The Stock Market Facts and theories.
Shares and values :  Introduction. <ul><li>Shares  : </li></ul><ul><ul><li>Some words on history. </li></ul></ul><ul><ul><...
Questions…… <ul><li>The curious outsider’s view : dynamics /stock prices   </li></ul><ul><ul><li>Random walk (Bachelier…) ...
Facts :aggregate evolution  of stock prices A century’s evolution..
Long period returns : US
Long period returns…
US : Volatility of returns.
US : Volatility of returns,  next..
The predictability of  returns…… ?
Theoretical tools… Fundamental value,  Riskiness,  Market « efficiency ».
  Stock valuation :  the standard theory… <ul><li>Two polar models for valuation :  </li></ul><ul><ul><li>No dividend :  <...
The fundamental value-1 <ul><li>Setting :  </li></ul><ul><ul><li>Certain dividend, </li></ul></ul><ul><ul><li>Common point...
  Remark on the  fundamental value : <ul><li>It is the perfect foresight equilibrium.   </li></ul><ul><ul><li>Assume p(t+1...
The fundamental value :  other formulaS..  <ul><li>The kernel : </li></ul><ul><ul><li>p(t) =   +∞ T=t+1  {1/(1+r} T-t  {E...
The fundamental value :  other formulaS..  <ul><li>The kernel : </li></ul><ul><ul><li>p(t) =   +∞ T=t+1  {1/(1+r} T-t  {E...
Complexification.  <ul><li>More complex processes.  </li></ul><ul><ul><li>ARMA, etc… </li></ul></ul><ul><ul><li>May depend...
Illustrations. <ul><li>Prices.- </li></ul>prix 4 cas1 t prix Cas 2 Cas 3 Cas 4
Risky assets <ul><li>Valuation of a risky asset.  </li></ul><ul><ul><li>q(j)/q(0) = [1/(1+r)][  s  A(j,s) P(s)],  </li></...
The theory of fundamental value and its predictions.  <ul><li>The evolution of prices Les prix et leur évolution: </li></u...
1-A : Price Difference and equal fundamental value.
1C: Unreasonable risk premium ? <ul><li>1-C :The risk premium is reasonable  </li></ul><ul><ul><li>US (1889-1978) </li></u...
1-C :  (Equity Premium Puzzle, EPP) <ul><li>US 1889-1978) </li></ul><ul><li>3 variables  </li></ul><ul><ul><li>Real return...
1D, 2C – Other predictions <ul><li>1-D : Prices vary less than reconstitued fundamental values.  </li></ul><ul><li>2-B : Y...
2-D : Objections to « efficiency ».
Excess volatility puzzle.  <ul><li>The diagram </li></ul><ul><ul><li>observed prices  : 1860 to-day.  </li></ul></ul><ul><...
No bubble… <ul><li>The tulip mania ; </li></ul><ul><ul><li>Feb. 1637 :  </li></ul></ul><ul><ul><ul><li>Bulb = 20 times a  ...
Others  <ul><li>Internet Bubble… </li></ul><ul><ul><li>2001 </li></ul></ul><ul><li>Crashes.  </li></ul><ul><ul><li>1929. <...
Aller plus loin ou abandonner le  paradigme ….. <ul><li>La première option  </li></ul><ul><ul><li>Garder l’hypothèse d’ant...
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The Stock Market Facts and theories.

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The Stock Market Facts and theories.

  1. 1. The Stock Market Facts and theories.
