Fin 3050 Exam 2

Errors in Information Processing

1.Forecasting Errors: Too much weight is placed on recent experiences. 2.Overconfidence: Investors overestimate their abilities and the precision of their forecasts. 3.Conservatism: Investors are slow to update their beliefs and under react to new information. 4.Sample Size Neglect and Representativeness: Investors are too quick to infer a pattern or trend from a small sample.

Suppose you forecast that the standard deviation of the market return will be 20% in the coming year. If the measure of risk aversion in is A = 4: a. What would be a reasonable guess for the expected market risk premium? b. What value of A is consistent with a risk premium of 9%? c. What will happen to the risk premium if investors become more risk tolerant?

A. Given that A = 4 and the projected standard deviation of the market return = 20%, we can use the below equation to solve for the expected market risk premium: A = 4 =Average(rM) - rf/Sample σM2 =Average(rM) - rf/(20%)2 E(rM) - rf = AσM2 = 4 × (0.20)2 = 0.16 = 16% B.Solve E(rM) - rf = 0.09 = AσM2 = A × (0.20)2, we can get A = 0.09/(0.04) = 2.25

Consider the following information: Portfolio Expected Return StandardDeviation Risk-free 10% 0% Market 18 24 A 20 22 a. Calculate the Sharpe ratios for the market portfolio and portfolio A. b. If the simple CAPM is valid, is the above situation possible?

A. Not possible. The reward-to-variability ratio for Portfolio A is better than that of the market, which is not possible according to the CAPM, since the CAPM predicts that the market portfolio is the most efficient portfolio. Using the numbers supplied: SA =20 - 10/22 = 0.4522 SM =18 - 10/24 = 0.3324 These figures imply that Portfolio A provides a better risk-reward tradeoff than the market portfolio. B. No.

Based on current dividend yields and expected capital gains, the expected rates of return on portfolios A and B are 11% and 14%, respectively. The beta of A is 0.8 while that of B is 1.5. The T-bill rate is currently 6%, while the expected rate of return of the S&P 500 Index is 12%. The standard deviation of portfolio A is 10% annually, while that of B is 31%, and that of the index is 20%. a-1. Calculate the return predicted by CAPM for a portfolio with a beta of 0.8. a-2. Calculate the return predicted by CAPM for a portfolio with a beta of 1.5. b. If instead you could invest only in bills and one of these portfolios, which would you choose?

A. Using the SML, the expected rate of return for any portfolio P is: E(rP) = rf + β[E(rM) - rf] Substituting for portfolios A and B: E(rA) = 6% + 0.8 × (12% - 6%) = 10.8% < 11% E(rB) = 6% + 1.5 × (12% - 6%) = 15.0% > 14% Hence, Portfolio A is desirable and Portfolio B is not. B. The slope of the CAL supported by a portfolio P is given by: S =E(rp) - rf/σP Computing this slope for each of the three alternative portfolios, we have: S(S&P 500) = (12% - 6%)/20% = 6/20 S(A) = (11% - 6%)/10% = 5/10 > S(S&P 500) S(B) = (14% - 6%)/31% = 8/31 < S(S&P 500) Hence, portfolio A would be a good substitute for the S&P 500

The risk-free rate of return is 10.0%, the expected rate of return on the market portfolio is 20%, and the stock of Xyrong Corporation has a beta coefficient of 2.6. Xyrong pays out 60% of its earnings in dividends, and the latest earnings announced were $25 per share. Dividends were just paid and are expected to be paid annually. You expect that Xyrong will earn an ROE of 22% per year on all reinvested earnings forever. A. What is the intrinsic value of a share of Xyrong stock? B-1.If the market price of a share is currently $59, and you expect the market price to be equal to the intrinsic value one year from now, calculate the price of the share after one year from now. B-2. What is your expected one-year holding-period return on Xyrong stock?

A. Xyrong Corporation k = rf + β[E(rM) - rf] = 0.10 + 2.6 × (0.20 - 0.10) = 0.3600 or 36.00% g = b × ROE = 0.4 × 0.22 = 0.088 or 8.80% V0=D0 × (1 + g)/k-g=$15.00 × (1+ 0.088)/.3600-0.088=$60.00 B-1. P1 = V1 = V0 × (1 + g) = $60.00 × (1 + 0.088) = $65.28 B-2. E(r)=D1 + P1 - P0/P0=$16.32 + $65.28 - $59/$59=0.3831=38.31%

When should you use the GAR and when should you use the AAR?

A1: When you are evaluating PAST RESULTS (ex-post): Use the AAR (average without compounding) if you ARE NOT reinvesting any cash flows received before the end of the period. Use the GAR (average with compounding) if you ARE reinvesting any cash flows received before the end of the period. A2: When you are trying to estimate an expected return (ex-ante return): Use the AAR

Weak-Form Tests: Anomalies

Could speculators find trends in past prices that would enable them to earn abnormal returns? Returns over the Short Horizon (3 - 12 months)Momentum: Good or bad recent performance continues over short to intermediate time horizons Returns over Long Horizons (up to 5-years)Mean return reversion: A run of positive returns eventually will tend to be followed by negative returns

13.5 Free Cash Flow Valuation Approaches

Free Cash Flow: Cash flows available to the firm or the equity holders net of capital expenditures -Useful for firms that don't pay dividends, -Helpful to understand sources and uses of cash -Free Cash Flows can provide very useful insights about firm value beyond DDM

Basic Dividend Discount Model

Intrinsic value of a stock can be found from as: -What happened to the expected sale price in this formula? -Why is this an infinite sum? -Is stock price independent of the investor's holding period? This equation is not useable because it is an infinite sum of variable CFs Therefore we have to make assumptions about the dividends to make the model tractable

Match each example to one of the following behavioral characteristics.

