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Stock Valuation Models 1. One-Period Valuation Model

Stock Valuation Models 1. One-Period Valuation Model (buy stock,… hold for 1 period,… collect dividend,…sell stock) P 0 = Div 1 + P 1 (1+K e ) (1+K e ) K e = required return on equity investment How is this calculated? Is it the same for everyone? 12-13% historically

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Stock Valuation Models 1. One-Period Valuation Model

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  1. Stock Valuation Models 1. One-Period Valuation Model (buy stock,… hold for 1 period,… collect dividend,…sell stock) P0 = Div1 + P1 (1+Ke) (1+Ke) Ke= required return on equity investment • How is this calculated? • Is it the same for everyone? • 12-13% historically • Function of uncertainty, cash flow risk, monetary policy, alternative asset returns etc….. Solve for Ke = Div1 + P1 - P0 P0 P0

  2. Stock Valuation Models 2. Generalized Dividend Valuation Model Value is present value of all future cash flows P0 = D1 + D2 + … + Dn + Pn (1+Ke)1 (1+Ke)2 (1+Ke)n (1+Ke)n P0 = Swt=1Dt (1+Ke)t (Stock price is determined by P.V of future dividend stream) Must have information about: • Level of Dt+i • Risk of Dt+i

  3. Stock Valuation Models 3. Gordon Growth Model Assume dividends grow at a constant growth rate, g, which is less than Ke P0 = D0 (1+g)1 + D0 (1+g)2 +… (1+Ke)1 (1+Ke)2 Let (1+g) / (1+Ke) = X < 1 P0 = D0 X + D0 X2 + D0 X3 + …. P0 = D0 [X + X2 + X3 + ….] P0 = D0 [X ( 1 + X + X2 + ….)] P0 = D0 [X (1/1-X)] P0 = D0 (1+g) = D1 Ke – g Ke - g

  4. How is PMKT Set? • Different investors have different levels of uncertainty over C.F.(t+1) => different Ke => different prices they are willing to pay. • Investor with lowest perceived risk is willing to pay most => establish PMKT • New info => D expected level and risk of Div(t+1) => DPMKT Information about C.F.(t+1) plays key role in asset pricing  C.F.(t+1) info => buyer discounts C.F.(t+1) at lower Ke =>  PMKT  Uncertainty of Div.(t+1) constancy and estimated growth rate, g, => risk =>  Ke =>  PMKT P0 = D1 Ke - g

  5. How are Expectations Formed? Stock price evaluations = F(C.F.Et+1) Recall,… RE = C + PEt+1 – Pt Pt • Adaptive Expectations(future is average of the past) qEt+1 = (1-l) Swj=0ljqt-j If l is small (0.10), then recent date is more relevant to forecast If l is large (0.90), then distant past is as important as recent data Implication: D in expectations occur slowly over time as data changes • Rational Expectations (R.E.)(John Muth – Monetary economist) 1. Expectations = Optimal forecast (best guess), using all available information PEt+1 = POFt+1=> RE = ROF (R.E. Equations)

  6. Rational Expectations (R.E.)(John Muth – Monetary economist) 1. Expectations = Optimal forecast (best guess), using all available information, A.A.I. PEt+1 = POFt+1 => RE = ROF (R.E. Equations) 2. Even with optimal forecast, prediction will not always be accurate (bound to be some randomness) 3. Not everyone will have R.E. - Some are too lazy to make best guess possible - Some are too stupid to use A.A.I. 4. Only need a few market participants to make R.E./O.F. 5. Strong incentives to make R.E./O.F. - better forecasts => higher income (P max. assumption) - accurate expectations are desirable - bad forecasts can be costly

  7. Example: Forecasting Inflation Adaptive Expectations (future is average of the past) qEt+1 = (1-l) Swj=0ljqt-j l = 0.25 (Small l, so distant past has little impact. New technology regulations, institutions make the past not relevant to predict the future. Past 4 years have material impact.) qEt+1 = 0.75*{1*3.0 + 0.25*1.4 + 0.06*2.8 + 0.02*-0.1+…} qEt+1 = 2.66% l = 0.50 (Past 9 years have material impact.) qEt+1 = 0.50*{1*3.0+0.5*1.4+0.25*2.8+0.13*-0.1+ 0.06*4.1+0.03*2.5+.02*3.5+0.01*3.3…} qEt+1 = 2.41% l = 0.75 (Big l, so past is important. No big change in structure of economy. Past 19 years have material impact.) qEt+1=0.25*{1*3.0+0.75*1.4+0.56*2.8+0.42*0.1+0.32*4.1+0.24*2.5+.18*3.5+0.13*3.3+0.1*1.9+0.08*2.4+0.06*1.6+0.04*3.4+0.03*2.6+0.02*1.6+0.02*1.7+0.01*3.3+…} qEt+1 = 2.37%

