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

–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

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

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) :

Lee-MyklandBrian Jansen Results XOMCOPCVX # of jumps % of returns that are jumps 0.282%0.4073%0.3593% # of days with a jump % of days with a jump Mean(L(i)) Mean(L(i)) if return is a jump Standard deviation of L(i)

Lee-MyklandBrian Jansen Results

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

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)

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)

Lee-MyklandBrian Jansen Corrections to the Test

Lee-MyklandBrian Jansen Corrections to the Test

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

Lee-MyklandBrian Jansen Results of Corrected Test

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

Factor AnalysisBrian Jansen Jump Component FactorEigenvalueDifferenceProportionCumulative

Factor AnalysisBrian Jansen Jump Component Factor 1Factor 2Factor 3Uniqueness Oil Futures ConocoPhillips Chevron ExxonMobil Baker Hughes Entergy Ford FedEx Goldman Sachs Proctor & Gamble Boeing Dell

Factor AnalysisBrian Jansen Instantaneous Volatility FactorEigenvalueDifferenceProportionCumulativeFactor

Factor AnalysisBrian Jansen Instantaneous Volatility Factor 1Factor 2Factor 3Factor 4Factor 5Factor 6Uniqueness Oil Futures ConocoPhillips Chevron ExxonMobil BakerHughes Entergy Ford FedEx GS Proctor & Gamble Boeing Dell

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

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

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

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

Lee-MyklandBrian Jansen Co-Jumps in the Oil Sector OILCOPCVXXOMBHIETRFFDXGSPGBADELL OIL COP CVX XOM BHI ETR F FDX GS PG BA DELL

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