Chapter 9 – Capital Asset Pricing Model Flashcards
CAPM
represents a prediction of the relationship between
the risk of an asset and its expected return
provides a benchmark rate of return for evaluating
possible investments
allows us to guess what should be the expected return of an asset
- -> How to price an IPO
- -> Required rate of return of a new project or firm stock price
which risk is rewarded with a risk premium?
why?
systematic risk
because it isa non diversifiable
Two sets of assumptions with CAPM
Individual Behaviour
Market Structure
Individual Behaviour CAPM assumption
Investors are rational and risk averse
–> they maximize the utility of
their wealth
Investors are price takers, their trades do not affect the price level of securities
Investors are myopic (Short sighted), one period investment horizon. Single period horizon
Investors have homogeneous expectations (all use the same input list)
Investors are alike
–> Information is costless and available to all investors
–> With common time horizon
Market Structure CAPM assumption are they CAPM
Returns are jointly normally distributed
There is a risk free rate from which investors can lend or borrow
All assets are marketable i.e. investments are limited to publicly traded financial assets
–> all assets are traded
Asset markets are frictionless (no transaction costs)
No market Imperfections: taxes, restrictions on short sales
Markets function well with no obstacles to trading
hnggg
nvrm
All investors will hold which same portfolio for risky asset?
the market portfolio
the market portfolio
contains all securities and the proportion of each security is its market value as a percentage of total
market value
An individual security’s risk premium is a function of what?
its contribution to the risk of the market portfolio
The covariance of returns with the assets that make up the
market portfolio
in CAPM, what is the difference between CML and CAL?
CAL become the CML
P becomes the market portfolio (optimal portfolio)
the market portfolio
optimal portfolio
is efficient
–> It maximizes the returns for a specific level of risk
mutual fund theorem
Investing in a passive index fund
how to invest in the market portfolio?
invest in index fund
the portfolio selection problem can be divided into which two parts?
A technological problem in which portfolio managers will
create their mutual funds
An asset allocation problem in which investors need to allocate their wealth between the RF and the risky portfolio
Considering the portfolio variance from a variance-covariance matrix perspective, we can say that the contribution of one stock (stock B for example) to the total portfolio (P) variance is equal to what?
is equal to the sum of all the of the covariance terms in the row corresponding to that stock (Stock B) multiplied by both the portfolio weights from its row and the portfolio weight from its column
As the number of stock increases in our portfolio, the
covariance of stock-B with all other stocks will dominate or be dominated by the contribution of stock-B variance to the portfolio variance?
will dominate the contribution of stock-B variance to the portfolio variance
If the covariance between stock “B” and our portfolio “P” is negative, then what will happen to the total variance after adding stock “B” to portfolio “P”?
will decrease the total variance of our portfolio
If the covariance between stock “B” and our portfolio “P” is positive, then what will happen to the total variance after adding stock “B” to portfolio “P”?
will increase the
total variance of our portfolio
𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝐵 𝑡𝑜 𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 “𝑷” 𝑒𝑥𝑐𝑒𝑠𝑠 𝑟𝑒𝑡𝑢𝑟n / 𝐶𝑜𝑛𝑡𝑟𝑖𝑏𝑢𝑡𝑖𝑜𝑛 𝑜𝑓 𝑠𝑡𝑜𝑐𝑘 𝐵 𝑡𝑜 𝑡ℎ𝑒 𝑡𝑜𝑡𝑎𝑙 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 “𝑷” 𝑣𝑎𝑟𝑖𝑎𝑛𝑐e
is equal to what formula
(𝐸R𝐵) − RF) / COV (RP, RB)
= (𝐸R𝐵) − RF) / COV (RM, RB)
the reward (excess return) an investor requests in order to invest in the risky stock “B” divided by the risk that stock “B” will add to our portfolio “P”
The reward the investor demands is the excess return (rb – rf)
Our benchmark is the RF
When adding a new stock, investors are only concerned with how this new stock will affect their current portfolio variance
In contrast to efficient portfolio where the variance itself is an
appropriate measure of risk,, what is the appropriate measure of risk for stocks, non efficient portfolios, and other components of the efficient portfolio?
their contribution to the
efficient portfolio variance
formula for the market price of risk
Market risk premium / Market Variance
= (𝐸R𝑀) − RF) / 𝜎^2𝑀
called the market price of risk because it quantifies the extra returns the investors demand to bear the portfolio risk
true or false
At market equilibrium all investor require the same reward to risk ratio for all assets?
