They found the MVHR was most eŒective at reducing the risk of a cash portfolio comprising the index underlying the futures contract.. While previous studies suggested the FTSE-100 contra
Trang 1The hedging eVectiveness of stock index
® xtures: evidence for the FTSE-100 and
FTSE-mid250 indexes traded in the UK
D A R R E N B U T T E R W O R T H and P H IL H O L M E S *{
Financial Services Team, London Economics Ltd, 66 Chiltern St, London W1M 1PR,
UK and {Department of Economics and Finance, University of Durham, 23/26 Old
Elvet, Durham, DH1 3HY, UK
E-mail: darren.butterworth @londonecon.co.u k and P.R.Holmes@ durham.ac.uk
This study provides the ® rst investigation of the hedging eŒectiveness of the
FTSE-Mid250 stock index futures contract In contrast to previous studies, the portfolios
to be hedged are actual diversi® ed portfolios in the form of investment trust
com-panies (ITCs) Furthermore, in addition to using the well established hedging
strategies, consideration is also given to hedge ratios estimated on the basis of the
Least Trimmed Squares approach Despite relatively thin trading, the FTSE-Mid250
contract is shown to be an important additional hedging instrument Surprisingly,
the new contract is more eŒective for hedging ITCs than is the established FTSE-100
contract The study also demonstrates that previous studies overstate the hedging
eŒectiveness of UK stock index futures, in that they assume the portfolio to be
hedged is one which underlies a broad market index
I IN T R O D U C T IO N
Futures contracts play an important practical role by
expanding the investor opportunity set through the
intro-duction of negative correlation not typically found in cash
markets The existence of stock index futures contracts
allows investors to avoid market risk, not easily avoided
using cash assets alone, due to short selling restrictions
Stock index futures were introduced in the UK in May
1984 when trading began in the FTSE-100 contract on
the London International Financial Futures Exchange
(LIFFE) This provided investors with the means to
hedge the risk associated with a broadly diversi® ed stock
portfolio However, since the contract relates to an index
comprising the 100 highest market capitalization ® rms, it is
questionable whether it is suitable for hedging risk
associ-ated with portfolios of smaller companies stocks To
expand the opportunity set further and allow the hedging
of the risk of such stocks, futures trading on the
FTSE-Mid250 (hereafter, FTSE-Mid250) index began in February 1994
To date trading has been thin compared to that in the FTSE-100 contract For example, open interest in the Mid250 contract is frequently only about 5% of that in the FTSE-100, while the value of each Mid250 contract typically has been less than 50% of that of the FTSE-100 Trading volume in the new contract suggests that while it oŒers new risk reduction opportunities in principle, its prac-tical signi® cance is limited in that it provides little extra hedging opportunit y compared to the FTSE-100 contract This study investigates whether the new contract is eŒec-tive for hedging a range of stock portfolios and compares its hedging performance with that of the FTSE-100 con-tract In addition to providing the ® rst test of hedging eŒectiveness of the new contract, the study oŒers improve-ments on previous studies of stock index futures hedging
In particular, a wide range of cash portfolios is used for assessing hedging performance, by using not only portfo-lios which mirror indexes underlying futures contracts, but
Applied Financial Economics ISSN 0960± 3107 print/ISSN 1466± 4305 online# 2001 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
57
*Corresponding author
Trang 2also a spread of investment trust companies (ITCs).1
Examining hedging eŒectiveness over such a range of
cash portfolios makes it possible to determine whether
the new contract adds substantially to investors’
oppor-tunity sets by markedly enhancing hedging performance
Previous studies of stock index futures hedging have
ex-amined performance for cash portfolios which underlie
broad market indexes or portfolios constructed speci® cally
for the analysis By utilizing ITCs, the contracts’
perform-ance is assessed for hedging actual diversi® ed portfolios,
rather than portfolios constructed by the researcher
Further-more, in addition to using the well established
hed-ging strategies, consideration is also given to hedge ratios
estimated on the basis of the Least Trimmed Squares
approach Further features are that the ® rst analysis of
daily hedging using UK futures is provided and, unlike
previous studies, consideration is given to using a
combi-nation of contracts (the Mid250 and the FTSE-100) to
hedge
The rest of the paper is organized as follows The next
section brie¯ y reviews previous empirical studies to identify
research issues requiring further investigation A section
