1. Formulating a Research Topic
Abhinay Sawant
February 18, 2009
Economics 201FS

2. Update from Last Time Fixed programs: Still Coarse Sampling: Z-Scores
Tri-Power Quarticity
Realized Volatility Signature Plots
Still Coarse Sampling:
Currently, sampling frequency = 8 min
Should be changed to 5 minutes in future with averaging

3. Homogeneity of Jumps

4. Homogeneity of Jumps

5. Homogeneity of Jumps
Let X1, X2, …, Xn be Bernoulli trials with probability p of success where success is defined as a jump day
Goal is to estimate p for pre-Lehman (1/1/06 – 9/12/08) and post-Lehman periods (9/15/08 – 1/7/09)
Conduct a t-Test to determine if a significance difference exists in parameter p in the two periods for individual equities

6. Homogeneity of Jumps
Assume a prior distribution ξ(θ) uniformly distributed on the interval [0, 1]
Posterior distribution is a Beta distribution with the following parameters:

7. Homogeneity of Jumps
Properties about estimated parameters can be determined as follows from Beta distribution:
t-Test is used to determine if difference is significant:

8. Homogeneity of Jumps Morgan Stanley (Tri-Power Quarticity):
Morgan Stanley (Quad-Power Quarticity):
Data Set
Total Days
Jump Days
p = 0.05
p = 0.01
p = 0.001
Entire Set
742
100 43 15
Pre-Lehman
664 92 39 14
Post-Lehman 78 8 4 1
Data Set
Total Days
Jump Days
p = 0.05
p = 0.01
p = 0.001
Entire Set
742
107 46 17
Pre-Lehman
664 98 42 16
Post-Lehman 78 9 4 1

9. Homogeneity of Jumps t Statistic measures the difference
Morgan Stanley t-Test:
Test is inconclusive but doesn’t suggest any significant difference in proportions
p = 0.05
p = 0.01
p = 0.001
TP Quarticity
-0.72
0.09
0.14
QP Quarticity
-0.60
-0.07
-0.03

10. Homogeneity of Jumps Company Name QRT p = 0.05 p = 0.01 p = 0.001
Conclusion
Bank of America TP
1.78
1.67
1.39
Slightly More QP
1.35
1.55
1.22
Citigroup
0.16
1.27
1.17
0.26
1.38
1.14
Goldman Sachs
-0.85
-0.60
-0.50
Homogeneous:
Slightly Less
-1.06
-0.69
J.P. Morgan
2.52
0.42
1.52
2.20
0.53
1.69
Morgan Stanley
-0.72
0.09
0.14
Homogenous
-0.07
-0.03

11. Homogeneity of Jumps Company Name QRT p = 0.05 p = 0.01 p = 0.001
Conclusion
Caterpillar
(Industrial Equipment) TP
-3.84
-2.84
-1.84
Significantly Less QP
-3.18
-2.91
-2.35
McDonald’s
(Restaurant)
-1.65
-1.15
0.00
Slightly Less
-2.03
-1.43
-0.22
Merck
(Pharmaceutical)
0.66
0.59
Homogeneous: Slightly More
0.37
0.31
0.80
Oracle
(Software)
-0.94
-0.15
0.69
Homogeneous
-0.50
-0.06
0.48
Wal-Mart
(Retail)
-2.28
-0.42
-2.62
-1.14
-0.83

12. Other Properties of Jumps

13. Other Properties of Jumps
Morgan Stanley data:
Mean Daily Return (QP)
p = 0.05
p = 0.01
p = 0.001
With Jumps
Without Jumps
Mean Realized Vol.(QP)
p = 0.05
p = 0.01
p = 0.001
With Jumps
Without Jumps

14. Other Properties of Jumps

15. Alternative Research Topics
Portfolio Risk
Constructing 2-asset portfolios and how does volatility change?
Realized Covariance:
How does investment process change for time-dependent volatility and correlation?

16. Alternative Research Topics
Risk Management
Incorporating time-dependent volatility for VaR model