Investments Exam 3

Implications of Weak Form EMH

**Technical Analysis is useless •Technical stock analysts (or "chartists") attempt to earn abnormal returns (positive alphas) by timing the market based on sophisticated charting techniques. •If markets are weak form efficient, these technicians should not be able to earn above average, risk-adjusted returns. •Weak form efficiency: Information in past market data does not predict returns. •Returns •Prices •Volume

Efficient Capital Market

A market in which prices reflect all available information.

Perfect Capital Market

A perfectly competitive and informationally efficient market in which there are no market frictions (e.g., no transaction costs or taxes).

What is the measure of systematic risk?

Beta

Beta Correlation

Cov(R(a), R(m))/Var(R(m)) Covariance of the asset and market/ Variance of the market

Market Risk Premium Equation

E(R(mkt)-R(f)

Fama-French 3 Factor Model Equation Break Down

E(r(i) )−r(f) = β(RMRF,i) E(r(RMRF)) +β(SMB,i) E(r(SMB)) +β(HML,i) E(r(HML))) -The factors are the excess returns (or return premiums) to the factor mimicking portfolios (**same across stocks). -The factor loadings, or betas, represent each stock's sensitivity to the factor. (**specific to stock i)

Risk Factors in Fama-French 3 Factor Model

E(r(i) )−r(f) = β(RMRF,i) E(r(RMRF))+β(SMB,i) E(r(SMB))+β(HML,i) E(r(HML))) -Market factor (RMRF): This is the market risk premium, and is the factor from CAPM: r(RMRF) = r(M) − r(f) -Size factor (SMB): This is the return difference between a portfolio of small stocks and a portfolio of large stocks ("Small minus Big"): r(SMB) = r(small) − r(big) -Book-to-market factor (HML): This is the return difference between a portfolio of high book-to-market stocks (e.g., high book value of equity relative to market value of equity) and a portfolio of low book-to-market stocks ("High minus Low"): r(HML) = r(highBM) − r(lowBM) Whether these additional factors do, in fact, measure actual sources of fundamental risk is still a matter of debate. -Empirically, the do help explain average returns. •Maybe book-to-market is a proxy for financial distress risk??? •High book-to-market stocks (e.g., firms with high book value of equity relative to market value of equity) may potentially be near financial distress.

Y axis on SCL

Excess rate of return on the stock (dependent)

What returns do portfolios of small stocks have

Higher average excess returns than large stocks

What returns do portfolios of high book-to-market stocks have

Higher average excess returns than low book-to-market stocks

Idiosyncratic news

How far away from the line the point is

Underpricing and Overpricing

Is relative to something else.

Psychology

Limits to arbitrage • If irrational traders cause deviations from fundamental value, rational traders will often be powerless to do anything about it. • Leaves open the question of what drives these deviations • Psychology • Catalogs the deviations from full rationality we might expect to see • Evidence on the systematic biases that influence: • Beliefs • Preferences

Good news for efficient market hypothesis: Semi-strong form

Money managers are earning an alpha of zero. *BUT this does not mean that markets are efficient because there are limits to arbitrage.

The Fama-French 3 Factor Model

Multifactor Model •Given the empirical evidence that: •small size stocks outperform large size stocks on average •high book-to-market (value) stocks outperform low book-to-market (growth) stocks Fama and French (1993) proposed a model that includes risk factors to address this finding: E(r(i) )−r(f) = β(RMRF,i) E(r(RMRF)) +β(SMB,i) E(r(SMB)) +β(HML,i) E(r(HML))) ***When doing expected return make sure to put risk free rate first then add the equation (risk free is subtracted in equation above from the left side, so add to the right side) CAPM: E(r(i) )−r(f) = β(RMRF,i) E(r(RMRF)) The rest is the added risk factors

MOST IMPORTANT PART OF EMH

Prices reflect all available info, therefore can't earn positive alpha/abnormal returns trading on information.

CAPM equilibrium expected return

R(f) +B(i)[E(R(m))-R(f)]

Alpha (α) Equation

R(i) - R(f) +B(i)[E(R(m))-R(f)] OR Expected return- CAPM

Slope of SML

Rise/Run OR E(R(mkt))-R(f)/1

Estimating Beta: Data and Proxies

To estimate beta, we need historical returns for the stock inquestion and for the market portfolio. We will use 60 monthlyexcess returns to estimate beta. Our proxy for the market portfolio will be the return on a value-weighted index of stocks on the NYSE, Amex, and Nasdaq. (Another proxy thatis often used in practice is the return on the S&P 500. Ourindex is even broader than the S&P 500.)