Investors are slow to update their beliefs when given new evidence. -Conservatism bias Investors are reluctant to bear losses due to their unconventional decisions. -Regret avoidance Investors exhibit less risk tolerance in their retirement accounts versus their other stock accounts. -Mental accounting Investors are reluctant to sell stocks with "paper" losses. -Disposition effect Investors disregard sample size when forming views about the future from the past. -Representativeness bias

Jill Davis tells her broker that she does not want to sell her stocks that are below the price she paid for them. She believes that if she just holds on to them a little longer, they will recover, at which time she will sell them. What behavioral characteristic does Davis display?

Loss aversion. Davis uses loss aversion as the basis for her decision making. She holds on to stocks that are down from the purchase price in the hopes that they will recover. She is reluctant to accept a loss.

Intrinsic Value and Market Price

Market Price -Consensus value of all traders -In equilibrium the current market price will equal intrinsic value Trading Signals -If V0 > P0Buy -If V0 < P0Sell or Short Sell -If V0 = P0Hold as it is Fairly Priced

If the simple CAPM is valid, is the following situation possible? Portfolio Expected Return StandardDeviation Risk-free 10% 0% Market 18 24 A 20 22

No. Not possible. Portfolio A clearly dominates the market portfolio. It has a lower standard deviation with a higher expected return.

If the simple CAPM is valid, is the following situation possible? Portfolio Expected Return Beta A 20% 1.4 B 25 1.2

No. Not possible. Portfolio A has a higher beta than Portfolio B, but the expected return for Portfolio A is lower.

Suppose that, after conducting an analysis of past stock prices, you come up with the following observations. Which would appear to contradict the weak form of the efficient market hypothesis?

One could have made superior returns by buying stock after a 10% rise in price and selling after a 10% fall. This is a filter rule, a classic technical trading rule, which would appear to contradict the weak form of the efficient market hypothesis.

Price-Earnings (P/E) Ratios

P/E Ratio and Growth Opportunities •P/E Ratios = Price / Earning per share -The lower the P/E the cheaper the stock is. But a high P/E might also mean that the stock is expected to grow so you would pay more for it. -High-P/E stocks are often referred to as growth stocks, -Low-P/E stocks are often referred to as value stocks •PEG ratio = (P/E ratio) / (growth rate, g) -Should be 1 -PEG is better than P/E. The lower the PEG the more undervalued the company is

MF Corp. has an ROE of 16% and a plowback ratio of 50%. If the coming year's earnings are expected to be $4 per share, at what price will the stock sell? The market capitalization rate is 12%. B. What price do you expect MF shares to sell for in three years?

ROE = 16%, b = 0.50, EPS = $4, k = 12% P0=D1=EPS × (1 − b)/k-(ROE x b)=$4 × (1 − 0.50)/0.12- (0.16 x .50)=$2.00/0.12 - 0.08= $50.00 B. P3=EPS × (1 − b) × (1 + g)3 /k-g= P0 × (1 + g)3 = $50 × (1.08)3 = $62.99

You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the reward-to-volatility (Sharpe) ratio for the equity fund?

Reward to volatility ratio =Portfolio risk premium/Standard deviation of portfolio excess return = 10%/14% = 0.7143

All of the following actions are consistent with feelings of regret except:

Selling losers quickly. Investors attempt to avoid regret by holding on to losers hoping the stocks will rebound. If the stock rebounds to its original purchase price, the stock can be sold with no regret. Investors also may try to avoid regret by distancing themselves from their decisions by hiring a full-service broker.

A share of stock is now selling for $100. It will pay a dividend of $9 per share at the end of the year. Its beta is 1. What must investors expect the stock to sell for at the end of the year? Assume the risk-free rate is 8% and the expected rate of return on the market is 18%.

Since the stock's beta is equal to 1.0, its expected rate of return should be equal to that of the market, that is, 18%. E(r) =D + P1 - P0/P0 18% = 9 + P1 - 100 /100⇒⇒ P1 = $109

Which of the following sources of market inefficiency would be most easily exploited?

Stocks are overvalued because investors are exuberant over increased productivity in the economy. If the stocks are overvalued, without regulative restrictions or other constraints on the trading, some investors observing this trend would be able to form a trading strategy to profit from the mispricing, thereby exploiting the inefficiency and forcing the price to the correct level.

14No Growth Model

Stocks that have earnings and dividends that are expected to remain constant over time (zero growth => g = 0) Why do you have to pay more for the constant growth stock? -Must pay for expected growth

Which version of the efficient market hypothesis focuses on the most inclusive set of information?

Strong-form. Strong-form efficiency includes all information: historical, public, and private.

The Historical Average Growth Rate

Suppose the Broadway Joe Company paid the following dividends: 2002: $1.50 2005: $1.80 2003: $1.70 2006: $2.00 2004: $1.75 2007: $2.20 The spreadsheet below shows how to estimate historical average growth rates, using arithmetic and geometric averages.