setting out the data and method used follows and the
results are then presented A ® nal section provides a
sum-mary and conclusions
II P R E V IO U S E M P IR IC A L S T U D IE S A N D
R E S E A R C H IS S U E S
The ® rst analysis of hedging eŒectiveness of stock index
futures was by Figlewski (1984) and considerable work
followed Researchers have concentrated on three hedge
strategies: the traditional one-to-one hedge; the beta
hedge; and the minimum variance hedge, proposed by
Johnson (1960).2 With all three strategies there is a need
to determine the hedge ratio, h, which measures the ratio of
the number of units traded in the futures market to the
number of units traded in the cash market The traditional
strategy involves hedgers adopting a futures position equal
in magnitude but opposite in sign to the cash position, i.e
hˆ ¡1 Implicit in such a strategy is the view that futures
and cash prices move closely together Indeed, if
propor-tionate price changes in one market exactly match those in
the other market, then price risk is eliminated The beta
hedge strategy is very similar, but recognizes that the cash
portfolio to be hedged may not match the portfolio
under-lying the futures contract With the beta hedge strategy, h is
calculated as the negative of the beta of the cash portfolio Thus, for example, if the cash portfolio beta is 1.5, the hedge ratio will be ¡1.5, since the cash portfolio is expected
to move by 1.5 times the movement in the futures contract Where the cash portfolio is that which underlies the futures contract, the traditional strategy and the beta strategy yield
the same value for h.
In practice, price changes in the two markets do not move exactly together and, therefore, the traditional or beta hedge will not minimize risk The minimum variance hedge ratio (MVHR) takes account of this imperfect cor-relation and identi® es the hedge ratio which minimizes risk
(as measured by variance) as h* in Equation 1:
h*ˆ ¡Cov Var …R s ; R f†
Again, the negative sign re¯ ects that to hedge a long stock position requires selling futures Using the MVHR as the basis for hedging implicitly assumes investors are in® nitely risk averse, i.e they will forgo an in® nite amount of expected return in exchange for an in® nitely small risk reduction While such an assumption about the risk-return trade-oŒ is unrealistic, the MVHR provides an unam-biguous benchmark against which to assess hedging performance.3
The majority of research on stock index futures hedging relates to the USA, although more recently work has been published in relation to the FTSE-100 contract This sec-tion aims to outline the main themes of previous research, and identify shortcomings and areas where further devel-opment is required Figlewski (1984) examined hedging eŒectiveness for the S&P 500 futures contract in relation
to portfolios underlying ® ve major stock indexes for the period June 1982 to September 1983 While all ® ve indexes represented diversi® ed portfolios, two included only the largest capitalization stocks, two included smaller com-panies and one contained only 30 stocks of very large
® rms Figlewski included dividend payments in the return series, but found that their inclusion did not alter the results Consequently, and given the relatively stable and predictable nature of dividends, subsequent studies have excluded dividends Figlewski showed that ex post MVHRs can be estimated by OLS using historical data
He found that for all indexes hedge performance was less good using the beta hedge ratio than when the MVHR was used With large capitalization portfolios, risk was reduced
1An ITC is a company formed for the purpose of holding investments It is a closed end fund which raises capital by issuing shares and uses that capital to buy shares in other companies The ITC is managed full-time by a specialist In the context of the USA, an ITC is similar to a mutual fund
2Other researchers associated with this approach include Stein (1961) and Ederington (1979)
3While some studies have incorporated expected returns into hedging decisions and developed risk-return measures of hedging eŒec-tiveness (see, for example, Howard and D’Antoniou (1984, 1987) and Chang and Shanker (1987)), such models suŒer from the same shortcoming in that they require a subjective assessment to be made in relation to investor preferences
Trang 3by 70% ± 80% using the MVHR For smaller stocks
port-folios, hedging eŒectiveness was considerably reduced
Hedging performance was less good for overnight hedges
than for one week and four week hedges
Figlewski (1985) investigated hedging performance for
three stock index futures for holding periods ranging
from one day to three weeks As with his earlier analysis,
eŒectiveness improved as the duration of the hedge
increased from days to weeks Once again, portfolios of
small stocks were hedged less eŒectively than were those
