Chapter 10 Flashcards
define probability distribution (Pr)
a graph that provides the probability of every possible discrete state
define expected (mean) return
weighted average of the possible returns, where the weights correspond to the probabilities
E[R] = sum of Pr x R
define variance
a method to measure the risk of a probability distribution, it’s the expected squared deviation from the mean
variance is a measure of how “spread out” the distribution of the return is
define standard deviation
a common method used to measure the risk of a probability distribution. it’s the square root of the variance, the expected squared deviation from the mean
SD = volatility of a return
what’s the variance and SD of the return distribution formula
Var(R) = E[9R-E[R])^2] = sum of Pr x (r-E[R])^2
SD(R) = squareroot of Var(R)
define realized return
the return that actually occurs over a particular time period
how to calculate realized annual returns
1 + Rannual = (1 + Rq1)(1 + Rq2) (1 + Rq3) (1 + Rq4)
define empirical distribution of the returns
a plot showing the frequency of outcomes based on historical data
define average annual returns
the arthmetic average of an investment’s realized returns for each year
R = (1/T)* (R1 + R2 ..+… Rt) = (1/T) sum of Rt
what’s unique about the average annual return
it’s the balancing point of the empirical distribution—in this case, the probability of a return occurring in a particular range is measured by the number of times the realized return falls in that range. Therefore, if the probability distribution of the returns is the same over time, the average return provides an estimate of the expected return.
how to calculate the difference in variability
estimate the standard deviation of the distribution of returns using the variance estimate using realized returns
Var R = [1/(T-1)] * sum of (Rt - R(average))^2
what’s the difficulties using past returns to predict the future returns
- We do not know what investors expected in the past; we can only observe the actual returns that were realized.
- he average return is just an estimate of the true expected return. If we assume that investors are neither overly optimistic nor overly pessimistic on average, however, then we can use a security’s historical average return to estimate its actual expected return. As with all statistics, however, an estimation error will occur. Given the volatility of stock returns, this estimation error will be large even when we have many years of data.
define standard error
the standard deviation of the estimated value of the mean of the actual distribution around its true value; that is, it’s the standard deviation of the average return
what’s the formula of the standard error of the estimate of the expected return
SD (average of independent, identical Risks) = SD(individual Risk)/ square root (number of observations)
Because the average return will be within two standard errors of the true expected return approximately 95% of the time,106 the standard error can be used to determine a reasonable range for the true expected value. = historical average return is +- (2 x standard error)
how to calculate the CAGR or the geometric average of the annual returns
[(1+R1)(1+R2)…*(1+Rt)]^(1/T) - 1
what are the limitations of expected return estimates
Individual stocks tend to be even more volatile than large portfolios, and many have been in existence for only a few years, providing little data with which to estimate returns. Because of the relatively large estimation error in such cases, the average return investors earned in the past is not a reliable estimate of a security’s expected return. Instead, we need to derive an alternative method to estimate the expected return—one that relies on more reliable statistical estimates
how are investors are risk averse
The benefit they receive from an increase in income is smaller than the personal cost of an equivalent decrease in income. This idea suggests that investors would not choose to hold a portfolio that is more volatile unless they expected to earn a higher return
define excess return
the difference between the average return for an investment and the average return for a risk-free investment
is there a relationship between investment size and risk?
yes, Larger stocks tend to have lower volatility overall. In addition, even the largest stocks are typically more volatile than a portfolio of large stocks
is there a relationship between volatility and return
While the smallest stocks have a slightly higher average return, many stocks have higher volatility and lower average returns than other stocks. And almost all stocks seem to have higher risk and lower returns than we would have predicted from a simple extrapolation of our data from large portfolios.
define common risk
perfectly correlated risk
define independent risk
risks that bear no relation to each other. if risks are independent, then knowing the outcome of one provides no information about the other. Independent risks are always uncorrelated, but the reverse need not be true
define diversification
the averaging of independent risks in a large portfolio to reduce risk
how do stock prices and dividends fluctuate due to 2 types of news
- Market-wide news is news about the economy as a whole and therefore affects all stocks.
- Firm-specific news is good or bad news about the company itself.
define firm-specific/idiosyncratic/unsystematic/unique/diversifiable risk
fluctuations of a stock’s return that are due to firm-specific news and are independent risks unrelated across stocks
define systematic/undiversifiable/market risk
fluctuations of a stock’s return that are due to market-wide news representing common risk
what’s the risk premium for diversifiable risk
zero, so investors aren’t compensated for holding firm-specific risk - earns only risk-free interest rate thus no arbitrage
Because investors can eliminate firm-specific risk “for free” by diversifying their portfolios, they will not require a reward or risk premium for holding it
does diversification reduce systematic risk
no - investor is exposed to risks that affect the entire economy so they demand a higher risk premium to be hold systematic risk
how is the risk premium of a security determined by
The risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk.
is a stock’s volatility useful in determining the risk premium that investors will earn
no
how to estimate a security’s expected return
need to find a measure of a security’s systematic risk.
how to determine how sensitive a stock’s return is to interest rate changes,
would look at how much the return tends to change on average for each 1% change in interest rates.
how to determine how sensitive a stock is to systematic risk
look at the average change in the return for each 1% change in the return of a portfolio that fluctuates solely due to systematic risk. find portfolio that contains only risk
define an efficient portfolio
a portfolio that contains only systematic risk - an efficient portfolio cannot be diversified further; no way to reduce the volatility of the portfolio without lowering its expected return. the efficient portfolio is the tangent portfolio, the portfolio with the highest sharpe ratio in the economy
define market portfolio
a value-weighted portfolio of all shares of all stocks and securities in the market
define Beta of a security
sensitivity of the security’s return of the overall market
The beta is the expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio.
Beta measures the sensitivity of a security to market-wide risk factors. For a stock, this value is related to how sensitive its underlying revenues and cash flows are to general economic conditions.
high vs low betas
Stocks in “cyclical” industries such as Energy and Materials, in which revenues tend to vary greatly with the business cycle, are likely to be more sensitive to systematic risk and have higher betas than stocks in less sensitive “defensive” industries such as Consumer Staples and Utilities.
what’s the market risk premium
market risk premium = E[Rmkt] -rf
the risk premium investors can earn by holding the market portfolio is the difference between the market portfolio’s expected return and the risk-free interest rate
what does the market interest rate and market risk premium reveal about the investors
market interest rate reflects investors’ patience and determines the time value of money, the market risk premium reflects investors’ risk tolerance and determines the market price of risk in the economy.
what’s the relationship between market risk premium and beta
market risk premium is the reward investors expect to earn for holding a portfolio with a beta of 1—the market portfolio itself
use the beta of the investment to determine the scale of the investment in the S&P/TSX Composite Index that has equivalent systematic risk.
what’s the estimated a traded security’s expected return from its beta
E[Ri] = risk free interest rate + Risk premium = Rf + Bi x (E[Rmkt] - rf)
is beta = volatility
no, volatility measures total risk - both market and firm-specific risks
what do stocks with negative beta mean?
stock with a negative beta will tend to do well when times are bad, so owning it will provide insurance against the systematic risk of other stocks in the portfolio.