true
Equal reward to risk ratios, leads to which equation for any stock
(ERi) - RF) / 𝑐𝑜𝑣(R𝑖, R𝑀) = (𝐸R𝑀 − RF) / 𝜎^2𝑀
–>
ERi = RF + (𝐸R𝑀 − RF) · 𝜷i
Beta (𝜷i)
measures the contribution of stock i to the variance of
the market portfolio as a fraction of the total variance of the market portfolio
a measure of risk
Beta is the appropriate measure of risk for individual assets and non-efficient portfolios
how do we calculate the Beta of our Portfolio
𝜷P = E wi𝜷i
on a graph, what does this equation form
ERi = RF + (𝐸R𝑀 − RF) · 𝜷i
the security market line (SML)
SML vs. CML
CML graphs the risk premiums of efficient portfolio as a function of the standard
deviation SD
–> SML graphs the risk premium of individual securities as a function of their beta
Both SML and CML, when used properly, will determine the required rate of return that will compensate investors for risk as well as the time value of money
alpha
The difference between the fair and actually expected return on securities
ERi = RF + (𝐸R𝑀 − RF) · 𝜷i + 𝛼i
where does an underpriced security lie?
above the SML
where does an overpriced security lie?
below the SML
The risk premium on the market portfolio will be
proportional to the risk of the market portfolio and the
market degree of risk aversion
how does tis translate into a formula
𝐸R𝑀) − RF = 𝐴̅𝜎^2M
𝑤ℎ𝑒𝑟𝑒 𝐴̅ 𝑖𝑠 𝑡ℎ𝑒 𝑎𝑣𝑒𝑟𝑎𝑔𝑒 𝑑𝑒𝑔𝑟𝑒𝑒 𝑜𝑓 𝑟𝑖𝑠𝑘 𝑎𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑎𝑐𝑟𝑜𝑠𝑠 𝑎𝑙𝑙 𝑖𝑛𝑣𝑒𝑠𝑡𝑜𝑟𝑠
how can we test whether the
market portfolio is efficient?
by testing whether it has the
highest reward-to-variability ratio compared to all other
portfolios
We can apply CAPM on realized returns instead of expected returns:
Ri = RF + (𝐸R𝑀 − RF) · 𝜷i + 𝛼i
CAPM implies that 𝛼i is equal to zero for every security in the market
𝛼i represents the expected return above or below the fair expected return predicted by CAPM
If a security is fairly priced according to CAPM, its I should be equal to zero
what is the 𝛼i of a fairly priced security
0
Is the CAPM testable?
Most tests related to the validity of the CAPM focus on testing whether the predictions related to CAPM are correct.
Two predictions are directly related to CAPM
- The market portfolio is mean-variance efficient
–> this is valid tho
–>The fact that active index funds, on average, fail to beat the market index, indicates that the market index is efficient
–> On average, active funds achieve a zero alpha
- The Securities’ alphas are zero
–> this can be concluded from the first
–> These tests usually reject the hypothesis that the average alpha values for all assets are uniformly zero
If CAPM fails empirical tests, why do we still rely on CAPM
to obtain our securities’ expected returns?
CAPM successfully divides the risk into systematic and nonsystematic components
–> It attributes excess returns to systematic risk components of securities
–> It is easy to implement and is still considered among the best models to assess risk premium relative to others
which portfolios on the efficient frontier have a companion portfolio on the bottom inefficient half of the frontier with which it is uncorrelated?
what are these companion portfolios referred as?
all portfolios except the minimum-variance-portfolio (MVP)
as zero-beta portfolios of this respective efficient portfolio
Merton and Roll independently reached which conclusions regarding the efficient frontier portfolio set?
Any portfolio that is a combination of two frontier portfolios is itself on the efficient frontier
The expected return of any security (i) can be expressed as an exact linear function of the expected return on any two efficient-frontier portfolios (P) and (Q)
the expected return of any security (i) expressed as an exact linear function of the expected return on any two efficient-frontier portfolios (P) and (Q)
what happens when we replace portfolio (P) by the market portfolio and portfolio (Q) by the zero-beta portfolio
corresponding to the market?
ERi - ERQ = (ERP - ERQ) · ((𝑐𝑜𝑣(R𝑖, R𝑃) − 𝑐𝑜𝑣(R𝑃, R𝑄)) / (𝜎^2𝑃 − 𝑐𝑜𝑣(R𝑃, R𝑄))
ERi - ERZ = (ERP - ERZ) · 𝜷i
–> ERi = ERZ + (ERP - ERZ) · 𝜷i
—-> the zero-beta portfolio replaces the risk-free
—-> the zero-beta CAPM equation
the zero-beta CAPM equation
when does this equation prevail’
ERi - ERZ = (ERP - ERZ) · 𝜷i
–> ERi = ERZ + (ERP - ERZ) · 𝜷i
the zero-beta portfolio replaces the risk-free
when investors face restrictions on borrowing and lending in the risk-free asset, this version of CAPM prevails
If a security is not traded, how can we properly estimate its
risk-return trade-off
For privately held firms, we can rely on risk-return trade-off of similar traded securities to hedge the risk taken when investing in privately held firms
For human capital, this is a real challenge to the traditional CAPM
ICAPM
Intertemporal CAPM
spans for more than one period
who invented the Intertemporal CAPM (ICAPM) model?
why?
