Final - FINA 469

Key Takeaways

- 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.

Equation 7.3 - Security Excess

- rit is the holding period return (HPR) i - asset t - period ai - intercept Bi - slope Equation 7.3 states that the realized excess return on any stock is the sum of the realized excess return due to market-wide factors, Bi(rMt - rFt), a nonmarket risk premium, ai, and a firm-specific outcome for that period summarized by eit.

CAPM serves two vital functions

1. Provides a benchmark rate of return for evaluating possible investments. EX: Security analyst might want to know whether the expected return she forecasts for a stock is more or less than its "fair" return given its risk. 2. CAPM model helps us make an educated guess as to the expected return on assets that have not yet been traded EX: How do we price an IPO of stock?

CAPM has two limitations:

1. Relies on the theoretical market portfolio, which includes all assets (including real estate, human capital foreign stocks, etc) 2. It applies to expected as opposed to actual returns. To implement and test the CAPM, we cast it in the form of an index model and use realized, not expected, returns.

Instances of persistent, positive significant CAPM alpha values

1. Small versus large stocks 2. Stocks of companies that have recently announced unexpectedly good earnings. 3. Stock with high ratios of book value to market value 4. Stocks with "momentum" that have experienced recent advance in price. These results pose meaningful challenges to the model.

Arbitrage

Arbitrage is the purchase and sale of an asset in order to profit from a difference in the asset's price between markets. It is a trade that profits by exploiting the price differences of identical or similar financial instruments in different markets or in different forms. Arbitrage exists as a result of market inefficiencies and would therefore not exist if all markets were perfectly efficient.

Beta

Beta is a measure of the volatility-or systematic risk-of a security or portfolio compared to the market as a whole. Beta is used in the capital asset pricing model (CAPM), which describes the relationship between systematic risk and expected return for assets (usually stocks). CAPM is widely used as a method for pricing risky securities and for generating estimates of the expected returns of assets, considering both the risk of those assets and the cost of capital. - Tells us how strongly the security responds to market-wide shocks. Beta > 1 exaggerate the response of the portfolio to broad market movements Beta < 1 dampen the response

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. - The Base Return + The Markets Excess Return * a factor (how risky your portfolio is relative to the market)

Equation 7.7 - Two-factor security market line for security i

Equation 7.7 is an expansion of the simple security market line. Once we generalize the single-index SML to multiple risk sources, each with its own risk premium, the insights are similar.

Fama and French Three Factor Model

The Fama and French Three-Factor Model (or the Fama French Model for short) is an asset pricing model developed in 1992 that expands on the capital asset pricing model (CAPM) by adding size risk and value risk factors to the market risk factor in CAPM. This model considers the fact that value and small-cap stocks outperform markets on a regular basis. By including these two additional factors, the model adjusts for this outperforming tendency, which is thought to make it a better tool for evaluating manager performance. The model is essentially the result of an econometric regression of historical stock prices. - The equation brings in size risk using Small minus Big (SMB) and the Book to Market Ration (BTM)(HML)

Risk Averse (Aversion)

The term risk-averse describes the investor who chooses the preservation of capital over the potential for a higher-than-average return. In investing, risk equals price volatility. A volatile investment can make you rich or devour your savings. A conservative investment will grow slowly and steadily over time. Low-risk means stability. A low-risk investment guarantees a reasonable if unspectacular return, with a near-zero chance that any of the original investment will be lost. Generally, the return on a low-risk investment will match, or slightly exceed, the level of inflation over time. A high-risk investment may gain or lose a bundle of money.

High Minus Low (HML)

The third factor in the Three-Factor model is High Minus Low (HML). "High" refers to companies with a high book value-to-market value ratio. "Low'" refers to companies with a low book value-to-market value ratio. This factor is also referred to as the "value factor" or the "value versus growth factor" because companies with a high book to market ratio are typically considered "value stocks." Companies with a low market-to-book value are typically "growth stocks." And research has demonstrated that value stocks outperform growth stocks in the long run. So, in the long run, a portfolio with a large proportion of value stocks should outperform one with a large proportion of growth stocks. - Long on portfolio with high book-to-market, short on portfolio with low book-to-market

Resistance and Support Levels

These values are said to be price levels above which it 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.

High Book-to-market ratios

Value stocks - Derive a larger share of their market value from assets already in place - Relatively mature firms

Semi-strong form hypothesis

all publicly available information regarding the prospects of a firm already must be reflected in the stock price. - Info includes past prices, data on firms product line, quality of management, balance sheet composition, patents held, earning forecasts, and accounting practices.

Value Premium

difference between value stock RoR and growth stocks RoR

Random Walk

price changes should be random and unpredictable

Logic of the CAPM

the only reason for a stock to offer an expected return greater than the risk-free rate is that stock imposes systematic risk for which the investor must be compensated. - However, a positive alpha promises reward without risk.

Fundamental Analysis

uses earnings and dividend prospects of the firm, expectations of future interest rates, and risk evaluation of the firm to determine proper stock prices - Ultimately, it represents an attempt to determine the present value of all the payments a stockholder will receiver frim each share of stcok

3 versions of the EMH

weak, semi-strong, strong

Alpha

"Alpha" (the Greek letter α) is a term used in investing to describe a strategy's ability to beat the market, or it's "edge." Alpha is thus also often referred to as "excess return" or "abnormal rate of return," which refers to the idea that markets are efficient, and so there is no way to systematically earn returns that exceed the broad market as a whole. Alpha is often used in conjunction with beta (the Greek letter β) , which measures the broad market's overall volatility or risk, known as systematic market risk.

Economic theory suggests factors that affect investor welfare in three possible ways:

1. factors that are correlated with prices of important consumption goods, such as housing or energy 2. factors that are correlated with future investment opportunities, such as interest rates, return volatility, or risk premiums 3. factors that correlate with the general state of the economy, such as industrial production and employment.