Parity

Trading at the correct ratios that they should be at. Mispricing is when its greater than parity. Look at example in PP (Royal Dutch and Shell: 1.5/1)

Mispricing Calculation

Use the Alpha Equation: R(i) - R(f) +B(i)[E(R(m))-R(f)] α > 0 = long α < 0 = short

Why can't we do a pure empirical test of CAPM?

We cannot measure the true market portfolio

Testing Semi Strong Form EMH: Post-Earnings Announcement Drift

What happens when good news is made public? •In efficient markets, the stock price should jump immediately. -Look at graph in PP -Firms placed into deciles (10 portfolios) based on their earnings surprise. •Standardized UnexpectedEarnings (SUE)= Actual Earnings -Expected Earnings •The market adjusts to the earnings information gradually.

CAPM Applications α > 0 α < 0

α > 0 = If the manager has exceeded the benchmark return α < 0 = If the manager has underperformed the benchmark -Of course, there are other benchmarks available besides CAPM. -Investment performance evaluation: CAPM can provide us with a benchmark return, based on the beta of the portfolio being managed. This allows us to compare the actual realized return to the CAPM equilibrium return.

Availability Bias

• Estimated probabilities may be biased by whether or not all 'memories' are equally retrievable.

Loss Aversion

• People are risk averse over gains but risk seeking over losses. • Potential losses are given more weight than potential gains, which is inconsistent with standard expected utility theory.

Anchoring Bias

• When forming estimates, people start with an (arbitrary?) value and adjust away from that.

Random Walk with a Positive Trend

•If stock prices follow a random walk, changes in stock prices are random. •But it is possible to have a random walk around a trend. •Expected price change is positive over time •Positive trend, but random around the trend **Look at PP for graph showing this trend (EMH PP) •On a day-to-day basis, the expected price change is close to zero •The trend is not very useful for stock price predictability. -Random walk with a drift: However, since the gain on the investment is greater than the loss on the investment, there is an upward trend to this process. The drift equals the expected value out of the outcome.

HML Risk Premium

Interpret HML as the risk premium that compensates investorsfor taking on the risk of owning high book-to-market stocks.

SMB Risk premium

Interpret SMB as the risk premium demanded by investors for taking on the additional risk of holding small firms relative to large firms.

Regret Avoidance

Investors are reluctant to bear losses due to their unconventional decisions.

Mental Accounting

Investors exhibit less risk tolerance in their retirement accounts versus their other stock accounts -Failure to consider total return (investor preference for dividends over capital gains)

Testing Weak Form Efficiency: Autocorrelation

Regress today's return on yesterday's return: r(i ,t) = α + γ(i) r(i ,(t−1)) + e(i ,t) *Symbol e is a different symbol on PP -Comparing yesterday's return with today's return -Look at Weak Form PP and look at the graph -Regress: -Independent: Yesterday's returns -Dependent: Today's returns -All info in yesterday's prices are in today's prices... no relationship between the 2 (no autocorrelation)

T-stat

T-stat > 2 : statistically significant: trust it more T-stat < 2: not statistically significant **T-stat is an absolute value so it doesn't matter if its positive or negative it just has to be greater than or less than 2. -Has to do with the precision of alpha and beta

Testing Weak Form EMH: Momentum Effects

**Test: Can I earn alpha by longing winners and shorting losers? •Generally, there is plenty of evidence suggesting that markets are weak form efficient. However, there is some more recent evidence related to momentum trading strategies that challenge this. •Ultimately, we have to consider whether or not any supposed deviations from efficiency (e.g., abnormal returns) are within arbitrage bounds (transactions costs). •There is evidence (Jegadeesh and Titman (1993)) that portfolios display momentum effects over intermediate horizons (3-12 months). •This evidence shows that both good and bad performance is persistent (for portfolios) over this horizon.

