Beta By Hao Sun. JPM: Realized Beta JPM: Bi-Power Beta

BetaBy Hao Sun

JPM: Realized Beta

Apr 09, 1997 Sep 11, 2000 Mar 01, 2004 Aug 01, 2007 Dec 30, 2010-1

0

1

2

3

4

5

6JPM: Realized Beta

Date

Cor

rela

tion

JPM: Bi-Power Beta


0

1

2

3

4

5

6JPM: Bipower Beta

Date

Cor

rela

tion

JPM Beta: Relative Contribution of Jumps


-20

-15

-10

-5

0

5

10

15

20

25JPM Beta: Relative Contribution of Jumps

Date

Rel

ativ

e C

ontri

butio

n

𝑀𝑒𝑎𝑛=0.0684

Price Jump: Merger

Oct 10, 2000 Oct 13, 2000 Oct 17, 2000 Oct 20, 2000 Oct 24, 200031

32

33

34

35

36

37

38

39

40JPM: Price

Date

Pric

e

Realized vs. Bi-power Beta

-1 0 1 2 3 4 5 6-1

0

1

2

3

4

5

6Different Covariance Measures

Realized Beta

Bi-p

ower

Bet

a

JPM: Realized Beta


-0.5

0

0.5

1

1.5

2JPM: Realized Beta

Date

Cor

rela

tion

JPM: Bi-Power Beta


-0.5

0

0.5

1

1.5

2JPM: Bipower Beta

Date

Cor

rela

tion

JPM Beta: Relative Contribution of Jumps


-15

-10

-5

0

5

10

15

20

25JPM Beta: Relative Contribution of Jumps

Date

Rel

ativ

e C

ontri

butio

n

𝑀𝑒𝑎𝑛=0.0606

Realized vs. Bi-Power Beta

-0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4Different Covariance Measures - JPM

Realized Beta

Bi-p

ower

Bet

a

JPM&SPFU: Realized Covariance (w/o 0’s)


0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000JPM&SPFU: Realized Covariance

Date

Cov

aria

nce

𝑀𝑒𝑎𝑛=1.3007×252=327.78326.74

JPM&SPFU: Bi-Power Covariance (w/o 0’s)


0

2000

4000

6000

8000

10000

12000

14000

16000

18000

20000JPM&SPFU: Bipower Covariance

Date

Cov

aria

nce

𝑀𝑒𝑎𝑛=1.2711×252=320.32319.31

Relative Contribution of Jumps


-20

-15

-10

-5

0

5

10

15

20

25JPM&SPFU: Relative Contribution of Jumps

Date

Rel

ativ

e C

ontri

butio

n

𝑀𝑒𝑎𝑛=0.0122

BAC&SPFU: Realize Covariance

Apr 09, 1997 Sep 11, 2000 Mar 01, 2004 Aug 01, 2007 Dec 30, 2010

0

5000

10000

15000

20000BAC&SPFU: Realized Covariance

Date

Cov

aria

nce

𝑀𝑒𝑎𝑛=1.2870×252=324.32

BAC&SPFU: Bi-Power Covariance


0

5000

10000

15000

20000BAC&SPFU: Bipower Covariance

Date

Cov

aria

nce

𝑀𝑒𝑎𝑛=1.2555×252=316.39

Relative Contribution of Jumps


-20

-15

-10

-5

0

5

10

15

20

25BAC&SPFU: Relative Contribution of Jumps

Date

Rel

ativ

e C

ontri

butio

n

𝑀𝑒𝑎𝑛=−0.0086

BAC: Realized Beta

𝑀𝑒𝑎𝑛=0.8717


0

1

2

3

4

5

6BAC: Realized Beta

Date

Cor

rela

tion

BAC: Bi-Power Beta

𝑀𝑒𝑎𝑛=0.9348


0

1

2

3

4

5

6BAC: Bipower Beta

Date

Cor

rela

tion

BAC Beta: Relative Contribution of Jumps

𝑀𝑒𝑎𝑛=−0.1682


-1000

-500

0

500

1000

BAC Beta: Relative Contribution of Jumps

Date

Rel

ativ

e C

ontri

butio

n

Realized vs. Bi-Power Beta

-1 0 1 2 3 4 5 6-1

0

1

2

3

4

5

6Different Covariance Measures - BAC

Realized Beta

Bi-p

ower

Bet

a

BAC: Realized Risks

𝑀𝑒𝑎𝑛=444.6055 𝑀𝑒𝑎𝑛=1020.2

𝜇𝜎𝑀2 =315.1512 𝜇𝜎𝑀

2 =297.1584

𝛽 𝐽𝑃𝑀2 𝜎𝑀

2 +𝜎𝜖2


1

2

3

4

5

6

7

8

9x 10

4 BAC: Realized Systematic Variance

Date

Var

ianc

e


1

2

3

4

5

6

7

8

9x 10

4 BAC: Realized Idiosyncratic Variance

DateV

aria

nce

BAC: Bi-Power Risks

𝑀𝑒𝑎𝑛=463.8418 𝑀𝑒𝑎𝑛=908.2782


2 +𝜎𝜖2


1

2

3

4

5

6

7

8

9x 10

4 BAC: Bipower Systematic Variance

Date

Var

ianc

e


1

2

3

4

5

6

7

8

9x 10

4 BAC: Bipower Idiosyncratic Variance

DateV

aria

nce

JPM: Realized Risks

𝑀𝑒𝑎𝑛=393.0049 𝑀𝑒𝑎𝑛=905.5298


2 +𝜎𝜖2


0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4 JPM: Realized Systematic Variance

Date

Var

ianc

e


0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4 JPM: Realized Idiosyncratic Variance

Date

Var

ianc

e

JPM: Bi-Power Risks

𝑀𝑒𝑎𝑛=414.9356 𝑀𝑒𝑎𝑛=799.8714


2 +𝜎𝜖2


0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4 JPM: Bipower Systematic Variance

Date

Var

ianc

e


0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

4 JPM: Bipower Idiosyncratic Variance

Date

Var

ianc

e

Documents

Beta By Hao Sun. JPM: Realized Beta JPM: Bi-Power Beta