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
III. Literature review
IV. Methodology
V. Data description
VI. Estimation results
VII. Conclusions
2
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
3
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
4
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.
5
IV. Methodology
There is a maturity mismatch and the hedge position is closed at some time t
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
ℎ.���� ��������−1 = ������������ ��������.���� ��������−1 + ℎ ������������ ��������.���� ��������−1 − 2ℎ������������(��������.���� , ��������.���� ��������−1 )
(2)
The minimum variance hedge ratio (MVHR):
������������(��������.���� , ��������.���� ��������−1 )
ℎ∗ = (3)
������������ ��������.���� ��������−1
6
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.
7
IV. Minimum variance hedge ratio
HEDGING EFFECTIVENESS
Ederlington measure (1979)
The risk reduction was measured as:
2 2
�������� − ����ℎ (8)
���� = 2
��������
σu and σh are standard deviations of the unhedged and hedged portfolio, respectively.
8
V. Data description
Underlying asset No. of contracts % Nominal value of the
contracts traded (lei)
BSE futures EUR/RON 15,586 99.83% 67,039,1
market in 2009 SIF 2 4 0.03% 1,1
(Source: Annual report) SIF 5 23 0.15% 8,7
Total 15,613 100% 67,049,1
No. Contract Total % of total
1 DESIF5 2,106,791 86.96
2 DESIF2 200,838 8.29
3 EUR/RON 95,837 3.96
4 DETLV 8,861 0.37
5 DESNP 6,608 0.27
6 DEBRD 1,400 0.06
SMFCE futures 7 DEEBS 968 0.04
8 DERRC 657 0.03
market in 2009 9 DEBRK 479 0.02
(Source: Annual report) 10 SIBGOLD 129 0.01
11 RON/EUR 99 0.00
12 CFD-SIF1 72 0.00
13 CFD - TLV 10 0.00
14 DESIF3 8 0.00
15 DESIF4 2 0.00
16 EUR/USD 1 0.00
9
V. Data description
SIF Oltenia – SIF5 Daily Spot and Futures prices
5.50
(3 Jan 2005 - 25 Jun 2010)
Sources: 5.00
- www.ktd.ro for end-of-day spot prices 4.50
4.00
(SIF5 is traded on the Bucharest Stock 3.50
Exchange (BSE)) 3.00
2.50
- www.sibex.ro for end-of-day prices for the 2.00
futures contract (DESIF5 trading started in 1.50
2004 on the Futures exchange in Sibiu 1.00
0.50
(Sibex) and since 2008 it is also traded on 0.00
the BSE) 3-Jan-05 3-Jan-06 3-Jan-07 3-Jan-08 3-Jan-09 3-Jan-10
Futures Spot
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;
10
V. Data description
Daily spot and futures returns
0.10
(3 Jan 2005 - 31 Mar 2010)
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
-0.08
-0.10
4-Jan-05 4-Jan-06 4-Jan-07 4-Jan-08 4-Jan-09 4-Jan-10
Futures log returns Spot log returns
Indicators Daily log returns Weekly log returns
Futures Spot Futures Spot
Observations 1321 1321 265 265
Mean 0.00048 0.00046 0.00227 0.00241
Maximum 0.16450 0.20153 0.26023 0.27242
Minimum -0.16127 -0.19889 -0.27675 -0.31067
Std. deviation 0.03216 0.03459 0.07977 0.07925
Skewness -0.15750 -0.25964 -0.41303 -0.35080
Kurtosis 7.17721 8.03594 4.36734 4.77928
Jarque-Bera 965.8876 1410.7340 28.1781 40.3915
Probability 0.0000 0.0000 0.0000 0.0000
Augmented Dickey Fuller -32.06174 -33.04338 -14.32664 -14.41091
11
V. Data description - cointegration
Cointegration test for daily Cointegration test for weekly
Spot and Futures prices Spot and Futures prices
12
VI. Estimation results - OLS
Daily Spot and Futures prices Weekly Spot and Futures prices
13
VI. Estimation results - BEEK
Daily Spot and Futures prices
14
VI. Estimation results - BEKK
Weekly Spot and Futures prices
15
VI. Estimation results
For each hedging strategy :
16
VI. Estimation results
Static hedge
Unhedged Naïve OLS BEKK
Daily returns for the hedging period 1 April – 25 June 2010
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%
Weekly returns for the hedging period 1 April – 25 June 2010
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%
17
VI. Estimation results
Dynamic hedge - weekly futures position changes – 1 April -23 June 2010
Unhedged Naïve OLS BEKK
Ratio Return Ratio Return Ratio Return Ratio Return
Week 1 (01.04 - 07.04) 0 0.02788 1 0.00367 0.92273 0.00554 0.79769 0.00857
Week 2 (08.04 - 14.04) 0 0.00448 1 -0.00294 0.92341 -0.00237 0.77603 -0.00128
Week 3 (15.04 - 21.04) 0 -0.02286 1 -0.00173 0.92141 -0.00339 0.78528 -0.00627
Week 4 (22.04 - 28.04) 0 -0.00949 1 -0.00311 0.92213 -0.00361 0.81296 -0.00431
Week 5 (29.04 - 05.05) 0 -0.02468 1 -0.01425 0.92583 -0.01502 0.82212 -0.01611
Week 6 (06.05 - 12.05) 0 0.01986 1 0.02055 0.92594 0.02050 0.83410 0.02044
Week 7 (13.05 - 19.05) 0 -0.11613 1 0.00015 0.92143 -0.00899 0.76448 -0.02724
Week 8 (20.05 - 26.05) 0 -0.08364 1 -0.00684 0.92551 -0.01256 0.83917 -0.01919
Week 9 (27.05 - 02.06) 0 -0.00386 1 0.00805 0.92856 0.00720 0.86750 0.00647
Week 10 (03.06 - 09.06) 0 -0.00783 1 0.00979 0.92831 0.00853 0.86733 0.00745
Week 11 (10.06 - 16.06) 0 0.06920 1 -0.00270 0.92786 0.00248 0.85377 0.00781
Week 12 (17.06 - 23.06) 0 0.02613 1 0.00617 0.92874 0.00759 0.88476 0.00847
Average return -0.01008 0.00140 0.00049 -0.00126
Sum of returns -0.12096 0.01681 0.00590 -0.01518
Variance 0.002475 0.000081 0.000103 0.000194
Std. deviation 4.97% 0.90% 1.01% 1.39%
Efficiency - 97% 96% 92%
18
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.
19
References
- Alexander, C. (2008), Futures and Forwards, Market Risk Analysis Volume III - Pricing, Hedging and Trading Financial Instruments, 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
Finance, 14: 3, 243 – 270.
- Laws, J. and Thompson, J. (2005), “Hedging effectiveness of stock index futures”, European Journal of Operational Research 163 177–
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.
20