1. 2/20/08Brian Jansen Co-jumps in the Oil Industry

2. –Introducing the Lee-Mykland Test –Results for XOM, COP, and CVX –Problems with the test –Possible corrections to the test –Results for corrected test –Factor Analysis Jump Component Instantaneous Volatility –Co-jumps in the oil sector and the market –Extensions Co-Jumps in OilBrian Jansen Outline

3. Lee-MyklandBrian Jansen Intro to the Lee-Mykland Jump Test -Creates a statistic L(i), for each price, comparing the change in price on the interval [ t i-1, t i ] to an instantaneous volatility measure using the previous 270 returns

4. Lee-MyklandBrian Jansen Rejection Region -The distribution of L (i) is normal under the null hypothesis that no jumps occur over a given set A n {1,2,….n} -The asymptotic distribution of the absolute value of the maximum L (i) in a given day is exponential -Where C n and S n, given n= and c=sqrt(2/pi) :

5. Lee-MyklandBrian Jansen Results XOMCOPCVX # of jumps288416367 % of returns that are jumps 0.282%0.4073%0.3593% # of days with a jump223328298 % of days with a jump0.1659230.2440480.221726 Mean(L(i)).0010.00068.00067 Mean(L(i)) if return is a jump -1.17-.5865-.6676 Standard deviation of L(i) 1.30231.31311.3097

6. Lee-MyklandBrian Jansen Results

7. Lee-MyklandBrian Jansen Problems of the Test -The window size they suggest for 5-minute data is K=270 observations -Thus, they calculate the instantaneous volatility going back 2.5 days -While this accounts for changes in local volatility on a larger scale, it does not adequately correct for intra- and inter-day changes in volatility -Specifically, inter-day volatility follows a U-shape, with higher volatility in the morning and lower volatility in the afternoon

8. Lee-MyklandBrian Jansen Problems of the Test -Average BV j =(1/K) ∑ |R t,j-1 |^(1/2)*|R t,j |*|R t,j+1 |^(1/2)

9. Lee-MyklandBrian Jansen Corrections to the Test -Let t=day and j=observation number in a given day -So, R 4,5 refers to the return of the 9:55 observation of the 4 th day -If we scale the return R t,j by the average BV j at time interval j, the resulting return should account for the daily trend in volatility -Thus, we could try R*= R t,j / sqrt(BV j) -Then, we can re-calculate the instantaneous volatility using the adjusted returns -Average BV j =(1/K) ∑ |R t,j-1 |^(1/2)*|R t,j |*|R t,j+1 |^(1/2)

10. Lee-MyklandBrian Jansen Corrections to the Test

11. Lee-MyklandBrian Jansen Corrections to the Test

12. Lee-MyklandBrian Jansen Results of Corrected Test XOMCOPCVX # of jumps219249223 % of returns that are jumps.2%.25%.22% # of days with a jump164190168 % of days with a jump12.20%14.14%12.50% Mean(L(i)).0042.0037.0039 Standard deviation of L(i) 1.2991.3001.298 Mean(L(i)) if return is a jump -1.4306-.3710-.9927

13. Lee-MyklandBrian Jansen Results of Corrected Test

14. Lee-MyklandBrian Jansen Factor Analysis -Oil Futures -Oil Companies: ExxonMobile, ConocoPhillips, and Chevron -Drilling/Exploration/Oil-field Company: Baker Hughes -Energy Company: Entergy -Businesses with products related to oil: FedEx, Ford, and Boeing -Miscellaneous companies: Goldman Sachs, Proctor and Gamble, and Dell

15. Factor AnalysisBrian Jansen Jump Component FactorEigenvalueDifferenceProportionCumulative 1 3.172782.304160.9673 2 0.868620.864190.26481.2321 3 0.004430.031630.00141.2335 4 -0.02720.01115-0.00831.2252 5 -0.038350.03583-0.01171.2135 6 -0.074190.00573-0.02261.1909 7 -0.079920.01264-0.02441.1665 8 -0.092560.00211-0.02821.1383 9 -0.094680.01137-0.02891.1094 10 -0.106050.01216-0.03231.0771 11 -0.11820.01646-0.0361.0411 12 -0.13466.-0.04111

