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Market hypotheses
- 1. Market Hypotheses and Models
- 2. The Five Pillars 2 Nobel Prize winner and former Univ. of Chicago professor, Merton Miller, published a paper called the “The History of Finance” Miller idenDfied five “pillars on which the field of finance rests” These include 1. Miller-‐Modigliani ProposiDons • Merton Miller 1990 and Franco Modigliani 1985 2. Capital Asset Pricing Model • William Sharpe 1990 3. Efficient Market Hypothesis • Eugene Fama 2013 Paul Samuelson, Harry Roberts, Benoit Mandelbrot 4. Modern PorWolio Theory • Harry Markowitz 1990 5. OpDons • Myron Scholes and Robert Merton 1997
- 3. Hypotheses and Models ¨ Explanations of phenomenon ¤ Hypothesis n A proposed explanation for a phenomenon ¤ Law n Statement of cause and effect without explanation n Newton’s Universal Law of Gravitation ¤ Theory n A well-established explanation for a phenomenon n Einstein’s theory of gravity ¨ A model is a mathematical or physical representation of a phenomenon’s hypothesis, theory, or law ¤ The “Bohr atomic model” ¤ Newton’s inverse square law of gravity ¤ Einstein’s Theory of General Relativity 3 2 21 r mm GF ⋅ ⋅=
- 4. The Efficient Market Hypothesis Market price is different but related to our earlier concepts of book value and fair value ¤ Book value from accounDng ¤ Fair value for discounted cash flow ¤ How do prices emerge from market dynamics ? “A market in which prices always fully reflect available informaDon is called efficient.” Prof. Eugene Fama University of Chicago 4
- 5. EMH Commentary “There is an impressive body of empirical evidence which indicates that successive price changes in individual common stocks are very nearly independent. Recent papers by Mandelbrot and Samuelson show rigorously that independence of successive price changes is consistent with an ‘efficient’ market i.e., a market that adjusts rapidly to new informaDon.” Fama, Fisher, Jensen, and Roll, “The Adjustment of Stock Prices to New InformaDon”, Interna>onal Economic Review, Feb. 1969. 5
- 6. EMH Commentary “I believe there is no other proposiDon in economics which has more solid empirical evidence supporDng it than the Efficient Market Hypothesis. That hypothesis has been tested and, with very few excepDons, found consistent with the data in a wide variety of markets: the New York and American Stock Exchanges, the Australian, English, and German stock markets, various commodity futures markets, the Over-‐the-‐Counter markets, the corporate and government bond markets, the opDon market, and the market for seats on the New York Stock Exchange.” Prof. Michael Jensen Some Anomalous Evidence Regarding Market Efficiency, 1978 6
- 7. EMH Commentary “ … the Efficient Markets Hypothesis (EMH), one of the most controversial and well-‐studied proposiDons in all the social sciences. It is disarmingly simple to state, has far-‐reaching consequences for academic pursuits and business pracDce, and yet is surprisingly resilient to empirical proof or refutaDon. Even aker three decades of research and literally thousands of journal arDcles, economists have not yet reached a consensus about whether markets -‐ parDcularly financial markets -‐ are efficient or not.“ Prof. Andrew Lo, MIT, 1997 7
- 8. EMH Commentary 8 “If the market is efficient, prices will only change when new, unanDcipated informaDon is released to the market. Since unanDcipated informaDon is as likely to be good or bad, the resulDng movement in stock prices is random … the probability that stocks will go up or down is completely random and cannot be predicted. Prof. Jeremy Seigel Stocks for the Long Run, 2002
- 9. EMH Commentary “The more efficient the market, the more random the sequence of price changes generated by the market, and the most efficient market of all is one in which price changes are completely random and unpredictable.” Campbell, Lo, MacKinlay The Econometrics of Financial Markets, 1997 9
