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Principal components of stock market dynamics

Principal components of stock market dynamics. Methodology and applications in brief (to be updated … ). Andrei Bouzaev, bouzaev@ya.ru. Why principal components are needed. Objectives

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Principal components of stock market dynamics

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  1. Principal components of stock market dynamics Methodology and applications in brief (to be updated…) Andrei Bouzaev, bouzaev@ya.ru

  2. Why principal components are needed Objectives • understand the evidence of more thanone factor driving the stock market, market factor should be supplemented with others, possibly less significant • identify set of factor components driving stock market and its basic segments • set up multi-factor model that is better than one-factor for monitoring of market dynamics, hedge, pricing, risk-valuation • consider stock returns dynamics as well as stock prices (levels)

  3. Similar to modeling the shape of the yield curve • Modelling the shape of the yield curve – very similar process • evidence of more than one factor driving the term structure • principal components of dynamics are needed to hedge the shape of the yield curve in practice The folowing three factors are used: level, slope, curvature Sensitivities of zero-couponyields to the three factors

  4. In reality, do we have only onefactor in stock returns? Correlation between USA stock market portfolios formed on size. Data: Fama-French decile portfolios’ returns formed on market equity, based on monthly yeilds, 1926-2010 • Correlation matrix indicates that difference in return dynamics is increasing by the difference in market equity. • Are there underlying factors that influence different portfolios in different manner?

  5. The same result is for pricelevel dynamic… Correlation between Russia stock market portfolios formed on size. Data: MICEX capitalisation indices, based on daily price levels (left) and daily returns (right), 2005-2011 • Correlation matrix indicates that difference in price dynamics is increasing by the difference in market equity. • Are there underlying factors that influence different portfolios in different manner?

  6. Identifying principal components* • Let us find 3 factors that explain thedynamics of the ME portfolios • The analysis for more than 3 factors is astraightforward extension • Assume the following dynamics of portfolios yields … meaning that each factor impacts all of the yields with sensitivities β. *The approach is adopted from modeling the shape of the yield curve, Fixed Income lecture notes at NES, professor Dmitri Makarov

  7. Principal component analysis • We look for factors that are implicit in the movements over time of thevarious yields • To determine them we are going apply PrincipalComponent Analysis • Finding first principal componentmeans that we are maximizing a weightedaverage of the R-square-s of the above regressions • After computing the first component, we canfind the residuals, applying them instead of yields, and find the second factor, and so on • For price levels the same approach can be used

  8. Principal components in practice (returns) • Using monthly returns for the US stock market between 1926 and 2000, we have thefollowing sensitivities of size-based portfolios yields to the three factors Correlation matrix

  9. Principal components in practice (price levels) Using dailyprice levels for the Russia stock market between 2005 and 2011, we have thefollowing sensitivities of size-based portfolios’ price level (1) and returns (2) to the three factors Correlation matrix, price levels Correlation matrix, returns

  10. Empirical components’ description • First factor has roughly thesame effect on all portfolio yields/prices. For this reason, it can be referred to as parallelshift/level.It explains most of the variation • Second factor has negative impact on small stocks and positive impact on big stocks. This is a slopefactor • The third factor is positive at the small and big stocks, and negative at the medium stocks. It can be referred to as curvature

  11. Principal components in dynamics • Three factor component in dynamic, based on Russia stock market (daily price levels), 2005-2011.

  12. Constructing “market curve” • Based on three factor components (price level factores are more appropriate) we can construct “stock market curve” which indicates underpriced/overpriced segments. Normal shape of the curve: all market segments around their average F3 curvature factor F2 slope factor F1 parallelshift Based on Russia stock market data (daily price levels), 2005-2011.

  13. Application (1) -“updating” CAPM with new factors

  14. Further development • Factor components methodology and components’ values are published on http://fmlab.hse.ru/ • Ready for any discussion and cooperation with individuals/academics/financial instituties of further development and calculation of the presented factor components in form of stock indices or returns. • Contacts: Andrei Bouzaev, bouzaev@ya.ru, (495) 9696 225

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