Robert Merton
When our investment horizon spans more than one period and possibly till our retirement, then more risk factors appear to play an important role in our investment decision
–> more securities are appearing (new innovations) or disappearing (bankruptcy)
–> The relation among securities themselves may be changing in the future
–> Inflation rates would be changing in the future
ICAPM equation
ERi = 𝜷i,M · ERM + E (𝜷i,k · ERk)
ERi = ri - RF
ERM = rM - RF
ICAPM reduces to CAPM under which assumptions?
Sources of risk are limited to uncertainty about the market portfolio return (eg.: no inflation risk)
Investment opportunity set do not change through time (eg.: no changes in the relationship of securities)
who invented the Consumption-Based CAPM (CCAPM)
Mark Rubinstein
Robert Lucas
Douglas Breeden
what is the assumption of the Consumption-Based CAPM (CCAPM)
the utility value
of an additional dollar of consumption today must be equal to the discounted utility value of the expected future
consumption that can be financed by that additional dollar of wealth
basically, $1 today more of consumption should be equal to the PV of additional $ of consumption in the future
–> so PV of additional consumption in the future should be $1
In CCAPM, what are assets prices based on?
on how they will increase or decrease our future consumptions
in a CCAPM framework, the excess return of a security should be a positive or negative function of its covariance with the consumption streams (or what we can call its consumption risk)?
a positive function
ERi = 𝜷i,C· RPC
ERi = ri - RF
RPC = ERC - RF
C: a consumption tracking portfolio
RPC: the risk premium associated with the consumption uncertainty, which is nothing but the excess return on the consumption tracking portfolio
Problems with CCAPM
Aggregate consumption figures are published infrequently relative to asset prices
Consumption figures may contain some measurement errors
Advantages in CCAPM
It has a very robust derivation scheme that does not require as much assumptions as CAPM
When empirically tested, it sometimes why explains stock realized returns better then CAPM
Liquidity
the ease and speed at which a security can be sold at fair market value in a timely
fashion
the three components of liquidity
Bid-ask spread
Price impact
Immediacy
Bid-ask spread of liquidity
represents the cost of engaging in a transaction
the difference between the price at which liquidity providers are willing to buy
or sell an security
Price impact of liquidity
how much a large trade may affect the prices
Immediacy of liquidity
how much of an asset can we sell quickly without causing a fire-sale decline in prices
illiquidity
the discount from fair market value a seller must accept if he wants to sell his asset quickly
investors are increasingly asking for excess returns that compensate them for the level of illiquidity they bear when purchasing an asset
the higher the illiquidity of an asset, the higher or lower the excess return requested by investors to invest in this asset
higher
Liquidity based models for CAPM
who came up with it?
They add the liquidity factor(s) to the usual market factor in the CAPM formula
Acharia and Pedersen (2005)
Liquidity based models for CAPM
formula
(don’t insist too much on this we will have the formula sheet)
𝐸(𝑅𝑖) = 𝑘𝐸(𝐶𝑖) + 𝜆(𝛽 + 𝛽𝐿1 − 𝛽𝐿2 − 𝛽𝐿3)
𝑅𝑖 = 𝑟𝑖 − RF
𝑅𝑀 = 𝑟𝑀 − RF
𝜆 = 𝐸(𝑟𝑀 − R𝑓 − 𝐶M)
𝛽 = 𝐶𝑜𝑣(𝑅𝑖, 𝑅𝑀) / 𝑉𝑎𝑟(𝑅𝑀 − 𝐶𝑀)
𝛽𝐿1 = 𝐶𝑜𝑣(𝐶𝑖, 𝐶𝑀) / 𝑉𝑎𝑟(𝑅𝑀 − 𝐶𝑀)
𝛽𝐿2 = 𝐶𝑜𝑣(𝑅𝑖, 𝑅𝑀) / 𝑉𝑎𝑟(𝑅𝑀 − 𝐶𝑀)
𝛽𝐿3 = 𝐶𝑜𝑣(𝐶𝑖, 𝐶𝑀) / 𝑉𝑎𝑟(𝑅𝑀 − 𝐶𝑀)
𝛽 = 𝛽𝐿2
𝛽𝐿1 = 𝛽𝐿3
in the bid_ask spread, why do liquidity providers put on bid/ask quotes?
These quotes indicate their willingness to buy/sell a specific security
what created the bid_ask spread?
Liquidity providers buying securities at lower prices than at the prices they sell those securities
the three components of the bid_ask spread
Inventory costs
Adverse selection cost
Order processing costs
Inside Spread
the difference between the higher price at which some investor (liquidity provider) is willing to purchase a security (highest bid) and the lowest price they are willing to sell this same security (lowest ask)
Inside spread is within the bid-ask spread
the two main types of traders
Noise traders or inventory driven traders or liquidity traders
–> could be non-informed traders
Informed traders or private information driven traders or traders that create asymmetric information in the trading
industry
the dangers of asymmetric information being highly feared by investors
can lead to the cease of trading altogether
