Every single investment decision you ever face,
I mean, whether you're just picking a single
stock for your own portfolio or, you know, evaluating
a huge corporate acquisition, it all requires
you to make one fundamental calculation. It's
that tradeoff between risk and return. Exactly.
We all instinctively know it, right? If you want
a shot at a higher return, you have to accept
higher risk. But the question that really launched
modern financial economics was. How do we objectively
price that risk? Right. How do you put a number
on it? Exactly. How do you precisely quantify
how much extra return is required for taking
on, say, one more unit of market volatility?
And that core problem, that search for the objective
price of risk, well, that's the entire mission
of the capital asset pricing model, or CAPM,
as everyone calls it. And that is our deep dive
today. We are getting into a formula that is,
and this isn't an exaggeration, truly foundational.
I mean, CAPM is the cornerstone model that corporations
use to figure out their cost of equity. And that
portfolio managers use to justify their investment
choices, or in many cases, fail to justify them.
Right. It's this incredible intellectual structure,
and it's all built on the idea of a perfectly
rational investor. Fundamentally, what CAPM is,
it's a tool. It's designed to determine the theoretically
appropriate required rate of return for any given
asset. Okay. The rate you should be demanding.
Precisely. And crucially, and this is a point
we'll come back to again and again, it assumes
that asset is being added to an already well
-diversified portfolio. That's a huge assumption.
A huge one. And what makes it so powerful and
so popular, really, is its simplicity. It gives
you a mathematically derived cost of equity capital,
and it's determined by just one single factor.
And that factor is the asset's exposure to non
-diversifiable risk. The thing that the entire
financial industry just calls beta. And here
is the paradox. I mean, we have to acknowledge
this right at the start because it's what makes
this dive so fascinating for any learner. CAPM
is ubiquitous. It's simple. It's elegant. It's
taught in every single business school on the
planet. Yet. As our sources show, decades and
decades of empirical tests have proven that the
model, well, in its purest form, it often fails
to predict real world returns. It really does.
It is the formula that failed, but somehow still
rules the world of finance. And that's its enduring
legacy. To understand why it still rules, you
really have to appreciate the purity of its theory.
The model itself was built upon the shoulders
of Harry Markowitz's earlier work. On modern
portfolio theory. Exactly. The key architects
who really developed CEPM as we know it today
were Jack Traynor. William F. Sharp, John Lintner
and Jan Mawson. And they were all working independently
in the early 1960s. It was just this rapid intellectual
explosion, wasn't it? All centered around like
1961 to 1966. And of course, that work secured
its permanent place in history when Sharp, along
with Markowitz and Merton Miller, received the
1990 Nobel Memorial Prize in Economic Sciences.
Of a landmark achievement, no question. A landmark,
even if its actual performance in the real world
is, well, it's questionable. OK, so. Let's unpack
this concept of risk because CAPM doesn't view
all risk equally. Before we even touch the formula,
we have to establish which risks we actually
care about and which ones we should just, you
know, get rid of. That distinction is the true
genius of modern portfolio theory, which, as
you said, CAPM inherited. We're dealing with
the two faces of risk that any investor is going
to encounter. Let's start with the face we can
actually control, unsystematic risk. Right. This
is often called idiosyncratic risk or maybe more
helpfully diversifiable risk. The key characteristic
here is that it's unique to a specific company
or a specific asset. So like a scandal. A perfect
example. If a pharmaceutical company fails a
phase three drug trial or a CEO gets caught in
an accounting scandal, that event really only
affects that security. It's just asset specific
noise. And then there's the other phase, the
risk we can't escape, which is systematic risk.
That's the big one. non -diversifiable risk or
just market risk. This is the macroeconomic risk
that's common to all securities, just to varying
degrees. OK, so what are we talking about here?
Think of the big drivers, inflation spiking,
the Federal Reserve hiking interest rates, a
sudden global recession, a major geopolitical
shock. If the overall economy contracts, almost
every single stock drops. You just can't diversify
away from that kind of decline within that market.
And this leads us directly to the great mandate
of CAPM, right? The power of diversification.