The Sustainable Growth Rate (cont.)

Sustainable growth rate: A dividend growth rate that can be sustained by a company's earnings. •Return on Equity (ROE) = Net Income / Equity •Payout Ratio = Proportion of earnings paid out as dividends = D/EPS •Retention Ratio = Proportion of earnings retained for investment

Semistrong Tests: Anomalies

These findings are difficult to reconcile with EMH, and therefore are called anomalies P/E Effect: Low P/E ratio stocks provide higher returns Small Firm Effect (January Effect): Small stock outperform large stocks Neglected Firm Effect and Liquidity Effects: Neglected firms (usually small firms) are riskier so they will provide higher returns Book-to-Market Ratios: High book-to-market portfolios provide higher returns Post-Earnings Announcement Price Drift: Stock prices respond very slowly to earning announcements

The Behavioral Critique

Two categories of irrationalities: 1.Investors do not always process information correctly. •Result: Incorrect probability distributions of future returns. 2.Even when given a probability distribution of returns, investors may make inconsistent or suboptimal decisions. •Result: They have behavioral biases.

Observations on Dividend Discount Models, II

Two-Stage Dividend Growth Model: •More realistic in that it accounts for two stages of growth •Usable when g > k in the first stage •Not usable for firms that do not pay dividends •Is sensitive to the choice of g and k •k and g may be difficult to estimate accurately.

A stock has an expected return of 6%. What is its beta? Assume the risk-free rate is 8% and the expected rate of return on the market is 18%.

Using the SML: 6% = 8% + β(18% - 8%) ⇒⇒ β = -2/10 = -0.2

The stock of Business Adventures sells for $40 a share. Its likely dividend payout and end-of-year price depend on the state of the economy by the end of the year as follows: Dividend Stock Price Boom $2.00 $50 Normal economy 1.00 43 Recession 0.50 34 a. Calculate the expected holding-period return and standard deviation of the holding-period return. All three scenarios are equally likely. b. Calculate the expected return and standard deviation of a portfolio invested half in Business Adventures and half in Treasury bills. The return on bills is 4%.

We use the below equation to calculate the holding period return of each scenario: HPR =Ending Price − Beginning Price + Cash Dividend/Beginning Price A. The holding period returns for the three scenarios are:Boom: (50 - 40 + 2)/40 = 0.30 = 30% Normal: (43 - 40 + 1)/40 = 0.10 = 10% Recession: (34 - 40 + 0.50)/40 = -0.1375 = -13.75% E(HPR)= =[(1/3) × 0.30] + [(1/3) × 0.10] + [(1/3) × (-0.1375)] =0.0875 or 8.75% Var(HPR)= =[(1/3) × (0.30 - 0.0875)2] + [(1/3) × (0.10 - 0.0875)2] + [(1/3) × (-0.1375 - 0.0875)2] =0.031979 SD(r)=√319.79= 0.1788 or 17.88% B. E(r) = (0.5 × 8.75%) + (0.5 × 4%) = 6.375% σ = 0.5 × 17.88% = 8.94%

Arithmetic Average Finding the average HPR for a time series of returns:

Without compounding (AAR or Arithmetic Average Return): Cons: Ignores compounding Pros: is the best forecast of performance for the next period

If the simple CAPM is valid, is the following situation possible? Portfolio Expected Return Standard Deviation A 30% 35% B 40 25

Yes. Possible. If the CAPM is valid, the expected rate of return compensates only for systematic (market) risk as measured by beta, rather than the standard deviation, which includes nonsystematic risk. Thus, Portfolio A's lower expected rate of return can be paired with a higher standard deviation, as long as Portfolio A's beta is lower than that of Portfolio B.

Limits to Arbitrage

•Behavioral biases would not matter if rational arbitrageurs could fully exploit the mistakes of behavioral investors. •Several factors limit the ability to profit from mispricing a)Fundamental Risk: -"Markets can remain irrational longer than you can remain solvent." -Intrinsic value and market value may take too long to converge. b)Implementation Costs: -Transactions costs and restrictions on short selling can limit arbitrage activity. c)Model Risk:-What if you have a bad model and the market value is actually correct?

Bubbles and Behavioral Economics

•Behavioral schools claims that bubbles are a case of a market moving by irrational investor sentiment •Bubbles are easier to spot after they end. -Dot-com bubble: -Housing bubble: •Other evidence: companies that added .com to their names during the dot-com bubble enjoyed significant stock price increase. That does not sound like rational valuation, right? Example supporting rational behavior •Rational explanation for stock market bubble using the dividend discount model: •S&P 500 is worth $12,883 million if dividend growth rate is 8% (close to actual value in 2000). •S&P 500 is worth $8,589 million if dividend growth rate is 7.4% (close to actual value in 2002).

Behavioral Biases

•Biases result in less than rational decisions, even with perfect information. Examples: 1.Framing: -How the risk is described, "risky losses" vs. "risky gains", can affect investor decisions. 2.Mental Accounting: •Investors may segregate accounts or monies and take risks with their gains that they would not take with their principal .•Example: They are more likely to sell stocks with gains than those with losses (contrary to a tax-minimizing strategy) 3.Regret Avoidance: •Investors blame themselves more when an unconventional or risky bet turns out badly. •John Nofsinger: "We are afraid to do anything, because we are afraid we will regret it." 4.Prospect Theory: -Conventional view: Utility depends on level of wealth. -Behavioral view: Utility depends on changes in current wealth. •Behavioral Biases that we talk earlier affect investor behavior

Types of Stock Analysis

•Fundamental Analysis - using economic and accounting information to predict proper stock prices -Try to find firms that are better than everyone else's estimate. -Try to find poorly run firms that are not as bad as the market thinks.

