Chapter 6: Risk and Return Flashcards
Intrinsic value of a company
Preset value of it’s expected future free cash flows discounted at the weighted average cost of capital
all else holding equal higher risk increases WACC (reducing the firm’s overall value)
risk aversion
a higher level of risk aversion leads an investor to require a higher rate of return as inducement to buy riskier securities
Dollar return
= amount to be received less amount invested
not very meaningful
- need to know scale of investment and timing of return to know if return was good
Rates of return
= dollar return / amount invested
standardizes the dollar return to consider annual return per unit of investment
Risk
“Exposure to an unfavorable event”
analyzed in two ways for asset risk
- considering each asset in isolation
- as part of a collection of assets (portfolio)
Asset’s stand-alone risk
Risk an investor would face if they held only this one asset
Discrete probability distribution
a list of all possible events/ outcomes, with a probability assigned to each event (total probabilities must sum to 100%)
can be used to calculate expected risk and return
Payoff matrix
Shows the various potential scenarios and lists the:
- probability of the scenario
- market rate of return given the scenario
- expected return (probability x return)
- standard deviations:
- deviation from expected return (market rate -1)
- Squared deviation
- probability of scenario x squared deviation
sum of this last one = variance
Weighted average of outcomes
sum of all (possible outcomes * probability of occurrence)
R-hat
r
expected rate of return
mean of the probability distribution
= sum of all (probability potential outcome * return if outcome returns)
measure of tightness of probability distribution
standard deviation (represented by signma)
larger = wider dispersal from expected value
Calculating standard deviation
square root of sum of all (probability of occurrence * (deviation between expected rate and possible outcome rate squared)
Variance is the calculation before taking the square root
standard deviation gives an idea of how far above or below the expected value an actual value is likely to be
SAMPLE standard deviation denoted by s
Continuous probability distributions
probability distributions that have an infinite number of possible outcomes, often shown as a curve. Area under the curve must = 100%. can only show the probability that an outcome will be between two outcomes, less than or equal to or greater than or equal to.
more used than discrete distribution
normal distribution often used
common to use historical data to estimate standard deviation
normal distribution
bell-shaped, symmetrical continuous probability distribution
actual return will be within +/- 1 standard deviation of the expected return 68.26% of the time
use of historic data to estimate standard deviation
historical standard deviation may be used as an estimate of future variability (variability often repeated)
it is INCORRECT to use the historic average return to estimate expected rate of return
annualize monthly standard deviation
multiply the monthly standard deviation by the square root of 12
historic trade off between risk and return
highest average returns also have highest standard deviations (widest ranges of returns)
Weight of an asset in a portfolio
the percentage of the portfolio’s total value that is invested in that asset
weight more meaningful than dollar value
total weights sum to 1
Actual return on a portfolio for a particular period
weighted average of the actual return in the stocks in the portfolio
= sum of all (weight * return) for each stock
Average portfolio return over a number of period
weighted average of the stock’s average return
= sum of all (weight * average return) for each investment
why might adding a risky asset to a safer asset reduce risk
(combined portfolio standard deviation lower than the less risky asset’s standard deviation)
changes in returns balance out
Correlation
tendency of two variables to move together
measured by the correlation coefficient
range from +1 (two variables move in perfect sych) to -1 (two variables move in directly opposite directions). 0 means variables are completely independent
Estimating correlation from sample data
called “R”
sum of all (actual return stock 1- average return stock 1) * (actual return for stock 2 - average return for stock 2)
DIVIDED BY
square root of (sum of all (actual return stock 1- average return stock 1) squared) *(sum of all (actual return for stock 2 - average return for stock 2)squared)
CORREL in excel
negative correlation = moving in opposite directions
correlation and the benefits of diversification
if returns for stocks have a negative correlation investing in both may reduce volatility of the portfolio (makes portfolio’s standard deviation less than the weighted average of the individual stock’s standard deviation)
zero risk portfolio
where correlation between stock 1 and 2 is -1 such that the deviations from the mean completely cancel each other out.
expected return = weighted average of stock’s expected return
Correlation and risk
- for correlation between -1 and +1 the porfolio’s standard deviation is less than the weighted average of the stock’s standard deviation
effects of portfolio size on portfolio risk for average stocks
The risk of a portfolio consisting of stocks declines (approaching a limit which is market risk) as the number of stocks in the portfolio increases.
market portfolio
a portfolio consisting of all shares of all stocks
Market risk
stock risk that can not be eliminated even with a well diversified portfolio
risk remaining after diversification: nondiversifiable or systematic risk
measured by the beta coefficient (beta risk)
stems from factors that affect most firms (war, inflation, recession, interest rates)
Diversifiable risk
that part of a security’s total risk that is associated with random events not affecting the market as a whole. Risk that can be eliminated by diversification
aka company specific risk - from events that are unique to a particular firm and “random” so far as the portfolio is concerned
importance of diversification
“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.
