UFL Investments: Chapters 9-13

*Chapter 10: Arbitrage Pricing Theory* Factor Loadings / Factor betas

*find answer on page 326)

*Chapter 11: Efficient Market Hypothesis* Weak-form hypothesis of EMH

- only trade and volume data in stock prices Claims that past price movements and volume data do not affect stock prices, and that stock prices already reflect all information that can be derived by examining market trading data such as history of past prices, trading volume or short interest. Trend analysis is fruitless. The signals are already known and therefore lose their value because a buy signal, for example, would result in an immediate price increase.

*Chapter 11: Efficient Market Hypothesis* Strong-Form Hypothesis

- public and insider in prices Claims that stock prices reflect all info relevant to the firm, even including info available only to the company insiders. This degree of market efficiency implies that profits exceeding normal returns cannot be realized regardless of the amount of research or information investors can access. Strong form efficiency is a component of the efficient market hypothesis and is considered part of the random walk theory. Strong form efficiency states that securities prices and, therefore, the overall market are not random and are influenced by past events. This efficiency is the opposite of weak form efficiency, which states that past events have no effect on current securities prices and price movements.

*Chapter 13: Empirical Evidence on Security Returns* Liquidity embodies which characteristics

1. Trading costs 2. ease of sale 3. necessary price concessions to effect a quick transaction 4. market depth 5. price predictability

*Chapter 12: Behavioral Finance & Technical Analysis* Behavioral Biases

A. *Framing*: Decisions are affected by how choices are described, such as uncertainty is posed as potential gains from a low baseline level, or as losses from a higher baseline value. B. *Mental Accounting*: Where people segregate certain decisions. Statman argues that mental accounting is consistent with some investors' irrational stock preferences, where they sell those with gains than those with losses -- contrary to tax minimizing strategies. The "house money effect" contributes here -- see page 392 C. *Regret Avoidance*: People blame themselves more when a decision turns for the worst, and it was a more unconventional decision. This idea is linked to the size and book-to-market effect, because those firms are "out-of-favor" and more likely to be in a precarious position/are less conventional investments. D. *Affect*: A feeling of good or bad that consumers may attach to a potential purchase/stock. pg 393 for examples E. *Prospect Theory*: Conventional view says that utility depends on the LEVEL of wealth, whereas the Behavioral view says that investor utility depends on CHANGES in current wealth.

*Chapter 9: CAPM* Why is the Capital Allocation Line (CAL) the same as the Capital Market Line (CML) here?

Because the market portfolio is the aggregation of all these identical risky portfolios, it too will have the same weights. So, if all investors choose the same risky portfolio, then it must be the market portfolio, which is the value-weighted portfolio of all the assets.

*Chapter 11: Efficient Market Hypothesis* Random Walk

Changes in the price of stocks should be random and unpredictable.

*Chapter 13: Empirical Evidence on Security Returns* Consumption growth and market rates of return ICAPM

Consumption model implies that what matters to investors is not their wealth per se, but their lifetime flow of consumption. So, we are better off using the covariance of returns with aggregate consumption to measure security risk (CCAPM).

*Chapter 9: CAPM* Determine the fair risk premium of stock X

E(Rx) = [COV(Rx,Rm) / σ2,m] X E(Rm) Or, you could use: E(Rx) = rf + βx[E(Rm) - rf]

*Chapter 13: Empirical Evidence on Security Returns* Measurement error in Beta

If right hand side variable of a regression equation is measured with error (beta), then the slope coefficient of this equation will be biased downward and intercept biased upward.

*Chapter 9: CAPM* The reward-to-risk ratio, or Market Price of Risk, for investments in a market portfolio is:

Market risk premium / market variance [E(rM) - r𝑓] / σ2,m

*Chapter 10: Arbitrage Pricing Theory* Would interest rate betas be negative or positive as interest rates increase?

Negative, as a rise in interest rates is bad news for most firms. (denoted by, ei)

*Chapter 13: Empirical Evidence on Security Returns* Momentum: A fourth factor

On top of the Fama-French three-factor model, a fourth factor has come to be added to the standard controls for stock return behavior = the MOMENTUM FACTOR. (Jegadeesh, Titma, Carhart) Added this momentum effect to the 3 factor model to evaluate MUTUAL FUND PERFORMANCE. Carhart found that much of what appeared to be the alpha of many mutual funds could in fact be explained as due to their loadings or sensitivities to market momentum.

*Chapter 10: Arbitrage Pricing Theory* Law of One Price

States that if two assets are equivalent in all economically relevant respects, they should have the same market price. Should there be a difference in price of Stock A on NYSE vs. on NASDAQ, arbitrage activity will take advantage of that "riskless" opportunity, yet in the process, will build up the price where it is lower until, eventually, the arbitrage opportunity is eliminated.

*Chapter 11: Efficient Market Hypothesis* Technical analysis vs. fundamental analysis

Technical analysis uses price and volume to predict future stock prices. Fundamental analysis Economic and accounting information

*Chapter 11: Efficient Market Hypothesis* What is the Efficient Market Hypothesis (EMH)?

The Efficient Market Hypothesis, or EMH, is an investment theory whereby share prices reflect all information and consistent alpha generation is impossible. Theoretically, neither technical nor fundamental analysis can produce risk-adjusted excess returns, or alpha, consistently and only inside information can result in outsized risk-adjusted returns. According to the EMH, stocks always trade at their fair value on stock exchanges, making it impossible for investors to either purchase undervalued stocks or sell stocks for inflated prices. As such, it should be impossible to outperform the overall market through expert stock selection or market timing, and the only way an investor can possibly obtain higher returns is by purchasing riskier investments. Real world implication: Proponents of the Efficient Market Hypothesis conclude that, because of the randomness of the market, investors could do better by investing in a low-cost, passive portfolio.

*Chapter 9: CAPM* Liquidity

The ease and speed with which an asset can be sold at fair market value.

*Chapter 9: CAPM* Mutual fund theorem

The mutual fund theorem is an investing strategy suggesting the use of mutual funds exclusively in a portfolio for diversification and mean-variance optimization.