  8. Example: Forecasting Inflation Rational Expectations (R.E.)(John Muth – Monetary economist) Expectations = Optimal forecast (best guess), using all available information PEt+1 = POFt+1=> RE = ROF (R.E. Equations) Inflation: • Inflation typically lags money supply growth by 3.5 years. • Noble prize winning economist Milton Friedman’s famous quote: ”Inflation is everywhere and always a monetary phenomenon”. • The Federal Reserve may not be willing or able to tighten monetary policy at the appropriate time. • If the Federal Reserve actions don’t lead to inflation, then massive spending by the Treasury will. • Foreign investors’ concerns over the U.S. fiscal position could lead to a significant drop in the value of the dollar and a jump in import prices. • Deleveraging periods are typically followed by periods of rapid debt accumulation and spending. • The current period is looking eerily similar to the 1970s: resurgence of Keynesian policy prescription, volatile commodity prices, loose monetary policy. • Historically, severe economic contractions have been followed by rapid economic expansions. • Rapid emerging market economic growth will create upward pressure on commodity prices and worldwide inflation. • Congressman Ron Paul has put forth legislation for the GAO to audit the Fed’s FOMC decision making activities. This could erode the Fed’s independence and increase market participants’ inflation expectations. Deflation: • The slack (output gap) in the U.S. economy is the largest its been since the early 1970s. • Significant slowdown in worldwide economic activity. • Continued worldwide wage differentials and a huge savings glut will keep disinflation in effect. • The bursting of an asset bubble has historically been deflationary. • No possibility of a wage-price spiral with unemployment rate above 8%. • Global decline in market based inflation expectations. • World wide economic growth will remain below potential for the next few years. • The Federal Reserve will counteract inflationary pressures caused by rising private sector demand by withdrawing bank liquidity and raising short-term rates. • New financial regulations will lower the velocity of money (rate of money turnover). Hence, today’s large increase in the supply of money is offset by lower velocity of money and the “money multiplier”. • Resurgence of the Ricardian Equivalence Theorem: Large government deficits are offset by rising household expectations of higher future taxes and savings rates.

  9. Efficient Market Hypothesis (EMH) Application of R.E. to the pricing of securities => EMH Need a way to measure RE => understanding of DPS Recall from supply/demand analysis that R* (equilibrium return) equates Q.S. with Q.D. of a security (equilibrium condition) D risk/liquidity factors =>DS/DD => DR* Assume, RE = ROF = R* (efficient market condition,… equation that describes pricing behavior in efficient markets) Why? Market participants are searching for unexploited profit opportunities, UPOs Determine R* to determine RE

  10. Characterization of Pricing Behavior • Pt will be set so that ROF = R* • In an efficient market, Pt reflects all available information Recall,… RE = C + PEt+1 – Pt Pt If ROF > R* =>  Pt =>  ROF until = R* (Efficient market condition is satisfied) If ROF < R* =>  Pt =>  ROF until = R* In an efficient market, all UPOs will be eliminated

  11. Implications for Investing 1. Published reports of financial analysts not very valuable 2. Should be skeptical of hot tips 3. Stock prices may fall on good news 4. Prescription for investor 1. Shouldn’t try to outguess market 2. Therefore, buy and hold 3. Diversify with no-load mutual fund Evidence on Rational Expectations in Other Markets 1. Bond markets appear efficient 2. Evidence with survey data is mixed Skepticism about quality of data 3. Following implication is supported: change in way variable moves, change way expectations are formed changes

  12. Evidence on Efficient Markets Hypothesis Favorable Evidence 1. Investment analysts and mutual funds don’t beat the market 2. Stock prices reflect publicly available information: anticipated announcements don’t affect stock price 3. Stock prices and exchange rates close to random walk If predictions of P big, Rof > R* predictions of P small 4. Technical analysis does not outperform market Unfavorable Evidence 1. Small-firm effect: small firms have abnormally high returns 2. January effect: high returns in January 3. Market overreaction 4. Excessive volatility 5. Mean reversion 6. New information is not always immediately incorporated into stock prices Overview Reasonable starting point but not whole story

  13. Econ 330 Homework 5Due Thursday, February 20, before exam Chapter 7 Questions & Applied Problems 4, 9, 16, 22, 23, 24, 25

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