- 10. ImplicaDons of the EMH • “Always fully reflected” implies that all new informaDon is immediately reflected in the price • InformaDon drives supply and demand for a security • But what is ‘informaDon’ ? What is noise? What informaDon is relevant? • Type of informaDon • Technical informaDon • Prices, volume, correlaDon, volaDlity • Fundamental informaDon • Free cash flow growth, cost of capital • Public and private informaDon • Might imply that informaDon is ra>onally reflected, but doesn’t define ra>onal other than maybe as a tautology • Arguable of course 10
- 11. ImplicaDons of the EMH ¨ Markets are almost surely ‘complex systems’ ¤ Laws or general theories of markets seem improbable n Other than the “law of one price” ¤ Markets might be modeled as complex systems to gain insights ¨ Market research remains focused on ¤ hypotheses and tesDng and ¤ models that provide some predicDve value ¨ The previous commentary indicates ¤ Hypotheses have not become theories ¤ Standard pricing models are stochasDc 11
- 12. EMH Discussion • How can a result emerging from a complex system be defined as ‘correct’ ? • How can a random variable in a stochasDc system be defined as ‘correct’ ? • Maybe the price is the fair value plus or minus some standard deviaDon ? • Common mis-‐interpretaDons of the EMH • Prices are always ‘correct’ or ‘correctly’ reflect ‘value’ • Investors should ‘buy and hold’ a stock • The NYSE and the NASDAQ are efficient markets • Price change rates in an efficient market are not predictable which means the rates are uncorrelated, but not necessarily independent • The EMH does imply that a trading strategy will not consistently outperform a buy and hold strategy 12
- 13. Example Mis-‐interpretaDons The EMH says something very simple, which is that shares are always correctly priced. p. 57. The EMH states that every security’s price equals its investment value at all Dmes. p. 204 If markets are efficiently priced, then shares must always be at fair value and it follows that there can be no difference between price and value. p. 59. Andrew Smithers, Wall Street Revalued, 2009. 13
- 14. EMH TesDng: Original Taxonomy ¨ Prices are informa>on efficient with respect to what informa>on? ¨ ”The 1970 review divides work on market efficiency into three categories: ¤ (1) weak-‐form tests n How well do past returns predict future returns?, ¤ (2) semi-‐strong form tests n How quickly do security prices reflect public informaDon announcements?, ¤ (3) strong-‐form tests n Do any investors have private informaDon that is not fully reflected in market prices?” ¨ Note that there is no menDon of “correct price” or “price equal to (fair) value” in any test Prof. Eugene Fama, 1991 14
- 15. EMH TesDng: Updated Taxonomy ¨ “Instead of weak-‐form tests, which are only concerned with the forecast power of past returns, the first category now covers the more general area of tests for return predictability … ¨ For the second and third categories, I propose changes in Dtle, not coverage. ¤ Instead of semi-‐strong form tests of the adjustment of prices to public announcements, I use the now common Dtle, event studies. ¤ Instead of strong-‐form tests of whether specific investors have informaDon not in market prices, I suggest the more descripDve Dtle, tests for private informa>on.” ¨ Note that there is no menDon of “correct price” or “price equal to (fair) value” in any test Prof. Eugene Fama, 1991 15
- 16. Event Studies 16 hpp://freerisk.org/wiki/index.php/Efficient-‐markets_hypothesis
- 17. EMH Models ¨ The core EMH certainly implies that ¤ Markets are informaDon efficient ¤ Security prices immediately include all informaDon n There are no people issues like over-‐reacDon, irraDonality, inapenDon, ¤ Rates of return are unpredictable ¤ But rates of return are not necessarily independent n Rates of return are uncorrelated n Rate of return volaDliDes (and other funcDons of rate) may be correlated ¤ If randomness of new informaDon is expected to be ‘symmetric’, then the best esDmate of the ‘next’ price is the previous price n This view holds at least in the short run where price or rate ‘trend’ is insignificant ¨ The EMH does not clearly state that markets are alloca>on efficient ¤ It is not certain that informaDon efficiency necessitates allocaDon efficiency ¤ We’ll consider this issue subsequently 17