Interpreting Anomalies

-Again, the biggest challenge is interpreting the evidence. There are a few different interpretations: •Mispricing: market inefficiencies with profit opportunities •Mispricing, but still inside arbitrage bounds. •Not profitable after costs. •Risk premiums •Joint hypothesis problem: need a better model for expected returns. •Data mining concerns •Behavioral interpretations to explain inefficient mispricings.

Testing Semi Strong Form EMH: Event Studies

-Aim to test whether or not stock prices react quickly and efficiently to new information. -They measure abnormal returns (alphas) around certain information events, and test for such things as overreaction, underreaction, and delayed reactions around the "event". •These studies have been applied to various types of supposed information events: •Dividend announcements •Earnings announcements •Mergers •Changes in CEOs •Security offerings

Testing CAPM

-CAPM is one of many asset pricing models that characterizesequilibrium rates of return. •We can test how well its predictions hold up in reality. •We run a regression of historical excess stock returns onto the historical excess returns of the market portfolio Note that E(ei ,t ) = 0 •CAPM predicts: •ˆαi = 0 •ˆβi = βi

Capital Budgeting NPV > 0 NPV < 0

-CAPM provides us with the required rate of return, or hurdle rate, of a capital project based on the project's beta. -If the project's actual expected return exceeds the CAPM return, the project has NPV > 0. -If the actual expected rate of return is less than the CAPM required return, then NPV < 0.

Security Market Line (SML)

-Describes the equilibrium relationship between the systematic risk of any individual asset (or portfolio) and its expected return. -It is the expected return-beta relationship for any asset or portfolio since beta is our measure of systematic risk.

Relationship between Efficient and Perfect Capital Markets

-Efficient markets are not necessarily perfect markets. A perfect capital market is a stronger condition. •Many theories in finance assume perfect capital markets.

Pricing Anomalies

-Empirical research has identified so-called pricing "anomalies" thatsuggest markets may be inefficient. •Small-firm effect (Small vs. large firms) •Book-to-market effect (Value vs. growth firms) •January effect •IPO performance •Large underpricing on day of issuance •Long-term underperformance •Momentum effects •Past winners outperform past losers •Post earnings announcement drift •And others...

Testing Semi Strong Form EMH: Performance Evaluation Tests

-Evaluation tests examine whether professional money managers (e.g., active mutual fund managers) can out perform on a risk-adjusted basis. •In general, the results show that active managers do not, on average, outperform broad-based indices or passively managed index funds after costs. -Look at PP for Mutual Fund Performance graph

Information Signals

-Firm: Financial statements, business plans, specific announcements -Competitors and Suppliers: Competition, Market share, product quality -Macroeconomy: GDP growth, Employment, Industrial production -Investment and brokerage community: Security analysis, earnings and dividends forecasts, value assessments, buy and sell recommendations

Behavioral Finance: Limits to Arbitrage Theory

-Investment strategies that attempt to take advantage of mispricing can be risky and costly: Implies mispricing may persist. •Fundamental risk: •Recall a true arbitrage opportunity is riskless. •In practice, investors use another risky asset as an (imperfect) hedge, retaining some firm-specific risk. •Noise trader risk: •Temporary mispricings may get worse. •If the arbitrageur is a portfolio manager, naive investors may see negative returns, withdraw their funds, and force the arbitrageur to close the position early. •Implementation costs: •Commissions •Bid-ask spreads •Price impact •Costly to learn about mispricing

Disposition Effect

-Investors are reluctant to sell stocks with "paper" losses. -Ignore the tax benefits and focus on a reluctance to realize losses. Alternatives are evaluated not in terms of final outcomes but rather in terms of gains and losses relative to the original price. Manipulation by changing the reference point. -Investors reluctant to sell stocks that are losers, but quick to sell stocks that are winners. • Inconsistent with tax considerations • Stocks that are sold outperform those that are held onto • Related to momentum in stock returns?

α (ALPHA) < 0

-Negative abnormal return -Security is overpriced relative to CAPM -BELOW THE SML -Short

Belief Perseverance Bias

-Once people form an opinion, they hold onto it tightly and for too long. • View evidence that contradicts their beliefs with skepticism. • Confirmation bias: -People misinterpret evidence that contradicts their beliefs as being supportive. -If people start out believing in EMH, they may continue to believe even after finding evidence against it.

