OFD Session_4 Hedging With Futures Contracts -Com Futures - Students
Short-term Hedging with Futures Contracts
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Short-term Hedging with Futures Contracts Supervisor: Professor Moisă Altăr MSc Student Iacob Călina-Andreea The Academy of Economic Studies Bucharest DOFIN - Doctoral School of Finance and Banking July 2010
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The Academy of Economic Studies Bucharest DOFIN - Doctoral School of Finance and Banking. Short-term Hedging with Futures Contracts. Supervisor: Professor Moisă Altăr MSc Student Iacob Călina-Andreea. July 2010. Contents. I. The use of the optimal hedge ratio. II. Objectives. - PowerPoint PPT Presentation
Transcript of Short-term Hedging with Futures Contracts
Short-term Hedging with Futures Contracts
Supervisor: Professor Moisă Altăr
MSc Student Iacob Călina-Andreea
The Academy of Economic Studies BucharestDOFIN - Doctoral School of Finance and Banking
July 2010
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 Assess the relationship between the Romanian spot and futures markets
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Estimate the optimal hedge ratio (minimum variance hedge ratio) Estimate the optimal hedge ratio (minimum variance hedge ratio)
Test the out-of-sample efficiency of the hedging strategies considered Test the out-of-sample efficiency of the hedging strategies considered
III. Literature reviewThe 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. MethodologyThere is a maturity mismatch and the hedge position is closed at some time t<T, 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,t=Rs,t – hRf,t (1)
Minimising the portfolio risk:
(2)
The minimum variance hedge ratio (MVHR):
(3)
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𝑉𝑎𝑟ሺ𝑅ℎ.𝑡ȁ𝐹𝑡−1ሻ=𝑉𝑎𝑟ሺ𝑅𝑠.𝑡ȁ𝐹𝑡−1ሻ+ℎ2𝑉𝑎𝑟൫𝑅𝑓.𝑡ห𝐹𝑡−1൯−2ℎ𝐶𝑜𝑣(𝑅𝑠.𝑡,𝑅𝑓.𝑡ห𝐹𝑡−1) ℎ∗=𝐶𝑜𝑣(𝑅𝑠.𝑡,𝑅𝑓.𝑡ห𝐹𝑡−1)𝑉𝑎𝑟൫𝑅𝑓.𝑡ห𝐹𝑡−1൯
IV. Minimum variance hedge ratio
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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𝑟𝑆𝑡 = 𝜇𝑆𝑡 +𝑒𝑆𝑡 𝑟𝐹𝑡 = 𝜇𝐹𝑡+𝑒𝐹𝑡
ESTIMATION APPROACHES
𝑟𝑆𝑡 =𝛼+𝛽෨𝑟𝐹𝑡 +𝜀𝑡
IV. Minimum variance hedge ratio
HEDGING EFFECTIVENESS
Ederlington measure (1979)
The risk reduction was measured as:
(8)
σu and σh are standard deviations of the unhedged and hedged portfolio, respectively.
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𝐸=𝜎𝑢2−𝜎ℎ2𝜎𝑢2
V. Data description
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BSE futures market in 2009(Source: Annual report)
No. Contract Total % of total1 DESIF5 2,106,791 86.962 DESIF2 200,838 8.293 EUR/RON 95,837 3.964 DETLV 8,861 0.375 DESNP 6,608 0.276 DEBRD 1,400 0.067 DEEBS 968 0.048 DERRC 657 0.039 DEBRK 479 0.0210 SIBGOLD 129 0.0111 RON/EUR 99 0.0012 CFD-SIF1 72 0.0013 CFD - TLV 10 0.0014 DESIF3 8 0.0015 DESIF4 2 0.0016 EUR/USD 1 0.00
SMFCE futures market in 2009(Source: Annual report)
Underlying asset No. of contracts % Nominal value of the contracts traded (lei)
EUR/RON 15,586 99.83% 67,039,175
SIF 2 4 0.03% 1,135
SIF 5 23 0.15% 8,790
Total 15,613 100% 67,049,100
V. Data description
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SIF Oltenia – SIF5Sources:
- 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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3-Jan-05 3-Jan-06 3-Jan-07 3-Jan-08 3-Jan-09 3-Jan-10
Daily Spot and Futures prices (3 Jan 2005 - 25 Jun 2010)
Futures Spot
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V. Data description
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4-Jan-05 4-Jan-06 4-Jan-07 4-Jan-08 4-Jan-09 4-Jan-10
Daily spot and futures returns(3 Jan 2005 - 31 Mar 2010)
Futures log returns Spot log returns
IndicatorsFutures Spot Futures Spot
Observations 1321 1321 265 265
Mean 0.00048 0.00046 0.00227 0.00241Maximum 0.16450 0.20153 0.26023 0.27242Minimum -0.16127 -0.19889 -0.27675 -0.31067Std. deviation 0.03216 0.03459 0.07977 0.07925Skewness -0.15750 -0.25964 -0.41303 -0.35080Kurtosis 7.17721 8.03594 4.36734 4.77928
Jarque-Bera 965.8876 1410.7340 28.1781 40.3915Probability 0.0000 0.0000 0.0000 0.0000
Augmented Dickey Fuller -32.06174 -33.04338 -14.32664 -14.41091
Daily log returns Weekly log returns
V. Data description - cointegration
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Cointegration test for dailySpot and Futures prices
