The Academy of Economic Studies Bucharest DOFIN Doctoral

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 Ø Assess the relationship between the Romanian spot and futures markets Ø Estimate the optimal hedge ratio (minimum variance hedge ratio) ØTest 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<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 – h. Rf, t Minimising the portfolio risk: (1) (2) The minimum variance hedge ratio (MVHR): (3) 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 specified as: Ht is a (2 x 2) conditional variance-covariance matrix (7) where matrixes A 1 and G 1 are diagonal. 7

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. 8

V. Data description BSE futures market in 2009 (Source: Annual report) SMFCE futures market in 2009 (Source: Annual report) 9

V. Data description SIF Oltenia – SIF 5 Sources: - www. ktd. ro for end-of-day spot prices (SIF 5 is traded on the Bucharest Stock Exchange (BSE)) - www. sibex. ro for end-of-day prices for the futures contract (DESIF 5 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; 10

V. Data description 11

V. Data description - cointegration Cointegration test for daily Spot and Futures prices 12 Cointegration test for weekly Spot and Futures prices

VI. Estimation results - OLS Daily Spot and Futures prices 13 Weekly Spot and Futures prices

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 17

VI. Estimation results Dynamic hedge - weekly futures position changes – 1 April -23 June 2010 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, 101133. - 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), 4659. - 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, 433465. - 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