EMH and Competition

•Information: The most precious commodity on Wall Street -Competition among investors should imply that stock prices fully and accurately reflect publicly available information very quickly. Why? -Else there are unexploited profit opportunities. -Once information becomes available, market participants quickly analyze it & trade on it & frequent, low cost trading assures prices reflect information. Questions arise about efficiency due to: •Unequal access to information •Structural market problems •Psychology of investors (Behavioralism)

Active or Passive Management

•It is clear that casual efforts to pick stocks are not likely to pay off •Active Management: EHM believe this is wasted effort -An expensive strategy -Suitable only for very large portfolios •Passive Management: No attempt to outsmart the market -Accept EMH -Index Funds and ETFs -Very low costs

Efficient Market Hypothesis (EMH)

•Maurice Kendall (1953) found no predictable pattern in stock prices. •Prices are as likely to go up as to go down on any particular day. •How do we explain random stock price changes? -At first, this result seemed to suggest that markets behave erratically -Then later, economists realized that it indicated a well-functioning market •EMH says stock prices already reflect all available information Explanation: •Assume that stock prices are predictable. -Then, a forecast about favorable future performance leads to favorable current performance, as market participants rush to trade on new information. -Result: Prices change until expected returns are exactly commensurate with risk.

Suppose you buy one share of a stock today for $45 and you hold it for two years and sell it for $52. You also received $8 in dividends at the end of the two years.

•PB = $45 , PS = $52 , CP = $8•HPR = (52 - 45 + 8) / 45 = 33.33%-Annualized w/out compounding:HPRann= 0.3333/2 = 16.66%, -Annualized HPR assuming annual compounding is (n = 2 ):HPRann = (1+0.3333)1/2 - 1 = 15.47%

Stock Analysis

•Technical Analysis - searching for predictable patterns in stock prices using prices and volume information -It assumes prices follow predictable trends -Success depends on a sluggish response of stock prices to fundamental supply-and-demand factors •This of course is opposed to the notion of EMH If the markets are weak form efficient or semi-strong form efficient or strong form efficient will technical analysis be able to consistently predict price changes?NO

Technical Analysis and Behavioral Finance

•Technical analysis attempts to exploit recurring and predictable patterns in stock prices. -Prices adjust gradually to a new equilibrium. -Market values and intrinsic values converge slowly. •One well known behavioral tendency is the disposition effect: The tendency of investors to hold on to losing investments. -So stock prices will move slowly toward their fundamental values, consistent with the central motivation of technical analysis

The Search for Momentum

•Technical analysis seeks to uncover trends in market prices, and that is in fact a search for momentum: -Relative strength statistics are used to discover these trends Dow Theory: 3 forces simultaneously affect stock prices 1.Primary trend : Long-term movement of prices, lasting from several months to several years. 2.Secondary or intermediate trend: short-term deviations of prices from the underlying trend line and are eliminated by corrections. 3.Minor trends: Daily fluctuations of little importance.

Capital Asset Pricing Model (CAPM)

•The model gives us a precise prediction of the relationship that we should observe between the risk of an asset and its expected return -It is the equilibrium model that underlies all modern financial theory -Derived using principles of diversification with simplified assumptions •Markowitz, Sharpe, Lintner and Mossin are researchers credited with its development

Market Efficiency & Portfolio Management

•Then, why do we need portfolio management? Why not choose a portfolio randomly? •Even if the market is efficient a role exists for portfolio management: -Diversification -Appropriate risk level -Tax considerations

Random Price Changes

•Why are price changes random? -In very competitive markets prices should react to only NEW information -Flow of NEW information is random -Therefore, price changes are random Therefore, stock price changes follow a random walk.

Suppose you have a 5% HPR on a 3 month investment. What is the annual rate of return with and without compounding?

•Without: n = 12/3 = 4 so HPRann= HPR*n = 0.05*4 = 20% •With: HPRann = (1.05^4) - 1 = 21.55%

Valuation models using comparable

Look at the relationship between price and various determinants of value for similar firms

Here are data on two companies. The T-bill rate is 4% and the market risk premium is 6%. Company $1 Discount Store Everything $5 Forecast return 12% 11% Standard deviation of returns 8% 10% Beta 1.5 1.0 Based on the fair return and according to the capital asset pricing model (CAPM), is each firm properly priced?

$1 Discount Store is overpriced; Everything $5 is underpriced.

Are Markets Efficient?

-Not surprisingly, EMH is not very popular on Wall Street It implies that portfolio management - the search for undervalued securities - is at best wasted effort, and maybe even harmful to clients because it costs money. -Three factors that imply that this debate will probably never be settled: Magnitude issue Selection bias issue Lucky event issue Magnitude Issue -Stock prices are very close to fair values and only managers of large portfolios can earn enough trading profits to make the exploitation of minor mispricing worth the effort.So the question is: How efficient are markets?Selection Bias Issue -Only unsuccessful investment schemes are made public; good schemes remain private.We cannot evaluate the true ability of managers that generate profits Lucky Event Issue -The probability of a lucky event is 50% (random). Then out of 10,000 managers, statistically speaking 2 out of 10,000 are expected to win

Fundamental Stock Analysis

-studying a company's accounting, financial & economic information to estimate the economic value of a company's stock (identify "undervalued" stocks to buy and "overvalued" stocks to sell) -In practice however, such stocks may in fact be correctly priced for reasons not immediately apparent to the analyst.