  2. 2. Shares and values : Introduction. <ul><li>Shares : </li></ul><ul><ul><li>Some words on history. </li></ul></ul><ul><ul><ul><ul><li>Risk Sharing. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Liquidity. </li></ul></ul></ul></ul><ul><ul><li>Ownership rights / firms. </li></ul></ul><ul><ul><ul><ul><li>Residual claimant, but limited liability. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Formal control outside bankruptcy. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Tradable. </li></ul></ul></ul></ul><ul><li>The stock market and the firm. </li></ul><ul><ul><li>Financing (Modigliani Miller) </li></ul></ul><ul><ul><li>Governance… </li></ul></ul>
  3. 3. Questions…… <ul><li>The curious outsider’s view : dynamics /stock prices </li></ul><ul><ul><li>Random walk (Bachelier…) ? </li></ul></ul><ul><ul><li>« Fat tail » (Mandelbrot) ? </li></ul></ul><ul><li>The investors’ eyes : how to make money ? </li></ul><ul><ul><ul><li>Can you predict future stock prices ? </li></ul></ul></ul><ul><ul><ul><li>Can you beat the market ? </li></ul></ul></ul><ul><ul><ul><ul><li>Bachelier no. </li></ul></ul></ul></ul><ul><ul><ul><ul><li>Modern version : is the market efficient ? </li></ul></ul></ul></ul><ul><li>The economist’s questions : </li></ul><ul><ul><li>The same i.e </li></ul></ul><ul><ul><ul><li>What determines prices and their dynamics.. </li></ul></ul></ul><ul><ul><li>Plus financing the firm and governance.. </li></ul></ul>
  4. 4. Facts :aggregate evolution of stock prices A century’s evolution..
  5. 5. Long period returns : US
  6. 6. Long period returns…
  7. 7. US : Volatility of returns.
  8. 8. US : Volatility of returns, next..
  9. 9. The predictability of returns…… ?
  10. 10. Theoretical tools… Fundamental value, Riskiness, Market « efficiency ».
  11. 11. Stock valuation : the standard theory… <ul><li>Two polar models for valuation : </li></ul><ul><ul><li>No dividend : </li></ul></ul><ul><ul><ul><li>value = selling asset value. </li></ul></ul></ul><ul><ul><ul><li>Fixed or random selling date, liquidation ? </li></ul></ul></ul><ul><ul><li>Standard theory : </li></ul></ul><ul><ul><ul><li>Shares give rigth to get dividents. </li></ul></ul></ul><ul><ul><ul><li>A share identified to an infinite sequence of dividends. : d(t). </li></ul></ul></ul><ul><li>Intermediate theories. </li></ul><ul><ul><ul><li>Choice : self finance, distribute dividends. </li></ul></ul></ul><ul><ul><ul><li>Endogenous, logic of dividends, profitability of reinvested funds. . </li></ul></ul></ul><ul><li>Option : </li></ul><ul><ul><li>Standard theory … </li></ul></ul><ul><ul><li>And elementary ….. </li></ul></ul>
  12. 12. The fundamental value-1 <ul><li>Setting : </li></ul><ul><ul><li>Certain dividend, </li></ul></ul><ul><ul><li>Common point expectations on next period price, </li></ul></ul><ul><ul><li>Safe interest rate r </li></ul></ul><ul><li>The basic connection. </li></ul><ul><ul><li>p(t) = {1/(1+r)}{p e (t+1/t) + d(t+1)} </li></ul></ul><ul><ul><li>The asset price depends on its price to-morrow, etc… </li></ul></ul><ul><ul><li>True with uncertainty : </li></ul></ul><ul><ul><li>p(t) = {1/(1+r)}{E (p e (t+1) + E( d(t+1 )} </li></ul></ul><ul><li>The dynamics with common point expectations </li></ul><ul><ul><li>p e (t+1/t) ) = {1/(1+r)}{p e (t+2/t+1) + d(t+2)} … </li></ul></ul><ul><ul><li>p(t) =  t+S t+1 {1/(1+r} T-t {d(T)} + {1/(1+r)} t+S p e (t+S/t+S+1)+d(t+S)}. </li></ul></ul><ul><ul><li>Si for S large, p e (t+S) grows more slowly than (1+r) S, the 2d term tends to zero </li></ul></ul><ul><ul><li>p(t) =  +∞ T=t+1 {1/(1+r} T-t {d(T)} , is the fundmental value. </li></ul></ul><ul><li>Partial equilibrium, common expectations… </li></ul>
  13. 13. Remark on the fundamental value : <ul><li>It is the perfect foresight equilibrium. </li></ul><ul><ul><li>Assume p(t+1)= p e (t+1 ), </li></ul></ul><ul><ul><li>Then, the above formula holds true. </li></ul></ul><ul><ul><li>Also the rational expectations equilibrium .. </li></ul></ul><ul><li>But not the only one … </li></ul><ul><ul><li>Bubble solution : </li></ul></ul><ul><ul><li>p(t)+ Δ , p(t+1)+(1+r) Δ , …p(t+t’)+(1+r) t’ Δ , is also a solution. </li></ul></ul><ul><li>It is a locally SREE . (« eductively stable ») </li></ul><ul><ul><li>It is CK that p (t+S) and d(t+S) grow less quickly than (1+r) S : </li></ul></ul><ul><ul><ul><li>p(t+S)  I, I/ (1+r) S «small », for some S when </li></ul></ul></ul><ul><ul><ul><li>d (t+S)<D, D/(1+r) S </li></ul></ul></ul><ul><ul><li>Argument </li></ul></ul><ul><ul><ul><li>p(t+S-1)  I/(1+r) +d(t+S)/(1+r)….. </li></ul></ul></ul><ul><ul><ul><li>p(t+S-2)  I/(1+r) 2 +d(t+S-1)/(1+r) +d(t+S)/(1+r) 2 </li></ul></ul></ul><ul><ul><li>It is almost CK that p(t) =valeur fondamentale . </li></ul></ul><ul><li>Stochastic version. </li></ul><ul><ul><li>p (t+S) and d(t+S) grow < than (1+r) S , p(t+S)  I </li></ul></ul>
  14. 14. The fundamental value : other formulaS.. <ul><li>The kernel : </li></ul><ul><ul><li>p(t) =  +∞ T=t+1 {1/(1+r} T-t {E( d(T ))} </li></ul></ul><ul><ul><li>Price equals the expectation of the fundamental value. </li></ul></ul><ul><li>Illustrations. d eterministic case. </li></ul><ul><ul><ul><li>Dividends grow at the rate g </li></ul></ul></ul><ul><ul><ul><li>P(t) = d(0)(1+g) t /(r-g) =d(t)/(r-g). </li></ul></ul></ul><ul><ul><ul><li>g=0 </li></ul></ul></ul><ul><li>Comments. </li></ul><ul><ul><li>r increases, P decreases : intuition. </li></ul></ul><ul><ul><li>If r=0,05, g=0,02, p =33 times the dividend, </li></ul></ul><ul><ul><li>Si g=0,03, 50 fois, si g=0,04, 100, si 0,01, 25 times. </li></ul></ul><ul><ul><li>Sensitivity to forecasts . </li></ul></ul><ul><li>Illustrations : stochastic dvidends iid </li></ul><ul><ul><ul><li>d(t) = d +  ;  zero mean, finite variance. </li></ul></ul></ul><ul><ul><ul><li>p(t) = d /r, price constant. </li></ul></ul></ul>
  15. 15. The fundamental value : other formulaS.. <ul><li>The kernel : </li></ul><ul><ul><li>p(t) =  +∞ T=t+1 {1/(1+r} T-t {E( d(T ))} </li></ul></ul><ul><ul><li>Price equals the expectation of the fundamental value. </li></ul></ul><ul><li>Illustrations : stochastic case b : </li></ul><ul><ul><li>d(t) = d +a ( d(t-1) - d ) +  </li></ul></ul><ul><ul><li>p(t) = d /r + a( d(t)- d )/(1+r- a), a =1, 0 </li></ul></ul><ul><li>Markov Chain : </li></ul><ul><ul><li>d takes two values, h, b=0, </li></ul></ul><ul><ul><li>Markov transition, c probab. Change. « ergodic » prob. : P =(1/2, 1/2) </li></ul></ul><ul><ul><li>P(t) two values Markov chain Stationary. </li></ul></ul><ul><ul><li>support between 0 et (h/r), fluctuates like dividends. </li></ul></ul>
