Strategies Using Futures dfdf

Lec 3 Hedging Strategies Using Futures At time T, Suppose spot rates are: ST = 0.72$/₤, ➀ Receive ₤50 M from A/R, sell it in the spot market = ₤50 M(0.72 $/₤) = $36 M, ➁ Close Futures position. Suppose FT = 0.725$/€ CF from Futures = - [ 0.725$/€ - 0.78$/€ ]€125,000(400) = +$2.75 M, And ➂ Total $CF from the A/RT$ = $36M + $2.75M = $38.75 M As of t=0: Expected A/RT$ = $39 M, As of t=1: Ex-post actual A/RT$ = $38.75 M. The difference is due to Basis Risk. Lec 3 Hedging Strategies Using Futures dfdf

Lec 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, βSMF = 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? Lec 3 Hedging Strategies Using Futures dfdf

Lec 3 Hedging Strategies Using Futures We need to short Futures. Sell NF such that Δ Portfolio Value + Δ Futures = 0 Assumptions: ▸ NO Basis Risk (i.e., F1 = S1 ) ➀ SMF Portfolio Value0 = $5.05 M, βSMF = 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: RORSMF = Rf + β(RORI - Rf) ➟ RORSMF = β(RORI ) ▸ SP500 Futures Index is at F0 = $1,000. $Notional Value of 1 SP500 Futures = = 250*F0 = 250*$1000 = $250,000 Lec 3 Hedging Strategies Using Futures dfdf

Lec 3 Hedging Strategies Using Futures From APT: Δ Futures Value = $250,000 x (%ΔSP500) From CAPM: Δ Portfolio Value = RORSMF V0 = [β x RORI ] V0 Goal is to find NF such that ΔP + NF ΔF = 0 ➟ NF ( $250,000) x (%ΔSP500) + β (RORI) V0 = 0 solve for NF ➟ NF = - 1.5(5.05M)/0.25M = - 30.30 (Short 30 SP Futures) Lec 3 Hedging Strategies Using Futures dfdf

Lec 3 Hedging Strategies Using Futures Cash Flow Analysis. Possible scenarios at time T: What is the beta of the Hedged Portfolio = ? SP500 IndexT %ΔSP Index RorSMF Unhedged SMF ValueT SP Futures Price, FT CF from {-F} -30.3(FT - F0) Hedged ValueT $ 900 ➀ -10% -15% $4.2925M $ 900 $0.7575 M $5.05M $ 950 ➁ -5% -7.5% $4.671M $ 950 $0. 37875M $1,000 ➂ 0% $5.05 M $1,000 $0 1,050 ➃ +5% +7.5% $5.429M $1,050 -$0. 37875M 1,100 ➄ +10% +15% $5.808M $1,100 -$0.7575 M Lec 3 Hedging Strategies Using Futures dfdf

Lec 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, βSMF = 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? Lec 3 Hedging Strategies Using Futures dfdf

Lec 3 Hedging Strategies Using Futures Assumptions: ▸ NO Basis Risk (i.e., F1 = S1 ) ➀ SMF Portfolio Value0 = $5.05 M, βSMF = 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: RORSMF = Rf + β(RORI - Rf) ➟ RORSMF = β(RORI ) ▸ SP500 Futures Index is at F0 = 1,000. ▸ $N0 = Notional $Value of 1 SP500 Futures contract = 250*F0 = 250*1000 = $250,000 From CAPM: Expected Δ in Portfolio Value = βOLD (RORI) V0 Desired Δ in Portfolio Value = βNEW (RORI) V0 From APT: Expected Δ Futures Value = NF ( $250,000) x (%ΔSP500) Lec 3 Hedging Strategies Using Futures dfdf

Lec 3 Hedging Strategies Using Futures Set βOLD (RORI) V0 + NF ( $250,000) x (%ΔSP500) = βNEW (RORI) V0 ➟ βOLD V0 + NF ( $250,000) = βNEW V0 and solve for NF ➟ NF = (2 - 1.5) (5.05M)/0.25M = + 10.10 (Long 10 SP Futures) Lec 3 Hedging Strategies Using Futures dfdf

Lec 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 IndexT %ΔSP Index RorSMF Unhedged SMF ValueT SP Futures Price, FT CF from {-F} +10.1(FT - F0) Hedged ValueT $ 900 ➀ -10% -15% $4.2925M $ 900 -252,500 $4.04M $ 950 ➁ -5% -7.5% $4.671M $ 950 -126,250 $4.545M 1,000 ➂ 0% $5.05 M $1,000 $0 $5.05M 1,050 ➃ +5% +7.5% $5.429M $1,050 +126,250 $5.55M 1,100 ➄ +10% +15% $5.808M $1,100 +252,500 $6.06M Lec 3 Hedging Strategies Using Futures dfdf

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