C214 Topic 8
Suppose the covariance between the dependent variable and independent variable is 3.5 and the variance of the independent variable is 2. What is the slope of this regression line?
Answer: 1.75 Slope = 3.5/2 = 1.75
Given the information below, what is the expected return for Stock X? Economic State Probability π Returns for Stock X Recessionary .15 -4% Normal .60 12% Expansionary .25 21%
Answer: 11.85 =0.15*-0.04+0.6*0.12+0.25*0.21
Suppose returns over the last three years were 12%, 13%, and 11%. What is the standard deviation of these returns?
Answer: 1 σ = 1% Expected return: =(0.12+0.13+0.11)/3 = 12% Standard deviation: =sqrt(((.12-.12)^2+(.13-.12)^2+(.11-.12)^2)/2)
Suppose the covariance between the dependent variable and independent variable is 4.2 and the variance of the independent variable is 3. What is the slope of this regression line?
Answer: 1.4 Slope = 4.2/3 = 1.4
Suppose returns over the last three years were 13%, 12%, and 10%. If the mean return over the past five years was 7%, what was the return four years ago?
Answer: -7 (13+12+10+X)/4 = 7% Solving for X yields X = 28-35 = -7%
Suppose the variance of the independent variable is 2.5 and the covariance between the dependent variable and independent variable is 1. What is the slope of this regression line?
Answer: .4 Slope = 1/2.5 = .4
UniFy Inc. has an expected return of 14.5%. If the market risk premium is 11.5% and the risk free rate is 3%, what is the beta for this company?
Answer: 1 14.5% = 3% + B(11.5%). Solve for B, B = 1
Given the information below, what is the standard deviation of expected return for Stock A? Economic State Probability π Returns for Stock A Recessionary .25 -4% Expansionary .75 29%
Answer: 14.289 σE[R] = 14.289% =0.25*-0.04+0.75*0.29 = 20.75% =SQRT(0.25*(-0.04-.2075)^2+0.75*(0.29-.2075)^2) = 14.289%
POLO Outerwear has a beta of 1.1. The expected return on the market is 14% while the risk free rate is 4%. According to the CAPM, what is the required return by shareholders of POLO in percent?
Answer: 15 E[R] = 4% + 1.1(14%-4%)= 15%
Suppose Crill Co. has a beta of 1.4. The expected return on the market is 12% while the risk free rate is 3%. Given this information, what is the expected return for this company in percent?
Answer: 15.6 E[R] = 3% + 1.4(12%-3%) = 15.6%
Suppose GrungeRock.com has a beta of 1.2. The expected return on the market is 14% while the risk free rate is 3%. Given this information, what is GrungeRock's required return by shareholders in percent?
Answer: 16.2 E[R] = 3% + 1.2(14% -3%)= 16.2%
Given the information below, what is the expected return for Stock Z? Economic State Probability π Returns for Stock Z Recessionary .25 3% Normal .35 16% Expansionary .40 26%
Answer: 16.75 =.25*.03+.35*.16+.4*.26
YouWatch.com has a beta of 1.2. The market risk premium is 12.5% while the expected return on the market is 15%. Given this information what is the expected return for this company in percent?
Answer: 17.5 E[R] = (15%-12.5%) + 1.2(12.5%) = 17.5%
Given the information below, what is the expected return for Stock A? Economic State Probability π Returns for Stock A Recessionary .40 10% Expansionary .60 23%
Answer: 17.8 =0.4*0.1+0.6*0.23
XFly Inc. has a beta of 1.5. The market risk premium is 11% and the expected return on the market is 14%. Given this information, what is the required return by shareholders of XFly in percent?
Answer: 19.5 E[R] = (14%-11%) + 1.5(11%)= 19.5%
Suppose returns over the last four years were 15%, 12%, 27%, and 21%. If the mean return over the past five years was 20%, what was the return five years ago?