*Chapter 9: CAPM* Concept 9.1: If there are only a few investors who perform security analysis, and all others hold the market portfolio, M, would the CML still be the efficient CAL for investors who do not engage in security analysis?

We can characterize the entire population by two representative investors: uninformed, one who doesn't engage in security analysis and holds the market portfolio, and informed, who optimizes the Markowitz algorithm with input from security analysis. The uninformed investor doesn't know what input the informed investor uses to make portfolio purchases. The uninformed investor knows, however, that if the other investor is informed, the market portfolio proportions will be optimal. Therefore, to depart from these proportions would constitute an uninformed bet, which will, on average, reduce the efficiency of diversification with no compensating improvement in expected returns.

*Chapter 10: Arbitrage Pricing Theory* When does an *Arbitrage* opportunity arise?

When an investor can earn riskless profits without making a net investment

*Chapter 11: Efficient Market Hypothesis* Selection bias issue

When one holds a successful investment strategy to themselves instead of sharing it with everyone --- contradictory to the EMH. It is evident that successful investment strategies are not being reported to the public, only those which do not provide investment rewards are available to the mass investors.

*Chapter 9: CAPM* The reward-to-risk ratio for investments in a particular stock is:

X's contribution to risk premium / X's contribution to variance w,xE(Rx) / w,xCOV(Rx, Rm) = E(Rx)/COV(Rx, Rm)

*Chapter 10: Arbitrage Pricing Theory* Is a portfolio well diversified if... it's invested in a large N number of shares. However, half the securities are weighted at 1.5N and the other shares are .5/n?

Yes. Even though some stocks have three times the weight of the other stocks (1.5/n vs. .5/n), the weight on all stocks approches zero as n increases. The impact of any individual stock's firm-specific risk will approach zero as n becomes ever larger. A portfolio that includes a variety of securities so that the weight of any security is small. The risk of a well-diversified portfolio closely approximates the systematic risk of the overall market, and the unsystematic risk of each security has been diversified out of the portfolio.

*Chapter 13: Empirical Evidence on Security Returns* Behavioral explanations

(Chan, Karceski, Lakonishok) The value premium is a manifestation of market irrationality, stemming largely from overreaction. They found that past growth is extrapolated and then impounded in price -- so, high past growth leads to higher prices and lower B/M ratios, but B/M at the beginning of a 5-year period shows little or even positive associations with growth; in other words, the firms with lower B/M experience no better or even worse average future income growth than other firms. (La Porta, Lakonishok, Shleifer, Vishny) Examine stock price performance when actual earnings are released to the public. THey found that growth stocks underperform value stocks surrounding earnings announcements.

*Chapter 13: Empirical Evidence on Security Returns* Size and B/M as Risk Factors

(Liew and Vassalou) Returns on style portfolios (HML or SMB) seem to predict GDP growth, and thus may, in fact, capture some aspects of business cycle risk. HML = high minus low investment factor SMB = small minus big investment factor (Petkova and Zhang) Also tried to tie the average return premium on the value (high B/M) portfolios to risk premiums, where they used a conditional CAPM. Pg 429 - They found a countercyclical vale beta: the beta of the HML portfolio is negative in good economies, meaning that the beta of value stocks (high book-to-market) is less than that of growth stocks (low B/M), but the reverse is true in recessions.

*Chapter 10: Arbitrage Pricing Theory* Using the factor portfolios below, find the equilibrium rate of return on a portfolio with β1 = .2 and β2 = 1.4 E(r1) = 10% E(r2) = 12% rf = 4%

**E(Ri) = rf + βp1 [E(r1) - rf] + βp2 [E(r2) - rf]** E(Ri) = 4 + .2(10-4) + 1.4(12-4) E(Ri) = 4 + 1.2 + 11.2 E(Ri) = 16.4%

*Chapter 9: CAPM* CAPM additional assumptions:

*1. Individual behavior* A. Investors are rational, mean-variance optimizers B. Investors use identical input lists, referred to as homogenous expectations C. Their planning horizon is a single period D. Investors are price takers *2. Market structure assumptions* A. All assets are publicly traded (short positions are allowed) and investors can borrow or lend at a common risk-free rate B. All information is publicly available C. No taxes D. No transaction costs

*Chapter 9: CAPM* Excess return on any stock and risk premium and variance of excess return on stock

*Excess return on any stock* Ri = αi + βi,Rm + εi Ri = excess stock returns εi = firm-specific, zero-mean residual (excess) *Risk premium on excess return* E(Ri) = αi + βi,E(Rm) *Variance on excess returns* σ2,i = βi,σ2m + σ2(εi) *Return on a portfolio "Q"* Rq = αq + βq,Rm + εq

*Chapter 10: Arbitrage Pricing Theory* Two-Factor risk model

*Ri = E(Ri) + βi,GDP + β(of i,IR)(IR) + ei* IR = any change in interest rates ei = firm-specific influences Macroeconomic factors being used here: 1. Uncertainties surrounding the state of the business cycle (measuring changes in GDP) 2. Changes in interest rate EX: R = .133 + 1.2(GDP) - .3(IR) + e Northeast airlines is highly susceptible to GPD swings, but not inflation swings. So, this info tells us that Expected Excess rate of return for Northeast is 13.3%, but that for every % point increase in GDP the return shares increase, on av, by 1.2%, while for every unanticipated % point the interest rate increases, its shares fall by .3%. *However, the multifactor model only describes the factors that affect security returns -- there is no theory in the equation. So, we turn to the APT to better determine the expected value E(R) *

*Chapter 12: Behavioral Finance & Technical Analysis* Kondratieff Waves

- Described how the economy moves in long waves lasting for 48 - 60 years. A Kondratieff Wave is a long-term economic cycle believed to result from technological innovation and produce a long period of prosperity. Nikolai D. Kondratieff noticed agricultural commodity and copper prices experienced long-term cycles. Kondratieff believed that these cycles involved periods of evolution and self-correction.