Capital asset pricing model
CAPM
one way to measure the risk of an individual stock
based on the proposition that any stock’s required rate of return is equal to the risk-free rate of return plus a risk premium reflecting only the risk remaining after diversification
[ ] = items in subscript
r[i] = r[RF]+b[i] (r[M] - r[RF])
relevant risk
the relevant risk of a stock is it’s contribution to a well-diversified portfolio’s risk (much smaller than stand-alone risk)
Relevant risk of an individual stock per CAPM
the amount of risk the stock contributes to the market portfolio (containing all stock)
Beta coefficient
measure of risk
beta coefficient for stock i = ( standard deviation of stock i’s return / standard deviation of the market’s return) * correlation between stock i’s return at the market return
estimated using past data (4-5 years of monthly data or 52 weeks of weekly data)
Estimate may vary by analyst - analysts may calculate their own or average published betas
proper measure of relevant risk in a well-diversified portfolio
beta coefficient meaning
stock with a high deviation will tend to have a high beta: other things held constant the stock contributes a lot of risk to a well diversified portfolio (destabilizes)
a stock with a high correlation with the market will also tend to have a large beta; be risky (high correlation does not help diversification)
beta of a portfolio
the weighted average of the beta values of all the stocks in the portfolio (weighted by the proportion of the stock)
= sum of all (weight of stock * beta of stock)
variance and beta relationship
variance of a well diversified portfolio is approximately equal to the product of its squared beta and the market’s variance
standard deviation and beta
(only considering portfolios with positive betas)
the standard deviation of a well-diversified portfolio is approximately equal to the production of the portfolio’s beta and the market standard deviation
a portfolio with:
- beta > 1 will have a larger standard deviation (more risk) than the market
- beta = 1 will have the same standard deviation (risk) as the market
- beta < 1 will have a smaller standard deviation (less risk) than the market
contribution of a single stock to portfolio standard deviation
(in a well diversified portfolio)
each stock contributes weight of stock * beta of stock* standard deviation of market
Beta, Key points:
- beta determines how much risk a stock contributes to a well-diversified portfolio
- average of all stock’s betas = 1 (beta of the market = 1) because the market return is the average of all stock’s risk
- stock with beta >1 contributes more risk than does the average stock and a stock with beta < 1 contributes less
- stocks with more risk (higher beta) tend to do better than average stock when market does well and worse than average when market does poorly
- most stocks have betas between 0.4 and 1.6
Ex ante model
variables represent before-the-fact expected values
beta coefficient expectation
beta coefficient used by investors should reflect the relationship between a stock’s expected return and the market’s expected return in the future
beta is calculated using data from the past, assuming the stock[’s risk will be the same in the future
Alternate calculation of beta
Beta of stock i = covariance of stock i and the market / variance of the market
formula for slope of a regression line if stock’s return on y axis and market portfolio’s return on the x axis
Covariance of stock i and the market = correlation of stock i and the market * standard deviation stock i * standard deviation of the market
Using a regression line to calculate beta
stock’s returns on y axis
market’s returns on x axis
regression line for formula
y= mx+b+ error gives estimate of beta
using trendline in excel shows regression equation and Rsquared
estimated beta is the m part of the mx+b function (slope)
can just calculate using excel’s slope formula
R squared value
measures the proportion of variation that is explained by the regression equation
R squared of 1 = all points lie exactly on the regression line (all variation in the y variable explained by the x variable)
What the R squared value means for a beta estimate
R squared gives the percentage of variation in the stock return that is explained by the market return
Risk premium on “the market”
= require rate of return on the market portfolio - risk free rate of return
the additional return over the risk-free rate (US Treasury bonds) required to induce an average investor to invest in the market portfolio (as opposed to purchasing risk-free securities)
aka equity premium or equity risk premium
primarily depends on average investor’s degree of risk aversion, higher when investors are more risk averse
usually ranges 4%-7%
Risk premium on stock i
= Risk premium on “the market” * beta of stock i
the extra rate of return an investor requires to invest in a particular stock
Required return on stock i
generally conceptualized as the risk-free rate + the risk premium needed to induce the investor to hold the stock
Security market line
represents in graphical form the relationship between the risk of an assets as measured by its beta and the required rates of return for individual securities