Testing Weak Form EMH: Negative Autocorrelation

-Periods with positive (negative) returns are followed by periods with negative (positive) returns. •Reversal effect -Different signs -SELL (short)

α (ALPHA) > 0

-Positive abnormal return -Security is underpriced relative to CAPM -ABOVE THE SML -Buy

X axis on SCL

Excess rate of return on the market index (independent)

R^2

-R^2 = Systematic risk/Total Risk = β(i)^2*Var(R(mkt))/Var(R(i)) =β(i)^2*Var(R(mkt))/β(i)^2* Var(R(mkt))+Var(E(i)) -Steeper the slope, higher the R^2, less idiosyncratic risk, points are closer to the line. More systematic risk... goes with the market -Flatter the slope, lower the R^2, more idiosyncratic risk, points are farther away from the line. Less systematic risk... doesn't go with the market

Testing Semi Strong Form EMH: Market Efficiency in Real Time

-Study stock price reaction and trading after a stock is featured on CNBC's Morning Call or Midday Call (322 observations: 6/2000 - 10/2000). •Price reaction is quick: •Response to positive announcement occurs within 1 minute •Response to negative announcement more gradual, around 15 minutes •Higher cost of short selling? -Some viewers trade on this information •Trading intensity more than doubles in first minute after announcement •Traders who execute within 15 seconds of the initial mention generate small but significant short-term profits for positive reports during Midday call. -Look at graph in PP

Weak Form

-The weak-form information set (Φw) includes the history of all security prices and returns. -Historical Prices and returns info -Useless to use technical analysis with this form -Weak form efficiency is generally synonymous with the random walk theory. •A random walk is a statistical process under which successive prices are independent of each other. •According to this theory, changes in stock prices are statistically random, implying that there is no pattern to stock prices. -Stocks fall at a random walk... last step does not tell you where the next step is P(t)= P(t−1) + E (rt) + e(t) *Note the lowercase e is a symbol from PP you need to look at •Intuitively, in an informationally efficient market, stock prices are only sensitive to new information, which by definition, arrives at random intervals. •Changes in price must also be random. -TEST AUTOCORRELATION AND MOMENTUM

Three Forms of EMH

-To determine whether or not markets are efficient, we need to define the information set. -There are three forms of the EMH that differ according to their definition of the relevant information set. -Weak-Form -Semistrong Form -Strong Form -Look at illustration in PP and notes of the circles of the 3 Forms -All of the forms are what info you are given and how you are not able to earn abnormal, risk-adjusted returns with that info.

Estimating CAPM

-To estimate beta, we use historical returns as our proxy for expected returns. We estimate beta by running a regression of excess stock returns onto the excess returns of the market portfolio: r(i ,t) −r(f ,t) = α(i) + β(i) (r(M ,t) −r(f ,t) ) + e(i ,t) -e(i ,t) = standard error (points that aren't on the SCL), residual return -α(i) (ALPHA) = interception -β(i) = slope of SCL and sensitivity -β(i)= Cov (r(i ,t) ,r(M ,t) )Var (r(M ,t) ) -Estimating the above regression gives us the security characteristic line (SCL), where the slope of this line is the estimated beta coefficient:

SML Return equation

E(r)= R(f) + B(E(R(mkt))-R(f))

Fundamental Risk

Even if a security is mispriced, it still can be risky to attempt to exploit the mispricing because the correction to price could happen after the trader's investing horizon. This limits the actions of arbitrageurs who take positions in mispriced securities.

Testing Weak Form EMH: Evidence of Weak Form Efficiency

r(i ,t) = α + γ(i) r(i ,(t−1)) + e(i ,t) *Symbol e is a different symbol on PP -γ: Gamma: not statistically significant from 0. Consistent with a random walk •For individual securities, γ is close to zero (random walk) •For portfolios, γ shows evidence of positive autocorrelation at weekly frequencies •Momentum strategies •Effect is small in magnitude: economically meaningful? •Over long horizons (3 - 5 years) γ shows evidence of negative autocorrelation •Contrarian strategies -How do we interpret long-term negative autocorrelation? •Mean reversion ("fads hypothesis") •Time-varying risk premiums?