- 18. MarDngale Process ¨ The standard model for security price, S, in an informaDon efficient market is a mar>ngale stochasDc process ¤ Simple return rates ¤ Natural log return rates ¤ represents all informaDon available through period i-‐1 ¤ The condiDonal expected price at the end of period i is the price at the end of period i-‐1 ¨ The condiDonal expected return rate during period i is zero ¤ The actual return rate during period i is most likely not zero ¨ Prof. Paul Samuelson first used the marDngale model for the EMH in 1965 18 ( ) [ ] [ ] 0... I ,I | rE S... ,I ,I | S E r1SS 2i1i-‐i1i-‐2i1i-‐ii1i-‐i ==+⋅= −− ( ) ( ) ( )[ ] ( ) [ ] 0... I ,I | vE Sln... ,I ,I | Sln E vSlnSln 2i1i-‐i1i-‐2i1i-‐ii1i-‐i ==+= −− 02i1i-‐ I..., ,I ,I − Si-‐1 Si Period i ΔSi Ii vi ri
- 19. MarDngale Process ¨ Return rate processes are not necessarily sta>onary ¤ StaDsDcs of rates not necessarily constant over Dme ¤ The distribuDon of rates over Dme is not necessarily IID ¨ The sequence of return rates does represent a fair game ¨ The EMH weak form (with simple rates) can be modeled as ¨ This model has value regarding the tesDng of the EMH but liple value in decision making ¤ Define the rate process (not just characterize it) and ¤ Define the probability distribuDon of rates 19 ( ) [ ] [ ] 0... S ,S | rE S... ,S ,S | S E r1SS 2i1i-‐i1i-‐2i1i-‐ii1i-‐i ==+⋅= −−
- 20. Random Walk Process ¨ A first step towards a useful model is to define the rate process as staDonary and the rate distribuDon to be IID/ FV ¤ This does specify that rates and funcDons of rates are uncorrelated – so this restricts the EMH ¨ The process is a (1-‐D) random walk ¨ This is sDll insufficient so we’ll further assume that the distribuDon is characterized by two staDsDcs, mean A and standard deviaDon, B ¨ Also assume for now -‐ no trend, so the mean rate is zero 20 Karl Pearson [ ] [ ]1,0IIDε BεSS B ,0IID~SΔ SΔSS iiii 2 i i1i-‐i =⋅+= +=
- 21. Brownian MoDon ¨ Now following tradiDonal approaches, its reasonable to try a normal distribuDon as the IID/ FV distribuDon ¤ IID/ FV rates do sum to a normal distribuDon ¤ Historical rates have a ‘normal appearance’ n Unimodal n ExponenDal tails ¤ Prices may in fact follow a diffusion process ¨ Again ignoring a rate trend ¨ Louis Bachelier first modeled security prices as Brownian moDon, Univ. of Paris 1900 21 [ ] [ ]1,0Nz BzSS B ,0N~SΔ SΔSS iiii 2 i i1i-‐i =⋅+= +=
- 22. Brownian MoDon 22 Note the negaDve prices AUY weekly standard deviaDon, B = $0.66, S0 = $2.27, 10,000 52 week simulaDons [ ]1,0Nz BzSS ii1i-‐i =⋅+=
- 23. Geometric Brownian MoDon ¨ Stock price models are actually rate based and simplest when using natural log rates of return ¨ The model in discrete Dme with no mean return rate (no drik) is ¨ Geometric Brownian moDon (GBM) results in a lognormal distribuDon in price. 23 ( ) ( ) [ ] [ ]2 s,0Nv 2 i1i-‐i e~e s,0N~v vSln Sln += [ ] i 2 zs 1ii s,0N 1i i eSS e~ S S ⋅ − − ⋅= This is not an exact soluDon for price S
- 24. Geometric Brownian MoDon 24 AUY weekly standard deviaDon rate, s = 7.283%, S0 = $2.27, 10,000 52 week simulaDons [ ]1,0Nz eSS i zB 1ii i =⋅= ⋅ −
- 25. The RaDonal Market Hypothesis “One of the central tenets of modern financial economics is the necessity of some trade off between risk and expected return, and although the marDngale hypothesis places a restricDon on expected returns, it does not account for risk in any way. If an asset’s expected price change is posiDve, it may be the reward necessary to apract investors to hold the asset and bear the associated risks. Therefore despite the intuiDve appeal that the fair game interpretaDon might have, it has been shown that the marDngale property is neither necessary nor sufficient condiDon for raDonally determined asset prices. “ Campbell, Lo, MacKinlay The Econometrics of Financial Markets, 1997 25