Price Ratio Analysis

.Price-Earnings Ratios •Price-earnings ratio (P/E ratio) -Current stock price divided by annual earnings per share (EPS) Expected share price = P/E*Projected EPS= = P/E*EPS0*(1+EPS growth rate)

Why would you want to annualize returns?

1. Annualizing HPRs for holding periods of > than 1 year: -Without compounding (Simple or APR): HPRann = HPR/n -With compounding: EARHPRann = [(1+HPR)1/n]-1, where n = number of years held 2.Annualizing HPRs for holding periods of < 1 year:-Without compounding (Simple): HPRann= HPR x n -With compounding: HPRann = [(1+HPR)n] - 1 where n = number of compounding periods per year

Annualizing Standard Deviation. Why would you want to annualize St.Dev?

1. Annualizing St.Dev for holding periods of > than 1 year: St.Devann = St.Dev / SQRT(n) where n = number of years held 2. Annualizing St.Dev for holding periods of < than 1 year: St.Devann = St.Dev * SQRT(n) where n = number of periods in 1 year

Versions of the EMH

1. Weak -Stock prices reflect all market trading data •The relevant information is historical prices and other trading data such as trading volume. •If the markets are weak form efficient, use of such information provides no benefit "at the margin." 2. Semi-strong -Stock prices reflect all publicly traded information (trading data, accounting data, earning forecasts, etc.) •The relevant information is "all publicly available information, including past price and volume data." •If the markets are semi-strong form efficient, then studying past price and volume data & studying earnings and growth forecasts provides no net benefit in predicting price changes at the margin. 3. Strong -Stock prices reflect all information relevant to the firm (including insider information) •The relevant information is "all information" both public and private or "inside" information. •If the markets are strong form efficient, use of any information (public or private) provides no benefit at the margin. •SEC Rule 10b-5 limits trading by corporate insiders, (officers, directors and major shareholders). Inside trading must be reported.

Resulting Equilibrium Conditions

1.All investors will hold the same portfolio for risky assets - market portfolio (M) a)Market portfolio contains all securities b)Market portfolio is the tangency point of the CAL with the efficient frontier Eg: Assume investors refuse to include IBM into their portfolio -IBM's price decreases to the point that is attractive to investors to include it

Assumptions

1.Individual investors are price takers-Security prices are unaffected by their own trades 2.Single-period investment horizon 3.Investments are limited to publicly traded assets 4.No taxes on returns & no transaction costs on trades 5.Information is costless and available to all investors 6.Investors are rational mean-variance optimizers 7.There are homogeneous expectations -All investors will use the same expected returns and covariance matrix of security returns

What is the expected rate of return for a stock that has a beta of 1 if the expected return on the market is 15%?

15%. Its expected return is exactly the same as the market return when beta is 1.0.

In an efficient market, professional portfolio management can offer all of the following benefits except which of the following?

A superior risk-return trade-off. It is not possible to offer a higher risk-return trade off if markets are efficient.

Note whether the following phenomena would be consistent with or a violation of the efficient market hypothesis. a. Nearly half of all professionally managed mutual funds are able to outperform the S&P 500 in a typical year. b. Money managers that outperform the market (on a risk-adjusted basis) in one year are likely to outperform in the following year. c. Stock prices tend to be predictably more volatile in January than in other months. d. Stock prices of companies that announce increased earnings in January tend to outperform the market in February. e. Stocks that perform well in one week perform poorly in the following week.

A. Consistent. Half of all managers should outperform the market based on pure luck in any year. B. Violation. This would be the basis for an "easy money" rule: Simply invest with last year's best managers. C. Consistent. Predictable volatility does not convey a means to earn abnormal returns. D. Violation. The abnormal performance ought to occur in January, when the increased earnings are announced. E. Violation. Reversals offer a means to earn easy money: Simply buy last week's losers.

Real Stock Value vs Market Price

Decide on whether a stock is worth buying or not 1.Expected Rate of Return versus Required Return 2.Intrinsic Value versus its Market Price

Suppose the market can be described by the following three sources of systematic risk. Each factor in the following table has a mean value of zero (so factor values represent realized surprises relative to prior expectations), and the risk premiums associated with each source of systematic risk are given in the last column. Systematic Factor Risk Premium Industrial production, IP 6% Interest rates, INT 2 Credit risk, CRED 4 beta on IP = 1.0 beta on INT = 0.5 beta on CRED = .75 rf = 6% a. Calculate the equilibrium expected excess return on this stock using the APT? b. Is the stock overpriced or underpriced?

A. Expected excess rate of return on the stock based on the factor betas is: E(R) = (1 × 6) + (0.5 × 2) + (0.75 × 4) = 10% B. According to the equation for the return on the stock, the actually expected return on the stock is 6% (because the expected surprises on all factors are zero by definition). Because the actually expected return based on risk is less than the equilibrium return, we conclude that the stock is overpriced.

