MINGWEI LEIECON 201

Final Presentation

Research Idea

Past research have shown evidence of high asset correlations in the period of heightened market volatility: Campbell, Koedijk, and Kofman- 2002 Butler Joaquin

This phenomenon is also well known in the business industry

Empirical exploration of the relationship between asset returns correlation and market (SPY) volatility

The Process

Pair up stocks to be analyzed along with SPYMatch up data of stocks and SPYPartition data into periods (1-day, 5-days, 20 days)

to be analyzedFind the optimal sampling frequency to calculate

returns correlation for each partitionPlot correlation against market standard deviationPerform transformations (log, Fisher) to attain a

more linear relationshipPerform regression analysis

Correlation Signature (Period- 1 day)

Correlation Signature (Period- 5 days)

Correlation Signature (Period- 20 days)

BAC & GS Correlation vs. Market Standard Deviation (Period – 1 day)

-1-.

50

.51

corr

0 .02 .04 .06 .08 .1mktstd

BAC & GS Correlation vs. Ln(MktStd) (Period – 1 day)

-1-.

50

.51

-6 -5 -4 -3 -2lnmktstd

corr Fitted values

_cons 1.139872 .0401475 28.39 0.000 1.061145 1.218599 lnmktstd .1483584 .0084539 17.55 0.000 .1317807 .164936 corr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .24517 R-squared = 0.0955 Prob > F = 0.0000 F( 1, 2404) = 307.97Linear regression Number of obs = 2406

BAC & GS Fisher Transformed Correlation vs. MktStd (Period – 1 day)

-2-1

01

2

0 .02 .04 .06 .08 .1mktstd

fishercorr Fitted values

_cons .3611695 .0127188 28.40 0.000 .3362286 .3861104 mktstd 15.51104 1.104211 14.05 0.000 13.34573 17.67634 fishercorr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .33454 R-squared = 0.1083 Prob > F = 0.0000 F( 1, 2404) = 197.32Linear regression Number of obs = 2406

BAC & GS Fisher Transformed Corr vs. Ln(MktStd) (Period – 1 day)

-2-1

01

2

-6 -5 -4 -3 -2lnmktstd

fishercorr Fitted values

_cons 1.600523 .0610846 26.20 0.000 1.480739 1.720307 lnmktstd .2285885 .01262 18.11 0.000 .2038414 .2533356 fishercorr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .33235 R-squared = 0.1200 Prob > F = 0.0000 F( 1, 2404) = 328.09Linear regression Number of obs = 2406

BAC & GS Correlation vs. Market Standard Deviation (Period – 5 days)

-.5

0.5

1co

rr

0 .05 .1 .15mktstd

BAC & GS Correlation vs. Ln(MktStd) (Period – 5 days)

-.5

0.5

1

-5 -4 -3 -2lnmktstd

corr Fitted values

_cons .9560543 .0537485 17.79 0.000 .8504423 1.061666 lnmktstd .1289958 .013579 9.50 0.000 .1023139 .1556777 corr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .17969 R-squared = 0.1131 Prob > F = 0.0000 F( 1, 479) = 90.24Linear regression Number of obs = 481

. regress corr lnmktstd, robust

BAC & GS Fisher Transformed Correlation vs. MktStd (Period – 5 days)

-.5

0.5

11.

5

0 .05 .1 .15mktstd

fishercorr Fitted values

_cons .3910024 .0193258 20.23 0.000 .3530286 .4289761 mktstd 5.507461 .712153 7.73 0.000 4.108131 6.906791 fishercorr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .23933 R-squared = 0.1150 Prob > F = 0.0000 F( 1, 479) = 59.81Linear regression Number of obs = 481

BAC & GS Fisher Transformed Corr vs. Ln(MktStd) (Period – 5 days)

-.5

0.5

11.

5

-5 -4 -3 -2lnmktstd

fishercorr Fitted values

_cons 1.247548 .0755015 16.52 0.000 1.099193 1.395904 lnmktstd .1878076 .0187676 10.01 0.000 .1509305 .2246847 fishercorr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .23664 R-squared = 0.1348 Prob > F = 0.0000 F( 1, 479) = 100.14Linear regression Number of obs = 481

BAC & GS Correlation vs. Market Standard Deviation (Period – 20 days)

-.2

0.2

.4.6

.8co

rr

0 .05 .1 .15 .2mktstd

BAC & GS Correlation vs. Ln(MktStd) (Period – 20 days)

-.2

0.2

.4.6

.8

-4 -3.5 -3 -2.5 -2 -1.5lnmktstd

corr Fitted values

_cons .8687509 .0746249 11.64 0.000 .7209732 1.016529 lnmktstd .131358 .0228952 5.74 0.000 .0860193 .1766967 corr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .16104 R-squared = 0.1338 Prob > F = 0.0000 F( 1, 118) = 32.92Linear regression Number of obs = 120

. regress corr lnmktstd, robust

BAC & GS Fisher Transformed Correlation vs. MktStd (Period – 20 days)

-.5

0.5

1

0 .05 .1 .15 .2mktstd

fishercorr Fitted values

_cons .380091 .0307682 12.35 0.000 .3191617 .4410203 mktstd 2.76328 .529945 5.21 0.000 1.713845 3.812716 fishercorr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .21073 R-squared = 0.1343 Prob > F = 0.0000 F( 1, 118) = 27.19Linear regression Number of obs = 120

BAC & GS Fisher Transformed Corr vs. Ln(MktStd) (Period – 20 days)