The model assumes the investor is rational. And
a rational investor should never, ever take on
diversifiable risk. Why? Because the model states
very clearly that only non -diversifiable risk
is rewarded with a premium return. You don't
get paid for holding on to company -specific
bad luck. That's the critical insight. It's so
important. When you assemble a portfolio, the
specific risks of those individual assets, they're
designed to average out or cancel each other
out. So the good news from one company offsets
the bad news from another. Exactly. Therefore,
the required return on any single asset is only
linked to its contribution to the overall portfolio
riskiness, not its own unique standalone risk.
That standalone risk becomes irrelevant once
you diversify. So practically speaking, what
does it take to get diversified enough to satisfy
this model? I mean, do you, the investor, need
to own 5000 different stocks from all over the
world? Well, our sources suggest that, you know,
in large developed markets like the U .S. or
the U .K., the bulk of the benefits are actually
achieved pretty quickly. A portfolio of about,
say, 30 to 40 randomly selected non -correlated
securities is usually sufficient. 30 to 40 stocks.
That's it. That's usually enough to essentially
eliminate the vast majority of that unsystematic
risk. At that point, your risk exposure is primarily
the systematic market -wide kind. Okay, but there's
a catch, I assume. There's a big caveat, yes.
In less developed emerging markets, asset volatilities
are much higher and the correlations between
them can be, well, they can be strange. You'd
likely need a significantly larger number of
assets to achieve that same level of protection.
Okay, so once we've assumed the investor has
successfully diversified away all that idiosyncratic
risk, we're left with only systematic risk. And
that's where we need a measure. We need a ruler.
A ruler. And that measure is beta. I always see
beta as like a financial Geiger counter. It measures
an asset's unique exposure to that remaining
inescapable market risk. That's a perfect way
to put it. Beta is the one and only variable
CIPM uses to justify why different assets should
have different required returns. It measures
an asset's sensitivity to that non -diversifiable
market movement. Okay. Technically speaking,
it quantifies the sensitivity of the expected
excess asset returns to the expected excess market
returns. Let's lay out the benchmarks then, because
beta numbers are basically a universal shorthand
in finance. What's the baseline? The baseline,
by definition, is a beta of 1. The market as
a whole, which we usually proxy with a broad
index like the S &P 500, has a beta of exactly
1. So an asset with a beta of 1 just moves perfectly
in sync with the market. That's the idea. So
if the S &P 500 goes up 10 % in a year... A stock
with a beta of one is also expected to go up
10%, all else being equal. What about the higher
risk assets? Well, if an asset has a beta greater
than one, let's say 1 .5, it means the asset
is fundamentally leveraged to market movements.
What kind of stocks are we talking about? Think
aggressive growth stocks, cyclical tech companies,
luxury consumer goods, things people buy. When
the economy is booming, if the market rises 10
percent, that stock with a 1 .5 beta might rise
15 percent. It carries more systematic risk exposure
and therefore it's expected to generate a higher
return to compensate the investor. And then conversely,
you have the defensive lower risk plays. Exactly.
Assets with a beta less than one indicate they
are less sensitive than the market average. So
beta of 0 .7, for instance. And these would be?
These are your classic defensive stocks utilities.
Establish consumer staples like toothpaste companies
or big telecom providers. If the market drops
10%, these stocks might only drop 7%. They're
associated with lower systematic risk and therefore
imply a lower required return. Okay, to really
appreciate beta, I think we have to look at the
math behind it. You defined it using covariance
and variance. And for the learner, that can sound
a little dense. So let's look at the formula
and then maybe translate it into simple movement.
Sure. The formula is the covariance of the assets
return and the markets return divided by the
variance of the markets return. And what's fascinating
here is what that ratio is actually doing. Right.
The numerator covariance that just measures how
much the assets returns and the markets returns
move together. Are they highly correlated? Do
they surge and fall in unison? And the denominator,
the variance of the market return, is simply
a measure of the market's total volatility. It's
just its own internal movement. So we're taking
the degree to which our specific asset is sensitive
to the market's ups and downs, and we're dividing
it by the market's own total movement. Precisely.
And by doing that division, beta gives you a
clear standardized ratio. If a stock's movements,
its covariance, are twice as large as the market's
own movements, its variance, then that stock
has a beta of two. It's just a simple ratio.
It strips away all the noise and tells us exactly
how sensitive that stock is to the big macroeconomic
tides. It gives us a really robust measure of
its systematic risk contribution. So with beta
established as the one and only driver of price
risk, we can now assemble. the standard CAPM
framework. This is the central equation, the
one that connects that systematic risk directly
to the expected return an investor has to demand.
