1. 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
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2. 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
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3. 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) = $39 M,
➟ NF = 400 contracts (short)
Lec 3 Hedging Strategies Using Futures
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4. Lec 3 Hedging Strategies Using Futures
At time T, Suppose spot rates are: ST = 0.72$/₤,
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$/€ $/€ ]€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
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5. 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
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6. 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
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7. 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 =
(Short 30 SP Futures)
Lec 3 Hedging Strategies Using Futures
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8. 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
$ M
$5.05M
$ 950 ➁
-5%
-7.5%
$4.671M
$ 950
$ M
$1,000 ➂ 0%
$5.05 M
$1,000 $0
1,050 ➃
+5%
+7.5%
$5.429M
$1,050
-$ M
1,100 ➄
+10%
+15%
$5.808M
$1,100
-$ M
Lec 3 Hedging Strategies Using Futures
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9. 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
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10. 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
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11. 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 = ( ) (5.05M)/0.25M =
(Long 10 SP Futures)
Lec 3 Hedging Strategies Using Futures
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12. 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
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13. Lec 3 Hedging Strategies Using Futures
Thank You!
(A favara)
Lec 3 Hedging Strategies Using Futures
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