Chapter 2: Risk and Return: Part I
The Impact on Required Return Due to Changes in the Risk-Free Rate, Risk Aversion, and Beta
*Changes in the Risk-Free Rate*: as it changes, so will the required return on the market, and this will, other things held constant, keep the market risk premium stable *Risk Aversion*: The steeper the slope of the line, the greater the average investor's aversion to risk -As risk aversion increases, so does the risk premium, and this causes the slope of the SML to become steeper *Beta*: the higher a stock's beta, the higher its required rate of return
Investment Returns and Risk:: Stand-Alone Risk versus Portfolio Risk
*Risk:* "a hazard; a peril; exposure to loss or injury"; refers to the chance that some unfavorable event will occur -For an investment in financial assets or in new projects, the unfavorable event is ending up with a lower return than you expected An asset's risk can be analyzed in two ways: *(1)* on a stand-alone basis, where the asset is considered in isolation; and *(2)* on a portfolio basis, where the asset is held as one of a number of assets in a portfolio *stand-alone risk:* the risk an investor would face if she held only this one asset
Risk in a Portfolio Context: Creating a Portfolio
*portfolio:*a collection of assets -The weight of an asset in a portfolio is the percentage of the portfolio's total value that is invested in the asset (*example:* you invest $1,000 in each of 10 stocks, your portfolio has a value of $10,000, and each stock has a weight of $1,000/$10,000= 10%) -The average portfolio return over a number of periods is also equal to the weighted average of the stock's average returns
Using Historical Data to Estimate Risk: Calculating the Historical Standard Deviation
*realized rates of return:* are denoted as ("r bar t"), where t designates the time period *average annual return over the last T periods* is denoted as r bar avg *The historical standard deviation is often used as an estimate of future variability* -Because past variability is often repeated, past variability may be a reasonably good estimate of future risk
Measuring Stand-Alone Risk: The Standard Deviation of a Discrete Distribution
*standard deviation:* the symbol pronounced "sigma" -large standard deviation means that possible outcomes are widely dispersed, -a small standard deviation means that outcomes are more tightly clustered around the expected value *variance:* a weighted average of the squared deviations from the expected value* The standard deviation provides an idea of how far above or below the expected value the actual value is likely to be*
risk aversion
*the basic premise that investors like returns and dislike risk* people will invest in relatively risky assets only if they expect to receive relatively high returns—the higher the perceived risk, the higher the expected rate of return an investor will demand
expected return on a portfolio
*the weighted average of the expected returns on the individual assets in the portfolio* *required return on a portfolio:* the weighted average of the required returns on the individual assets in the portfolio
The Relevant Risk of a Stock: Contribution to Market Risk: Beta
A well-diversified portfolio has only market risk *the CAPM defines the relevant risk of an individual stock:* the amount of risk that the stock contributes to the market portfolio, which is a portfolio containing all stocks *Beta: The relevant measure of risk *a stock with a high standard deviation, will tend to have a high beta*, which means that, other things held constant, the stock contributes a lot of risk to a well-diversified portfolio *a stock with a high correlation with the market, will also tend to have a large beta and hence be risky* ( the stock performing well when the portfolio is also performing well, and the stock performing poorly when the portfolio is also performing poorly) *beta of a portfolio, bp.:* the weighted average of the betas of the stocks in the portfolio, with the weights equal to the same weights used to create the portfolio *standard deviation of a well diversified portfolio* = equal to the product of the portfolio's beta (or the absolute value if beta is negative) and the market standard deviation *(1)* a portfolio with a beta greater than 1 will have a bigger standard deviation than the market portfolio; *(2)* a portfolio with a beta equal to 1 will have the same standard deviation as the market; and *(3)* a portfolio with a beta less than 1 will have a smaller standard deviation than the market
The Relevant Risk of a Stock: Estimating Beta
The CAPM is an *ex ante model:* all of the variables represent before-the-fact, expected values anther way to estimate beta: *COVim* = covariance between Stock i and the market
Investment Returns and Risk: Returns on Investments
The concept of return provides investors with a convenient way to express the financial performance of an investment *Dollar return = Amount to be received -Amount invested* =$1,100 -$1,000 =$100 two problems arise: *(1)* To make a meaningful judgment about the return, you need to know the scale (size) of the investment [EX: a $100 return on a $100 investment is a great return (assuming the investment is held for 1 year), but a $100 return on a $10,000 investment would be a poor return] *(2) You also need to know the timing of the return (EX: a $100 return on a $100 investment is a great return if it occurs after 1 year, but the same dollar return after 20 years is not very good) The solution to these scale and timing problems is to express investment results as *rates of return, or percentage returns* *Rate of return = Amount received-Amount invested/Amount invested* (EX: the rate of return on the 1-year stock investment, when $1,100 is received after 1 year: 1100-1000/1000 = .10= 10%)
Forms of the Efficient Markets Hypothesis
*Weak-Form Efficiency*: of the EMH asserts that all information contained in past price movements is fully reflected in current market prices; the fact that a stock has risen for the past three days, would give us no useful clues as to what it will do today or tomorrow) -*technical analysts (chartists)*: believe that past trends or patterns in stock prices can be used to predict future stock prices (EX: If a stock has fallen for three consecutive days, its price rose by 10% (on average) the following day. The technician would then conclude that investors could make money by purchasing a stock whose price has fallen three consecutive days) -weak-form efficiency implies that any information that comes from past stock prices is too rapidly incorporated into the current stock price for a profit opportunity to exist *Semistrong-Form Efficiency*: current market prices reflect all publicly available information -would do no good to pore over annual reports or other published data because market prices would have adjusted to any good or bad news contained in such reports back when the news came out -investors should expect to earn returns commensurate with risk, but they should not expect to do any better or worse other than by chance - whenever information is released to the public, stock prices will respond only if the information is different from what had been expected (*EX*: if a company announces a 30%, the stock price would probably fall if analysts had expected earnings to increase by more than 30%, but it probably would rise if they had expected a smaller increase) *Strong-Form Efficiency*: states that current market prices reflect all pertinent information, whether publicly available or privately held -If this form holds, even insiders would find it impossible to earn consistently abnormal returns in the stock market