Miltmar Corporation will pay a year-end dividend of $4, and dividends thereafter are expected to grow at the constant rate of 6% per year. The risk-free rate is 6%, and the expected return on the market portfolio is 12%. The stock has a beta of 0.86. A. Calculate the market capitalization rate. B. What is the intrinsic value of the stock?

A. Market capitalization rate = k = rf + β[E(rM) − rf]= 0.06 + 0.86(0.12 − 0.06) = 0.1116 = 11.16% B. Intrinsic value = V0=D1/k − g=$4/0.1116 − 0.06 = $77.52

Multistage Growth Models

As firms progress through their industry life cycle, earnings and dividend growth rates (ROE) are likely to change. A two stage growth model: g1 = first growth rate g2 = second growth rate T = number of periods of growth at g1

Price Ratio Analysis

B. Price-Cash Flow Ratios •Price-cash flow ratio (P/CF ratio) -Current stock price divided by current cash flow per share •Most analysts agree that in examining a company's financial performance, cash flow can be more informative than net income. Expected share price = P/CF*Projected CFPS= = P/CF*CFPS0*(1+CFPS growth rate)

Models of Equity Valuation

Basic Types of Equity Valuation Models -Balance Sheet Models -Dividend Discount Models -Price/Earnings Ratios -Free Cash Flow Models Measures of Valuation Methods -Book value -Market value -Liquidation value -Replacement cost

Measures of Valuation Methods into Depth

Book value -Value of common equity on the balance sheet •Market value -Market value based on stock price •Liquidation value -Net amount realized from sale of assets and paying off all debt •Replacement cost -Replacement cost of the assets less the liabilities

You know that firm XYZ is very poorly run. On a scale of 1 (worst) to 10 (best), you would give it a score of 3. The market consensus evaluation is that the management score is only 2. Should you buy or sell the stock?

Buy. You should buy the stock. The firm's management is not as bad as everyone else believes it to be, therefore, the firm is undervalued by the market. You are less pessimistic about the firm's prospects than the beliefs built into the stock price.

Expected Return vs Required Return

CAPM gave us required return given its risk, call it k: -k = market capitalization rate If the stock is priced correctly -Required return, E(r) should equal expected return, k

Observations on Dividend Discount Models, I.

Constant Growth Model: Simple to compute •Not usable for firms that do not pay dividends•Not usable when g > k •Is sensitive to the choice of g and k •k and g may be difficult to estimate accurately. •Constant perpetual growth is often an unrealistic assumption.

Behavioral Finance

Conventional Finance •Prices are correct; equal to intrinsic value. •Resources are allocated efficiently. •Consistent with EMH Behavioral Finance •What if investors don't behave rationally?

A common stock pays an annual dividend per share of $5.20. The risk-free rate is 7% and the risk premium for this stock is 3%. If the annual dividend is expected to remain at $5.20, what is the value of the stock?

Cost of equity = rf + E(Risk premium) = 7% + 3% = 10% Because the dividends are expected to be constant every year, the price can be calculated as the no-growth-value per share: P0 =D/ke=$5.20/.10 =$52.00

Constant Growth Model

Dividends are expected to grow at a constant rate, g For a stock whose Intrinsic Value = Market Value

What must be the beta of a portfolio with E(rP) = 20%, if rf = 5% and E(rM) = 15%?

E(rP) = rf + β[E(rM) - rf] Given rf = 5% and E(rM)= 15%, we can calculate β: 20% = 5% + β(15% - 5%) ⇒⇒ β = 1.5

Constant Growth Model

EX: A common stock share just paid a $2.00 per share dividend and the stock has a required return of 10%. Dividends are expected to grow at 6% per year forever. -What is the most you should be willing to pay for the stock?

Which of the following would most appear to contradict the proposition that the stock market is weakly efficient?

Every January, the stock market earns abnormal returns. This is a predictable pattern of returns, which should not occur if the stock market is weakly efficient.

Types of Stock Analysis

Examples of technical Analysis -Relative strength: compare stock performance to that of the market or other stocks -Support level: A price level below which it is supposedly unlikely for a stock or stock index to fall. -Resistance levels: Price levels above which stock prices are difficult to rise, or price levels below which it is unlikely for them to fall

You manage an equity fund with an expected risk premium of 10% and a standard deviation of 14%. The rate on Treasury bills is 6%. Your client chooses to invest $60,000 of her portfolio in your equity fund and $40,000 in a T-bill money market fund. What is the expected return and standard deviation of your client's portfolio?

Expected return for your fund = T-bill rate + risk premium = 6% + 10% = 16% Expected return of client's overall portfolio = (0.6 × 16%) + (0.4 × 6%) = 12% Standard deviation of client's overall portfolio = 0.6 × 14% = 8.4%

Are the following statements true or false? a. Stocks with a beta of zero offer an expected rate of return of zero. b. The CAPM implies that investors require a higher return to hold highly volatile securities. c. You can construct a portfolio with beta of .75 by investing .75 of the investment budget in T-bills and the remainder in the market portfolio.

False. According to CAPM, when beta is zero, the "excess" return should be zero. False. CAPM implies that the investor will only require risk premium for systematic risk. Investors are not rewarded for bearing higher risk if the volatility results from the firm-specific risk, and thus, can be diversified. False. We can construct a portfolio with the beta of 0.75 by investing 0.75 of the investment budget in the market portfolio and the remainder in T-bills.