Overconfidence Bias

• Evidence shows people have too much confidence in their abilities. • Two forms of overconfidence: 1. Higher expected returns 2. Lower variances • Poor estimation of probabilities • Self-attribution bias: • Past successes due to ability. • Past failure due to bad luck. • People think they are very talented .• Investors with good results think they are skilled • Hindsight Bias: • After an event occurs, people think they predicted it before it happened. • If they think they predicted the past, they might think they can predict the future. -Risk seeking behavior -Excessive trading usually linked to this

Representativeness Bias

• Kahneman and Tversky have conducted many experiments aimed at uncovering biases. • "Linda is 31 years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in anti-nuclear demonstrations." • Which of the following is more likely? 1 Linda is a bank teller. 2 Linda is a bank teller and is active in the feminist movement. -1 is correct because you are relying too much on the data given if you say 2. You don't know if she's a feminist. • What does our theory of probability tell us is the more likely answer? Prob(statement 1|description) = Pr (description|statement 1)Pr (statement 1)/ Pr (description) • Sample size neglect • People will infer the data generating process too quickly based on too few data points. • Is a financial analyst with four good stock picks talented? • "Hot Hand" fallacy -Investors disregard sample size when forming views about the future from the past.

Conservatism Bias

• Opposite of representativeness • If data doesn't seem to be representative, people don't react enough and rely too much on their priors. -Investors are slow to update their beliefs when given new evidence.

CAPM Problems

•CAPM is a single-factor asset pricing model, where the factor is the excess return on the market portfolio. •The empirical evidence suggests this factor alone does not fully explain asset returns. •SMALL stocks and VALUE stocks have higher returns than predicted by CAPM. •Perhaps there are other risk factors, in addition to market-risk (β(mkt) ), that influence returns.

Behavioral Finance: Limits to Arbitrage

•Efficient Markets •"Prices are right": Prices reflect the information of investors who are doing the best they can. •"No free lunch": No investment strategy can earn excess risk-adjusted returns (alphas are zero). •If investors observe a mispriced security, they will undertake a strategy to take advantage of the mispricing. •Limits to arbitrage: Difficult for rational traders to undo the dislocations caused by less rational traders.

Testing Semi Strong Form EMH: Event Study Methodology

•Identify a sample of events (e.g., merger announcements). •For each event, collect a time series of security returns (and market index returns) surrounding the event date (designated t = 0). •Estimate the abnormal return (α(i ,t)) for each security i for each period t around the event day. (can be before or after event) •Form "portfolios" by aligning the time series for each security in "event time." •For example, you might analyze data from 10 trading daysbefore and after a merger announcement (−10 ≤t ≤10). •Compute average abnormal returns for each period in "event time": Take alphas of both stocks in the event at whatever date before/after event and divide by amount of stocks to get average alpha. -Compute cumulative abnormal returns (CAR) -If the sample size (N) is large, any cross-sectional correlation between alphas should be event-related. •If the market is semistrong-form efficient, we should expect α(t) ≈0 for t > 0. •In other words, the market response to new information should be quick and accurate. •Joint hypothesis problem •Event studies are tests of a joint hypothesis •Markets are semistrong-form efficient and the asset pricing model (CAPM) is correct. •Rejection of the hypothesis may be attributable to the failure of either or both of the joint hypotheses.

Testing Weak Form EMH: Random Walks and Autocorrelation

•If the market is weak-form efficient, then security returns innon-overlapping periods should be uncorrelated. •Either positive or negative autocorrelation implies a violation of weak-form EMH. -You want 0 autocorrelation for weak-form EMH. •Essentially, tests for autocorrelation are tests for random walks in stock prices.

Efficient Market Hypothesis (EMH)

•In the New Palgrave Dictionary of Money and Finance, Burton Malkiel offers the following definition of market efficiency: •A capital market is said to be efficient if it fully and correctly reflects all relevant information in determining security prices. •Formally, the market is said to be efficient with respect to some information set ... if security prices would be unaffected by revealing that information to all participants. •Moreover, efficiency with respect to an information set ...implies that it is impossible to make economic profits by trading on the basis of that information set. -Economic profits = α > 0 = abnormal returns

Behavioral Finance: Traditional Framework

•Investors are rational: Standard assumptions behind all our models •Two components •When investors receive new information, they update their beliefs in a way that's consistent with our models of probability. •Suppose a bucket has 40 red balls and 40 white balls. If you pick a ball at random, what's the probability you pick a red ball? 50% •Add 20 green balls to the bucket. Now what's the probability you pick a red ball? 40% •Agents make choices that are consistent with our rules for maximizing expected utility. •Suppose you prefer apples to oranges. And you prefer oranges to bananas. •What would you rather have: apple or banana?: Apple -Either of these two assumptions can fail

Interpreting the Evidence CAPM: Mispricing Argument

•Large stocks are overpriced relative to small stocks. •Growth stocks are overpriced relative to value stocks.

