Initial Stock Analysis Andrew Bentley February 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 Split

AAPL: Stock Splits  Three 2:1 Stock Splits  June 15, 1987  June 21, 2000  February  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 Dec. 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 IV t  Bipower Variation (BV):  Threshold/Truncated Variation (TV)

Bipower Volatility BV t (AAPL)

Bipower Volatility, BV t (F*)

Truncated Variation, TV t (AAPL)  AAPL, cutoff of 4 standard deviations

Truncated Variation, TV t (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” 

RV t after Sub-Sampling (AAPL)…RV SS

RV t after Sub-Sampling (F*)…RV SS

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 RV t by BV t and other measures of intraday variance

AAPL: Volatility Signatures

F: Volatility Signatures

RV t - BV t (AAPL)

RV t - BV t (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.