*Chapter 12: Behavioral Finance & Technical Analysis* Elliott Wave Theory

- Describes pattern of actual price movements Elliott proposed that trends in financial prices resulted from investors' predominant psychology. He found that swings in mass psychology always showed up in the same recurring fractal patterns, or "waves," in financial markets Elliott made detailed stock market predictions based on reliable characteristics he discovered in the wave patterns. An impulse wave, which net travels in the same direction as the larger trend, always shows five waves in its pattern. A corrective wave, on the other hand, net travels in the opposite direction of the main trend. On a smaller scale, within each of the impulsive waves, five waves can again be found

*Chapter 11: Efficient Market Hypothesis* Semi-Strong Form Hypothesis

- public info in prices Claims that all public info regarding the prospects of a firm must already be reflected in the stock price, or the prices adjust rapidly to all new info. Info such as past stock price, fundamental data on the firm's product line, quality of management, balance sheet composition, patents held earning forecasts and accounting practices. If we had access to all this info, you'd expect it to be reflected in the stock prices. Semi-strong form efficiency contends that security prices have factored in available market and non-public market information (NMPI). It concludes that neither fundamental nor technical analysis can be used to achieve superior gains and suggests that only material nonpublic information (MNPI) would benefit investors seeking to earn above average returns on investments.

*Chapter 13: Empirical Evidence on Security Returns* The effect of liquidity on an asset (is composed of 2 factors)

1. *Transaction costs* that are dominated by the bid-ask spread that dealers set to compensate for losses incurred when trading with informed traders 2. *Liquidity risk* resulting from covariance between changes in asset liquidity cost with bond changes in market-index liquidity cost and with market-index rates of return

*Chapter 11: Efficient Market Hypothesis* EMH tenants

1. All investors perceive all available information in precisely the same manner. 2. No single investor is ever able to attain greater profitability than another with the same amount of invested funds: their equal possession of information means they can only achieve identical returns. 3. No investor should ever be able to beat the market, or the average annual returns that all investors and funds are able to achieve using their best efforts.

*Chapter 10: Arbitrage Pricing Theory* APT Key Propositions

1. Security returns can be described as a factor model 2. There are sufficient securities to diversify away idiosyncratic risk 3. well-functioning security markets do not allow for the persistence of arbitrage opportunities

*Chapter 9: CAPM* What are some challenges to the CAPM? pg. 305

1. Short positions are not as easy to take as long ones (because... A. The liability of investors who hold a short position in an asset is potentially unlimited, since the price may rise without limit. Hence a large short position requires large collateral, and proceeds cannot be used to invest in other risky assets. B. There is a limited supply of shares of any stock to be borrowed by would-be short sellers. It often happens that investors simply cannot find shares to borrow in order to short. C. Many investment companies are prohibited from short sales. the US and other countries further restrict short sales by regulation. 2. Unrealistic assumptions A. All assets trade (challenged on pg 313) B. There are no transaction costs C. A single time horizon

*Chapter 13: Empirical Evidence on Security Returns* What were some of the difficulties to the tests of the CAPM?

1. Stock returns are volatile, which lessons the precision of any test of av return 2. Fundamental concerns about the validity of the tests (market index probably different from the one used with the CAPM).

*Chapter 13: Empirical Evidence on Security Returns* 3 Measures of Liquidity

1. price reversals? (Pastor, Stambaugh) If stock price movements tend to be partially reversed on following day, then we can conclude that part of the original price change was not due to perceived changes in intrinsic value, but instead a symptom of price impact associate with the original trade. PG 433 2. Association between large trades and price movements. ILLIQ = Monthly average of daily [absolute value (stock return) / dollar volume] (Amihud) -- this can be used to estimate both liquidity cost and risk. (Acharya and Pederson) use Amihud's measure to test for price effects associated with average LEVEL of liquidlity as well as liquidity risk premium. They demonstrate that expected stock returns depends on the av level of illiquidity. 3. Trade-by-trade data via asymmetric information (Sadka). He uses regression analysis to break out the component of price impact that is due to information issues. The liquidity of firms can wax or wane as the prevalence of informationally motivated trades varies, giving rise to liquidity risk.

*Chapter 10: Arbitrage Pricing Theory* Factor Portfolio

A "tracking portfolio": A well-diversified portfolio constructed to have a beta of 1.0 on one factor and a beta of 0 an any other factor. A tracking portfolio where the returns on such a portfolio track the evolution of particular sources of macro risk but are uncorrelated with other sources of risk. Multifactor model (here, two factors F1, F2): *Ri = E(Ri) + β1,F1 + β2,F2 + εi* **E(Ri) = rf + βp1 [E(r1) - rf] + βp2 [E(r2) - rf]** ^^ use to determine the total return on the portfolio, with two assets or things to compare (factors).

*Chapter 11: Efficient Market Hypothesis* Post-Earnings-Announcement Price Drift By Ball and Brown

A fundamental principle of EMH is that any new info ought to be reflected in stock prices very rapidly. However, price responses to earnings announcements is rather sluggish. And, once released, positive-surprise firms have returns that gradually increase overtime, whereas negative-surprise firms returns gradually decrease overtime. This should not be possible in EMH -- the prices should adjust almost abruptly and stay that way.

*Chapter 12: Behavioral Finance & Technical Analysis* Breadth

A measure of the extent to which movement in the market index is reflected widely in the price movements of the stocks in the market (i.e. the spread between the number of stocks that advance and decline in price).

*Chapter 11: Efficient Market Hypothesis* Book-to-Market Ratios by Fama and French

A powerful predictor of returns across securities is the ratio of the book value of the firm's equity to the market value of equity. They found that beta was not indicative of of average security returns; rather, the book-to-market ratio was more capable of predicting future returns. This is interesting because it would challenge the notion of rational markets, because it seems to imply that systematic risk, which should affect returns, seems to not matter as much as one would assume.

*Chapter 13: Empirical Evidence on Security Returns* Q: If stocks with high liquidity betas have higher average returns, we conclude that liquidity is?

A priced factor, meaning that exposure to it offers higher expected return as compensation for the risk. (Pastor and Stambaugh) conclude that liquidity risk is in fact a priced factor and that the risk premium associated with it is quantitatively significant. and they suggest that liquidity risk factor may account for a good part of the apparent profitability of the momentum strategy.

