Stock Price Behavior. Stock Price Behavior

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1 Major Topics Statistical Properties Volatility Cross-Country Relationships Business Cycle Behavior Page 1 Statistical Behavior Previously examined from theoretical point the issue: To what extent can the past history of a common stock s price be used to make meaningful predictions of its future price? Page 2 Page 1

2 Concluded from weak-form efficiency that stock prices follow a random walk process The future path of the price level of a security is no more predictable than the path of a series of randomly generated numbers Statistically, successive price changes are independent, identically distributed random variables» Series of price changes have no memory Page 3 Hypothesized components of random walk theory Successive price changes are independent The price changes conform to some probability distribution Page 4 Page 2

3 Hypotheses (Continued) Independence» The probability distribution for price changes during period t is independent of the sequence of changes during previous periods» Can never have perfect independence so theory cannot be completely accurate description of reality There is some level of dependence in the real economic world Page 5 Hypotheses (Continued) Independence (Continued)» What may lead to dependence? Dependence in noise generating process or in process generating new information May lead to dependence in successive price changes Page 6 Page 3

4 Hypotheses (Continued) Independence (Continued)» Even if there are dependencies, there may be offsetting market mechanisms that still induce independence Some traders may be better at predicting appearance of new information and incorporate it into prices Some may be better at statistical analysis Page 7 Hypotheses (Continued) Independence (Continued)» Issue What is the minimal acceptance level of dependence? Page 8 Page 4

5 Hypotheses (Continued) Distribution» Merely states that price changes conform to some distribution» The general theory of random walks states that the form or shape of the distribution need not be specified Any distribution is consistent with the theory as along as it correctly characterizes the price change process Page 9 Hypotheses (Continued) Distribution (Continued)» Form of distribution is important, however, for investors because it is a major factor in determining the riskiness of an investment in common stocks» Form also important for academic work and for statistical work such as done by Wall Street financial analysts Page 10 Page 5

6 Empirical Evidence Independence» Numerous tests for all different time intervals (hourly, daily, monthly) show that amount of dependence is extremely slight or non-existent» Conclusion: the independence assumption of the random walk model seems to be adequate description of reality Page 11 Empirical Evidence (Continued) Independence (Continued)» Implication When successive price changes are independent, there can be no technical analysis which makes the expected profits of the investor greater than what would be earned under a buy-and-hold strategy We saw this claim before Page 12 Page 6

7 Empirical Evidence (Continued) Independence (Continued)» Application Mutual funds claim two things They pool funds of many investors to diversify away unsystematic risk Because of the funds management's closeness to the market, they are better able to earn above market profits Page 13 Empirical Evidence (Continued) Independence (Continued)» Application (Continued) First claim probably true given portfolio arguments Second claim can be tested Page 14 Page 7

8 Empirical Evidence (Continued) Independence (Continued)» Application (Continued) Extensive tests have shown that funds in general do no better than the market Individual funds do not seem to do better than their competitors Conclusion: if there really is a sophisticated analyst, he/she has escaped detection Page 15 Empirical Evidence (Continued) Distribution of Price Changes» Previous research has shown that the distribution of price changes are Gaussian normal Gaussian normal is symmetric about the mean with thin tails that asymptotically approach the x-axis Page 16 Page 8

9 Empirical Evidence (Continued) Distribution of Price Changes» More sophisticated techniques have questioned Gaussian normality Empirical distributions of price changes conform better to a stable Paretian distribution Paretian distribution like a normal but with fatter tails that asymptotically approach the x-axis at a much greater value than for the normal Page 17 Empirical Evidence (Continued) Distribution (Continued)» Implication Empirical distribution of price changes has longer tails than normal That is, the empirical distributions have more relative frequency in their extreme tails than under the Gaussian normal Held for every stock tested!! Page 18 Page 9

10 Empirical Evidence (Continued) Distribution (Continued)» Implication (Continued) The combination of independence and Gaussian normality implies that stock price values do not often change by large amounts However, the combination of independence and a stable Paretian distribution implies that values often change by large amounts during very short periods Page 19 Empirical Evidence (Continued) Distribution (Continued)» Implication (Continued) Large changes are observed consistent with independence and a stable Paretian distribution These abrupt changes imply that the market is riskier than a Gaussian market The variability of a given expected return is higher than in a Gaussian market Page 20 Page 10

11 Empirical Evidence (Continued) Distribution (Continued)» Implication (Continued) Probability of large gains/losses is greater than in a Gaussian market Page 21 Empirical Evidence (Continued) Distribution (Continued)» Implication (Continued) At the same time, speculators cannot protect themselves from large losses by a stop-loss order once market starts to fall. Once market starts to fall, it will fall rapidly and impossible to carryout stop-loss at intermediate prices Page 22 Page 11

