Short-term Hedging with Futures Contracts

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Short-term Hedging with Futures Contracts
The Academy of Economic Studies BucharestDOFIN
- Doctoral School of Finance and Banking

• Supervisor Professor Moisa Altar
• MSc Student Iacob Calina-Andreea

July 2010
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Contents
I. The use of the optimal hedge ratio
II. Objectives
III. Literature review
IV. Methodology
V. Data description
VI. Estimation results
VII. Conclusions
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I. The use of the optimal hedge ratio

• Hedging with futures contracts
• A hedger who has a long (short) position in a
  spot market and wants to lock in the value of its
  portfolio can take an opposite position in a
  futures market so that any losses sustained from
  an adverse price movement in one market can be in
  some degree offset by a favorable price movement
  on the futures market.
• Maturity mismatch hedging instrument vs.
  hedging period
• Less than perfect correlation futures spot
  markets
• Proxy hedge hedging a portfolio with a futures
  on correlated a stock index
• Basket Hedge hedging a portfolio with a
  portfolio of futures contracts

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II. Objectives

• Assess the relationship between the Romanian
  spot and futures markets

• Estimate the optimal hedge ratio (minimum
  variance hedge ratio)

• Test the out-of-sample efficiency of the hedging
  strategies considered

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III. Literature review

• The optimal hedge ratio has been a subject of
  interest for economic and econometric studies for
  many years. The focus shifting from establishing
  the most appropriate hedging criteria to finding
  the best econometric estimation method to
  estimate the optimal hedge ratio. Chen, Lee and
  Shrestha (2002) and Lien and Tse (2002) provide
  an overview of the specialised literature on this
  topic.
• Approaches to setting the hedging objective
• minimum variance hedge ratio
• mean-variance framework
• the use of different utility functions in the
  mean-variance framework
• maximise the Sharpe ratio
• minimise the mean Gini coefficient
• minimisation of the generalized semi-variance or
  higher partial moments.
• Numerous approaches to the estimation of the
  hedge ratio ranging from the OLS method to
  sophisticated GARCH specifications.

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IV. Methodology

• There is a maturity mismatch and the hedge
  position is closed at some time tltT, where T is
  the expiry date of the futures.
• Let Rs,t and Rf,t denote the one-period returns
  of the spot and futures positions, respectively.
• The return on the portfolio, Rh, is given by
• Rh,tRs,t hRf,t
  
  (1)
• Minimising the portfolio risk
• 
  
  
  (2)
• The minimum variance hedge ratio (MVHR)
• 
  
  
  (3)

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IV. Minimum variance hedge ratio
ESTIMATION APPROACHES

• I. OLS
• 
  
  (4)
• II. Bivariate GARCH the BEKK parameterisation
  proposed by Engle and Kroner (1995)
• 
  
  (5)
• 
  
  (6)
• where Ht is a
  (2x2) conditional variance-covariance matrix
  specified as
• 
  
  (7)
• where matrixes A1 and G1 are diagonal.

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IV. Minimum variance hedge ratio

• HEDGING EFFECTIVENESS
• Ederlington measure (1979)
• The risk reduction was measured as
• 
  
  (8)
• su and sh are standard deviations of the unhedged
  and hedged portfolio, respectively.

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V. Data description
BSE futures market in 2009 (Source Annual
report)
SMFCE futures market in 2009 (Source Annual
report)
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V. Data description

• SIF Oltenia SIF5
• Sources
• www.ktd.ro for end-of-day spot prices (SIF5 is
  traded on the Bucharest Stock Exchange (BSE))
• www.sibex.ro for end-of-day prices for the
  futures contract (DESIF5 trading started in 2004
  on the Futures exchange in Sibiu (Sibex) and
  since 2008 it is also traded on the BSE)

• Period 3 January 2005 31 March 2010
• daily spot and futures prices 1322 daily
  observations
• the futures series was built using the closest
  contract to maturity and switching to the next
  closest to maturity contract 7 days before expiry
  (only contracts traded on Sibex have been
  included in the sample)
• weekly spot and futures prices (Wednesday prices)
  - 266 weekly observations
• Period 1 April 2010 25 June 2010 used for
  hedging efficiency testing
• 60 daily prices 12 Wednesday prices

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V. Data description
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V. Data description - cointegration
Cointegration test for daily Spot and Futures
prices
Cointegration test for weekly Spot and Futures
prices
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VI. Estimation results - OLS
Daily Spot and Futures prices
Weekly Spot and Futures prices
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VI. Estimation results - BEEK
Daily Spot and Futures prices
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VI. Estimation results - BEKK
Weekly Spot and Futures prices
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VI. Estimation results
For each hedging strategy
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VI. Estimation results
Static hedge
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VI. Estimation results
Dynamic hedge - weekly futures position changes
1 April -23 June 2010
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VII. Conclusions

• The best hedging strategy was the naïve hedge
  which incorporates also the benefit of reduced
  transaction costs.
• Weekly data provides more information when
  constructing short term hedge strategies but
  using fewer observations may introduce
  instability into the estimates.
• All hedging methods considered can effectively
  reduce risk. The MVHR obtained were close to
  unity, the higher the hedge ratio the more
  efficient the hedge.
• As in the case of many other papers on this
  subject, result are very much data specific
  especially due to the fact that the futures
  market in Romania is still in development. Only
  in the last couple of year some new products were
  launched showing an increased interest of
  investors in alternative investment solutions.

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References

• Alexander, C. (2008), Futures and Forwards,
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• Alexander, C. and Barbosa, A. (2007), The impact
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  on the effectiveness of minimum variance
  hedging, Journal of Portfolio Management, 33,
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• Alexander, C. and Barbosa, A. (2007),
  Effectiveness of Minimum-Variance Hedging, The
  Journal of Portfolio Management, 33(2), 46-59.
• Baillie, R. and Myers (1991), Bivariate GARCH
  Estimation of the Optimal Commodity Futures
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• Brooks, C. (2008), Modeling volatility and
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• Chen, S., C. Lee, and Shrestha, K. (2003),
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• Ederington, L. H. (1979), The hedging
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• Engle, R. F. and Kroner, K. F. (1995),
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