Transcript Optimal hedge ratio – an application on the Romanian

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
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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
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.
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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 – hRf,t

Minimising the portfolio risk:
2
 𝑉𝑎𝑟 𝑅
ℎ.𝑡 𝐹𝑡−1 = 𝑉𝑎𝑟 𝑅𝑠.𝑡 𝐹𝑡−1 + ℎ 𝑉𝑎𝑟 𝑅𝑓.𝑡 𝐹𝑡−1 − 2ℎ𝐶𝑜𝑣(𝑅𝑠.𝑡 , 𝑅𝑓.𝑡 𝐹𝑡−1 )

(1)
(2)
The minimum variance hedge ratio (MVHR):
ℎ∗ =
6
𝐶𝑜𝑣(𝑅𝑠.𝑡 , 𝑅𝑓.𝑡 𝐹𝑡−1 )
𝑉𝑎𝑟 𝑅𝑓.𝑡 𝐹𝑡−1
(3)
IV. Minimum variance hedge ratio
ESTIMATION APPROACHES

I. OLS
𝑟𝑆𝑡 = 𝛼 + 𝛽 𝑟𝐹𝑡 + 𝜀𝑡


II. Bivariate GARCH
(4)
–
the BEKK parameterisation proposed by Engle and
Kroner (1995)



𝑟𝑆𝑡 = 𝜇𝑆𝑡 + 𝑒𝑆𝑡
(5)
𝑟𝐹𝑡 = 𝜇𝐹𝑡 + 𝑒𝐹𝑡
(6)
where
specified as:
Ht is a (2x2) conditional variance-covariance matrix

(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:
𝜎𝑢2 − 𝜎ℎ2
𝐸=
𝜎𝑢2
(8)
σu and σh are standard deviations of the unhedged and hedged portfolio, respectively.
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V. Data description
Underlying asset
BSE futures
market in 2009
(Source: Annual report)
No. of contracts
15,586
99.83%
Nominal value of the
contracts traded (lei)
67,039,1
SIF 2
4
0.03%
1,1
SIF 5
23
0.15%
8,7
Total
15,613
100%
67,049,1
EUR/RON
No.
SMFCE futures
market in 2009
(Source: Annual report)
9
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
Contract
DESIF5
DESIF2
EUR/RON
DETLV
DESNP
DEBRD
DEEBS
DERRC
DEBRK
SIBGOLD
RON/EUR
CFD-SIF1
CFD - TLV
DESIF3
DESIF4
EUR/USD
%
Total
% of total
2,106,791
86.96
200,838
8.29
95,837
3.96
8,861
0.37
6,608
0.27
1,400
0.06
968
0.04
657
0.03
479
0.02
129
0.01
99
0.00
72
0.00
10
0.00
8
0.00
2
0.00
1
0.00
V. Data description

SIF Oltenia – SIF5
Sources:
-
-
5.50
Daily Spot and Futures prices
(3 Jan 2005 - 25 Jun 2010)
5.00
www.ktd.ro for end-of-day spot prices
(SIF5 is traded on the Bucharest Stock
Exchange (BSE))
4.50
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)
2.50
4.00
3.50
3.00
2.00
1.50
1.00
0.50
0.00
3-Jan-05
3-Jan-06
3-Jan-07
Futures
3-Jan-08
3-Jan-09
3-Jan-10
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;
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V. Data description
Daily spot and futures returns
(3 Jan 2005 - 31 Mar 2010)
0.10
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
Futures log returns
Indicators
Observations
11
Daily log returns
Futures
Spot
1321
1321
4-Jan-08
4-Jan-09
4-Jan-10
Spot log returns
Weekly log returns
Futures
Spot
265
265
Mean
Maximum
Minimum
Std. deviation
Skewness
Kurtosis
0.00048
0.16450
-0.16127
0.03216
-0.15750
7.17721
0.00046
0.20153
-0.19889
0.03459
-0.25964
8.03594
0.00227
0.26023
-0.27675
0.07977
-0.41303
4.36734
0.00241
0.27242
-0.31067
0.07925
-0.35080
4.77928
Jarque-Bera
Probability
965.8876
0.0000
1410.7340
0.0000
28.1781
0.0000
40.3915
0.0000
-32.06174
-33.04338
-14.32664
-14.41091
Augmented Dickey Fuller
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
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VI. Estimation results
For each hedging strategy :
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VI. Estimation results
Static hedge
Unhedged
Naïve
OLS
Daily returns for the hedging period 1 April – 25 June 2010
0
1
0.77681
Hedging ratio
0.000414
0.000072
0.000101
Variance
2.0350%
0.8482%
1.0052%
Std. deviation
83%
76%
Efficiency
Weekly returns for the hedging period 1 April – 25 June 2010
0
1
0.92273
Hedging ratio
0.002475
0.000081
0.000103
Variance
4.9749%
0.8992%
1.0158%
Std. deviation
97%
96%
Efficiency
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BEKK
0.74379
0.000108
1.0376%
74%
0.79769
0.000197
1.4036%
92%
VI. Estimation results
Dynamic hedge - weekly futures position changes – 1 April -23 June 2010
Week 1 (01.04 - 07.04)
Week 2 (08.04 - 14.04)
Week 3 (15.04 - 21.04)
Week 4 (22.04 - 28.04)
Week 5 (29.04 - 05.05)
Week 6 (06.05 - 12.05)
Week 7 (13.05 - 19.05)
Week 8 (20.05 - 26.05)
Week 9 (27.05 - 02.06)
Week 10 (03.06 - 09.06)
Week 11 (10.06 - 16.06)
Week 12 (17.06 - 23.06)
Average return
Sum of returns
Variance
Std. deviation
Efficiency
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Unhedged
Ratio
Return
0
0.02788
0
0.00448
0
-0.02286
0
-0.00949
0
-0.02468
0
0.01986
0
-0.11613
0
-0.08364
0
-0.00386
0
-0.00783
0
0.06920
0
0.02613
-0.01008
-0.12096
0.002475
4.97%
-
Naïve
Ratio
1
1
1
1
1
1
1
1
1
1
1
1
OLS
Return
0.00367
-0.00294
-0.00173
-0.00311
-0.01425
0.02055
0.00015
-0.00684
0.00805
0.00979
-0.00270
0.00617
0.00140
0.01681
0.000081
0.90%
97%
Ratio
0.92273
0.92341
0.92141
0.92213
0.92583
0.92594
0.92143
0.92551
0.92856
0.92831
0.92786
0.92874
Return
0.00554
-0.00237
-0.00339
-0.00361
-0.01502
0.02050
-0.00899
-0.01256
0.00720
0.00853
0.00248
0.00759
0.00049
0.00590
0.000103
1.01%
96%
BEKK
Ratio
Return
0.79769
0.00857
0.77603
-0.00128
0.78528
-0.00627
0.81296
-0.00431
0.82212
-0.01611
0.83410
0.02044
0.76448
-0.02724
0.83917
-0.01919
0.86750
0.00647
0.86733
0.00745
0.85377
0.00781
0.88476
0.00847
-0.00126
-0.01518
0.000194
1.39%
92%
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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