The standard CAPM formula for the expected return
on an asset is the risk -free rate plus beta
times the market return minus the risk -free
rate. Okay, let's walk through this piece by
piece because every component is important. Everything
is what we're solving for, right? The expected
or required return on our asset. This is the
minimum return an investor demands to even consider
holding that asset. And we begin with true dollars,
the risk -free rate. This represents the absolute
floor of returns. It's the reward you get just
for committing capital over time with absolutely
zero systematic risk. And in the real world,
what do we use for that? Typically, this is proxied
by the return on short -term government debt,
like a U .S. Treasury bill. Okay, so that's our
baseline. Then we define the engine of the market,
ERM as well as the expected return of the market
portfolio. What do we generally expect the whole
market to deliver? And that term in the parentheses,
the market return minus the risk -free rate,
that is absolutely crucial. This is the market
premium. Or sometimes called the market risk
premium. Right. It's the generalized reward the
market offers just for accepting average market
risk over and above that risk -free floor. If
you had a beta of 1, this entire amount would
be your reward for taking on risk. But because
we have individual assets with different sensitivities,
we scale that market premium using the asset's
unique beta. So if your beta is 0 .5, you only
get to claim half of that market premium. And
if your beta is 2, you claim double the market
premium. It's perfectly proportional. The logic
is that the asset's reward is... perfectly calibrated
by its unique sensitivity. And we can express
this even more clearly if we rearrange the equation
a bit. Okay. So if we just subtract the risk
-free rate from both sides. We get what's called
the risk premium form. It states that the individual
risk premium an asset delivers, that's its return
above the risk -free rate, must be exactly equal
to the market premium scaled by beta. Which just
confirms that central idea. It confirms the central
theoretical thesis. The reward for risk has to
be perfectly linear and proportional to systematic
risk across every single asset in the market.
OK, so if the formula is the brain, then the
security market line, or SML, is the visual body
of CAPM. It's the graph that analysts use to
translate all this theoretical math into practical
investment decisions. It's where you can spot
potential market errors. The SML is just a graph
of the CAPM formula. It's that simple. On the
x -axis, we plot risk and remember only systematic
risk measured by beta. And on the y -axis, we
plot the expected return. And if you look at
that line, you can immediately see the structure
of the formula. The intercept where beta is zero,
that has to be the nominal risk -free rate, $4.
That's the reward floor for taking no market
risk. And the slope of that line, how steep it
is, that represents the market risk premium.
A steeper slope just means the market is demanding
a higher compensation for taking on risk. And
this line, in theory, defines perfect market
equilibrium. And this visualization is where
the rubber meets the road for anyone interested
in active management, isn't it? Because in a
theoretical CPM world, every single security
should plot directly on the SML. They should
all line up perfectly. But in reality, they don't.
So if we plot an asset's expected return in its
beta and we find it sits above the SML, CAPM
tells us that that asset is undervalued. Why
undervalued? Because it means that for the level
of systematic risk it carries, its beta, it is
currently offering a return that is greater than
what the market theoretically requires. The market
is basically giving you a bonus return for that
level of risk. So if an asset is offering a 12
% return for a risk level where the SML says
it should only offer 10%, an active investor
would see that 2 % difference as a clear buying
signal. Exactly. The expectation is that demand
for that asset will push its price up. Which
in turn drives the expected future return back
down until it lands on the SML. Right. And conversely,
if an asset plots below the SML, it's overvalued.
You are accepting a return that is less than
what the market demands for that specific amount
of systematic risk. The expectation is that the
asset's price will fall, which naturally drives
its future expected returns back up toward that
equilibrium line. That deviation, that vertical
distance between where the asset's actual return
is and where the theoretical SML says it should
be, is so important that it earned its own famous
measure, Jensen's alpha. Jensen's alpha, or just
alpha, is the formal measurement of that abnormal
return relative to the SML. It's essentially
a mathematical way of measuring the error term
in the model. Or, for a portfolio manager, it's
a measure of their skill. And we can incorporate
alpha right into the CAPM equation as a sort
of residual term, can't we? We can. A positive
alpha means the asset has outperformed the return
expected based purely on its systematic risk
and the market premium. It suggests the asset
is undervalued or maybe the manager found a true
market inefficiency. This is the return that
cannot be explained by beta alone. And generating
positive alpha is what active fund managers are
paid, you know, massive sums of money to do.
