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**Money, Banking & Finance Lecture 2**

The Stock Market, Rational Expectations and Efficient Markets

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**Aims Explain the theory of valuing stocks.**

Explore how expectations influence affect the value of stocks. Understand the theory of rational expectations Understand the concept of the Efficient Markets Hypothesis

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Common Stock Common stock is the principal way that listed companies raise equity capital. Common stock holders have an ownership interest in the enterprise in the form of a bundle of rights. The right to vote at the AGM. The right to be the residual claimant of all cash flows into the company. The right to sell stock. Dividends are paid quarterly or six monthly

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One period valuation An analyst makes a forecast for the price of a particular stock. Does the current price accurately reflect the Analysts forecast? Need to discount the expected future cash flow. This is a one-period model where P0 = current price of the stock P1 = the price of the stock in the next period D1 = the dividend paid at the end of next period. ke = required return on investments in equity

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One period valuation

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**Generalised dividend valuation model**

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Dividend Model The price of a stock depends only on the discounted flow dividend payments. Some don’t pay out a dividend and so the valuation is based on the expectation of dividends to be paid out some time. Some stock are zero dividend stocks. Valuation is based on expected capital gain.

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Dividend growth Valuation of stocks is based on expected dividend stream Difficult to estimate. Many companies aim to increase dividends at a constant stream each year. Let g = the expected constant growth in dividends.

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Gordon growth model

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**Gordon growth model continued**

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**Assumptions and Implications**

Dividends are assumed to continue growing at a constant rate forever. The growth rate is assumed to be less than the required return on equity. We can see how this model can be applied to the setting of stock prices. Let expected dividend payout next year be £2 per share. Market analysts expect firm growth to be 3% but there is uncertainty about the constancy of the dividend stream. To compensate for the higher risk the required rate of return is 15% for investor A Investor B has researched industry insiders and is more confident and therefore has a required rate of 12%. Investor C has inside information and feels that 10% is acceptable to compensate for risk.

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**Stock prices setting Investor A valuation = [2/(.15-.03)]=£16.67**

Investor B valuation = [2/( ]=£22.22 Investor C valuation = [2/( ]=£28.57 If investor A holds stock, he/she would sell it to C. The market price would depend on which investor holds the stock, how much stock and the market orders for the stock.

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Implications Expectations about the firm changes as new information is made available. Expectations of future dividends or growth will affect investor valuations. Interest rates affect the market valuation of stock prices. When interest rates are lowered the rate on bonds (and other safe assets) decline. As these are substitutes to equity, the required return on equities decline also and drive up stock prices. Lower rates also stimulate the economy and help the real economy to expand which also helps firms and raise stock prices.

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Risk and Return Expected return of a share is the sum of the earnings per share and expected percentage capital gain. For example if the current price of a share is 100 and the expected price of the share in one years time is 114 and the dividend is 3. The expected return is [( )/ /100]= 17% But in this exercise the expectation will not be held by all people or the expectation will be state-conditional. A distribution of estimates of expected return will exist based on differing information state contingency

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Expected return

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**Example The current price of a common stock is 100**

State contingency is, good, average, bad Expected future price in each state is, 128,117, 105 respectively Expected dividends are, 7, 3, 0 respectively The state contingent expected returns are; [( )+7]/100=0.35; [( )+3]/100=.2; [( )+0]100=.05. Probability of each state; 0.3, 0.4, 0.3.

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**Expected return over all contingencies**

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**Calculation of expected return and risk**

E(r) = (35%x0.3) + (20%x0.4) + (5%x0.3) = 20% Variance of returns calculation [(35%)2x(0.3) + (20%)2x(0.4) + (5%)2x(0.3)] – (20%)2 = 535 – 400 = 135. Standard deviation = √135 = 11.62% This is an example of three contingencies only

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**Distribution of returns**

Frequency - Return E(r) + Return

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**Expectations Stock price valuation depends on expectations**

But how are expectations formed? One model of expectations formation is the theory of rational expectations. John Muth ‘Expectations will be identical to optimal forecasts (the best guess of the future) using all available information’

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Optimal forecast Rational expectation is the optimal forecast using all the available information but the forecast will not always be right. Why? Each forecast has an error that is given by all the possible outcomes. But it will be an optimal forecast meaning it will be unbiased. Unbiasedness means that there is no bias in any forecast.

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Rational Expectation

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**Implications of RE theory**

1. If there is a change in the way a variable moves, the way in which expectations of this variable are formed will change as well. 2. The forecast errors will on average be zero and cannot be predicted ahead of time.

