ECON 3303 Ch. 7 notes

The Gordon Growth Model:

P(0) = (D(0)(1+g))/(k(e)-g) = D(1)/(k(e)-g) D(0) = the most recent dividend paid g = the expected constant growth rate in dividends k(e) = the required return on an investment in equity - Dividends are assumed to continue growing at a constant rate forever. - The growth rate is assumed to be less then required return on equity

Rational Behind the Hypothesis

R(of) > R(*) -> P(t) increases -> R(of) decreases R(of) < R(*) -> P(t) decreases -> R(of) increases until R(of) = R(*) - In an efficient market, all unexploited profit opportunities will be eliminated.

Computing the Price of Common Stock

The One-Period Valuation Model: p(0) = (Div(1)/(1+k(e))) + (P(1)/(1+k(e))) P(0) = the current Price of the stock Div(1) = the dividend paid at the end of year 1 k(e) = the required return on investment in equity P(1) = the sale price of the stock at the end of the first period

The Generalized Dividend Valuation Model:

The value of stock today is the present value of all future cash flows. P(0) = (D(1)/((1+k(e))^1)) + (D(2)/((1+k(e))^2)) +...+ (D(n)/((1+k(e))^n)) + (P(n)/((1+k(e))^n)) - if P(n) is far in the future, it will not affect P(0). P(0) = - The price of the stock is determined only by the present value of the future dividend stream.

The Efficient Market Hypothesis: Rational Expectations in Financial Markets (cont'd)

- At the beginning of the period, we know P(t) and C. - P(t+1) is unknown and we must form an expectation of it. - The expected return then is: R(e) = (P(et+1)-P(t)+C)/ P(t) - Expectations of future prices are equal to optimal forecasts using all currently available information so: P(et+1) = P(oft+1) -> R(e) = R(of) - Supply and Demand analysis states R(e) will equal the equilibrium return R(*), so R(of) = R(*).

The Theory of Rational Expectations

- Expectations will be identical to optimal forecasts using all available information. - Even though a rational expectation equals the optimal forecast using all available information, a prediction based on it may not always be perfectly accurate: *It takes too much effort to make the expectation the best possible. * Best guess will not be accurate because predictor is unaware of some relevant information

Application: The Global Financial Crisis and the Stock Market

- Financial crisis that started in August 2007 led to one of the worst bear markets in 50 years - Downward revision of growth prospects: decrease in g - Increased uncertainty: increase in k(e) required return -Gordon model predicts a drop in stock prices

How Valuable are Published Reports by Investment Advisors?

- Information in newspapers and in the published reports of investment advisers is readily available to many market participants and is already reflected in market prices. - Acting on this information will not yield abnormally high returns, on average. - The empirical evidence for the most part confirms that recommendations from investment advisers cannot help us outperform the general market.

How the Market Sets Stock Prices

- Information is important for individuals to value each asset - When new information is released about a firm, expectations and prices change - Market participants constantly receive information and revise their expectations, so stock prices change frequently.

The Efficient Market Hypothesis: Rational Expectations in Financial Markets

- Recall. The rate of return from holding a security equals the sum of the capital gain on the security, plus any cash payments divided by the initial purchase price of the security. R = (P(t+1)-P(t)+C)/ P(t) R = the rate of return on the security P(t+1) = price of the security at time t+1, the end of the holding period P(t) = price of the security at time t, the beginning of the holding period C = cash payment (coupon or dividend) made during the holding period

Why the Efficient Market Hypothesis Does Not Imply That Financial Markets Are Efficient

- Some financial economists believe all prices are always correct and reflect market fundamentals (items that have a direct impact on future income streams of the securities) and so financial markets are efficient. - However, prices in markets like the stock market are unpredictable. This casts serious doubt on the stronger view that financial markets are efficient.

Rationale Behind the Theory

- The incentives for equating expectations with optimal forecasts are especially strong in financial markets. In these markets, people with better forecasts of the future get rich - The application of the theory of rational expectations to financial markets (where it is called the efficient market hypothesis or the theory of efficient capital markets) is thus particularly useful

Behavioral Finance

- The lack of short selling (causing over-priced stocks) may be explained by loss aversion. - The large trading volume may be explained by investor overconfidence. - Stock market bubbles may be explained by overconfidence and social contagion.

Asset Price Bubbles

- The present value model of stock can be applied to any asset. - The price or value of an asset today is the discounted present value of future cash flows (CF) P(0) = (CF(1)/((1+k(e))^1)) + (CF(2)/((1+k(e))^2)) +...+ (CF(n)/((1+k(e))^n)) + (P(n)/((1+k(e))^n)) - Normally P(n) will not affect P(0) because the growth rate in P must be less than (1+k(e)) so as n -> ∞, P(n)/((1+k(e))^n) -> 0 - When this condition is violated we may observe deviations of the current asset price P(0) from its fundamental value implied by the present value relationship. Such deviations of the market price from its fundamental value are called asset price bubbles.

How the Market Sets Stock Prices

- The price is set by the buyer willing to pay the highest price. - The market price will be set by the buyer who can take best advantage of the asset. - Superior information about an asset can increase its value by reducing its perceived risk.

The Efficient Market Hypothesis: Rational Expectations in Financial Markets (cont'd)

- current prices in a financial market will be set so that the optimal forecast of a security's return using all available information equals the security's equilibrium return - In an efficient market, a security's price fully reflects all available information

The One-Period Valuation Model:

- k(e) the required rate of return, will be different for each person based on that individual's preferences. - If Pat is risk averse, an increase in the riskiness of ABC stock will cause Pat's k(e) or required return to rise, Pat needs a greater return to be willing to hold the stock. That in turn will cause Pat to lower the discounted present value of the future cash flows associated with ABC. This ultimately results in Pat reducing the value placed on ABC stock today, P(0) decreases.

Adaptive expectations:

-Expectations are formed from past experience only. -Changes in expectations will occur slowly over time as data changes. -However, people use more than just past data to form their expectations and sometimes change their expectations quickly.

Implications of the Theory

-If there is a change in the way a variable moves, the way in which expectations of the variable are formed will change as well. * changes in the conduct of monetary policy (e.g. target the federal funds rate) -The forecast errors of expectations will, on average, be zero and cannot be predicted ahead of time.

Efficient Market Prescription for the Investor

-Recommendations from investment advisors cannot help us outperform the market -A hot tip is probably information already contained in the price of the stock -Stock prices respond to announcements only when the information is new and unexpected -A "buy and hold" strategy is the most sensible strategy for the small investor

What does the one-period valuation model tell us about asset pricing?

Three things: 1) The higher the expected dividend (or other periodic cash flow payments), ceteris paribus, the higher will be the asset price today. 2) The higher the (expected) future selling price the higher will be the current selling price. 3) the greater the discount factor, k(e) , the lower will be the asset price, ceteris paribus. So the current price P(0) reflects both judgments about future values (expectations) and about risk.

Formal Statement of Theory

X(e) = X(of) X(e) = expectation of the variable that is being forecast X(of) = optimal forecast using all available information - Under rational expectations the expected value is equal to the optimal statistical forecast using all available data. - This means that rational expectations cannot be improved upon given the current information.