16. Factor AnalysisBrian Jansen Jump Component Factor 1Factor 2Factor 3Uniqueness Oil Futures 0.09845-0.34280.04010.87118 ConocoPhillips 0.65299-0.31282-0.008050.47568 Chevron 0.72422-0.27534-0.022450.39918 ExxonMobil 0.74788-0.20726-0.018320.39739 Baker Hughes 0.54126-0.319560.025710.60425 Entergy 0.401790.20636-0.010070.79588 Ford 0.297740.156690.0240.88622 FedEx 0.460790.278510.010230.71 Goldman Sachs 0.524480.280130.012560.64629 Proctor & Gamble 0.45880.27677-0.010840.71279 Boeing 0.455280.266010.003870.72194 Dell 0.452370.248650.013620.73335

17. Factor AnalysisBrian Jansen Instantaneous Volatility FactorEigenvalueDifferenceProportionCumulativeFactor 1 7.083535.75410.8171 1.104697 2 1.329430.862260.15340.97050.092609 3 0.467170.325050.05391.0244-0.335237 4 0.142130.076810.01641.0408-0.758011 5 0.065320.053190.00751.0483-1.153504 6 0.012130.020950.00141.0497-1.556563 7 -0.008830.02827-0.0011.0487-1.955003 8 -0.03710.01822-0.00431.0444-2.359276 9 -0.055310.028-0.00641.038-2.761669 10 -0.083310.01613-0.00961.0284-3.170523 11 -0.099440.04732-0.01151.0169-3.572822 12 -0.14675.-0.01691-12.2935

18. Factor AnalysisBrian Jansen Instantaneous Volatility Factor 1Factor 2Factor 3Factor 4Factor 5Factor 6Uniqueness Oil Futures -0.079090.289940.412850.032010.097670.036140.72736 ConocoPhillips 0.73578-0.575760.175920.03565-0.048210.03380.09144 Chevron 0.8366-0.491750.05333-0.023120.091830.008950.04639 ExxonMobil 0.9214-0.240930.02123-0.034730.020470.012680.09073 BakerHughes 0.79533-0.225290.10050.1916-0.05447-0.049740.26444 Entergy 0.85950.097090.04047-0.22421-0.1121-0.021380.18691 Ford 0.77670.3099-0.047890.00416-0.100280.068520.28363 FedEx 0.840570.16444-0.12190.118260.00028-0.014480.23735 GS 0.815750.01948-0.2307-0.130510.11041-0.006990.25168 Proctor & Gamble 0.751190.304660.2765-0.071440.0516-0.033560.25755 Boeing 0.711950.534830.104670.06947-0.01574-0.009910.19096 Dell 0.754510.22696-0.30490.100720.062570.018140.27185

19. Factor AnalysisBrian Jansen Instantaneous Volatility -XOM in Red, CVX in Blue

20. Factor AnalysisBrian Jansen Instantaneous Volatility -XOM in Red, Oil in Black

21. Factor AnalysisBrian Jansen Instantaneous Volatility -XOM in Red, Goldman Sachs in Blue

22. Sector vs. MarketBrian Jansen Co-Jumps in the Oil Sector -Hypothesis: oil sector stocks will jump simultaneously due to the common factor price of oil -Many oil stocks in fact do jump at the same time, on the same day. -However, the price of oil futures does not frequently jump simultaneously -Possible explanation: When the price of oil increases, the upstream sector sees huge profits while the downstream sector is hampered by decreased demand and increased input costs. -Following table: number of days experiencing common price jumps

23. Lee-MyklandBrian Jansen Co-Jumps in the Oil Sector OILCOPCVXXOMBHIETRFFDXGSPGBADELL OIL 17400000000000 COP 391370000000000 CVX 2256130000000000 XOM 29405511100000000 BHI 25332125990000000 ETR 3634322717188000000 F 3731 24164720500000 FDX 3032 311939341630000 GS 2130374022343528129000 PG 22283027173638394013900 BA 213028272139252734331370 DELL 2641 331843 40 4638181

24. More familiarity with the practices of the oil industry, especially their trading desk operation to determine how they deal with oil price volatility –Suggestions for investigating day-to-day operations Correcting the Lee-Mykland test Volatility correlation with small lag times Can we use the implied volatility of same industry companies and oil futures to forecast volatility using the HAR-RV-CJ model? ConclusionBrian Jansen Extensions