If a fund manager generates a 15 percent return
in a market that gave 10 percent and their funds
beta was exactly one, they have 5 percent alpha.
They generated excess return that the standard
model couldn't predict. And a negative alpha
is, of course, the dreaded opposite. underperformance.
It often suggests overvaluation, or simply that
the manager destroyed value relative to the risk
they took on. And if an asset has a zero alpha,
it's considered fairly valued and plots directly
on the SML. So we've established that CAPM outputs
this required return, EWAR. Let's turn to the
practical application now. Why is this number
so essential in corporate finance and investment
banking? Because it is the required discount
rate, the year use entry that CAPM generates.
provides the asset appropriate required return.
And this number becomes the critical component
for determining a company's cost of equity. Which
then feeds into the WACC, the weighted average
cost of capital. Exactly. And without that rate,
companies can't accurately assess whether a new
project, building a new factory, launching a
new product, is actually going to create shareholder
value. It's a really intuitive relationship,
isn't it, between risk and discounting? If I
need a higher return to take on higher risk,
then that higher return must translate into a
higher discount rate that I apply to any future
cash flows. It has to. A stock with a high beta
will have a high required return, and therefore
its future cash flows will be discounted at a
higher rate. Less sensitive stocks with lower
betas are discounted at a lower rate. This reflects
a fundamental aspect of investor behavior, which
is described by what economists call the concave
utility function. OK, that's a bit of academic
jargon. Can you break down what the concave utility
function means for someone just learning this?
Sure. It just means that investors are risk averse.
They value the first dollar they gain much more
than the hundredth dollar they gain. Therefore,
to persuade a risk averse investor to take on
a higher level of risk, you have to offer them
a disproportionately larger amount of expected
return. The more risk I take, the more you have
to pay me, and at an increasing rate. At an accelerating
rate, exactly. So the higher discount rate we
use for high beta stocks just reflects this behavioral
requirement for compensation. So once that required
return, it's established via CAPM, it is plugged
directly into the foundation of all fundamental
valuation. calculating an asset's intrinsic value
based on its expected future cash flows. This
is the classic present value calculation. We
take all those future cash flows we anticipate
the company will generate and we shrink them
back to today's dollar value using that CAPM
derived rate. The formula for the intrinsic present
value, or PV, is just the sum of all those discounted
future cash flows. And the resulting PV is the
theoretical fair price for that asset today.
This gives you the most important valuation comparison
you can make. If the PV you calculate is higher
than the current market price, then the asset
is undervalued. It's undervalued. You are essentially
buying its future cash flows at a discount relative
to their systematic risk. And if the current
market price is higher than the intrinsic value
calculated, then the asset should be considered
overvalued. This is the mechanism, the nuts and
bolts by which CAPM translates risk into a tangible,
actionable price tag. And I should probably mention
our sources note that CAPM can also calculate
the asset price using an alternative structure.
It's sometimes called the certainty equivalent
pricing formula. OK, that sounds a little esoteric.
How is that different from the standard present
value calculation we just discussed? It's just
another way to frame the exact same idea. Instead
of adjusting the discount rate, the denominator
for risk, the certainty equivalent method adjusts
the expected cash flows. The numerator. How does
it do that? It calculates the certainty equivalent
cash flows. That's the guaranteed amount of money
today that an investor would accept instead of
the risky future cash flows. Then you just discount
that guaranteed amount at the risk free rate.
So you either adjust the cash flow for risk or
you adjust the discount rate for risk. Exactly.
Both the methods lead to the same result. But
the certainty equivalent approach focuses on
risk adjusting the cash flow itself instead of
the rate. So we have the year I, the rate that
CAPM demands we earn, and it's derived purely
from beta. How do we turn that into an actual
investment decision? Well, you have to compare
that CAPM required rate of return to an independent
estimate of the asset's actual return outlook.
Right. CAPM can't tell you what the future cash
flows will be. You have to do that work yourself.
So you need separate analysis. You need fundamental
analysis, maybe technical indicators, looking
at PE ratios, comparing it to similar firms,
using market -to -book ratios, and so on. Okay,
let's put some numbers on it to make it concrete.