After Polly Shrum sells a stock, she avoids following it in the media. She is afraid that it may subsequently increase in price. What behavioral characteristic does Shrum have as the basis for her decision making?

Fear of regret. Shrum refuses to follow a stock after she sells it because she does not want to experience the regret of seeing it rise. The behavioral characteristic used for the basis for her decision making is the fear of regret.

Dividend Discount Models

For now assume price = intrinsic value

Using Table 5.3 as your guide, what is your estimate of the expected annual HPR on the market index stock portfolio if the current risk-free interest rate is 3%?

From Table 5.3, we find that for the period 1926 - 2016, the mean excess return for S&P 500 over 1-month T-bills is 8.48%.E(r) = Risk-free rate + Risk premium = 3% + 8.48% = 11.48%

Example: Calculating and Using the Sustainable Growth Rate

In 2007, American Electric Power (AEP) had an ROE of 10.17%, projected earnings per share of $2.25, and a per-share dividend of $1.56. What was AEP's: -Retention rate? -Sustainable growth rate? •Payout ratio = $1.56 / $2.25 = 0.693 So, retention ratio = 1 - .693 = 0.307 or 30.7% Therefore, AEP's sustainable growth rate = g = 0.1017 x 0.307 = 0.03122, or 3.122%

Example: Price/Earnings Analysis

Intel Corp (INTC) - Earnings (P/E) Analysis 5-year average P/E ratio 27.30 Current EPS$.86 EPS growth rate 8.5% Expected stock price = historical P/E ratio x projected EPS $25.47 = 27.30 x($.86 x 1.085) Mid-2007 stock price = $24.27

A firm pays a current dividend of $2, which is expected to grow at a rate of 7% indefinitely. If the current value of the firm's shares is $214, what is the required return applicable to the investment based on the constant-growth dividend discount model (DDM)?

Intrinsic value = V0=D0 × (1 + g)/(k − g) $214=$2 × 1.07/k − 0.07 ⇒⇒ k = 0.08 or 8%

Jand, Inc., currently pays a dividend of $1.62, which is expected to grow indefinitely at 6%. If the current value of Jand's shares based on the constant-growth dividend discount model is $44.41, what is the required rate of return?

Intrinsic value = V0=D0 × (1 + g)/k − g $44.41=$1.62 × 1.06/k − 0.06 ⇒⇒ k = 0.098667 or 9.87%

Deployment Specialists pays a current (annual) dividend of $1 and is expected to grow at 25% for two years and then at 5% thereafter. If the required return for Deployment Specialists is 11.0%, what is the intrinsic value of its stock?

Intrinsic value = V0=D1+D2+ ... +DH + PH1 + k(1 + k)2(1 + k)H =$1 × 1.25+$1 × 1.252+$1 × 1.252 × 1.051 + 0.110(1 + 0.110)2(0.110 − 0.05) × (1 + 0.110)2 = $24.59

Which of the following statements are true if the efficient market hypothesis holds?

It implies that prices reflect all available information. This is the definition of an efficient market.

Suppose you find that prices of stocks before large dividend increases show on average consistently positive abnormal returns. Is this a violation of the EMH?

No. No, this is not a violation of the EMH. This empirical tendency does not provide investors with a tool that will enable them to earn abnormal returns; in other words, it does not suggest that investors are failing to use all available information. An investor could not use this phenomenon to choose undervalued stocks today. The phenomenon instead reflects the fact that dividends occur as a response to good performance. After the fact, the stocks that happen to have performed the best will pay higher dividends, but this does not imply that you can identify the best performers early enough to earn abnormal returns.

No Growth Model

Special case: Preferred Stock -A preferred stock pays a $2.00 per share dividend and the stock has a required return of 10%. What is the most you should be willing to pay for the stock?

13-8Intrinsic Value, V0

The PV of a firm's expected future net CFs discounted by a risk adjusted required rate of return The cash flows on a stock are? -Dividends (Dt) -Sale price (Pt) Intrinsic Value today (time 0) is denoted V0 and for a one year holding period may be found as: V0=E(D1)+E(P1)/(1+k)

Strong-Form Tests: Inside Information

The ability of insiders to trade profitability in their own stock has been documented in studies by Jaffe, Seyhun, Givoly, and Palmon SEC requires all insiders to register their trading activity

Estimating Discount Rates forDividend Discount Models

The discount rate for a stock can be estimated using the capital asset pricing model (CAPM ). We can estimate the discount rate for a stock as: (k) = U.S. T-bill Rate + (Stock Beta x Stock Market Risk Premium) T-bill Rate:Risk free rate/return on U.S. T-bills (Rf) Stock Beta:risk relative to an average stock (how much does my stock move if the market moves 1%) Stock Market:risk premium for an average stock Risk Premium:(Rm-Rf)

The Dividend Discount Model:1. Estimating the Growth Rate

The growth rate in dividends (g) can be estimated in a number of ways: 1.Using the company's historical average growth rate. 2.Using an average growth rate per industry 3.Using the sustainable growth rate

So, Are Markets Efficient?