*Chapter 12: Behavioral Finance & Technical Analysis* Limits to Arbitrage and the Law of One Price (where identical assets should have identical prices)

A. *Siamese Twin Companies*: Two companies that merged should sell at the price of their agreed profit split, 60/40. However, when this happened in real life with Dutch Petroleum and Shell, Shell sold at 10% over its 40 ratio and the premium widened to nearly 17% after 6 years. pg 396 B. *Equity Carve-Outs*: The inability of investors to sell short certain positions, if all are already borrowed or sold short when you needed. C. *Close-ended funds*: These funds incur expenses that ultimately are paid for by investors, and these will reduce share price (such as overhead expenses). Lee, Shleifer and Thaler say that discounts on various funds move together and are correlated with the return on small stocks. These funds are good examples of how apparent anomalies may also have rational explanations. (price/NAV)/NAV = α-E/ σ+E-α

*Chapter 12: Behavioral Finance & Technical Analysis* Investor Sentiment Indicators

A. *Trin Statistic*: Market volume is sometimes used to measure the strength of a market's rise or fall. Trin = (Volume declining/Number declining) / (Volume advancing/Number advancing) Ratios above 1.0 are bearish, or below 1.0 as negative. B. *Confidence Index*: Barron's computes a confidence index using data from the bond market. Confidence index is the ratio of the average yield on 10 top-rated corporate bonds dividend by the average yield on 10 intermediate-grade bonds. Higher values of the confidence index are bullish signals. C. *Put/Call Ratio*: The ratio of outstanding put options to outstanding call options, which typically hovers around 65%. Put options do well in falling markets, call options do well in rising markets, so this can be insightful into market sentiment/predictive of market movements.

*Chapter 13: Empirical Evidence on Security Returns* Example: Determine a sample period of 60 monthly holding periods (5 years). For each of the holding periods, collect the rates of return on 100 stocks, a market portfolio proxy (sp500) and 1-month (risk-free) T-bills. Your data consists of: r,it = 6000 returns (100 stocks over 60 periods) r,Mt = 60 observations of the return over the sample period r,ft = 60 observations of the risk-free rate. A. How many regression estimates of the SCL do we have from the sample? B. How many observations are there in each of the regressions? C. According to the CAPM, what should be the intercept in each of these regressions?

A. How many regression estimates of the SCL do we have from the sample? The SCL is estimated for each stock; so we need to estimate 100 equations. B. How many observations are there in each of the regressions? This sample consists of 60 monthly rates of return for each of the 100 stocks and for the market index. So each regression is estimated with 60 observations. C. According to the CAPM, what should be the intercept in each of these regressions? The SCL should pass through the origin, that is, have a zero intercept

*Chapter 13: Empirical Evidence on Security Returns* EXAMPLES estimating the SML. A. What is the implication of the empirical SML being "too flat"? B. Do high or low beta stocks tend to outperform the predictions of the CAPM? C. What is the implication of the estimate of y2?

A. What is the implication of the empirical SML being "too flat"? When the SML has a positive intercept and its slope is less than the mean excess return on the market portfolio, it is flatter than predicted by the CAPM. B. Do high or low beta stocks tend to outperform the predictions of the CAPM? Low-beta stocks therefore have yielded returns that, on average, were higher than they should have been on the basis of their beta. Conversely, high beta stocks were found to have yielded, on average, lower returns than they should have on the basis of their betas. C. What is the implication of the estimate of y2? The positive coefficient on y2 implies that stocks with higher values of firm-specific risk had on average higher returns. This pattern, of course, violates the predictions of the CAPM.

*Chapter 13: Empirical Evidence on Security Returns* Roll's Critique (Richard Roll)

An economic idea that suggests that it is impossible to create or observe a truly diversified market portfolio. This is an important idea because a truly diversified portfolio is one of the key variables of the capital asset pricing model (CAPM), which is a widely used tool among market analysts. 1. There is a single testable hypothesis with the CAPM: the market portfolio is mean-variance efficient 2. All other implications of the model, the best-known being the linear relation between expected return and beta, follow the market portfolio's efficiency 3. In any returns sample, there will be an infinite number of ex post mean-variance efficient portfolios using the sample period returns and covariances. 4. The CAPM is not testable unless we know the exact composition of the true market portfolio and use it in the tests. This implies that the theory is not testable unless ALL individual assets are included in the sample. 5. Using an index proxy for the portfolio is subject to two difficulties: it might be mean-variance efficient even when the true market isn't and the proxy itself may turnout to be inefficient. *benchmark error* = the use of an incorrect benchmark (market proxy) portfolio in the tests of a theory. 6. (Roll, Ross, Kandel, Stambaugh then added that tests that reject a positive relatinoship between av return and beta, point to inefficiency of the market proxy used in those tests, rather than refuting the theoretical expected return-beta relationship. Fast Facts Roll's critique suggests that one can never fully diversify a portfolio and that even a "market portfolio," such as the S&P 500, is only a proxy for a fully-diversified portfolio. The capital asset pricing model offers a solid foundation for choosing investments to diversify portfolios, but it's limited because it relies on the S&P 500 to simulate the overall market return.

*Chapter 10: Arbitrage Pricing Theory* What is the main idea of the APT?

Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset's returns can be predicted using the linear relationship between the asset's expected return and a number of macroeconomic variables that capture systematic risk. It is a useful tool for analyzing portfolios from a value investing perspective, in order to identify securities that may be temporarily mispriced. *APT formula: E(Rx) = Rf + ∑[βn(RPn - Rf)]* Where: E(Ri): expected return on asset i Rf: risk-free rate ßn : Sensitivity of the asset price to macroeconomic factor n RPn : risk premium associated with factor i The beta coefficients in the APT model are estimated by using linear regression. In general, historical securities returns are regressed on the factor to estimate its beta.

