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K.Cuthbertson and D.Nitzsche1
Lecture
Stock Index Futures
Version 1/9/2001
FINANCIAL ENGINEERING:
DERIVATIVES AND RISK MANAGEMENT(J. Wiley, 2001)
K. Cuthbertson and D. Nitzsche
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K.Cuthbertson and D.Nitzsche2
Topics
Basic Concepts
Speculation
Hedging
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Basic Concepts
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Stock Index Futures:Terminology
Hold, TVS0= $2m in diversified equity portfolioand stockindexS0=
200
Number of index units in stocks,Ns =TVS0/S0=10,000shares
ie. For each unit change in the index S, then the valueof the
stock portfolio changes by $10,000 (DOLLARS)
(TVS)t = Ns St
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F0= 202z = contract size= $500 per index point - for S&P
500
Then the face value of one futures contract isFVF0= z F0= $500 (
202 ) = $101,000
Fear a fall in equity prices : what do I do to
hedge ?Short the futuresHow many futures contract do I short
?
Stock Index Futures:Terminology
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Specualtion
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Figure 3.2 : Speculation: Nikkei index (Leeson)
12000
14000
16000
18000
20000
22000
24000
03/01/94 03/07/94 03/01/95 03/07/95 03/01/96 03/07/96
Leeson buys
Leeson closes out / sellsFive eights make $1.4bn ?
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Hedgingwith
Stock Index Futures
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Minimum Variance Hedge Ratios
V
= change in spot market position + change in futures position=
Ns.(S1-S0) + Nf(F1- F0) z
= Ns. S + Nf(F) z
where, z= contract multiple ($500 for S&P 500)S = S1-
S0,
F = F1- F0The variance of the hedged portfolio is
FSzfNsNFzfNSsNV ,.222
).(2
)2
(2
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Minimum Variance Hedge Ratio(1)
0tatindexspotofValue
PositionSpotofValue .
. 0
0
Sz
TVSNf
is the regression beta for the absolute changein your portfolio
price S regressed on theabsolute change in F:
ie. = (S, F)/2(F) = (S)/(F)
Choose Nfto minimize variance, gives:
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Minimum Variance Hedge Ratio-(2)
0.
tatfuturesofFaceValue
PositionSpotofValue
pfFVFTVSN .
0
0
p
pis the regression beta for thepercentage change inyour
portfolio S (ie. the portfolio return)regressed on thepercentage
change in F. In practice hedging error arisesbecause pis an
estimate and may not hold over the
future.
Equivalent expression
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End of Slides