require rate of return for stock i = risk free rate of return + (beta coefficient for stock i * risk premium on the market)
aka = risk free rate + risk premium for stock i
SML
Graphing SML
Y axis: required rates of return
x axis: risk, measured by beta
y-axis intercept = portfolio with a beta of 0 (riskless) required return = risk-free rate
slope reflects degree of risk aversion in the economy (average investor)
- greater average aversion to risk = steeper slope (= greater risk premium on all stocks = higher required rate of return on all stocks)
so gives (for different stocks) the required rate of return given the beta (and a given risk free return and required return on market)
Impact on required return: changes in the risk-free rate
change in risk-free rate will not necessarily cause a change in market risk premium so required rate of return only changes identically to risk-free rate
Impact on required return: changes in risk aversion
changes in risk aversion change the slope of the security market line. Greater risk aversion = steeper slope
increased risk aversion = increased market risk premium (slope of SML line)
Impact on required return: changes in a stock’s beta coefficient
moves the point for required return along the given SML line
given risk aversion + a positively sloped SML the higher a stock’s beta the higher it’s required rate of return
firm can change its beta through changes in composition of assets and through use of debt
Expected rate of return on a portfolio
weighted average of the expected returns on individual stocks
= sum of (weight of stock i * expected return on stock i ) for all stock’s held
Required rate of return on a portfolio
weighted average of the required returns on individual stocks
= sum of (weight of stock i * required return on stock i ) for all stock’s held
required return on a portfolio expressed using beta
= risk-free rate of return + (beta of the portfolio * risk premium on the market)
beta of a portfolio
weighted average of beta of individual stocks
evaluating portfolio managers
key is evaluating the portfolios return against the return the manager should have made given the risk of the investments
intrinsic value vs market price
intrinsic value incorporates all relevant available information about expected cash flow and risks
market prices are based on investors’ selected and interpretation of information
when market price is lower than intrinsic value there is opportunity for rate of return in excess of required return (which drives up price, and drives down yield)
Market equilibrium
the condition under which the intrinsic value of a security is equal to its price; when a security’s expected return equals its required return
aka equilibrium
When a security’s price is below its intrinsic value demand increases (people buy) and drives the price up (and yield down) until expected = required return
when a security’s price is above its intrinsic value demand decreases (people sell) which drives the price down (and yields up) until expected = required return
market equilibrium equation
Expected return = required return
or
market price = intrinsic value
Efficient markets hypothesis
asserts that:
- stocks are always in equilibrium (changes in value are adjusted to so quickly that there isn’t time to take advantage before the change)
- it is impossible for an investor to consistently “beat the market” by getting a higher return than is justified by the stock’s risk
assumes that all important information regarding a stock is reflected in the price of that stock
Three forms of the Efficient Market Hypothesis
Weak-form
semistrong-form
strong-form
Weak-form EMH
asserts that all information contained in past price movements is fully reflected in current market prices
means that information about recent trends in stock prices is of no use in selecting stocks
implies that any information that comes from past stock prices is too rapidly incorporated into the current stock price for opportunity to exist
semistrong form of EMH
States that market prices reflect all publicly available information
implies it would do no good to exam annual reports/ other published data because market prices would have adjusted to any public information when the information became public
investors should expect to earn returns commensurate with risk and only do better or worse by chance
stock prices will only respond to new information if the information is unexpected
strong-form EMH
states that current market prices reflect all pertinent information, whether publicly or privately held, making it impossible for even insiders to earn consistently abnormal returns
market bubbles
strings of events where:
1. prices climb rapidly (to heights previously considered unlikely)
2. volume of trading is much higher than in the past
3. many new investors (speculators) enter the market
4. prices suddenly fall precipitously leaving many investors with huge losses
past experience suggests that in the height of these booms market prices far exceed intrinsic values (aka the market is not efficient)
How do people make money when a market bubble bursts?
