Chapter 10

Question 1

define probability distribution (Pr)

Answer 1

a graph that provides the probability of every possible discrete state

Question 2

define expected (mean) return

Answer 2

weighted average of the possible returns, where the weights correspond to the probabilities

E[R] = sum of Pr x R

Question 3

define variance

Answer 3

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

Question 4

define standard deviation

Answer 4

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

Question 5

what’s the variance and SD of the return distribution formula

Answer 5

Var(R) = E[9R-E[R])^2] = sum of Pr x (r-E[R])^2

SD(R) = squareroot of Var(R)

Question 6

define realized return

Answer 6

the return that actually occurs over a particular time period

Question 7

how to calculate realized annual returns

Answer 7

1 + Rannual = (1 + Rq1)(1 + Rq2) (1 + Rq3) (1 + Rq4)

Question 8

define empirical distribution of the returns

Answer 8

a plot showing the frequency of outcomes based on historical data

Question 9

define average annual returns

Answer 9

the arthmetic average of an investment’s realized returns for each year

R = (1/T)* (R1 + R2 ..+… Rt) = (1/T) sum of Rt

Question 10

what’s unique about the average annual return

Answer 10

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.

Question 11

how to calculate the difference in variability

Answer 11

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

Question 12

what’s the difficulties using past returns to predict the future returns

Answer 12

1. We do not know what investors expected in the past; we can only observe the actual returns that were realized.
2. 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.

Question 13

define standard error

Answer 13

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

Question 14

what’s the formula of the standard error of the estimate of the expected return

Answer 14

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)

Question 15

how to calculate the CAGR or the geometric average of the annual returns

Answer 15

[(1+R1)(1+R2)…*(1+Rt)]^(1/T) - 1

Question 16

what are the limitations of expected return estimates

Answer 16

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

Question 17

how are investors are risk averse

Answer 17

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

Question 18

define excess return

Answer 18

the difference between the average return for an investment and the average return for a risk-free investment

Question 19

is there a relationship between investment size and risk?

Answer 19

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

Question 20

is there a relationship between volatility and return

Answer 20

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.

Question 21

define common risk

Answer 21

perfectly correlated risk

Question 22

define independent risk

Answer 22

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

Question 23

define diversification

Answer 23

the averaging of independent risks in a large portfolio to reduce risk

Question 24

how do stock prices and dividends fluctuate due to 2 types of news

Answer 24

1. Market-wide news is news about the economy as a whole and therefore affects all stocks.
2. Firm-specific news is good or bad news about the company itself.

Question 25

define firm-specific/idiosyncratic/unsystematic/unique/diversifiable risk

Answer 25

fluctuations of a stock’s return that are due to firm-specific news and are independent risks unrelated across stocks

Question 26

define systematic/undiversifiable/market risk

Answer 26

fluctuations of a stock’s return that are due to market-wide news representing common risk

Question 27

what’s the risk premium for diversifiable risk

Answer 27

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

Question 28

does diversification reduce systematic risk

Answer 28

no - investor is exposed to risks that affect the entire economy so they demand a higher risk premium to be hold systematic risk

Question 29

how is the risk premium of a security determined by

Answer 29

The risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk.

Question 30

is a stock’s volatility useful in determining the risk premium that investors will earn

Answer 30

no

Question 31

how to estimate a security’s expected return

Answer 31

need to find a measure of a security’s systematic risk.

Question 32

how to determine how sensitive a stock’s return is to interest rate changes,

Answer 32

would look at how much the return tends to change on average for each 1% change in interest rates.

Question 33

how to determine how sensitive a stock is to systematic risk

Answer 33

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

Question 34

define an efficient portfolio

Answer 34

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

Question 35

define market portfolio

Answer 35

a value-weighted portfolio of all shares of all stocks and securities in the market

Question 36

define Beta of a security

Answer 36

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.

Question 37

high vs low betas

Answer 37

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.

Question 38

what’s the market risk premium

Answer 38

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

Question 39

what does the market interest rate and market risk premium reveal about the investors

Answer 39

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.

Question 40

what’s the relationship between market risk premium and beta

Answer 40

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.

Question 41

what’s the estimated a traded security’s expected return from its beta

Answer 41

E[Ri] = risk free interest rate + Risk premium = Rf + Bi x (E[Rmkt] - rf)

Question 42

is beta = volatility

Answer 42

no, volatility measures total risk - both market and firm-specific risks

Question 43

what do stocks with negative beta mean?

Answer 43

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.