  16. 16. Complexification. <ul><li>More complex processes. </li></ul><ul><ul><li>ARMA, etc… </li></ul></ul><ul><ul><li>May depend on the past. </li></ul></ul><ul><li>Asymetric information ? </li></ul><ul><ul><li>« Smart et noisy traders », ..(Campbell, Shiller..) </li></ul></ul><ul><ul><li>Smart infinitely lived </li></ul></ul><ul><ul><li>Dividends sum of Brownian and AR1, </li></ul></ul><ul><ul><li>P(t) = VF(t) –h/(r-g) + y(t). </li></ul></ul><ul><li>Common property : </li></ul><ul><ul><li>Price fluctuate less than reconstituted fundamental value !! </li></ul></ul><ul><ul><li>v(t) =  T=t+1 {1/(1+r} T { d(T ))} </li></ul></ul><ul><ul><li>P(t) = E( v(t )), v(t)=p(t)+e(t), Var(p)<Var(v), ergodicity </li></ul></ul>
  17. 17. Illustrations. <ul><li>Prices.- </li></ul>prix 4 cas1 t prix Cas 2 Cas 3 Cas 4
  18. 18. Risky assets <ul><li>Valuation of a risky asset. </li></ul><ul><ul><li>q(j)/q(0) = [1/(1+r)][  s A(j,s) P(s)], </li></ul></ul><ul><ul><li>P(s) =  (s)/   (s)  is the «  risk-neutral probability  ».. </li></ul></ul><ul><ul><li>Price = expectations of the discounted value of incomes </li></ul></ul><ul><ul><ul><li>with corrected probabilities. </li></ul></ul></ul><ul><ul><ul><li>(probability marginal utility of income). </li></ul></ul></ul><ul><ul><li>Hence take corrected probability of the fundamental value… </li></ul></ul><ul><li>Relative valuation of assets : (CAPM) </li></ul><ul><ul><li>[(ER(j) – (1+r)] = [E(R(  *)-(1+r)][Cov[(R(  *),R(j)]/[Var (R(  *)] </li></ul></ul><ul><ul><li>* is the market portfolio. … </li></ul></ul><ul><li>A stock return. </li></ul><ul><ul><li>q= E ( A )/(1+r) – [Cov( A,c(m )]/ [(1+r)T(.)]. </li></ul></ul><ul><li>Market efficiency and asymetric information. </li></ul>
  19. 19. The theory of fundamental value and its predictions. <ul><li>The evolution of prices Les prix et leur évolution: </li></ul><ul><ul><li>1-A: 2 firms with the same flow of dividends have equal value. </li></ul></ul><ul><ul><li>1-C : The risk premium is reasonable….. </li></ul></ul><ul><ul><li>1-D : Statistical evolution : prices vary less than the reconstitued fundamental value.. </li></ul></ul><ul><ul><li>1-E : No bubble. </li></ul></ul><ul><li>Prix, information et stratégies des acteurs. </li></ul><ul><ul><li>2-A : No information in to-day prices ? </li></ul></ul><ul><ul><li>2-B : You cannot beat the market (ovm) </li></ul></ul><ul><ul><li>2-C : No (public) information to beat the market. </li></ul></ul><ul><ul><li>2-E : Crash : a lot of information . . </li></ul></ul><ul><li>The stock market and the firm. </li></ul><ul><ul><li>3-A : appropriate valuation. </li></ul></ul><ul><ul><li>3-B : good Signal for investment. </li></ul></ul><ul><ul><li>3-B « Discipline  » </li></ul></ul>
  20. 20. 1-A : Price Difference and equal fundamental value.