comprising large stocks Junkus and Lee (1985) tested
hed-ging eŒectiveness of three USA stock index futures
exchanges using four commodity hedging models They
found the MVHR was most eŒective at reducing the risk
of a cash portfolio comprising the index underlying the
futures contract Peters (1986) also con® rmed the
super-iority of the MVHR over the beta hedge
Graham and Jennings (1987) were ® rst to examine
hed-ging eŒectiveness for cash portfolios not matching an
index Random sampling techniques were used to form
90 equity portfolios each comprising ten stocks
Interestingly this study found that stock index futures
were less than half as eŒective at hedging non-index
port-folios as they were at hedging cash indexes Finally for the
USA, Lindahl (1992) examined hedge duration and hedge
expiration eŒects for the MMI and S&P 500 futures
con-tracts Lindahl’s results suggested that both hedge ratios
and hedging eŒectiveness increase as hedge duration
increases However, there was no obvious pattern in
terms of risk reduction in relation to time to expiration
Hedging eŒectiveness for the UK was ® rst examined by
Holmes (1995) , for the FTSE-100 contract Ex ante
MVHRs for the period 1984-199 2 were used and the cash
portfolio hedged was that underlying the futures contract
His results showed that even using ex ante hedge ratios, the
contract enabled risk reduction of more than 80% Holmes
(1996) investigated ex post hedging eŒectiveness for the
same contract and the same cash portfolio as in the earlier
paper and showed that standard OLS provided MVHR
estimates superior to those estimated by GARCH or
using an error correction method His results suggested
eŒectiveness increased with hedge duration, in line with
Figlewski and Lindahl for the USA, but that there was
no strong discernible pattern in expiration eŒects
The impact of portfolio composition on systematic risk
and hedging eŒectiveness was examined by Holmes and
Amey (1995) They constructed portfolios of UK stocks
and considered the FTSE-100 contract As the number of
stocks in portfolios increased from 1, through 5, 10, 15 and
20, to 25 hedging eŒectiveness increased markedly While
previous studies suggested the FTSE-100 contract removed
approximately 80% of cash portfolio risk when the
portfo-lio was the underlying index, risk reduction was only about
60% for portfolios comprising 25 stocks
There are a number of points to draw from the studies considered First, the MVHR provides superior hedging performance in terms of risk reduction Second, a duration eŒect is evident, with longer hedges more eŒective In con-trast, there is no strong evidence of expiration eŒects Third, the nature of the portfolio hedged is an important determinant of hedging performance For example, Figlewski (1984) found hedging eŒectiveness was less for portfolios comprising small stocks, Graham and Jennings (1987) found the hedging of portfolios comprising only ten stocks was much less eŒective than for portfolios matching
an index and Holmes and Amey (1995) found similar results for the UK While the composition of the cash portfolio is clearly important, previous studies have failed
to address true hedging eŒectiveness by examining per-formance for actual stock portfolios Portfolios used for examining hedging eŒectiveness have been either market indexes or constructed by the researcher In addition, to date no analysis has been undertaken of the eŒectiveness of
UK stock index futures when hedging small capitalization stocks Furthermore, in relation to the UK, no considera-tion has been given to performance over very short dura-tions It is also worth noting that as yet no attention has been given to the hedging eŒectiveness of the Mid250 con-tract and to whether this concon-tract provides market partici-pants with another important means by which to hedge stock portfolio risk
Finally, consideration needs to be given to the way in which hedge ratios are estimated In particular, while the OLS estimation of the MVHR has many desirable charac-teristics it is associated with the unattractive property of being sensitive to outliers Therefore, in order to allow for this problem and take account of the fact that futures prices are often characterized by kurtosis, it may be desir-able to generate hedge ratios using an approach which minimizes the impact of outliers One such approach is the Least Trimmed Squares (LTS) method employed by Knez and Ready (1997) The LTS approach trims a pro-portion of the most extreme observations and then ® ts the remaining observations using ordinary least squares Thus the LTS coe cient represents the value that minimizes the sum of the squared residuals where the sum is taken over all the observation s which are not trimmed If the MVHR
