17/01/2023, 19:14
10 November, 2022
Multivariate conditional volatility models
Download prices for Tesla stock and convert into returns
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Perform PCA analysis
Multivariate conditional volatility models
PC1 PC2 PC3 PC4 PC5 PC6
META 0.3549 0.2744 -0.5068 -0.7189 0.0364 0.1541
AMAZON 0.3200 0.2110 -0.2548 0.4499 -0.6983 0.3134
TESLA 0.6481 -0.7442 0.1445 -0.0677 -0.0252 -0.0021
APPLE 0.2480 0.0802 -0.3428 0.4903 0.7043 0.2795
NETFLIX 0.4729 0.5431 0.6827 -0.0310 0.1190 0.0163
ALPHABET 0.2579 0.1579 -0.2716 0.1866 -0.0161 -0.8943
Standard deviation 0.0444 0.0278 0.0214 0.0148 0.0132 0.0104
Proportion of Variance 0.5324 0.2081 0.1241 0.0594 0.0470 0.0291
Cumulative Proportion 0.5324 0.7406 0.8646 0.9240 0.9709 1.0000
https://moodle.lse.ac.uk/pluginfile.php/2194697/mod_resource/content/1/HW2.html
Interpretation of the first 3 PCs
1. We see that PC1 is the market factor
17/01/2023, 19:14 HW2
2. PC2 can be interpreted as the auto vs. tech factor (Tesla is more of an auto company and the rest of the firms are tech firms)
3. PC3 is hard to interpret, but it can be thought of as the entertainment (Netflix) vs. non-entertainment factor. (There¡¯s only a small loading on Tesla, to which we won¡¯t attach an important meaning)
Multivariate conditional volatility models
https://moodle.lse.ac.uk/pluginfile.php/2194697/mod_resource/content/1/HW2.html
GARCH(1,1) using all principal components
Since we are using all factors the error term Omega is zero.
17/01/2023, 19:14
Conditional correlation between Tesla and conditional volatility models
https://moodle.lse.ac.uk/pluginfile.php/2194697/mod_resource/content/1/HW2.html
Interpretation of the result, main observations:
1. The correlation is the highest during the initial period of COVID, consistent with how correlation tends to rise in times of greater volatility.
2. The correlation also tends to trend upward over time. There is no one right interpretation for this, but one could speculate that Apple¡¯s greater focus on self- driving technology and other larger tech products may increase its exposure to the same risk Tesla is exposed to.
17/01/2023, 19:14 HW2
Reducing dimensionallity
Multivariate conditional volatility models
## [1] “We need 3 principal components to explain at least 85% of v
https://moodle.lse.ac.uk/pluginfile.php/2194697/mod_resource/content/1/HW2.html
The results look very similar. This is because the first few PCs are most important in generating the correlations.
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