*Chapter 12: Behavioral Finance & Technical Analysis* Behavior Finance

Behavioral finance, a sub-field of behavioral economics, proposes psychology-based theories to explain stock market anomalies, such as severe rises or falls in stock price. The purpose is to identify and understand why people make certain financial choices. This thought argues that literature on trading strategies has missed the larger point: the correctness of security prices. This may be the more important implication because market economies rely on prices to allocate resources efficiently. *Assumptions*: 1. Investors are irrational 2. Arbitrageurs are limited and therefore insufficient to force prices to match intrinsic value. *Two irrationalities*: 1. They don't always process information correctly and therefore infer incorrect probability distributions about future rates of return 2. Given a probability distribution of returns, they often make inconsistent or systematically suboptimal decisions

*Chapter 11: Efficient Market Hypothesis* Bubbles and Market Efficiency

Bubbles seem to arise when a rapid run-up in prices creates a widespread expectation that they will continue to rise. It's hard to defend the position that security prices in these instances represented rational, unbiased assessments of intrinsic value. However, bubbles become obvious only in retrospect. At the time, prices may seem rationally defensible.

*Chapter 13: Empirical Evidence on Security Returns* CAPM review

CAPM predicts EXPECTED rates of returns on assets, relative to a market portfolio of all risky assets. *Expected Return-Beta Relationship* E(r,i) = rf + βi [E(r,M) - rf)] ^^ where β = COV(ri,rM)/σ2M To overcome the CAPM testing difficulties, we usually work with a multi-factor approach, such as a broad market market index (SP 500) and well diversified portfolios are often substituted for individual securities. Results of tests: 1. Expected rates of returns are linear and increase with Beta, the measure of systematic risk. 2. Expected rates of returns are not affected by nonsystematic risks.

*Chapter 9: CAPM* How are expected returns determined?

E(r) are determined by the prices investors must pay compared to the cash flow those investments might garner.

*Chapter 9: CAPM* Investors decide on capital allocation such that: y = [E(rM) - rf ] / A(σ2M) However, the risk premium of market in CAPM

E(rM) = E,A(σ2M) because net borrowing and lending across investors must be zero (they are perfectly offset by each other in CAPM), so the average position in the risky portfolio is 100% or y=1.

*Chapter 9: CAPM* Zero-Beta Model

E(ri) - E(rz) = (E,Rm - E,Rz)[COV(Ri, Rm)/σ2m] which also = βi(E,rm - E,rz) Efficient frontier portfolios have a number of interesting characteristics, independent from CAPM. 1. Any portfolio that's a combo of two frontier portfolios is itself on the efficient frontier 2. Every portfolio on the efficient frontier, except for the global min-variance portfolio, has a "companion" portfolio on the bottom (inefficient) half of the frontier with which it's uncorrelated.

*Chapter 9: CAPM* The CAPM implies that the risk premium on any individual asset or portfolio is the product of the risk premium on the market portfolio and the beta coefficient

E(ri) - r𝑓 = βi[E(rm) - r𝑓) ^^ where the β is the COV of the asset with the market portfolio as a fraction of the σ2 of the market portfolio: βi = COV(ri, rm) / σ2,m

*Chapter 9: CAPM* Multiperiod model --- multi-index model (challenge the single-time period)

E(ri) = βim(E,rm) + ∑(βik(E,rk) k = # sources of extra market risk

*Chapter 12: Behavioral Finance & Technical Analysis* Information processing errors

Error in info processing can lead investors to misestimate the true probabilities of returns. Four biases: A. *Forecasting errors/Memory Bias*: (Kahneman and Tversky) people give too much weight to recent experience vs. prior beliefs when making forecasts, which makes for extreme forecasts. Thus, high P/E firms tend to be poor investments. B. *Overconfidence Bias*: Overestimate the precision of their beliefs/forecasts, and tendency to overestimate abilities. (Barber and Odean) Young, single men with overconfidence trade more than young, single women and they note that high trading activity leads to lower overall performance. C. *Conservatism Bias*: Investors are too slow in updating their beliefs to respond to new evidence and might initially under-react to news about a firm. D. *Sample Size Neglect and Representativeness Bias*: People commonly don't take into account the size of a sample, acting as if a small sample is just as representative of an entire population, which overshoots the intrinsic value. So, they may infer a pattern too quickly and push trends too far into the future.

*Chapter 9: CAPM* Concept 9.3: Suppose that the risk premium on the market portfolio is estimated at 8% with a standard deviation of 22%. What is the risk premium on a portfolio invested 25% in Toyota and 75% in Ford, if they have betas of 1.10 and 1.25, respectively?

First, find the proportions of these investments: βp = wFord,βFord + wToyota,βToyota = (.75x1.25) + (.25x1.10) = .9375 + .2750 = 1.2125 Then, as the market risk premium, E(rm) - r𝑓, is 8%, the portfolio risk premium will be E(rp) - r𝑓 = βp[E(rm) - r𝑓] = 1.2125 x 8 = 9.7%

*Chapter 11: Efficient Market Hypothesis* Small-Firm Effect By Banz

If you divide the NYSE into 10 portfolios, each portfolio consisting of larger and larger stocks, you'd realize that the average annual returns are consistently higher on the small-firm portfolios. Diff between largest and smallest portfolios = 8.52% However, Keim, Reinganum, Blume and Stambaugh all showed that the small-firm effect is really concentrated in the first two weeks of January, so this size effect is basically a "small-firm-in-January" effect.

*Chapter 11: Efficient Market Hypothesis* Is the market efficiency dictated in the EMH possible or realistic?

It's safe to say the market is not going to achieve perfect efficiency anytime soon. For greater efficiency to occur, the following criteria must be met: (1) universal access to high-speed and advanced systems of pricing analysis, (2) a universally accepted analysis system of pricing stocks, (3) an absolute absence of human emotion in investment decision-making, (4) the willingness of all investors to accept that their returns or losses will be exactly identical to all other market participants. It is hard to imagine even one of these criteria of market efficiency ever being met.

*Chapter 11: Efficient Market Hypothesis* Strong-Form Tests: Inside Information by Jaffe, Seyhun, Givoly, and Palmon

Jaffe noticed that stock prices rose or fell marginally after insiders intensively bought or sold their shares in the firm. If markets are efficient though, others should not be able to make profit off these adjustments because once the information is known the price would adjust to FMV and all would become equal again. And, according to Seyhun, following insider transactions would be fruitless. The abnormal returns on such actions are not sufficient enough to overcome the transaction costs.