is considerably diŒerent to the hedge ratio generated using LTS, then this would strongly indicate that the MVHR is being driven by a small sample of extreme observations and raises concerns over the possible biasedness of the MVHR This would have important implications when ex ante hedge ratios are determined on the basis of estimations using historical data
This study addresses shortcomings of previous work in a number of important ways:
The ® rst assessment of hedging eŒectiveness of the Mid250 contract is presented In addition,
Trang 4compari-sons are made between the performance of this
con-tract and that of the FTSE-100 concon-tract for a number
of diŒerent portfolios Given that one aim of the
intro-duction of the new contract is to enable more eŒective
hedging of small capitalization stocks, this is clearly
important
In addition to assessing hedging performance for cash
portfolios mirroring broad indexes, cross hedging
per-formance is analysed by examining the hedging of
actual cash portfolios held by professional managers
in the form of ITCs Since returns on ITCs represent
the returns on professionally managed, well
diversi-® ed, portfolios, evaluation of hedging eŒectiveness in
relation to these portfolios provides new insights into
the capabilities for hedging actual portfolios
Consideration is given here not only to the hedging
eŒectiveness of the FTSE-100 and Mid250 when
used separately, but also to their use in combination
Not only are the well established hedging strategies
used, but consideration is also given to an alternative
method for generating hedge ratios by using the LTS
approach By comparing hedge ratios estimated by
OLS with those determined using LTS it should be
possible to determine the importance of outliers on
the estimated hedge ratios
The ® rst investigation of hedging eŒectiveness of stock
index futures in the UK over short periods is provided,
by examining daily hedges
II I D A T A A N D M ET H O D
Hedging performance is examined for the FTSE-100 and
Mid250 index futures contracts traded on LIFFE by using
cash and futures return data for February 1994 (date of
introduction of the Mid250 contract) to December 1996
The FTSE-100 represents the 100 largest companies traded
on the London Stock Exchange The Mid250 represents the
next 250 largest companies (i.e numbers 101 to 350 by
market capitalization) Both indexes are weighted by
mar-ket capitalization
Thirty-six cash portfolios comprising four indexes and
32 investment trusts are used The four indexes are the
FTSE-100, the Mid250, the FTSE-350 (comprising the
lar-gest 350 companies) and the FT Investment Trust (FTIT)
index The ITCs were chosen to provide a range of
portfo-lios which diŒer substantially in their composition Seven
categories of ITCs are used:4
(1) General funds: at least 80% of the assets are in UK
registered companies;
(2) Capital Growth funds: at least 80% of the assets are
in UK registered companies, with stocks chosen to accentuate capital growth;
(3) Income Growth funds: at least 80% of their assets are in UK equities whose policy is to accentuate income growth;
(4) High Income funds: at least 80% of assets are in equities and convertibles; the aim is to achieve a yield in excess of 125% of that of the FT Actuaries All-Share Index;
(5) Smaller Company (SC) funds: at least 50% of assets are in smaller and medium sized companies; (6) Venture and Development Capital (VDC) funds: a signi® cant portion of the trusts’ portfolio is invested
in securities of unquoted companies; and (7) Property funds: at least 80% of the assets of these funds are in listed property equities
For each of the ® rst six categories, returns on ® ve ITCs are used to analyse hedge eŒectiveness In the case of Property funds, only two ITCs were used due to a lack of appro-priate funds with su ciently long returns series To allevi-ate any problems arising from thin trading only funds with
a market capitalization in excess of £20 million at the beginning of the period under investigation are included The funds provide a broad range of portfolios, which diŒer
in terms of objectives and composition In particular, the
SC funds and the VDC funds represent investments in rela-tively low capitalization stock Hedging such funds is expected to be less eŒective with the FTSE-100 contract, given the composition of the underlying index It is there-fore of interest to determine if this is the case and whether the Mid250 contract adds markedly to hedging perform-ance for such portfolios
Analysis is carried out for two diŒerent hedge durations: daily and weekly Hedge durations of longer than a week are not considered due to problems of sample size After removing non-trading days the daily series consists of 715 observations, the weekly series 148 observations The returns series for each cash portfolio and each futures con-tract is calculated as the logarithmic price change:
R t ˆ log
³
P t
P t¡1
´
…2†
where, R tis the daily or weekly return on either the cash or
futures position and P t is the price at time t.