Let's say CAPM tells me that based on this asset's
beta, its required return is 9%. But based on
my own deep dive into the company's expected
growth and its dividend policy, I calculate that
the current market price will actually generate
an expected return of 11%. That 2 % discrepancy
is the key signal. If the expected return of
the asset, your 11%, is higher than what CAPM
says is required, the 9%, it implies that the
current market price must be too low. The asset
is undervalued. It's undervalued. Assuming, of
course, that the market is efficient enough to
eventually correct that price, which would pull
the expected return back down to the required
9%. The pricing implication is simple. Find assets
where the expected return exceeds the required
return and buy them. So we've spent a lot of
time admiring the simplicity and the utility
of CAPM, but now we have to confront its intellectual
foundation, because the model only works perfectly
if the real world adheres to a set of extremely
strict and often very unrealistic theoretical
assumptions. Oh, reading this list of assumptions
really makes it clear that CAPM is describing
a financial utopia. It's a frictionless world
where every single actor is a math genius. Let's
start with the behavioral side of things. Well,
the model requires investors to be perfectly
rational and risk -averse. They're always trying
to strictly maximize their economic utility.
And quickly, they must share what are called
homogenous expectations. What does that mean
in plain English? It means every single investor
has to agree on the probability distribution
of potential returns and risks for every single
asset. So if your expectation of Google's future
growth differs from mine, the model starts to
break down. That seems like an impossibility
right there. Everyone processes information differently,
but it gets even more restrictive, doesn't it?
They must also have all information available
at the same time, and no single investor can
influence prices. They're all price takers. Then
you hit the assumptions about the market structure
itself. The market has to be absolutely frictionless.
That means zero transaction costs, zero taxes.
And assets must be perfectly divisible and perfectly
liquid so you can trade fractions of a penny
instantly and without any cost. Wait, let me
stop you on the most famous or perhaps the most
infamous assumption of them all. The ability
for investors to lend and borrow unlimited amounts
of money at the exact same risk -free rate. I
mean, that just seems like a complete fantasy
for the average person. It's a profound abstraction
from reality. That one assumption, coupled with
all the others, is what allows every investor
to achieve an optimal, diversified portfolio
on what's called the efficient frontier. It leads
them all to hold the exact same market portfolio.
It's necessary for the math to work. It's essential
for the mathematics of the equilibrium to hold.
But it is deeply, deeply disconnected from financial
reality where lending rates are always higher
than borrowing rates. And nobody, nobody can
borrow unlimited money. So these nine core assumptions,
they create this elegant theoretical construct.
But it's one that demands a financial world that
just doesn't exist. It's really no wonder the
model started facing issues as soon as it hit
real world data. Right. And because that assumption
about the risk free asset. The ability to lend
and borrow freely at that one rate was such a
high hurdle. Fisher Black developed a really
influential variation back in 1972 to get around
it. This is the Black CPM or the zero beta CAPM.
OK, so if the model can't rely on the existence
of a perfect risk free asset that everyone can
borrow against, how did Black adjust the formula?
You replace the restrictive risk free rate, 10
authors, with the return of a theoretical zero
beta portfolio. We'll call it ERIZ. What exactly
is a zero beta portfolio? It's a portfolio that's
constructed from risky assets that when you combine
them have a weighted average beta of zero. Therefore,
it's a portfolio that has no correlation with
the movements of the overall market. So it's
not risk -free in the sense that it has no volatility.
No, not at all, because it is made of risky assets.
But its systematic risk contribution is nil.
So instead of benchmarking everything against
a government bond, you're benchmarking against
a basket of stocks and bonds whose systematic
movements just happen to cancel each other out.
The Black KPM formula looks just a little bit
different then. By substituting that zero beta
return for the risk -free race, Black created
a model that actually proved to be far more robust
when you tested it empirically. It was particularly
successful in addressing a major initial finding.