*Chapter 10: Arbitrage Pricing Theory* APT Key takeaways

Key Takeaways A. Arbitrage pricing theory (APT) is a multi-factor asset pricing model based on the idea that an asset's returns can be predicted using the linear relationship between the asset's expected return and a number of macroeconomic variables that capture systematic risk. B. Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. C. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value.

*Chapter 12: Behavioral Finance & Technical Analysis* Relative Strength

Measures the extent to which a security has outperformed or underperformed either the market as a whole or its particular industry. Ratio of the security's price / the price of the index for the industry

*Chapter 13: Empirical Evidence on Security Returns* Equity premium puzzle of risk aversion

Mehra and Prescott observed that historical excess returns on risky assets in the US are too large to be consistent with economic theory and reasonable levels of risk aversion. (pg 437) Fama and French (Pg 439) suggest that equity premium puzzle is a creature of modern times and suspect that estimating the risk premium from average realized returns may be the problem. They argued that dividend growth rates produce more reliable estimates of the capital gains investors actually expected to earn than the average of their realized capital gains for 3 reasons: 1. Av realized returns exceed internal rate of return on corporate investments 2. estimates from DDM are far higher than those using av historical returns 3. The reward to volatility (sharpe) ratio derived from DDM is far more stable that those derived from realized returns.

*Chapter 11: Efficient Market Hypothesis* The neglected-firm effect and liquidity effects by Arbel and Strebel

Neglected-Firm Effect: Working off of the small-firm-in-January effect, Arbel argued that small firms tend to be neglected by large institutional traders, therefore information about smaller firms is less available, which makes them more risky. As such, small firms HAVE to offer a greater risk premium to make up for their added risk. So, the neglected-firm is both a market inefficiency and a type of risk premium. Brand names, after all, are subject to much greater public scrutiny and accountability. because small-firm and neglected-firms are less-analyzed stocks, they are less liquid, and this liquidity effect means investors are only interested in these options if they offer a rate-of-return premium to off-set the risk and trading costs.

*Chapter 10: Arbitrage Pricing Theory* Is a portfolio well diversified if it's invested in a large N number of shares. However, one half of the portfolio is invested in stock 1, and the rest equally divided among the other n-1 shares?

No. The weight on the first security doesn't decline as N increases. Regardless of how much diversification there is in the rest of the portfolio, you will not shed the firm-specific risk of this security. A portfolio that includes a variety of securities so that the weight of any security is small. The risk of a well-diversified portfolio closely approximates the systematic risk of the overall market, and the unsystematic risk of each security has been diversified out of the portfolio.

*Chapter 11: Efficient Market Hypothesis* Magnitude issue

Only managers of large portfolios can earn enough trading profits to making exploiting minor misprinting worth the effort. To make .1% on a 5billion acct would make you $5mill/year. Worth it. But not worth it if your acct is only worth $10k. According to this view, the actions of intelligent investment managers are the driving force behind the constant evolution of market prices to fair levels.

*Chapter 9: CAPM* What does the CAPM primarily ask and what is is about?

Primarily asks: What would happen if all investors shared an identical investable universe and used the same input list to draw their efficient frontiers. The Capital Asset Pricing Model (CAPM) describes the relationship between systematic risk and expected return for assets, particularly stocks. CAPM is widely used throughout finance for pricing risky securities and generating expected returns for assets given the risk of those assets and cost of capital. Formula for calculating the expected return of an asset and its given risk: *ERi = R𝑓 + βi(ERm - r𝑓)* ERi = Expected return of investment R𝑓 = Risk-free rate βi = Beta of the investment ERm = Expected return of market (ERm - R𝑓) = Market risk premium. Using the CAPM to build a portfolio is supposed to help an investor manage their risk. If an investor were able to use the CAPM to perfectly optimize a portfolio's return relative to risk, it would exist on a curve called the efficient frontier. If a portfolio existed on the efficient frontier it would be providing the maximal return for its level of risk.

*Chapter 9: CAPM* The expected return-beta relationship can be portrayed graphically as the security market line (SML), where the slope is the risk premium of the market portfolio.

SML graphs the individual asset risk premiums as a function of asset risk -- so it provides the required rate of return necessary to compensate investors for risk, as well as the TVM. α (alpha) = the difference between fair and actually expected rates of return on a stock α ... so, if the market return is expected to be 14%, a stock has a β of 1.2, and rf is 6%, the SML would predict the E(ri) = 6 + 1.2(14-6) = 15.6%. ... if one believed the stock would've provided an expected return of 17%, then the implied α would be 1.4% (17-15.6).

*Chapter 12: Behavioral Finance & Technical Analysis* Limits to Arbitrage

Several factors limit the ability to profit from mispricing, such as A. *Fundamental risk*: Risk that even if an asset is mispriced, there is still no arbitrage opportunity, because the mispricing can widen before price eventually converges to intrinsic value. B. *Implementation Costs*: short-selling a security entails costs. Ex: you may have to return the borrowed security on little notice, rendering the horizon of the short sale uncertain. This can limit the ability of arbitrage activity to force prices to FMV. C. *Model Risk*: Some apparent risks may be more apparent than real, depending on whether or not you're using a faulty model.