Price is the daily or weekly closing price All data were obtained from Datastream
Four hedging strategies are considered First, the tradi-tional hedge is examined Second, the MVHR, as shown in Equation 1, is used Figlewski (1984) showed the MVHR can be estimated by regressing cash returns on futures
4The de® nitions of these categories of ITCs are taken from the Association of Investment Trust Companies’ monthly report
Trang 5returns using historical information, with h* the negative of
the slope coe cient, b, in the following equation:
where RS tis the return on the cash portfolio in time period
t; RF t is the return on the futures contract in time period t;
e t is an error term and a, b are regression parameters, where
¡b is the MVHR, h*.
Third, the LTS hedge ratio is investigated In order to
generate the LTS hedge ratio the residual series from the
estimated equation (e tin Equation 3) is collected Both the
cash and futures returns are then ranked in relation to the
absolute size of their associated residual term The ® rst
observation in both the cash and futures return series are
associated with the smallest residual in absolute size and
the ® nal observation in both the cash and futures returns
series is associated with the largest residual in absolute size
In view of the ® ndings of Knez and Ready (1997) and the
number of observations in our daily and weekly samples we
adopt a trimming coe cient of 10% 5This trims away the
10% of cash and futures returns which are associated with
the largest residuals, measured in absolute size This
pro-duces a trimmed daily sample of 643 observations and a
trimmed weekly sample of 132 observations Having
trimmed away the extreme outliers from both samples,
the LTS hedge ratios are then estimated by employing
OLS to the remaining 90% of observations
Finally, given that cross hedges are being considered, the
beta hedge is used The beta hedge ratio is calculated as the
negative of in the following equation:6
RS t ˆ ¬ ‡ RIND t‡ "t …4†
where RIND t is the return on the index underlying the
futures contract; "t is an error term and all other terms
are as previously de® ned
Consideration is given to mean and standard deviation
of returns of the unhedged and the hedged positions In
addition, the degree of risk reduction will be determined as:
Risk reduction ˆ¼u¼¡ ¼h
where ¼u is the standard deviation of returns on the
unhedged (i.e cash) position; ¼h is the standard deviation
of returns on the hedged position
The eŒectiveness of the four strategies is investigated using the FTSE-100 and the Mid250 contracts individually
In addition, for the MVHR and LTS strategies composite hedges are examined, where the two futures contracts are combined into a `synthetic’ FTSE-350 contract Returns on the synthetic futures are the weighted average of returns on the FTSE-100 and Mid250 contracts, with the weights attached to the two contracts varying from 2 : ¡1 to
¡1 : 2 Weights always sum to 1 and change at intervals
of 0.25 Thus, 13 composite hedges are considered for each of the thirty-six cash portfolios.7
IV EM P IR IC A L R E S U L T S
Stock market indexes
Empirical analysis begins by investigating whether the new contract adds markedly to the ability to hedge broad based cash portfolios Therefore, the reduction in risk achieved
by the FTSE-100 and Mid250 futures when the cash port-folio is an index is examined The four indexes described above are considered Results using traditional and beta hedge strategies for daily and weekly hedge durations are presented in Tables 1 and 2 respectively For each table, panel A shows the mean and standard deviation of returns for cash portfolios;8 panel B shows results when hedging with the FTSE-100 contract; and panel C shows results when using the Mid250 contract In panels B and C the hedge ratio, mean and standard deviation of returns and percentage reduction in the standard deviation from the unhedged position are shown
In relation to daily data, Table 1, panel A shows that the four cash portfolios diŒer considerably in terms of their risk-return pro® les over the sample period For example, the FTSE-100 index gave an annual mean return of 7.7% , with a standard deviation of returns of 10.9% , compared