-.5

0.5

1

-4 -3.5 -3 -2.5 -2 -1.5lnmktstd

fishercorr Fitted values

_cons 1.097684 .1016551 10.80 0.000 .8963793 1.298989 lnmktstd .1857677 .0304402 6.10 0.000 .1254878 .2460476 fishercorr Coef. Std. Err. t P>|t| [95% Conf. Interval] Robust

Root MSE = .20804 R-squared = 0.1562 Prob > F = 0.0000 F( 1, 118) = 37.24Linear regression Number of obs = 120

Regression Results (Period- 1 day)

Regressand

Regressor β1 t-stat

β0 t-stat R2

BAC and GS Corr ln(MktStd) 0.148 17.55 1.140 28.39 0.0955

Fisher Corr MktStd 15.51 14.05 0.362 28.40 0.1083

Fisher Corr ln(MktStd) 0.229 18.11 1.600 26.20 0.1200

JPM & GS Corr ln(MktStd) 0.134 15.77 1.098 27.36 0.0835

Fisher Corr MktStd 14.15 13.66 .416 34.43 0.0908

Fisher Corr ln(MktStd) 0.214 16.51 1.572 25.06 0.1058

Regression Results Cont. (Period- 1 day)

Regressand

Regressor β1 t-stat

β0 t-stat R2

WMT and JPM

Corr ln(MktStd) 0.1563 18.68 1.086 27.76 0.1019

Fisher Corr MktStd 13.94 14.27 0.255 21.67 0.1028

Fisher Corr ln(MktStd) 0.2070 18.54 1.373 25.92 0.1151

WMT and KO Corr ln(MktStd) 0.1475 15.29 0.983 21.59 0.0851

Fisher Corr MktStd 12.96 12.11 0.189 15.32 0.0915

Fisher Corr ln(MktStd) 0.1877 15.55 1.206 21.02 0.0975

WMT and VZ Corr ln(MktStd) 0.1954 22.66 1.243 30.42 0.1634

Fisher Corr MktStd 16.0287 14.39 0.192 15.05 0.1496

Fisher Corr ln(MktStd) 0.2469 21.97 1.53 28.30 0.1768

Regression Results (Period- 5 days)

Regressand

Regressor β1 t-stat

β0 t-stat R2

BAC and GS Corr ln(MktStd) 0.1290 9.50 0.956 17.79 0.1131

Fisher Corr MktStd 5.507 7.73 0.391 20.23 0.1150

Fisher Corr ln(MktStd) 0.1878 10.01 1.248 16.52 0.1348

JPM & GS Corr ln(MktStd) 0.1004 8.42 0.881 18.44 0.0860

Fisher Corr MktStd 4.420 7.89 0.462 28.85 0.0829

Fisher Corr ln(MktStd) 0.1537 8.85 1.161 10.45 0.1014

Regression Results Cont. (Period- 5 days)

Regressand

Regressor β1 t-stat

β0 t-stat R2

WMT and JPM

Corr ln(MktStd) 0.1233 10.17 0.832 17.82 0.1336

Fisher Corr MktStd 4.688 8.82 0.275 18.17 0.1341

Fisher Corr ln(MktStd) 0.1531 10.31 0.976 16.84 0.1431

WMT and KO Corr ln(MktStd) 0.1242 8.78 0.768 13.97 0.1298

Fisher Corr MktStd 4.822 6.36 0.194 10.11 0.1463

Fisher Corr ln(MktStd) 0.1504 8.65 0.889 13.02 0.1439

WMT and VZ Corr ln(MktStd) 0.1725 13.14 0.987 18.91 0.2462

Fisher Corr MktStd 6.185 10.57 0.195 12.70 0.2426

Fisher Corr ln(MktStd) 0.210 12.88 1.156 17.68 0.2679

Regression Results (Period- 20 days)

Regressand Regressor β1 t-stat Β0 t-stat R2

BAC and GS Corr ln(MktStd) 0.1314 5.74 0.869 11.64 0.1338

Fisher Corr MktStd 2.763 5.21 0.380 12.35 0.1343

Fisher Corr ln(MktStd) 0.186 6.10 1.098 10.80 0.1562

JPM & GS Corr ln(MktStd) 0.0843 4.60 0.763 11.98 0.0858

Fisher Corr MktStd 1.980 5.44 0.470 22.13 0.0910

Fisher Corr ln(MktStd) 0.1316 5.03 0.979 10.67 0.1030

Regression Results Cont. (Period- 20 days)

Regressand

Regressor β1 t-stat

β0 t-stat R2

WMT and JPM

Corr ln(MktStd) 0.1229 6.69 0.735 12.59 0.2021

Fisher Corr MktStd 2.266 6.81 0.264 13.15 0.1908

Fisher Corr ln(MktStd) 0.1470 6.84 0.836 11.99 0.2084

WMT and KO Corr ln(MktStd) 0.1240 5.90 0.672 9.92 0.2040

Fisher Corr MktStd 2.426 5.95 0.180 8.73 0.2299

Fisher Corr ln(MktStd) 0.1463 5.80 0.756 9.20 0.2149

WMT and VZ Corr ln(MktStd) 0.1618 8.12 0.828 12.39 0.3351

Fisher Corr MktStd 3.156 11.44 0.183 10.92 0.3666

Fisher Corr ln(MktStd) 0.1947 8.06 0.951 11.70 0.3593

Conclusions

The results definitely suggest that there exists a negative relationship between asset correlations and market volatility

Results imply that diversification works the least when it is needed the most

Portfolio managers and risk management practices must allow for time variant asset correlations and understand how asset correlations change with the market