*Chapter 13: Empirical Evidence on Security Returns* A Macro Factor Model (Chen, roll, ross)

Several possible variables that might proxy for systematic factors (sources of risk): IP = Growth in rate in industrial production EI = Changes in E,i measured by changes in Tbill rates UI = Unexpected inflation defined as the difference between actual and expected inflation CG = Unexpected changes in risk premiums measured by the difference between the returns on corporate Baa-rated bonds and long-term government bonds GB = Unexpected changes in the term premium measured by the difference between the returns on long and short term govt bonds r = a + βM,rM + βEI,EI + βUI,UI + βCG,CG + βGB,GB + e m=market index

*Chapter 10: Arbitrage Pricing Theory* Key Equations

Single factor model: *Ri = E(Ri) + βi,F + εi* Multifactor model (here, two factors F1, F2): *Ri = E(Ri) + β1,F1 + β2,F2 + εi* Single-Index Model (excess return on any security) Ri = αi + βi,Rm + εi *Ri = αi + βi,E(Rm)* Multifactor SML (here, two factors labeled 1, 2: E(Ri) = rf + β1 [E(R1) - rf)] + β2 [E(R2) - rf)] *E(Ri) = rf + β1,E(R1) + β2,E(R2)* ^^ where the risk premiums on the two factors are E(R1) and E(R2) Risk premium on portfolio i (risk premium = alpha): *E(Ri) = Wp, αp = αp(1 / 1-βp)* ^^ where, if βp<1 and the risk premium of 'i' is positive (implying that 'i' returns more than the risk-free rate), borrow and invest the proceeds in Z. ^^ however, if βp>1 and the risk premium of 'i' is negative (implying that 'i' returns less than the risk-free rate), so sell 'i' short and invest the proceeds in the risk-free rate.

*Chapter 9: CAPM* To calculate the variance of the market portfolio, use the bordered covariance matrix with the market portfolio weights.

Stock x ∑wi,COV(Ri, Rx) = COV(∑,wi,Ri, Rx) COV(∑,w1,R1, Rx) = w1(CovR1, Rx)+ w2(CovR2, Rx) +... Also, because ∑wi,Ri = R,M, then ∑wi,COV(Ri, Rx) = COV (Rm, Rx)

*Chapter 13: Empirical Evidence on Security Returns* Fama-French Type Factor Models

Systematic factors in FF are: firm size, book-to-market ratio, and market index. The FF innovation here is a method to quantify the size risk premium. PG 427 *Fama-French three factor asset pricing model* measures the TOTAL RISK PREMIUM. *E(ri) - r𝑓 = ai + βi[E(rM) - r𝑓] + si,E[SMB] + hi,E[HML] HML = high minus low investment factor SMB = small minus big investment factor βi, si, hi = "loading" coefficients *the intercept of the equation should be zero because all returns on the assets should be explained by the coefficients* (Goyal) ran an asset pricing test and confirmed that the FF model improved the CAPM.

*Chapter 10: Arbitrage Pricing Theory* The Treynor-Black (T-B) procedure

The Treynor-Black model is a portfolio-optimization model that seeks to maximize a portfolio's Sharpe Ratio by combining an actively managed portfolio built with a few mispriced securities and a passively managed market index fund. The Treynor-Black model, published in 1973 by Jack Treynor and Fischer Black, assumes that the market is highly, but not perfectly efficient. Some investors have information that can be used to generate abnormal returns, or alpha, from a few mispriced securities. The passively invested market portfolio contains securities in proportion to their market value, and it is assumed that the expected return and standard deviation can be estimated through macroeconomic forecasting. In the active portfolio — which is a long/short fund — each security is weighted according to the ratio of its alpha to its unsystematic risk (the industry-specific risk that is inherently unpredictable. This ratio is called the Treynor-Black ratio or appraisal ratio, and measures the value the security would add to the portfolio, on a risk-adjusted basis. The higher a security's alpha, the higher the weight assigned to it. The more unsystematic risk the stock has, the less weight is assigned to it. Process: 1. Estimate the risk premium (RPm) and SD (σm) of the benchmark portfolio (index). 2. Place all assets that are misplaced into an active portfolio. Call the alpha of the active portfolio αA, its systematic-risk coefficient βA, and its residual risk σ(eA). The optimal risky portfolio will allocate to the active portfolio a weight, w*A. W,0A = W,0A / [1 + W,0A (1-βA)] The allocation to the passive portfolio is then, W*M = 1 - W*A. With this allocation, the increase in the Sharpe ratio of the optimal portfolio, Sp, over that of the passive portfolio, Sm, depends on teh size of the info ratio of the active portfolio, IR,A=αA/σ2(e,A). The optimized portfolio can attain a Sharpe ratio of Sp = square root of: S,squared,of m + IR,squared,of A 3. To maximize the Sharpe ratio of the risky portfolio, you maximize the IR of the active portfolio. This is achieved by allocating each asset in the active portfolio a portfolio weight proportional to W,Ai = αi/σ2(e,i). When this is done, the square of the info ratio of the active portfolio will be the sum of the squared individual info ratios: IR,squared,of A = ΣIR,squared,of i.

*Chapter 10: Arbitrage Pricing Theory* How does APT work?

The arbitrage pricing theory was developed by the economist Stephen Ross in 1976, as an alternative to the CAPM. Unlike the CAPM, which assume markets are perfectly efficient, APT assumes markets sometimes misprice securities, before the market eventually corrects and securities move back to fair value. Using APT, arbitrageurs hope to take advantage of any deviations from fair market value. To an arbitrageur, temporarily mispriced securities represent a short-term opportunity to profit virtually risk-free. However, this is not a risk-free operation in the classic sense of arbitrage, because investors are assuming that the model is correct and making directional trades, so it's using a model to determine the "theoretical" FMV of an asset - rather than locking in true risk-free profits.

*Chapter 12: Behavioral Finance & Technical Analysis Moving averages

The moving average of a stock price is the average price over a given interval, where that interval is updated as time passes. After prices have fallen, the M.Av. will be above the current price. When prices are rising, the M.Av. will be below the current price. Prices breaking through (upwards) the moving average from below, is taken as a bullish signal, because it signifies a shift from a falling trend.

*Chapter 11: Efficient Market Hypothesis* Lucky event issue

The number of investors is so large, by chance some must make huge returns. A bet on a stock is simply a coin toss. There is equal possibility of winning or losing the bet. A doubter will call the result luck; the successful investor will call it skill.

*Chapter 11: Efficient Market Hypothesis* Resistance levels / support levels

The price levels above which it is difficult for stock prices to rise, or below which it is unlikely for them to fall, and they are believed to be levels determined by market psychology.

*Chapter 11: Efficient Market Hypothesis* Cumulative abnormal return

The sum of all abnormal returns over the time period of interest, which captures the total firm-specific stock movement for an entire period when the market might be responding to the new information.

