chapter 9: CAPM Flashcards
a risk premium
induces a risk averse person to enter into a risky situation
the expected payoff that induces a risk-averse person to enter into a risky situation
insurance premium
the payment to get out of a risky situation
where can we know for sure a reasonable investor’s portfolio will be, whether he is risk averse or nah?
on the efficient frontier
Zero risk
another way of describing a risk-free asset
the point on the graph containing the efficient fortier in which there is zero risk?
The origin
the point on the graph containing the efficient fortier in which there is zero rate of return?
the origin
formula of a portfolio containing one risk asset and a non risky asset (such as a T-bill)
what does this formula explain regarding the allocation of our in vestments in the risky asset?
σp = w · σA
the more we put in the risky asset, the more our risk increases, and vice versa
formula to find the wright put in the risky asset when we have a non risky asset
w = σp / σA
formula to find the return of a portfolio with a risky asset and a non risky asset
ERp = ((ERA - RF) / σA) · σp
or just do the weights
tangent portfolio
the risky portfolio on the efficient frontier whose tangent line cuts the vertical axis at the risk-free rate
–> touches just one point of the efficient fortier
new (or super) efficient frontier
portfolios composed of the risk-free rate and the tangent portfolio that offer the highest expected rate of return for any given level of risk
how to find our most efficient portfolio with a given efficiency fortier?
you find the point tangent with the ER formula given earlier that forms a straight line
short position in a risk-free asset
having a negative position
the investor achieves a short position by borrowing part of the asset’s purchase price from the stockbroker
how to achieve a shorted position?
to buy stocks on margin
what is buying stocks on margin?
the investor borrows part of the purchase price from the stockbroker
the separation theorem
states that the investment decision is separate from the financing decision
the investment decision
the decision on how to construct the portfolio of risky assets
the financing decision
the decision about how much should be invested or borrowed at the risk-free rate
the market portfolio
a portfolio that contains all risky securities in the market
the capital asset pricing model (CAPM)
a pricing model that uses one factor, market risk, to relate expected returns to risk
the capital asset pricing model (CAPM)’s creator
Professor William Sharpe
the best-known equilibrium asset pricing model
the capital asset pricing model (CAPM)
the capital asset pricing model (CAPM)’s basic assumptions
- All investors have identical expectations about expected returns, standard deviations, and correlation coefficients for all securities.
- All investors have the same one-period time horizon.
- All investors can borrow or lend money at the risk-free rate of return (RF).
- There are no transaction costs.
- There are no personal income taxes, so investors are indifferent whether they receive capital gains or dividends.
- There are many investors, and no single investor can affect the price of a stock through their buying and selling decisions. Therefore, investors are price-takers.
- Capital markets are in equilibrium.
the two CAPM important implications
- The “optimal” risky portfolio is the one that is tangent to the efficient frontier on a line that is drawn from RF
–> This portfolio will be the same for all investors
- This optimal risky portfolio will be the “market portfolio” (M), which contains all risky securities
–> The value of this portfolio will equal the aggregate of the market values of all the individual assets composing it
—-> the weights of these assets in the market portfolio will be represented by their proportionate weight in its total value
what is the market portfolio (M)
the optimal portfolio of risky securities that is combined with RF
capital market line (CML)
a line depicting the highest attainable expected return for any given risk level that includes only efficient portfolios
–> indicates an expected rate of return
all rational, risk-averse investors want to be on this line
it is the line formed by point RF and point M
what is the point RF on a graph
the point ton the y axis where x = 0
x is the standard deviation or risk, so it is when there is no risk
that point is the highest possible return we can obtain Risk Free
what is the slope for the capital market line (CML) on a graph?
slope of the CML = (ERM - RF) / σM
ERM: the expected return at point M, so at the most efficient portfolio at σM
RF: the risk free rate, so the point on the y axis when x = 0
σM: the standard deviations of returns on the market portfolio, the value on the x axis
the market price of risk for efficient portfolios or the equilibrium price of risk in the capital market
the slope for the capital market line (CML)
indicates the additional expected return that the market demands for an increase in a portfolio’s risk
formula to find the expected return of portfolio M at any given σM (point on x)
ERp = ((ERM - RF) / σM) · σp
ERM: the expected return at point M, so at the most efficient portfolio at σM
RF: the risk free rate
σM: the standard deviations of returns on the market portfolio
the standard deviations of returns on the efficient portfolio being considered
market price of risk
the incremental expected return divided by the incremental risk
indicates the additional expected return that the market demands for an increase in risk
the slope for the capital market line (CML)
required rate of return
the rate of return investors need to tempt them to invest in a security
basically, what is the Capital Market Line?