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**If information set θ changes then expectations of X changes**

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**Forecast errors are on average zero**

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**Concepts of efficiency**

Economics provides concepts of efficiency – allocative and operational efficiency An allocationally efficient market is one where prices are determined where market demand equals market supply. An operationally efficient market is one where transactions costs of moving resources around are zero. Eg: perfect capital markets

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**Efficient Capital Markets**

Efficient markets in finance is less restrictive than the concept of perfect capital markets. In an efficient capital market, prices fully and instantaneously reflect all available relevant information – informationally efficient. A capital market may be informationally efficient but not allocatively or operationally efficient. E.g. imperfect competition (allocatively inefficient) or transactions costs like the proposed Tobin tax (operationally inefficient).

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**Efficient Markets Hypothesis**

Expectations are unobserved and we need expectations of future stock price to calculate expected return. The theory of rational expectations tells us that expectations are the optimal forecasts based on all the available information. The supply and demand for securities will determine an equilibrium price of securities therefore the expected price of stocks will be given by the market equilibrium. The expected return on a security will equal the equilibrium return given by the market conditions for that particular security.

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Weak form efficiency Weak form efficiency – no investor can earn excess returns by developing trading rules based on historical price/returns data. So technical analysis or chartists rules cannot beat the market. All past information is reflected in the spot price of an asset.

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**Semi-strong form efficiency**

No investor can earn excess returns from trading rules based on any publicly available information. Implication is that all publicly available information is fully reflected in the actual asset price. Market reaction to new publicly available information is instantaneous and unbiased. No over- or under-reaction. Fundamental analysis based on publicly available information shouldn’t result in abnormal returns.

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**Strong form efficiency**

No investor can earn excess returns using any information – public or private. Strong form efficiency implies that all information is fully reflected in the price of the asset. Even private information! – Insider trading is ineffective

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**Implication of EMH Let equilibrium return for stock A is 10%.**

The current price Pt is lower than the optimal forecast price Pot+1 so that the optimal forecast return is actually 50%. This has created an unexploited profit opportunity. So investors buy more stock A and drive up the current price relative to expected future price thus lowering the optimal forecast return to equal the equilibrium return. Vice versa if the current price was above the expected future price. In an efficient market all unexploited profits are eliminated. Not all investors have to be informed or have rational expectations for the price to be driven to its equilibrium point.

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**Evidence in favour of EMH**

Empirical studies confirm that stock pickers or mutual fund managers cannot outperform the market over a long period of time. The EMH states that stock prices reflect all available information so that earnings announcements that are already known will not affect stock prices when the announcements are made. Only ‘new’ news causes stock prices to change. Future changes in stock prices should follow a random walk (future changes in prices are unpredictable).

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**Random Walk-assume expected dividend stream is constant**

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Random Walk Since the expectation of Pt conditional on information at time t is simply itself Pt. The difference between expected dividends in t+1 given information at time t and dividends in t+2 given information at time t+1 is ‘new’ news and is therefore unpredictable. Hence its expectation is ZERO.

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Random Walk

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**Empirical evidence against EMH**

Size effect – Empirical studies show that small firms earn abnormal returns over long periods. January effect – studies have confirmed an abnormal price rise from December to January. Market overreaction – over/under shooting following ‘new’ news. Excessive volatility – fluctuations in stock prices are greater than the fluctuations in the fundamentals. Mean reversion – low returns stock tend to be followed by high returns and vice versa. Stocks that have done poorly in the past tend to do better in the future. But the evidence on this is controversial. Lag in effect of ‘new’ news – stock prices do not always react to news instantly. Some evidence of autocorrelation. If capital markets are informationally efficient, why is there so much between people that take different views about the same future.

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Behavioural Finance Doubts about EMH particularly after the stock market crash of 1987 (and probably 2008) have led to the emergence of a new field in finance. Applies psychology, social anthropology and sociology to understand the behaviour of stock markets. One of the arguments of EMH is that unexploited profit is eliminated by knowledgeable investors. For this to happen they must engage in short selling. Short selling – borrowing the stock from brokers and then sell it in the market with the aim of making a profit by buying the stock back at a lower price. Psychologists suggest that people are subject to ‘loss aversion’. They are more unhappy from losses than happy with equivalent gains. Because the potential losses can be huge from short selling in reality short selling occurs only in special circumstances. Psychologists also find that people tend to be overconfident in their own judgements. Overconfidence and social contagion explain the creation of speculative bubbles.

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The final say? “Observing correctly that the market was frequently efficient they [academics, investment professionals, corporate mangers] went on to conclude incorrectly that it was always efficient” Warren Buffet “Economics is not so much the Queen of the social sciences but the servant, and needs to base itself on anthropology, psychology – and the sociology of ideologies” John Kay (FT 7/10/09)

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**Summary The theory of stock market valuation**

Expectations govern the valuation of stocks. Different expectations result in different expected returns and a distribution of expected capital gains. The theory of rational expectations provides a market equilibrium basis for expectations based on available information. The EMH is the application of rational expectations to the securities market.

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