*Chapter 12: Behavioral Finance & Technical Analysis* Disposition effect

The tendency of investors to hold on to losing investments. Behavioral investors seem reluctant to realize losses.

*Chapter 13: Empirical Evidence on Security Returns* Early versions of the Multifactor CAPM and APT

These theories provided little guidance concerning which factors (sources of risk) ought to result in risk premiums. A test of this hypothesis would require three stages 1. Specification of risk factors 2. Identification of portfolios that hedge these fundamental risk factors 3. Test of the explanatory power and risk premiums of the hedge portfolios

*Chapter 10: Arbitrage Pricing Theory* How are the T-B model and APT similar?

They both assume that when the residual risk of the active portfolio goes to zero, the position in it goes to infinity. This is precisely the same implication as the APT: When portfolios are well-diversified, you will scale up an arbitrage position without bound. Also, when the residual risk of an asset in the active TB portfolios is zero, it will displace all other assets from the portfolio and thus the residual risk of the active portfolio will be zero and elicit the same extreme portfolio response.

*Chapter 13: Empirical Evidence on Security Returns* Tests of the Multifactor CAPM and APT

Three factors increase the market risk factor in a multifactor SML: 1. Factors that hedge consumption against uncertainty in the prices of important consumption categories/general inflation (housing or energy) 2. Factors that hedge future investment opportunities (market risk premium) 3. Factors that hedge assets missing from the market (labor or private business) *Labor income*: (Mayers) determined that if you include aggregate labor income into the equation, the SML is flatter than the CAPM - this pushes the slope of SML below the return of the index portfolio. (Jagannathan and Wang pg 422-423) We learn through them: conventional first-pass estimates of security betas are greatly deficient, and human capital will be important in any version of the CAPM that better explains the systematic risk of securities.

*Chapter 13: Empirical Evidence on Security Returns* Private (Nontraded) business

Whereas Jagannathan and Wang focus on labor income, Heaton and Lucas estimate the importance of proprietary business. Heaton and lucas found that households with higher investment in private business do, in fact, reduce the fraction of total wealth invested in equity. And, they extended Jag/Wang's equation to include the rate of change in proprietary-business wealth. They find that this variable also is significant and improves the explanatory power of the regression.

*Chapter 9: CAPM* Concept 9.4 & 9.5: Stock XYZ has an expected return of 12% and risk of β=1. Stock ABC has expected return of 13% and β=1.5. The market's expected return is 11% and rf = 5%. a. According to the CAPM, which stock is a better buy? b. What's the alpha of each stock? Plot the SML and each stock's risk-return point on one graph. Show the alphas graphically. The risk free rate is 8% and the expected return on the market portfolio is 16%. A firm XYZ considers a project that is expected to have a beta of 1.3. a. What's the required rate of return on the project? b. If the E(IRR) of the project is 19%, should it be accepted?

a. According to the CAPM, which stock is a better buy? E(ri) - rf = βi[E(rm) - rf) XYZ.... 1(12-5) = 7 ABC... 1.5(13-5) = 12 **Stock ABC more attractive b. What's the alpha of each stock? Plot the SML and each stock's risk-return point on one graph. Show the alphas graphically. α = E(r) - [rf + β(E,rm - rf)] αXYZ = 12 - 5 + 1(11-5) αXYZ = 12 - 11 αXYZ = 1% αABC = 13 - 5 + 1.5(11-5) αABC = 13 - 14 αABC = -1% a. What's the required rate of return on the project? E(r,XYZ) = rf + βi[E(rm) - rf) = 8+ 1.3(16-8) = 18.4% b. If the E(IRR) of the project is 19%, should it be accepted? Yes, because that is much higher than the former 18.4%. Any project with an IRR equal or less than 18.4% should be rejected.

*Chapter 9: CAPM* Concept 9.2: Data from the last eight decades of the S&P500 index yield the following statistics: average excess return 7.9%; standard deviation 23.2%. a. To the extent that these averages approximated investors expectations for the period, what must have been the average coefficient of risk aversion? b. If the coefficient of risk aversion were actually 3.5, what risk premium would have been consistent with the market's historical standard deviation?

a. E(rM) = E,A(σ2M) .079 = A (.235)^.5 .079 = A (.0538) A = .079 / .0538 A = 1.47 b. E(rM) = E,A(σ2M) E(rM) = 3.5(.0538) E(rM) = .1883 or 18.8%

*Chapter 11: Efficient Market Hypothesis* Abnormal return

abnormal return = actual return - expected return given the return on a market index e,t = *r(t) - (a + br,Mt) r(t) = stock return during a given period a = average rate of return the stock would realize in a period with a zero market return b = measures sensititivy to the market e,t = the part of a security's return resulting from firm-specific events r,Mt= Market's rate of return *We measure the impact of an abnormal event on a stock at the moment the info becomes known to the market*

*Chapter 9: CAPM* Market Portfolio, M

proportion of each stock in this portfolio = (price per share X shares outstanding) / sum of the market value of all stocks

*Chapter 13: Empirical Evidence on Security Returns* First-pass regression equation (estimate SCL) (Estimation of betas of portfolios of securities using time series regression)

r,it - r,𝑓t = ai + bi(r,Mt - r,𝑓t) + e,it ri-r𝑓 = Sample averages of excess returns on # stocks bi = Sample estimates of the beta coefficients of each # stocks rM - r𝑓 = Sample average of the excess return of the market index σ2(e,i) = Estimates of the variance of the residuals of the # stocks

*Chapter 13: Empirical Evidence on Security Returns* Second-pass regression equation (estimate SML) (In the second pass, the independent variables are the first pass estimated betas. That is, you estimate 𝛽𝑖^βi^ in time series for every stock i.... A cross-sectional regression of portfolio returns on betas. The estimated slope is the measurement of the reward for bearing systematic risk during the period analyzed.) 𝑟𝑖,𝑡−𝑟𝑓,𝑡=𝛼𝑖+𝛽𝑖(𝑟𝑀,𝑡−𝑟𝑓,𝑡)+𝜖𝑡

rt - r𝑓= Y0 + Y1,βi