Answer: 25 (15+12+27+21+X)/5 = 20% Solving for X yields X = 100-75 = 25%
IVAT Inc. has a beta of 2. The market risk premium is 11.5% while the risk free rate is 3.5%. Given this information, what is the required return by shareholders of IVAT in percent?
Answer: 26.5 E[R] = 3.5% + 2(11.5%)= 26.5%
Given the information below, what is the standard deviation of expected return of the portfolio made up of 40% of stock A and 60% of stock B. Economic State Probability π Stock A Stock B Recessionary .35 12% 2% Expansionary .65 5% 22%
Answer: 4.388 σE[R] of the portfolio = 4.388% Expected return during recession: =0.4*0.12+0.6*0.02 = 6% Expected return during expansion: =0.4*0.05+0.6*0.22 = 15.2 % Expected return of portfolio: =0.35*6%+0.65*15.2% = 11.98% Standard Deviation of portfolio:=SQRT(0.35*(0.06-0.1198)^2+0.65*(0.152-0.1198)^2) = 4.3881%
Given the information below, what is the standard deviation of expected return for Stock X? Economic State Probability π Returns for Stock X Recessionary .15 -4% Normal .60 12% Expansionary .25 21%
Answer: 7.657 σE[R] = 7.657% Expected Return =0.15*-0.04+0.6*0.12+0.25*0.21 = 11.85% Standard Deviation =SQRT((0.15*(-0.04-0.1185)^2+0.6*(0.12-0.1185)^2+0.25*(0.21-0.1185)^2))
Given the information below, what is the standard deviation of expected return for Stock Z? Economic State Probability π Returns for Stock Z Recessionary .25 3% Normal .35 16% Expansionary .40 26%
Answer: 9.038 σE[R] = 9.038% Expected return of Stock Z: .25*.03+.35*.16+.26*.4 = 16.75 Standard deviation of Stock Z: sqrt(.25*(.03-.1675)^2+.35*(.16-.1675)^2+.4*(.26-.1675)^2)
Right Turn Industries has a standard deviation of return of 15% and a beta of 1.25. Left Ahead Co. has a standard deviation of return of 12.5% and a beta of 1.5. According to the CAPM, which stock will have a higher expected return?
Answer: Left Ahead Co. The CAPM model assumes the firm with a higher beta will have a higher required rate of return.
In a CAPM framework, why do investors hold the market portfolio
Any stock with higher expected returns, relative to risk, will converge to the market portfolio
According to the CAPM
If a firm has more systematic risk then the return required by shareholders will be higher
Entrepreneurial finance and capital budgeting frequently rely on time value of money (TVM) calculations . Since risk varies between projects, adjusting for riskiness is a key element of financial analysis. The most common way of adjusting for the risk of an investment is to
Increase the discount rate for riskier projects.
Entrepreneurial finance and capital budgeting frequently rely on time value of money (TVM) calculations. Since risk varies between projects, adjusting for riskiness is a key element of financial analysis. The most common way of adjusting for the risk of an investment is to:
Increase the discount rate for riskier projects.
Implications of the Capital Asset Pricing Model (CAPM)
Investors will hold the market portfolio The expected return of a stock depends on the stock's beta The expected return of a stock depends on the size of the market risk premium
Suppose you calculated the expected returns and standard deviations of expected returns for two stocks. Your calculations are given below: Stock 1 E[R] σE[R] 21.5% 8.74% Stock 2 18.4% 7.4%
Stock 1: 21.5/8.74 = 2.460 Stock2: 18.4/7.4 = 2.487 Choose Stock 2
beta (β)
ratio of the covariance of a stock's returns and market returns to the variance of market returns
The CAPM can be used to determine
return required by equity holders
The CAPM can be used to determine the
return required by equity holders (shareholders)
The CAPM suggests
a firm's expected return is only a function of the firm's level of systematic risk
A stock with a wider distribution has
a larger standard deviation
Regression analysis allows an analyst to estimate
a linear relationship between a dependent variable and an independent variable
The standard deviation measures the spread of the distribution, so a smaller or more narrow distribution results in
a lower standard deviation
According to the CAPM
all idiosyncratic risk can be diversified away
According to the Capital Asset Pricing Model
all investors will hold the market portfolio
Stocks with a greater deviation in returns
are said to be more volatile
The ratio of the covariance of a stock's returns and market returns to the variance of market returns is often referred to as
beta (β).