CAPM Empirical Evidence

•Large stocks earn lower returns than predicted by CAPM, and small stocks earn higher returns than predicted by CAPM. •Growth stocks (low book-to-market ratios) earn lower returns than predicted by CAPM, and value stocks (high book-to-market ratios) earn higher returns than predicted byCAPM. -***CAPM doesn't do small stocks and value stocks justice. -These results are problematic for CAPM, since CAPM posits that expected returns are determined completely by Beta, and not by size or book-to-market ratios.

Multifactor Models

•Multi-factor asset pricing models may more fully describe the determinants of expected returns. •Investors may demand additional risk premiums for additional risk factors. •Some models specify what the factors are; others do not.

Empirical Considerations when estimating Beta

•Note that we are using realized returns as a proxy for expectedreturns. This assumes that outcomes in the future will resemble outcomes from the past. •Estimating beta with past data assumes this is representativeof the "true" beta. •Our proxy for the market portfolio does not include certain assets that are in the theoretical market portfolio such as real estate, international stocks, risky bonds, and other nontradeable assets.

Testing Weak Form EMH: Positive Autocorrelation

•Periods with positive (negative) returns are followed by periods with positive (negative) returns. •Momentum effect -Same signs -BUY (long)

Strong Form Efficiency

•Prices reflect all information, both public and private. •Includes information held by corporate insiders. •Implications of strong form: •Even insiders with privileged information are unable to earn abnormal, risk-adjusted returns.

Semistrong Form Efficiency

•Security prices reflect all available public information. •Includes financial statements, annual reports, quarterly earnings reports, dividend announcements, and past changes in prices and volume. **Fundamental Analysis is useless •Implications of semistrong form: •Casts doubt on the usefulness of fundamental analysis. •Securities analysts examine publicly available information, such as financial statements, in an effort to identify undervalued stocks. •If semistrong efficiency holds, these analysts should not be able to produce above average, risk-adjusted returns. •Consider: •There are a large number of securities analysts •Money attracts brains

Interpreting the Evidence CAPM: Risk premium argument

•Small stocks have extra risks in relation to large stocks that are not captured by beta, so investors demand a risk premium for owning small stocks. •Value stocks have extra risks in relation to growth stocks that are not captured by beta, so investors demand a risk premium for owning value stocks.

Testing Weak Form EMH: Momentum and Efficiency

•The risk-adjusted return ( ˆαp ) for a momentum strategy thatis long winners and short losers is significantly positive. •Evidence of a market inefficiency: positive alpha shows markets are not weak form. •Various interpretations: •Mispricing: The positive alpha implies markets are not weak-form efficient •Risk premium: The model of expected returns is not complete. (Momentum may be related to some underlying risk factor we haven't accounted for.) -Joint Hypothesis Problem: A test of market efficiency is simultaneously a joint test of whether the asset pricing model is correct.

Testing Weak Form EMH: Portfolio Tests of the Weak Form EMH

•The weak-form of the EMH implies that portfolios formed using past price or return information shouldn't earn a positive abnormal return. -In order to test the EMH, the researcher must specify a model for expected returns. •In practice, the market or single-index model is frequently selected. = CAPM -Testing CAPM: pay attention to Alpha, market efficiency= alpha = 0 Methodology: •Choose a portfolio formation date. •Form portfolios using a trading rule based on past price or return information. •Estimate the abnormal return of each portfolio (alpha) (ˆα(p) ) by running a regression. r(p) −r(f) = α(p) + β(p) [r(M) −r(f) ] + e(p) r(p) −r(f) = α(p) + β(p) [r(M) −r(f) ] + β(SMB) r(SMB) + β(HML)r(HML) + e(p) *Symbol e is a different symbol on PP