  21. 21. 1C: Unreasonable risk premium ? <ul><li>1-C :The risk premium is reasonable </li></ul><ul><ul><li>US (1889-1978) </li></ul></ul><ul><ul><li>3 variables </li></ul></ul><ul><ul><li>Real return of stocks (SP 500) : 7% ( R s ) </li></ul></ul><ul><ul><li>Real return of safe bonds : 1% ( R s ) </li></ul></ul><ul><ul><li>Per capita consumption growth : 1,8% / an ( c t +1 / c t ) </li></ul></ul><ul><li>Cov( Rs , ct +1 / ct ) > 0 </li></ul>
  22. 22. 1-C : (Equity Premium Puzzle, EPP) <ul><li>US 1889-1978) </li></ul><ul><li>3 variables </li></ul><ul><ul><li>Real return of stocks (SP 500) : 7% ( R s ) </li></ul></ul><ul><ul><li>Real return of safe bonds : 1% ( R s ) </li></ul></ul><ul><ul><li>Per capita consumption growth : 1,8% / year ( c t +1 / c t ) </li></ul></ul><ul><li>Puzzle (Mehra-Prescott 1985) </li></ul><ul><ul><li>Incompatible with standard behaviour under risk. </li></ul></ul><ul><ul><li>Risk aversion and time preference. </li></ul></ul><ul><ul><li>Cov( R s , c t +1 / c t ) > 0, but small, justifies a small risk premium with iso-elastic utility and standard preferences. </li></ul></ul>
  23. 23. 1D, 2C – Other predictions <ul><li>1-D : Prices vary less than reconstitued fundamental values. </li></ul><ul><li>2-B : You cannot beat the market (ovm) </li></ul><ul><li>2-C : No public information to beat the market. </li></ul><ul><li>1-C : No bubble. </li></ul><ul><ul><li>Tulip mania </li></ul></ul><ul><ul><li>Internet bubble. </li></ul></ul><ul><li>2-E : Crash : a lot of information. </li></ul><ul><li>Doubts </li></ul><ul><ul><li>Crisis , Law… </li></ul></ul><ul><ul><li>1929, Crash 1987 </li></ul></ul><ul><ul><li>Change Crises. </li></ul></ul>
  24. 24. 2-D : Objections to « efficiency ».
  25. 25. Excess volatility puzzle. <ul><li>The diagram </li></ul><ul><ul><li>observed prices : 1860 to-day. </li></ul></ul><ul><ul><li>Fundamental values reconstituted. </li></ul></ul><ul><ul><ul><li>With several assumptions on the discount rate… </li></ul></ul></ul><ul><ul><ul><li>Or on future dividends. </li></ul></ul></ul><ul><li>Prices vary more than reconstituted f undamental values. </li></ul>
  26. 26. No bubble… <ul><li>The tulip mania ; </li></ul><ul><ul><li>Feb. 1637 : </li></ul></ul><ul><ul><ul><li>Bulb = 20 times a yearly craftsman income. </li></ul></ul></ul><ul><ul><ul><li>5 ha land. </li></ul></ul></ul><ul><ul><li>Facts.. </li></ul></ul><ul><li>Explanations. </li></ul><ul><ul><li>Law/ possibility of cancelllation of future contracts… </li></ul></ul>200 12-11 03-02
  27. 27. Others <ul><li>Internet Bubble… </li></ul><ul><ul><li>2001 </li></ul></ul><ul><li>Crashes. </li></ul><ul><ul><li>1929. </li></ul></ul><ul><ul><li>1987 </li></ul></ul><ul><ul><li>2008…. </li></ul></ul>
  28. 28. Aller plus loin ou abandonner le paradigme ….. <ul><li>La première option </li></ul><ul><ul><li>Garder l’hypothèse d’anticipations rationnelles </li></ul></ul><ul><ul><li>Tester encore version savante étendue: horizon court, multiplicité. </li></ul></ul><ul><ul><li>Introduire une dose limitée de « rationalité limitée ». </li></ul></ul><ul><ul><ul><li>Rationalité non standard :neu </li></ul></ul></ul><ul><ul><ul><li>Myopie, … </li></ul></ul></ul><ul><li>La seconde option : </li></ul><ul><ul><li>Rationalité limitée plus radicale au niveau individuel. </li></ul></ul><ul><ul><li>Ou au niveau collectif : test de la plausibilité de l’équilibre…. </li></ul></ul><ul><ul><ul><li>Divinatoire : conséquence de CK du modèle et de la rationalité), Mise en cause de la « rationnalisabilité » de l’équilibre. </li></ul></ul></ul><ul><ul><ul><li>Évolutive; </li></ul></ul></ul><ul><li>Première option : une galerie de phénomènes compatibles </li></ul><ul><ul><li>Fluctuations « erratiques » des cours. </li></ul></ul><ul><ul><li>Comportement « moutonnier » d’imitation… </li></ul></ul><ul><ul><li>Krachs de « multiplicité ». </li></ul></ul><ul><ul><li>Bulles en information asymétrique. </li></ul></ul><ul><ul><li>Bulles avec agents « irrationnels ». </li></ul></ul>

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