bet against an overvalued market
if everyone did this it would cause market prices to retreat to intrinsic values quickly
strategies for profiting from a failing market
- sell stocks (or the market index itself) short
- purchase a put option or write a call option
- take a short position in a futures contract on the market index
selling a stock short
selling a share of stock that has been borrowed from the broker
receive cash but owe the share
but when the price of the share falls can buy at the lower price and return to the broker and make the difference in profit (if price goes up would lose the increase)
put option
the option to sell a share at a fixed strike price
so if stock price falls below strike price can buy at lower price and sell at higher strike price
(if put expires before stock price falls the money spent on the put is a loss)
writing a call option
selling the obligation to sell a share (when called upon) at a given strike price
if price stays below strike price the sale is all profit
if price rises above strike price: seller must buy a share at the new higher price and sell it at the lower price, resulting in a net loss (including consideration of the call option price)
(generally settled for cash and not actual shares)
short position in a futures contract
obligated to sell a share at a fixed price
if market price falls below specified price: profit from buying a share at market price and selling at the higher fixed price
if market price increases: loss from buying share at higher price and selling it at lower fixed price
(generally settled for cash and not actual shares)
problem with market bubble puncturing strategies
(puncturing = capitalizing on an overvalued market & thus driving it back to equilibrium)
may take a long period of time for market to return to intrinsic value and cost of strategies employed could be prohibitive
why negative bubbles don’t persist
no potential for negative cash flows. Investors buy stock at too low market price and hold it until price eventually increases. losses are paper-only and not cash
book-to-market ratios
B/M ratios
book value of equity / market value of equity
companies with high B/M rations tend to have higher returns than predicted by CAPM
long-term reversals
studies show that portfolios of stocks with poor past long-term performance tend to do slightly better in the long-term future than predicted by CAPM (and vice versa)
momentum
stocks with strong performance in the short-term past tend to do slightly better in the short-term future than CAPM predicts
stocks with weak performance in the short-term past tend to do slightly worse (?) in the short term-future than CAPM predicts
Fama-french portfolios
Portfolios of similarly sized companies based on the company’s size as measured by the market value of its equity and the company’s book-to-market ratio
returns tend to increase as B/M ratio increases
Fama-french three-factor model
three factors for determining required return
- excess market return (market return minus risk-free rate)
- size (return on a portfolio of small firms - return on a portfolio of big firms)
- book-to-market effect (the return on a portfolio with high book-to-market ratio minus return on portfolio with a low B/M ratio)
accounts for many of the major violations of the efficient market hypothesis
useful in identifying the market’s reaction to news about a company
SMB portfolio
Small minus big portfolio
all actively traded stocks ranked by size and split into two portfolios: small stocks and big stocks
return on small portfolio - return on big portfolio = SMB portfolio
designed to measure the variation in stock returns caused by size effect
HML portfolio
High minus low portfolio
all stocks ranked according to their book-to-market ratios
30% of stocks with highest ratios = H portfolio
30% of stocks with lowest ratios = L portfolio
return of H portfolio - return of L portfolio = HML portfolio
using the fama-french model
can decompose an actual change in stock price to see what is explained by the environment (covered by the market, the SMB and HML portfolios) and what is explained by the company’s actions.
not as useful to estimate the required return on a stock (no well-accepted link provided between risk and required return)
unexplained return
= actual return - predicted return
meaning of b/m ratio
High BM ratio = low market value = lenders reluctant to extend credit = higher risk = higher return required
Behavioral finance
a field of study that analyzes investor behavior as a result of psychological traits. Assumes that investors do not necessarily behave rationally and instead focuses on irrational but predictable financial decisions
potential behavioral explanations for market bubble creation
- overconfidence (people are overconfident in their own abilities relative to those of others)
- anchoring bias
- herding
self-attribution bias
people’s tendency to ascribe their successes to their own talents and blame their failures on bad luck
repetition leads to conclusions of talent
hindsight bias
tendency of people to believe, after an event has occurred, that they predicted the past better than they actually did (leads to thinking can predict the future)
Anchoring bias
occurs when predictions of future events are influenced too heavily by recent events (vs all pertinent events including those past)
Herding behavior
when groups of investors emulate other successful investors and chase asset classes that are doing well
creates excess demand for asset classes, causing price increases that can induce additional herding behavior
being part of a large group may make the penalty for being wrong bigger than the reward for being correct
loss aversion
a behavioral phenomenon occurring when investors dislike a loss more than they like a gain of the same amount
preference of a sure gain over a higher risky gain
preference of a higher risk of loss over lower sure loss
operations relationship to stock market
because every project contributes to the size, timing and risk of the company’s cash flows the relevant risk and expected return of any project must be measured in terms of its effect on the stock’s risk and return
Use of CAPM for managers
Can be used to estimate the required return on a company’s stock, which will be the required return of any projects undertaken