Equation 7.2 Expected Return Beta Relationship

An assets risk premium equals the assets systematic risk measure (beta) times the risk premium of the (benchmark) market portfolio. This expected return (equivalently, mean return) - beta relationship is the most familiar expression of the CAPM. Equation 7.2 tell us that the total expected rate of return is the sum of the risk-free rate (compensation for "waiting,", the time value of money) plus a risk premium (compensation for "worrying" about investment returns)

Arbitrage

Arbitrage is the purchase and sale of an asset in order to profit from a difference in the asset's price between markets. It is a trade that profits by exploiting the price differences of identical or similar financial instruments in different markets or in different forms. Arbitrage exists as a result of market inefficiencies and would therefore not exist if all markets were perfectly efficient. - Arbitrage is a type of trade in which a security, currency, or commodity is nearly simultaneously bought and sold, in different markets. - The purpose of arbitrage is to take advantage of the difference in prices available for the same financial instrument being offered on different exchanges. - Arbitrage is not only legal in the United States, but is also considered useful to markets as it helps promote market efficiency and also provides liquidity for trading.

Arbitrage Pricing Theory (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.

Equation 7.6 - Excess Returns

BiTB is the sensitivity of stock i's excess return to that of the T-bond potfolio and RTBt is the excess return of the T-bond portfolio in month t.

Suppose the risk premium of the market portfolio is 8% and we estimate the Beta of Digital as 1.2. THe risk premium predicted for the stock is therefore 1.2 times the market risk premium, or 1.2 x 8% = 9.6%. The expected rate of return on Digital is the risk-free rate plus the risk premium. For example, if the T-bill rate were 3%, the expected rate of return would be 3% + 9.6% = 12.6%, or using Equation 7.2 directly,

If the estimate of Digital's beta were only 1.1, its required risk premium would fall to 8.8%. Similarily, if the market risk premium were only 6% and Beta= 1.2, Digital's risk premium would be only 7.2%.

Portfolio Beta and Risk Premium

If the market risk premium is 7.5%, the CAPM predicts that the risk premium on each stock is its beta times 7.5%, and the risk premium on the portfolio is .84 x 7.5% = 6.3%. This is the same result that is obtained by taking the weighted average of the risk premiums of the individual stocks.

CML vs SML

In the capital market line (CML), risk is measured by the portfolio's standard deviation. - The CML graphs the risk premiums of efficient complete portfolios (made up of the market portfolio and the risk-free asset) as a function of portfolio standard deviation. - This is appropriate because standard deviation is a valid measure of risk for portfolios that are candidates for an investor's complete portfolio In the security market line (SML), the individual asset's risk is measured by the beta coefficient. - Graphs individual asset risk premium as a function of asset risk. The relevant measure of risk for an individual asset (which is held as part of a diversified portfolio) is not the asset standard deviation but rather the asset beta. The SML is valid both for individual assets and portfolios - The SML provides a benchmark for evaluation of investment performance. The SML provides the required rate of return that will compensate investors for the beta risk of that investment, as well as for the time value of money.

The Security Market Line

The security market line (SML) is a line drawn on a chart that serves as a graphical representation of the capital asset pricing model (CAPM)—which shows different levels of systematic, or market risk, of various marketable securities, plotted against the expected return of the entire market at any given time. Also known as the "characteristic line," the SML is a visualization of the CAPM, where the x-axis of the chart represents risk (in terms of beta), and the y-axis of the chart represents expected return. The market risk premium of a given security is determined by where it is plotted on the chart relative to the SML. - The mean-beta relationship is represented by the security market line (SML). Its slope is the risk premium of the market portfolio. At the point where B=1 (the beta of the market portfolio), we can read off the vertical axis the expected return on the market portfolio.

As investors diversify, their exposure to the firm-specific risk of any individual security steadily diminishes, but their exposure to market wide movements remains.

True As a result, what will matter to diversified investors is the systematic risk of the portfolio and the contribution each stock makes to that risk.

Weak-from hypothesis

asserts that stock prices already reflect all information that can be derived by examining market trading data such as the history of past prices, trading volume, or short interest. - Holds that if such data ever conveyed reliable signals about future performance, all investors already would have learned to exploit them.

Low Book-to-market ratios

growth firms - market values derive from anticipated growth in future cash flows, rather than from assets already in place

Efficient Market Hypothesis (EMH)

is a hypothesis that states that share prices reflect all information and consistent alpha generation is impossible. According to the EMH, stocks always trade at their fair value on exchanges, making it impossible for investors to purchase undervalued stocks or sell stocks for inflated prices. Therefore, it should be impossible to outperform the overall market through expert stock selection or market timing, and the only way an investor can obtain higher returns is by purchasing riskier investments.

Small Minus Big (SMB)

is one of the three factors in the Fama/French stock pricing model. Along with other factors, SMB is used to explain portfolio returns. This factor is also referred to as the "small firm effect," or the "size effect," where size is based on a company's market capitalization. -Small minus big is the excess return that smaller market capitalization companies return versus larger companies. - Long on portfolio with small-cap stocks, shoty on portfolio with large-cap stocks.

What would happen to market efficiency if all investors attempted to follow a passive strategy?

sooner or later prices will fail to reflect new information. At this point there are profit opportunities for active investors who uncover mispriced securities. As they buy and sell these assets, prices again will be driven to fair levels.

Strong-form hypothesis

stock prices reflect all relevant information, even including information available only to company insiders

Technical Analysis AKA chartists

the search for recurrent and predictable patterns in stock prices. - Study records or charts of past stock prices, hoping to find patterns they can exploit to make a profit.