Which was what? That the observed security market
line in real markets was often flatter than the
standard CAPM predicted it should be. Wait, why
would the black CAPM lead to a flatter SML? That
seems counterintuitive. Well, in the real world,
the minimum rate you can earn without systematic
risk, that's the zero beta portfolio return,
is often higher than the theoretical risk -free
rate. Because you're still taking on some unsystematic
risk in that portfolio. OK, so the starting point
of the line is higher. Right. And at the same
time, high beta stocks often underperform what
CAPM predicts. So by raising the baseline return
and simultaneously acknowledging that the rewards
for high beta are often lower in practice, the
black KPM effectively pivots the SML, making
it flatter and a much better fit for real -world
observations. We've established the beauty, the
elegance, and the very strict theoretical requirements
of CAPM. Now we have to dive into the section
that, for me, provides the most crucial insight
for the learner. The undeniable evidence that
despite its intellectual pedigree, the model
simply does not work that well in the wild. And
this failure, it's not a matter of mild academic
debate. It's really the consensus view among
leading financial economists. It's perhaps best
summarized by Eugene Fama and Kenneth French,
whose work fundamentally challenged CAPM. And
what did they say? They stated in their 2004
review, and this is the quote, the failure of
the CAPM in empirical tests implies that most
applications of the model are invalid. Wow. That
is a staggering indictment for a Nobel Prize
winning framework that's taught globally. It
tells you right away that modern finance is built
on a foundation that we all know is cracked.
Let's look at some of those specific crack, the
empirical failures. The most direct failure lies
in that relationship between risk and return
itself. CAPM predicts the relationship is linear
and steep. You must take on proportionally more
beta risk to get a proportionally higher return.
But the data shows the S &L is often significantly
flatter than predicted. And this flatness points
directly to the biggest statistical anomaly that
challenged CAPM's dominance, doesn't it? The
low volatility anomaly. What does this pattern
look like in practice? It means that if you analyze
decades of market data, you find that low beta
stocks, the supposed low risk defensive assets
like utilities or consumer staples, often deliver
higher average returns than the CAPM model says
they should. They even outperform some high beta
stocks. Which is a complete contradiction. It's
a direct contradiction to the model's central
promise that only high systematic risk gets a
significant reward. But why would that happen?
Why would investors accept lower returns for
higher risk? If the model is wrong and low beta
stocks outperform, why are people still piling
into aggressive high beta tech stocks? That's
the behavioral gap. Researchers have found that
investors are often constrained. They may not
be able to borrow money at the risk -free rate
to leverage up their safe low beta portfolio.
So instead, they gravitate toward high beta stocks,
hoping to achieve high returns through volatility,
even if those stocks are statistically overpriced
relative to their true risk. It's also just optimism,
right? It's optimism and the hope of massive
outsized gains. The lottery ticket effect. So
beta was supposed to be the single unifying factor
that explained everything. But it was proven
to be insufficient because it just couldn't explain
historical outperformance in specific segments
of the market. Right. And those are the famous
size and value effects discovered primarily by
Fama and French. They observed systematic historical
outperformance from two specific types of stocks
that. Beta just couldn't account for it. And
those were? Small cap stocks companies with smaller
market capitalization. That's the size effect.
And value stocks, which are companies trading
at low multiples of their book value, the value
effect. These stocks consistently generated returns
that were higher than CAPM predicted for their
level of beta. And finally, there's the issue
of time. The model treats beta as this reliable
static constant. Yes. The convenience of the
model requires treating beta as a single fixed
number. But in the real world, beta is highly
time varying. It changes. It changes constantly.
A company in a cyclical industry, say heavy manufacturing,
might have a very high beta during a recession
when investor confidence is low, but a much lower
beta during a boom when its earnings are stable.
Relying on a historically calculated fixed beta
for a valuation model just breaks down when that
company's relationship to the market is changing
dynamically with the economic cycle. Beyond just
the statistical errors, some critics argue the
entire CAPM structure is theoretically flawed
from the ground up. And the most famous argument
here is Rolle's critique from 1977. This is where
it gets really fascinating. Rolle argued that
the entire model is practically untestable. And
the reason is that the anchor of the whole equation,
the true market portfolio, is completely unobservable.
Why is it unobservable? We use indices like the
S &P 500 all the time as a proxy for the market.
But that's just it. They're a proxy. The true
theoretical market portfolio must include all
assets held by all investors globally. Publicly
traded stocks, sure, but also private equity,
government bonds, real estate, precious metals,
commodities, and most importantly... Human capital.
Human capital. The present value of all future
labor income for every person on Earth. We simply
cannot construct a verifiable measure of this
total wealth market portfolio. So when analysts
use a proxy like the S &P 500, they aren't really
testing CAPM. They're just testing whether the
S &P 500 is efficient relative to itself, not
relative to the true total market. Precisely.