to ® gures for the Mid250 of 4.5% and 7.0% respectively In terms of hedging, the traditional hedge is very eŒective when the cash portfolio is that which underlies the contract under consideration, as expected For example, panel B shows that hedging the FTSE-100 cash index with the FTSE-100 contract achieves risk reduction of over 64% , while using the Mid250 contract to hedge the Mid250 index achieves risk reduction of 45.2% (see panel C) These
5
Knez and Ready generate separate regressions using ordinary least squares and then LTS for various trimming coe cients within the range of 5% to 50% of the sample They show that LTS slopes are similar using either 50% or 95% of the data This implies that the tendency for extreme observations to be in¯ uential is explained by a small percentage of the observations We therefore choose a 10% trimming coe cient
6
In the remainder of the paper the hedge ratio will be referred to as a positive number for convenience, even though in practice hedging
an established spot position is likely to require selling futures
7By creating various weighted `synthetic’ FTSE 350 contracts, the panel approach provides a detailed picture of the impact on hedging eŒectiveness arising from changes in the contribution made by the Mid 250 contract to the composition of the `synthetic’ hedge
8All mean and standard deviation ® gures reported in the tables and the text have been annualized to allow more convenient comparison between hedges of diŒerent durations
Trang 6results indicate the new contract is not as eŒective at
hedging its underlying index as is the more established
contract, using the naive strategy The new contract is also
less eŒective at hedging the FTSE-350 index Given the
composition of the FTSE-350 index, these results are not
surprising
Results for other cross hedges are of more interest First,
panel B shows that the FTSE-100 contract was not eŒective
at hedging either the Mid250 or the FTIT indexes using the
traditional hedge For both hedges the standard deviation
of returns is higher and mean returns lower for the hedged
position than for the unhedged position In contrast, the
Mid250 contract oŒers an eŒective means by which to
cross-hedge Table 1, panel C demonstrate s that using
this contract for a traditional hedge, when the cash
port-folio is the FTSE-100, achieves risk reduction of over 36%
Similarly, risk reduction in relation to the FTIT cash
port-folio is about one third
Now consider the beta hedge The traditional and beta
hedges are identical when the cash portfolio is that
under-lying the contract For cross-hedging, the FTSE-100 con-tract is superior when hedging the FTSE-350 (risk reduction of 61.4% for the FTSE-100 contract, compared
to 39.7% for the Mid250 contract) However the Mid250 contract again is superior for cross-hedging other indexes The FTSE-100 contract achieves risk reduction of below 29% when the cash portfolio is the Mid250 or the FTIT
In contrast, for the FTSE-100 and FTIT cash portfolios, the Mid250 index achieves risk reduction in excess of one third with the beta strategy The results suggest that for daily hedging the new contract provides an important additional hedging vehicle for some broadly diversi® ed portfolios
Table 2 shows results for traditional and beta weekly hedges Results are very similar to those for daily data, although the new contract’s value is more marked When the cash portfolio is that underlying the contract, risk reduction is substantial with both contracts (over 70% ),
as in previous studies for the FTSE-100 (see Holmes,
1995, 1996) Thus, hedging eŒectiveness improves as
Table 1 The hedging eVectiveness of the 100 and
FTSE-Mid 250 contracts: daily data
Hedge Mean S.D of Decrease ratio return returns in S.D.*
Cash portfolio
(A) Unhedged
(B) Hedging with the
FTSE100 contract
Traditional hedge
Beta hedge
(C) Hedging with the
FTSE-Mid 250 contract
Traditional hedge
Beta hedge
Note: *This measures the percentage of the standard deviation of
returns of the unhedged portfolio that is removed by hedging
Table 2 The hedging eVectiveness of the 100 and
FTSE-Mid 250 contracts: weekly data
Hedge Mean S.D of Decrease ratio return returns in S.D.* Cash portfolio
(A) Unhedged
(B) Hedging with the FTSE 100 contract Traditional hedge
Beta hedge
(C) Hedging with the FTSE-Mid 250 contract Traditional hedge
Beta hedge
Note: *As Table 1.
