Initial Stock AnalysisAndrew BentleyFebruary 8, 2012

Outline

Price and returns for Apple Inc. (AAPL) and Ford Motor Inc. (F)

Measures of Volatility RV, BV, Sub-Sampled RV, TV

Volatility Signatures RV and BV

Relative Contribution of Jumps Basic Comparison Between these Measures

Price and Returns

Unadjusted plots of price data against time Adjusted plots of price data against time after correcting backwards for

stock splits Minute-by-minute geometric returns

“Returns” graphs consider intraday minute-by-minute returns as well as overnight returns.

AAPL: Unadjusted Prices

2:1 Split2:1 Split

AAPL: Stock Splits

Three 2:1 Stock Splits

June 15, 1987

June 21, 2000

February 28 2005

The June 2000, and February 2005 splits fall in the data range

Price adjusts “backwards” to account for the splits

AAPL: Adjusted Prices

AAPL: Returns

F: Price

Nov. 2006Dec. 2008

F: Returns

Measures of Volatility Goal is to measure the integrated variation

for a process:

The realized variance:

AAPL: Realized Volatility (Annualized)

F: Realized Volatility (Annualized)

Estimators for IVt

Bipower Variation (BV):

Threshold/Truncated Variation (TV)

Bipower Volatility BVt (AAPL)

Bipower Volatility, BVt (F*)

Truncated Variation, TVt (AAPL) AAPL, cutoff of 4 standard deviations

Truncated Variation, TVt (F*) F, cutoff of 4 standard deviations

Relative Contribution of Jumps

Effects of Microstructure Noise Observed data is actually some price plus some noise term Look for ways to wash out the effect of the noise without

loosing the vast majority of the data Sub-Sampling

k can be thought of as an “offset”

RVt after Sub-Sampling (AAPL)…RVSS

RVt after Sub-Sampling (F*)…RVSS

Volatility Signatures Measure of the calculated unconditional variance of the stock

as a function of the sampling interval Δ For T time periods, the average realized variance is:

This number is then properly annualized. Replace RVt by BVt and other measures of intraday variance

AAPL: Volatility Signatures

F: Volatility Signatures

RVt- BVt (AAPL)

RVt- BVt (F)

Next Steps: Examine Relative Contribution of Jumps of AAPL vs. those of F Calculate correlation of the two vectors

Expected to be low. Look at stock that are both in the same industry

Examine volatility of Apple with that of Microsoft, Google, Intel, and other technology sector firms.

Examine volatility of Ford with other car manufacturers like GM. Examine correlation of intra-industry stocks

Expected to be high.