Gordon Growth Model
can estimate the return required by shareholders
Mean
can provide information about a distribution taken from a representative sample of a population
CAPM will be useful for an investment analyst trying to
determine the expected returns for stocks and will also be used in capital budgeting analysis
Implication of the Capital Asset Pricing Model (CAPM)
expected return of a stock depends on the stock's beta
As the market risk premium increases, the CAPM suggests
expected returns for individual stocks will increase as well
A distribution will
generally be centered around the mean of the sample
A well diversified portfolio should
have a lower standard deviation of expected returns than an undiversified portfolio
A higher beta implies
higher volatility and risk relative to the market which requires a higher return
Less variability
implies a lower standard deviation
If stock A has a higher expected return for a given level of risk than stock B,
investors will sell stock A and buy stock B.
The standard deviation
is a measure of the width of the distribution
In finance, the standard deviation
is also commonly used to approximate for volatility
Systematic risk
is also known as non-diversifiable risk because it affects all firms in the market
Stock X has a wider distribution of returns than Stock Y. Stock X is
more volatile
Ordinary Least Squares
most common type of regression analysis
The standard deviation of expected returns
provides information on the volatility and risk of the portfolio's expected return
Investors can eliminate the idiosyncratic risk through diversification
is called diversifiable risk
The CAPM model assumes idiosyncratic risk
is diversified away
The CAPM beta for the market
is equal to 1
The discount rate
is important in capital budgeting analysis because we will use this rate to discount projected cash flows that will come to the firm if the capital investment project is undertaken
The difference between the expected return for the market and the risk free rate
is often called the market risk premium
The mean
is the best estimate for the Expected Value
According to the Capital Asset Pricing Model, all investors will hold the
market portfolio.
The difference between the expected return for the market and the risk free rate is often called the
market risk premium.
A regression line
minimizes the squared distance from each historical data point to the line
According to the CAPM, only systematic risk affects
the expected return of an individual stock
In general, as riskiness of a portfolio increases
the expected return of the portfolio increases
If the firm is more risky than the market
the firm's β will be greater than one, and if the firm is less risky than the market, the firm's β will be less than one
If the dependent variable is the historical returns for a stock and the independent variable is the historical market returns,
the slope of a regression line is the estimate of the CAPM beta (assuming the risk free rate is zero).
Beta is
the slope of the regression line comparing a stock's returns to the market's return
If returns are higher for an expansionary economic state than a recessionary economic state,
then an increase in the probability of an expansionary economic state occurring will INCREASE the expected return.
If the firm is as risky (in systematic terms) as the market
then the firm's β will equal one
If the present value of the stream of future (projected) cash flows to the firm is greater than the initial cost of the investment project
then the project will be undertaken.
If the dependent variable is the historical returns for a stock and the independent variable is the historical market returns,
then the slope of a regression line is the estimate of the CAPM beta (assuming the risk free rate is zero).
When calculating the standard deviation of expected returns
we must account for the probabilities of various economic states.
there exists a portion of risk that is not diversifiable
which is called systematic (or non-diversifiable) risk
If a firm has more systematic risk, then, according to the CAPM, the return required by shareholders
will be higher
If a firm has more idiosyncratic risk, then, according to the CAPM, the return required by shareholders
will be higher.
The CAPM model assumes the firm with a higher beta
will have a higher required rate of return
As the market risk premium increases, the CAPM suggests that expected returns for individual stocks
will increase as well.
A larger standard deviation
will lead to a wider distribution
Higher risk projects are evaluated
with a higher discount rate
Investors generally prefer stocks
with high returns and low associated risk
In the CAPM
β measures the firm's systematic risk
