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Initial Stock Analysis

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.

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Initial Stock Analysis

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  1. Initial Stock Analysis Andrew Bentley February 8, 2012

  2. 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

  3. 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.

  4. AAPL: Unadjusted Prices 2:1 Split 2:1 Split

  5. 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

  6. AAPL: Adjusted Prices

  7. AAPL: Returns

  8. F: Price Nov. 2006 Dec. 2008

  9. F: Returns

  10. Measures of Volatility • Goal is to measure the integrated variation • for a process: • The realized variance:

  11. AAPL: Realized Volatility (Annualized)

  12. F: Realized Volatility (Annualized)

  13. Estimators for IVt • Bipower Variation (BV): • Threshold/Truncated Variation (TV)

  14. Bipower Volatility BVt(AAPL)

  15. BipowerVolatility, BVt(F*)

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

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

  18. Relative Contribution of Jumps

  19. 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”

  20. RVtafter Sub-Sampling (AAPL)…RVSS

  21. RVtafter Sub-Sampling (F*)…RVSS

  22. 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 BVtand other measures of intraday variance

  23. AAPL: Volatility Signatures

  24. F: Volatility Signatures

  25. RVt- BVt(AAPL)

  26. RVt- BVt(F)

  27. 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.

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