Trang 7hedge duration rises For cross hedges, the new contract
again achieves superior risk reduction for the FTIT (47%
compared to 20% for the FTSE-100 contract)
Tables 3 and 4 report daily and weekly results respect-ively for the mean and standard deviation of returns using the MVHR and LTS hedge ratio (LTSHR) Results relate to the same cash portfolios as in Tables 1 and 2 For convenience panel A again shows details of unhedged positions Panels B and C show results for hedging with the FTSE-100 and Mid250 contract respectively Panel D reports results for the `synthetic’ FTSE-350 contract In all cases the results for the MVHR are reported ® rst, followed
by the results for the LTSHR Results are also reported for the optimal combination of the two contracts.9 The opti-mal combinations of the FTSE-100 and Mid250 contracts for daily data for the four cash portfolios are 0.75 : 0.25 (FTSE-100), 0 : 1 (Mid250), 0.75 : 0.25 (FTSE-350) and 0.25 : 0.75 (FTIT) Thus, for example, in constructing a synthetic futures which minimizes the return variance when hedging the FTIT portfolio, the optimal mix involves
a weighting of 0.25 in the FTSE100 contract and 0.75 in the new contract First, the MVHR results for daily and weekly hedges are discussed and then these are compared with the LTSHR results
In relation to the MVHR, Table 3, panel B shows the FTSE-100 contract greatly reduces risk for the FTSE-100 (73% ) and FTSE-350 (70% ) cash portfolios for daily hedges For the other portfolios risk reduction of only about 30% is achieved The Mid250 contract is less successful at reducing risk for the FTSE-100 and FTSE-350 cash portfolios, as expected, given that the FTSE-100 dominates these indexes
by market capitalization However, for the other portfolios the new contract is superior for hedging Risk reduction of 52% and 36% is achieved for the Mid250 and FTIT cash portfolios Thus, for portfolios with smaller capitalization the new contract is a signi® cant additional hedging facility Results in relation to the construction of a synthetic futures are very interesting (see panel D) In all cases, the optimal combination involves some use of the new contract, while for the Mid250 cash portfolio the FTSE-100 contract should not be used Thus, even for the FTSE-100 cash portfolio, the introduction of the new contract adds to hedging eŒectiveness.10
In Table 4, once again hedging performance improves as hedge duration rises to a week However, the main results are unchanged: for the FTSE-100 and FTSE-350 portfo-lios, the FTSE-100 contract provides higher risk reduction than the Mid250 contract, with the new contract superior for other cash portfolios Optimal combinations for the synthetic contract are the same as for daily data Thus,
Table 3 Hedging eVectiveness using the MVHR and LTSHR
stra-tegies: daily data
ratio return returns in S.D.*
Cash portfolio
(A) Unhedged
(B) Hedging with
the FTSE 100 contract
MVHR
LTSHR
(C) Hedging with the
FTSE Mid 250 contract
MVHR
LTSHR
(D) Composite hedges**
MVHR
LTSHR
Note: *As Table 1.
**Results are reported for the optimal combination of FTSE-100
and FTSE-Mid 250 contract in terms of maximum risk reduction
The optimal combinations are 0.75 : 0.25, 0:1, 0.75 : 0.25 and
0.25 : 0.75 respectively
9All other combinations identi® ed in the previous section were used to identify the optimal mix The results for the other combinations are available from the authors on request
10This ® nding can, in part, be explained by the fact that the composition of the two cash indexes is revised on a regular basis re¯ ecting changes in market capitalization When changes are made, some stocks move out of the FTSE-100 into the Mid250 and others make the move in the opposite direction
Trang 8the new contract improves hedging eŒectiveness even when
the cash portfolio is that underlying the FTSE-100
con-tract
Tables 3 and 4 also provide an opportunity to compare the daily and weekly hedging results for the MVHR and the LTSHR when the cash portfolios consist of stock market indexes It is clear that when the cash portfolios are broad based market indexes trimming the sample to remove the largest 10% of outliers tends to result in very small changes