Cointegration test for weekly Spot and Futures prices
VI. Estimation results - OLS
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Daily Spot and Futures prices Weekly Spot and Futures prices
VI. Estimation results - BEEK
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Daily Spot and Futures prices
VI. Estimation results - BEKK
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Weekly Spot and Futures prices
VI. Estimation results
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For each hedging strategy :
VI. Estimation results
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Unhedged Naïve OLS BEKK
Hedging ratio 0 1 0.77681 0.74379
Variance 0.000414 0.000072 0.000101 0.000108
Std. deviation 2.0350% 0.8482% 1.0052% 1.0376%
Efficiency - 83% 76% 74%
Hedging ratio 0 1 0.92273 0.79769
Variance 0.002475 0.000081 0.000103 0.000197
Std. deviation 4.9749% 0.8992% 1.0158% 1.4036%
Efficiency - 97% 96% 92%
Daily returns for the hedging period 1 April – 25 June 2010
Weekly returns for the hedging period 1 April – 25 June 2010
Static hedge
VI. Estimation results
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Dynamic hedge - weekly futures position changes – 1 April -23 June 2010
Ratio Return Ratio Return Ratio Return Ratio ReturnWeek 1 (01.04 - 07.04) 0 0.02788 1 0.00367 0.92273 0.00554 0.79769 0.00857Week 2 (08.04 - 14.04) 0 0.00448 1 -0.00294 0.92341 -0.00237 0.77603 -0.00128Week 3 (15.04 - 21.04) 0 -0.02286 1 -0.00173 0.92141 -0.00339 0.78528 -0.00627Week 4 (22.04 - 28.04) 0 -0.00949 1 -0.00311 0.92213 -0.00361 0.81296 -0.00431Week 5 (29.04 - 05.05) 0 -0.02468 1 -0.01425 0.92583 -0.01502 0.82212 -0.01611Week 6 (06.05 - 12.05) 0 0.01986 1 0.02055 0.92594 0.02050 0.83410 0.02044Week 7 (13.05 - 19.05) 0 -0.11613 1 0.00015 0.92143 -0.00899 0.76448 -0.02724Week 8 (20.05 - 26.05) 0 -0.08364 1 -0.00684 0.92551 -0.01256 0.83917 -0.01919Week 9 (27.05 - 02.06) 0 -0.00386 1 0.00805 0.92856 0.00720 0.86750 0.00647Week 10 (03.06 - 09.06) 0 -0.00783 1 0.00979 0.92831 0.00853 0.86733 0.00745Week 11 (10.06 - 16.06) 0 0.06920 1 -0.00270 0.92786 0.00248 0.85377 0.00781Week 12 (17.06 - 23.06) 0 0.02613 1 0.00617 0.92874 0.00759 0.88476 0.00847Average return -0.01008 0.00140 0.00049 -0.00126Sum of returns -0.12096 0.01681 0.00590 -0.01518Variance 0.002475 0.000081 0.000103 0.000194Std. deviation 4.97% 0.90% 1.01% 1.39%
Efficiency - 97% 96% 92%
Unhedged Naïve OLS BEKK
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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101-133.- Alexander, C. and Barbosa, A. (2007), “The impact of electronic trading and exchange traded funds on the effectiveness of minimum
variance hedging”, Journal of Portfolio Management, 33, 46−59.- 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 Hedge”, Journal of Applied
Econometrics, 6(2) , 109-124.- Brooks, C. (2008), Modeling volatility and correlation, Introductory Econometrics for Finance, 428-450.- Brooks, C., Henry, O. T., and Persand, G. (2002), “The effect of asymmetries on optimal hedge ratios”, Journal of Business, 75,
333−352.- Chen, S., C. Lee, and Shrestha, K. (2003), “Futures Hedge Ratios: A Review”, The Quarterly Review of Economics and Finance, 43, 433-
465.- Ederington, L. H. (1979), “The hedging performance of the new futures markets”, Journal of Finance, 34, 157−170.- Engle, R. F. and Kroner, K. F. (1995), “Multivariate simultaneous generalized ARCH”, Econometric Theory, 11, 122–50. - Kavussanos, M. and Visvikis, I (2008) ,”Hedging effectiveness of the Athens stock index futures contracts”, The European Journal of
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191.- Lien, D. (2006), “A note on the hedging effectiveness of GARCH models”, Working Paper, College of Business, University of Texas at
San Antonio.- Lien, D., and Y.Tse (2002), “Some Recent Developments in Futures Hedging”, Journal of Economic Surveys, 16 (3), 357-396.- Lien, D., and Shrestha. K. (2008), “Hedging effectiveness comparisons: A note”, International Review of Economics and Finance 17,
391–396.- Lien, D., and Yang. Li. (2008), “Hedging with Chinese metal futures”, Global Finance Journal, 19 123–138- Myers, R. (1991), “Estimating time-varying optimal hedge ratios on futures markets”, Journal of Futures Markets, 11, 39−53.
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