- 26. The RaDonal Market Hypothesis ¨ “A market is efficient with respect to a parDcular set of informaDon if it’s impossible to make abnormal profits (other than by chance) by using the set of informaDon to formulate buy and sell decisions. “ Prof. William Sharpe ¨ “A market is efficient with respect to informaDon set, It ,if it is impossible to make economic profits by trading on the basis of informaDon set [It]. By economic profits, we mean the risk adjusted returns net of all costs. “ Prof. Michael Jensen ¨ “In my view, equity prices adjust to new informaDon without delay and, as a result, no arbitrage opportuniDes exist that would allow investors to achieve above average returns without accepDng above average risk. This hypothesis is associated with the view that stock price movements approximate those of a random walk. If new informaDon develops randomly, then so will market prices, making the stock market unpredictable apart from its long-‐run uptrend.” A Random Walk Down Wallstreet, Prof. Burton Malkiel 26
- 27. Brownian MoDon 27 AUY weekly standard deviaDon, B = $0.66, mean, A= $.0273, S0 = $2.27, 10,000 52 week simulaDons [ ] BzASS BA,N~S i1i-‐i 2 ⋅++=Δ With drik or with a trend represent expected return for taking risk The volaDlity or risk term is superimposed on the trend term -‐$2.00 $0.00 $2.00 $4.00 $6.00 $8.00 $10.00 $12.00 0 4 8 12 16 20 24 28 32 36 40 44 48 52 Weeks Note that price can sDll be negaDve
- 28. RMH and Geometric Brownian MoDon ¨ The raDonal market hypothesis (RMH) could be stated exactly as the EMH with the interpretaDon that efficient markets are informaDon efficient and allocaDon efficient in that price is the best representaDon of value ¤ AllocaDon efficiency requires the inclusion of a risk – return model defining a posiDve mean expected return – but which risk – return model ? CAPM ? ¤ Oken described as a joint hypothesis ¤ Its this joint hypothesis or raDonal market hypothesis that makes verificaDon perhaps impossibly difficult ¤ Using the notaDon from an earlier chapter ¤ GBM is the standard price model and is based on the raDonal market hypothesis 28 ( ) ( ) [ ] [ ]2 B,ANv 2 i1i-‐i e~e B,AN~v vSln Sln += [ ] i 2 zBA 1ii B,AN 1i i eSS e~ S S ⋅+ − − ⋅= This is not an exact soluDon
- 29. Geometric Brownian MoDon ¨ In the chapter on “Dynamic Equity Price” ¨ This is the standard market model, but is more restricDve than the EMH ¨ Model parameters ¤ u: expected mean return maybe from CAPM ¤ s, ρ, β: from historical data 29 ( ) ( ) [ ] [ ]2 s,uNv 2 i1i-‐i e~e s,uN~v vSln Sln += [ ] i 2 zsu 1ii s,uN 1i i eSS e~ S S ⋅+ − − ⋅= This is not an exact soluDon
- 30. Geometric Brownian MoDon 30 AUY weekly standard deviaDon rate, s = 7.283%, mean rate, u=.444%, S0 = $2.27, 10,000 52 week simulaDons szu 1ii i eSS ⋅+ − ⋅=
- 31. EssenDal Concepts ¨ This secDon focuses on the funcDoning of securiDes markets and the securiDes prices that emerge. This is a different perspecDve than security book and fair value. But market based variables e.g., cost of capital are included in fair value DCF calculaDons. ¨ The EMH states that markets are informaDon efficient and that security prices are unpredictable since they’re driven by randomly arriving informaDon. An important implicaDon is that investors cannot successful trade a security over the long run. ¨ The model best represenDng the EMH is the marDngale, but has no value to decision making ¨ The GBM is much more restricDve than the EMH and does have value to investors – but its certainly imperfect 31 Market – Price DescripDons • Laws • Law of One Price • Theories • Hypotheses • Efficient Market Hypothesis • RaDonal Market Hypothesis • Fractal Market Hypothesis StaDonary StochasDc Models (IID/FV) • Random Walk • Brownian MoDon • Geometric Brownian MoDon Non-‐StaDonary (not IID/FV) StochasDc Models • MarDngale • Can include IID/FV • Sub-‐marDngale • Can include IID/FV • ARCH • Correlated volaDlity • Levy Stable • Fat tails, skew, and kurtosis
- 32. Links ¨ Bachelier ¨ Bachelier ¨ Mandelbrot 32