to the size of the optimal hedge ratio and levels of risk reduction For instance, in the case of the hedge between the FTSE 100 contract and the FTSE 100 index (Table 3, panel B), the hedge ratio changes from 0.803 to 0.810 and the level of risk reduction falls from 72.875% to 72.864% For the cross hedges involving the FTSE 100 contract, the diŒerences between the MVHR and LTSHR remain small with the level of risk reduction being achieved by the LTSHR being within 0.3% of the MVHR In the case of the Mid250 contract (Table 3, panel C), the diŒerence between the MVHRs and the LTSHRs are of a similar magnitude to those involving the FTSE 100 contract with the diŒerences in the size of the hedge ratios being less than 0.05 and diŒerence in the levels of risk reduction being less than 0.2%
When hedges of weekly duration are considered (Table 4), the MVHRs and the LTSHRs are extremely similar, with the LTSHRs approaching those of the MVHR strat-egy For the hedge between the FTSE 100 contract and FTSE 100 index, the MVHR and LTSHR are 0.882 and 0.881, and levels of risk reduction are 81.860% and 81.859% respectively Similarly, in the case of the hedge between the Mid250 contract and the Mid250 index, the MVHR and LTSHR are 0.918 and 0.928, and levels of risk reduction are 73.228% and 73.0% respectively Hence it is clear that when the cash and futures series are highly cor-related removing the largest 10% of outliers makes little impact on hedging performance, demonstrating that the hedge ratios estimated by OLS are indeed robust
Investment trust companies
The hedging eŒectiveness of the two contracts when the cash portfolios are ITCs is now examined Given the super-iority of the MVHR and LTSHR strategies, only those strategies are considered Rather than report results for each of the thirty-two portfolios, average results for each category of ITCs11 are reported Tables 5 and 6 report results for ITCs for daily and weekly hedges respectively The format of the tables is similar to Tables 3 and 4 However, in addition to showing average risk reduction for each category of ITC, maximum and minimum stan-dard deviations for each category are also shown
Panel A in both tables demonstrates that the cash port-folios vary substantially in terms of mean and standard
Table 4 Hedging eVectiveness using the MVHR and LTSHR
stra-tegies: daily data
Hedge Mean S.D of Decrease ratio return returns in S.D.*
Cash portfolio
(A) Unhedged
(B) Hedging with the
FTSE 100 contract
MVHR
LTSHR
(C) Hedging with the
FTSE Mid 250 contract
MVHR
LTSHR
(D) Composite hedges**
MVHR
LTSHR
Note: *As Table 1.
**Results are reported for the optimal combination of FTSE-100
and FTSE-Mid 250 contract in terms of maximum risk reduction
The optimal combinations are 0.75:0.25, 0:1, 0.75:0.25 and
0.25:0.75 respectively
11Results in relation to traditional and beta hedge strategies and those relating to individual investment trust companies are available on request
Trang 9Table 5 Hedging investment trusts portfolios using the MVHR and LTSHR strategies: daily data
Standard deviation of returns
Cash portfolio
(A) Unhedged portfolio
(B) Hedging with the
FTSE 100 contract
MVHR
LTSHR
(C) Hedging with the
FTSE Mid 250 contract
MVHR
LTSHR
(D) Composite hedgesy
MVHR
LTSHR
Notes: * The decrease in the S.D of returns relates to a comparison of the average S.D of returns for the hedged position with that of the unhedged position.
y The optimal combinations of the FTSE-100 and FTSE-Mid 250 contract range from 0.25:0.75 to ¡0.5 to 1.5 For no portfolio did the weight given to the FTSE-Mid 250 contract fall below 0.75.
Trang 10Table 6 Hedging investment trusts portfolios using the MVHR and LTSHR strategies: weekly data
Standard deviation of returns
Cash portfolio
(A) Unhedged portfolio
(B) Hedging with the
FTSE 100 contract
MVHR
LTSHR
(C) Hedging with the
FTSE Mid 250 contract
MVHR
LTSHR
(D) Composite hedgesy
MVHR
LTSHR
Note: * The decrease in the S.D of returns relates to a comparison the average S.D of returns for the hedged position with that of the unhedged position.
y The optimal combinations of the FTSE-100 and FTSE-Mid 250 contract range from 0.5:0.5 to ¡0.75 to 1.75 For no portfolio did the weight given to the FTSE-Mid 250 contract fall below 0.5.