it is our required rate of return and at a certain level risk
it is Kp
can the CML slope downward?
why?
nah bro
because with risk-averse investors the risk premium must always be positive, and the CML predicts required returns
–> risk-averse investors will not invest unless they expect to be compensated for bearing risk
does the CML usually consider ex post or ex ante returns?
why?
ex ante returns
because it is based on expected rates of return
the Sharpe ratio
to assess portfolio performance
describes how well an asset’s return compensates investors for the risk taken
who is the inspirit of the Sharpe ratio?
William Sharpe
the Sharpe ratio usually considers ex post or ex ante returns?
ex post returns
because we are evaluating our past performances
the Sharpe ratio formula
(ERp - RF) / σp
can the CML be applied to individual securities?
no
only to portfolios
the appropriate measure of risk to determine the risk premium required by investors for holding a risky security
the market risk
thats why we have the CML
beta (βi)
a commonly used measure of market risk
relates the extent to which the return on a security moves with the return on the overall market
the characteristic line
a line of best fit through the returns on an individual security, plotted on the vertical axis, relative to the returns for the market, plotted along the horizontal axis
shows how the returns of one firm move alongside the returns of the entire market
the slope of the characteristic line
the beta (βi) coefficient
how do we estimate beta (βi) coefficients?
by using historical data, which assumes that what has happened in the past is a good predictor for the future
we usually use 60 months of monthly returns, but sometimes only 52 weeks of weekly returns are used
when are beta (βi) coefficients much more stable? why?
betas estimated for large portfolios or for industries are much more stable because they are averaged over many securities
how can we calculate the beta (βi) coefficient?
βi = (COViM) / (σ^2M) = (PiM · σi) / σM
A beta of 1 implies what?
hat if the market increased (or decreased) by 1 percent, the return on the security (or portfolio) would increase (decrease) by 1 percent on average
A security with a beta of 1.2 implies what?
that is has returns that are 1.2 times as volatile as market returns, either up or down
The risk-free asset has a beta of how much? why?
a beta of 0
because it has a covariance of zero with the market and has no risk
are negative betas possible?
yea, but they are rare
why do Betas tend to vary a great deal between companies in different industries?
because they possess different risk profiles
how to find the Beta of a portfolio βp?
βp = wn · βn
the security market line (SML)
the trade-off between market risk and the required rate of return for any risky investment, whether an individual security or a portfolio
ki
the price of for a single security
the security market line (SML) formula
ki = RF + (ERM - RF) · βi
ki: the required rate of return on a security (or portfolio) I
(ERM - RF) · βi : the risk premium
the most important and widely used contribution of the CAPM
the security market line (SML)
the security market line (SML) slopes upwards or downwards? why?
slopes upward
indicates that investors require a higher expected return on riskier securities
require securities with higher-betas
the market risk premium
the ERM − RF term in the the security market line (SML) formula
the risk premium as a function of market conditions
the expected return on the market minus the risk-free rate
In equilibrium, the expected return on all properly priced securities will lie on what?
on the SML
when is a security properly priced?
when investors expect a return equal to the required return
when are securities or portfolios undervalued according to CAPM?
when they have expected returns greater than their required rate of return
–> they provide investors with an expected return that is higher than the return required given their risk
–> will lie above the SML or CML
when are securities or portfolios overvalued according to CAPM?
when they have expected returns lower than their required rate of return
–> they provide investors with an expected return that is lower than the return required given their risk
–> will lie below the SML or CML
Alpha (α)
measures the risk-adjusted excess return (above or below that predicted by its beta) earned by a security or portfolio over a given period
the difference between the actual excess return on a security or portfolio during some period and the return that should have been earned according to its level of systematic risk (beta) and the use of the CAPM
how to find the alpha (α) of a security?
αi = (Ri - RF) - [βi(RM - RF)]
The two main differences between SML and CML
(1) the measure of risk
–> CML uses standard deviation, while SML uses beta
(2) the CML applies only to efficient portfolios, while the SML applies to individual stocks and portfolios
why should the _t-bill rate be used for the CAPM model?
because technically, the CAPM is a one-period model
–> T-bill is virtually guaranteed and does not fluctuate
what is the beta of the market?
one