12 Volatility Simple model to interpret stock price index movements Real stock prices equal present value of rationally expected or forecasted future real dividends discounted by a constant real discount rate» Sudden movements in stock prices attributed to new information about future dividends This is Efficient Markets Hypothesis Source: R.J. Shiller, AER, 6/81, p. 421 Page 23 Volatility (Continued) Can model stock prices as 0 E( D P i ) D S E rf i i = = i 1 1+ i 1 1+ rf i = = ( ) = ( ) Define forecast error so that * ( S) E P * 0 PS = PS + ε Forecast Actual Error Page 24 Page 12

13 Volatility (Continued) Then, assuming independence, taking variances, we have Var ( P * ) = Var ( P ) + S 0 2 S σ Page 25 Volatility (Continued) Therefore Conclusion: the variance of rationally derived expected stock prices is greater than the variance of actual stock prices Based on EMH * Var( PS ) > 0 Var( PS ) Page 26 Page 13

14 Volatility (Continued) Intuitive appeal Forecasts always have larger variances, especially the further out they are from today Page 27 Volatility (Continued) Problem: actual stock prices seem too volatile relative to projections Too much volatility to be rationally attributed to objective new information Movements seem too big relative to actual subsequent events Seem to contradict EMH Page 28 Page 14

15 Volatility (Continued) Stock Price Graph Here Page 29 Volatility (Continued) Insight from stock price graph Ex Post rational prices smooth while actual prices are volatile Real dividends did not vary greatly over this period to cause erratic movements in actual prices Is EMH in trouble? Possible answer lies with real interest rate as discount factor Page 30 Page 15

16 Volatility (Continued) What are principal factors influencing interest rate volatility of equities? Studies show these factors are:» Firm s cash flows» Amount and nature of the debt in the firm s capital structure» Degree to which cash flows covary with inflation and real interest rates Page 31 Volatility (Continued) Firm s cash flows Cash flows are at least to some extent indexed against inflation» Suppose interest rates rise due to an increase in expected inflation Effect on equity values partially offset by an increase in expected profit Equities are by no means a perfect hedge against inflation A better hedge than nominal bonds, however Page 32 Page 16

17 Volatility (Continued) Debt structure If the firm holds many forward contracts allowing it to borrow at a fixed rate, its stock will be less adversely or evenly favorably affected by a rise in interest rates relative to a firm that relies entirely on floating rate finance Page 33 Volatility (Continued) Earnings and interest rates Some firms (e.g., banks) have earnings that are positively related to interest rates» As rates rise, earnings rise and this offsets to some extent the increase in the discount rate Would expect financial firms to be partially hedged against interest rate changes Page 34 Page 17

18 Cross-Country Relationships TBW Page 35 Business Cycle Behavior Movement of stock and bond prices over course of business cycle important for investment decisions Rational investor will not invest when prices can be expected to fall What are the patterns of prices during expansions and contractions? Page 36 Page 18

19 Business Cycle Behavior (Continued) Business Cycle Plot of Stock Price Page 37 Business Cycle Behavior (Continued) Stock prices usually fall during recessions and rise during expansions Few sustained or substantial swings in stock prices that have not been closely associated with swings in the business cycle Page 38 Page 19

20 Business Cycle Behavior (Continued) Turn in stock prices usually occur prior to turn in business cycle Stock prices are a leading indicator» The average lead is 5-6 months but with wide variations Page 39 Business Cycle Behavior (Continued) Patterns At peak of business cycle» Stock prices usually declining for several months At trough of business cycle» Stock prices have usually already started to rise Page 40 Page 20

21 Business Cycle Behavior (Continued) Pattern explanations Stock prices function of profit expectations (reflected in dividends) and interest rates During late stages of business cycle expansion, level or rate of growth of profits, profit margins, new orders decline» Declines are harbingers of declining earnings» Expectations of earnings decline so stock prices fall before downturn in general business Page 41 Business Cycle Behavior (Continued) Pattern explanations (Continued) Profits and stock prices do not turn at precisely the same time but the tendency is clearly in that direction» Reasonable to suppose that promptly available information and astute guesses about profit trends would influence the market Would help to account for propensity to lead the business cycle Page 42 Page 21

22 Business Cycle Behavior (Continued) Pattern explanations (Continued) At late stages of expansion, money supply and credit tighten forcing up interest rates which lowers capital values» Investment in plant & equipment falls making common stock a less attractive security to hold» Higher rates also impact cost of doing business Inventory carrying costs Accounts receivable Page 43 Review Questions Page 44 Page 22

23 Key Concepts and Terms Page 45 Suggested Readings Page 46 Page 23