The Relevant Risk of a Stock: Interpreting the Estimated Beta
*a high-beta stock:* When the market is doing well, tends to do better than an average stock, and when the market does poorly, a high-beta stock also does worse than an average stock -*The opposite is true for a low beta stock:* When the market soars, the low-beta stock tends to go up by a smaller amount; when the market falls, the low-beta stock tends to fall less than the market
The Security Market Line (SML)
*a stock's risk premium is equal to the product of the stock's beta and the market risk premium* the three components of required return: *The risk-free rate:* a stock's required return begins with it; The yield on long-term Treasury bonds is often used to measure *The market risk premium:* the extra rate of return that investors require to invest in the stock market rather than purchase risk-free securities -When investors are *very risk averse* = the market risk premium is *high* -when investors are *less concerned about risk*= the market risk premium is *low* *The Risk Premium for an Individual Stock:* equal to the product of the stock's beta and the market risk premium
Risk in a Portfolio Context: Correlation and Risk for a Two-Stock Portfolio
*correlation:* The tendency of two variables to move together *correlation coefficient:* measures this tendency *can range from +1.0:* denoting that the two variables move up and down in perfect synchronization *to -1.0:* denoting that the variables always move in exactly opposite directions *zero indicates:* that the two variables are not related to each other at all—that is, changes in one variable are independent of changes in the other *If two stocks have a correlation of -1:* (the lowest possible correlation), when one stock has a higher than expected return then the other stock has a lower than expected return -Such a portfolio would have a zero standard deviation but *would have an expected return equal to the weighted average of the stock's expected returns* -For correlation of -1, the portfolio's standard deviation can be as low as zero if the portfolio weights are chosen appropriately *If the correlation were +1*: (the highest possible correlation), *the portfolio's standard deviation would be the weighted average of the stock's standard deviations* -*diversification doesn't help: For correlation of +1* *For any other correlation, diversification reduces, but cannot eliminate, risk:* - correlation between -1 and +1, the portfolio's standard deviation is less than the weighted average of the stocks' standard deviations *If a portfolio's standard deviation is less than the weighted average of the individual stocks' standard deviations, then diversification provides a benefit*
Required Returns versus Expected Returns: Market Equilibrium
*difference between the market price and intrinsic value* *intrinsic value:* incorporates all relevant available information about expected cash flows and risk - information about the company, the economic environment, and the political environment *market price :* based on investors' selection and interpretation of information -To the extent that investors don't select all relevant information and don't interpret it correctly, market prices can deviate from intrinsic values *When market prices deviate from their intrinsic values, astute investors have profitable opportunities* *market equilibrium*: expected return equals its required return -if a bond's market price were lower than its intrinsic value, an investor could purchase the bond and receive a rate of return in excess of the required return -demand for the bond would soar as investors tried to purchase it, driving the bond's price up. But as the price of a bond goes up, its yield goes down -If the bond's price were too high compared to its intrinsic value, then investors would sell the bond, causing its price to fall and its yield to increase until its expected return equaled its required return
Measuring Risk for Discrete Distributions: Expected Rate of Return for Discrete Distributions
*expected rate of return*: weighted average (r-hat) *a weighted average of outcomes:* multiply each possible outcome by its probability of occurrence and then sum these products -The weights are the probabilities (believes that the market would go up 37% in Best Case, 11% in Most Likely, and down 15% in worst case)
Risk in a Portfolio Context: Diversification and Multi-Stock Portfolios
*market portfolio:* a portfolio consisting of all stocks *almost half of the risk inherent in an average individual stock can be eliminated if the stock is held in a reasonably well-diversified portfolio, which is one containing 40 or more stocks in a number of different industries* -*market risk*: The part of a stock's risk that cannot be eliminated -factors that systematically affect most firms: war, inflation, recessions, and high interest rates -diversifiable risk:* the part that can be eliminated is called -caused by such random events as lawsuits, strikes, successful and unsuccessful marketing programs, winning or losing a major contract, and other events that are unique to a particular firm
Measuring Risk for Discrete Distributions: a Probability Distributions for Discrete Outcomes
An event's probability is defined as the chance that the event will occur (Example: a weather forecaster might state: "There is a 40% chance of rain today and a 60% chance that it will not rain) *probability distribution:* If all possible events, or outcomes, are listed, and if a probability is assigned to each event *the probabilities must sum to 1.0 or 100%* (see 2.2 in book)
The Relevant Risk of a Stock: The Capital Asset Pricing Model (CAPM)
How should the risk of an individual stock be measured? A stock might be quite risky if held by itself, but—because diversification eliminates about half of its risk— the stock's *relevant risk* is its contribution to a well-diversified portfolio's risk, which is much smaller than the stock's stand-alone risk
The Efficient Markets Hypothesis
asserts that: *(1)* stocks are always in equilibrium and *(2)* it is impossible for an investor to "beat the market" and consistently earn a higher rate of return than is justified by the stock's risk -*a stock's market price is always equal to its intrinsic value* (EX: suppose a stock's market price is equal to the stock's intrinsic value but new information that changes the stock's intrinsic value arrives. -The EMH asserts that the market price will adjust to the new intrinsic value so quickly that there isn't time for an investor to receive the new information, evaluate the information, take a position in the stock before the market price changes, and then profit from the subsequent change in price)