The performance of professional managers is broadly consistent with market efficiency. Most managers do not do better than the passive strategy. There are, however, some notable superstars: -Peter Lynch, Warren Buffett, John Templeton, George Soros

Expected Holding Period Return

The return on a stock investment comprises cash dividends and capital gains or losses •Assuming a one-year holding period

Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%.You estimate that a passive portfolio invested to mimic the S&P 500 stock index provides an expected rate of return of 13% with a standard deviation of 25%. a. What is the slope of the CML?

a. Slope of the CML =E(rM) − rf/σM =0.13 − 0.07/0.25 = 0.24

Suppose the yield on short-term government securities (perceived to be risk-free) is about 4%. Suppose also that the expected return required by the market for a portfolio with a beta of 1 is 12%. According to the capital asset pricing model: a. What is the expected return on the market portfolio? b. What would be the expected return on a zero-beta stock? Suppose you consider buying a share of stock at a price of $40. The stock is expected to pay a dividend of $3 next year and to sell then for $41. The stock risk has been evaluated at β = -0.5. c-1. Using the SML, calculate the fair rate of return for a stock with a β = -0.5. c-2. Calculate the expected rate of return, using the expected price and dividend for next year. c-3. Is the stock overpriced or underpriced?

a. Since the market portfolio, by definition, has a beta of 1.0, its expected rate of return is 12%. b. β = 0 means the stock has no systematic risk. Hence, the portfolio's expected rate of return is the risk-free rate, 4%. c-1. Using the SML, the fair rate of return for a stock with β = -0.5 is:E(r) = 4% + (-0.5) × (12% - 4%) = 0.0% c-2. The expected rate of return, using the expected price and dividend for next year:E(r) = ($41 + $3)/$40 - 1 = 0.10 = 10% c-3. Because the expected return exceeds the fair return, the stock must be under-priced.

Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 27%. The T-bill rate is 7%.A client prefers to invest in your portfolio a proportion (y) that maximizes the expected return on the overall portfolio subject to the constraint that the overall portfolio's standard deviation will not exceed 20%. A. What is the investment proportion, y? B.What is the expected rate of return on the overall portfolio?

a. Standard deviation of the complete portfolio = σC = y × 0.27 If the client wants the standard deviation to be equal or less than 20%, then: y = (0.20/0.27) = 0.7407 = 74.07% He should invest, at most, 74.07% in the risky fund. b. E(rC)=rf + y × [E(rP) − rf] =0.07 + 0.7407 × 0.10 = 0.1441 or 14.41%

Different Rates of Returns a. What rates of returns do we need to use? b. There are several candidates each with its own advantages and shortcomings:

a. What if you want to know how a fund has performed over a 5-year period? What if the fund experienced both cash inflows and outflows? b.-Arithmetic average returns -Geometric average returns -Dollar-weighted return -Time-weighted return

Consider the following information: Portfolio Expected Return Beta Risk-free 10% 0 Market 18 1.0 A 16 0.9 a. Calculate the expected return of portfolio A with a beta of 0.9. b. What is the alpha of portfolio A. c. If the simple CAPM is valid, is the above situation possible?

a.Not possible. Here, the required expected return for Portfolio A is: 10% + (0.9 × 8%) = 17.2% b. This is still higher than 16%. Portfolio A is overpriced, with alpha equal to: -1.2% c. No.

What do you think would happen to the expected return on stocks if investors perceived an increase in the volatility of stocks? Assuming no change in tastes, that is, an unchanged risk aversion, investors perceiving higher risk will demand a higher risk premium to hold the same portfolio they held before. If we assume that the risk-free rate is unaffected, the increase in the risk premium would require a________________ expected rate of return in the equity market.

higher

Time-Weighted Returns

ii.Time-weighted returns (TWR):TWRs assume you buy one share of the stock at the beginning of each interim period and sell one share at the end of each interim period. TWRs are thus independent of the amount invested in a given period. To calculate TWRs: •Calculate the return for each time period, typically a year. •Then calculate either an arithmetic (AAR) or a geometric average (GAR) of the returns.

The risk-free rate of return is 5%, the required rate of return on the market is 10%, and High-Flyer stock has a beta coefficient of 1.6. If the dividend per share expected during the coming year, D1, is $3.50 and g = 6%, at what price should a share sell?

k = rf + β[E(rM) − rf) = 0.05 + 1.6 × (0.10 − 0.05) = 0.130 or 13.0% P0 =D1/k-g=$3.50/.130-0.06 =$50.00

Portfolio Betas. If you put half your money in a stock with a beta of 1.5 and 30%of your money in a stock with a beta of 0.9 and the rest in T-bills, what is the portfolio beta?

βP = 0.50(1.5) + 0.30(0.9) + 0.20(0) = 1.02 •All portfolio beta expected return combinations should also fall on the SML. •All (E(ri) - rf) / βi should be the same for all stocks.

Examples of Resistance levels

•A resistance level may arise at say $31.25 if a stock repeatedly rises to $31.25 and then declines, indicating that investors are reluctant to pay more than this price for the stock. -A stock price above $31.25 would then indicate a 'breakout' which would be a bullish signal. •EHM states that any information that was ever available from analyzing past prices has already been reflected in stock prices -Assume there is a resistance level for a stock at $50. Then no one would buy the stock at $49.50. -If no one buys it at $49.50 then $49.50 would become the stock's new resistance level

Expected Return and Risk on Individual Securities

•An individual security's total risk (2i) can be partitioned into: -systematic (market risk) and -unsystematic (firm-specific) risk •Firm-specific risk is diversifiable •Individual security's market risk is measured by BETAcomputed as βi= [COV(ri,rM)] / sM2