1

Economics 201FS: Realized Covariance, Realized Betas,

“Bipower Betas”

Grace Shuting WeiSpring 2011

16 February 2011

2

Main Points• Goals• Stock Choices• Basic Properties of Stocks• Realized Covariance• Realized Correlation• Realized Betas• Bipower Volatility Measures• Extensions

3

Data• UPS, FDX, SPFU

– Nov 11 1999 – Dec 30 2010– 2763 days– Aligned time series

• Data Outliers– Measurement error: UPS– Data of erroneous day removed

4

FDX: Price & Returns

5

FDX: Realized, Bipower Volatility

6

UPS: Price & Returns

7

UPS: Realized, Bipower Volatility

8

SPFU: Price & Returns

9

SPFU: Realized, Bipower Volatility

10

Realized Covariance, Correlation, Beta• Realized Covariance

• Realized Correlation

• Realized Beta

11

FDX & Market: Realized Covariance, Corr

12

UPS & Market: Realized Covariance, Corr

13

FDX & UPS: Realized Covariance, Corr

14

Bipower Volatility, Beta• Bipower Covariance

– Backed out from portfolio approach• Bipower Beta

– =

15

FDX: Bipower Beta

16

FDX: Scatter of Betas

RealizedBeta

Bipower Beta

Mean 0.7140 0.7590

SD 0.3366 0.4022

Max 2.2849 3.2043

Min -0.7919 -1.0370

17

UPS: Bipower Beta

18

UPS: Scatter of Betas

RealizedBeta

Bipower Beta

Mean 0.5368 0.5736

SD 0.3116 0.3558

Max 1.6126 2.5496

Min -0.5104 -1.0697

19

Extensions• Comparison of “bipower” beta to βc• Use of simulated data

– “Right” answer• Effect of microstructure noise on betas

20

Realized Covariance Signature Plots