Roll's argument was that using any proxy leads
to flawed mathematical inferences. If the true
market portfolio is unobservable, then any test
of CPM's validity is just circular and inconclusive.
The model is perfect in theory, but its key variable
can't be measured in reality, which makes definitive
empirical confirmation impossible. There's also
a more philosophical issue with how CPM even
defines risk, isn't there? Yes. CPM assumes that
variant volatility is the sole measure of risk.
It treats upside volatility and downside volatility
as equally bad. Which doesn't make intuitive
sense. Not at all. It completely ignores asymmetric
downside risk. Most investors don't mind volatility
when a stock is going up. What they really fear
is the probability of returns falling below a
critical threshold, losing their capital. And
this links to the safety first approach to investing,
right? It does. Many practical investors prioritize
minimizing the probability of a major loss rather
than just minimizing overall variance. CAPM completely
fails to capture this psychological preference
for avoiding large losses, focusing instead on
a symmetrical statistical measure that doesn't
really reflect human fear. And finally, we have
to look at the factors introduced by behavioral
finance and just the messy reality of markets
that completely defy CPM's neat assumptions.
Let's start with the ideal world versus the reality
of market frictions. The assumption of a frictionless
world, no taxes, no transaction costs, perfectly
divisible assets is just a non -starter. Real
world trading costs. bid -ask spreads, capital
gains taxes, regulatory restrictions. They all
prevent investors from creating and maintaining
the perfectly optimized, efficient portfolios
that CAPM requires. And those frictions really
matter. They matter greatly, especially in small
transactions. They can completely erode the possibility
of the perfect arbitrage that keeps the model
in equilibrium. And then we introduce actual
human beings who are anything but rational. Behavioral
finance is arguably the biggest intellectual
challenger to CEPM because it shows that our
psychological biases drive significant market
inefficiencies. Absolutely. Biases like investor
overconfidence, hurting behavior, or just simple
emotional trading. They all cause price deviations
that the linear, purely rational CEPM cannot
possibly explain. If investors are driven by
emotion rather than utility maximization, the
entire efficient market equilibrium that CAPM
predicts just falls apart. A great example of
this irrationality and how people structure their
portfolios is mental accounting. CAPM requires
the investor to view all of their assets as one
single optimized portfolio. But in reality, people
silo their money, don't they? They have a safe
retirement account, a speculation fund and a
rainy day savings account. Right. They create
them all differently. They manage the risk profile
of each silo separately, which completely contradicts
the fundamental assumption that they're managing
one unified, risk -optimized entity to maximize
their total wealth. They apply different risk
tolerances to different pools of money. And this
leads to something called skewness preference,
which I think perfectly explains why people buy
lottery tickets even though they have a terrible
expected return. That's the lottery effect. Investors
may willingly accept a lower expected return
for assets that exhibit high positive skewness.
That just means there is a small but high impact
chance of an enormous rare payout. And the dream
of that huge win is enough. The potential for
that huge win compensates them for the statistically
lower average return. CAPM, which only looks
at variance, completely ignores this powerful
preference, which means it systematically undervalues
stocks that have lottery -like characteristics.
So the incredible utility of CPM's framework,
combined with its glaring empirical failures,
meant that finance couldn't just abandon it.
It had to try and fix it. The failures we just
talked about in part five were the direct engine
that drove the creation of more complex multi
-factor models. They just had to acknowledge
that a single measure beta was not sufficient
to describe the complexity of market returns.
Right. And the most famous and influential extension,
which is often considered the modern academic
successor to key APM, is the Fama -French three
-factor model. And this model was a direct response
to those empirical failures we discussed, wasn't
it? Specifically, the size and value anomalies.
Exactly. Instead of relying solely on market
risk or beta, Fama, and French, proposed adding
two new independent risk factors to the equation.
What are those factors? The first factor is SMB,
which stands for small minus big. It accounts
for the historical premium that we've observed
in small cap stocks. That's the size effect.
The second factor is HML. or high minus low,
which captures the premium associated with value
stocks, the value effect. So the Fama French
model is essentially saying Your required return
is determined not just by your sensitivity to
the overall market, but also by your exposure
to the systematic risk associated with being
a small company and being a value company. That's
it. And by including these three independent
sources of risk, the model significantly improved
the ability to explain the cross -section of
expected stock returns. It just fit the data
better. And we also saw extensions designed to
capture that behavioral flaw we mentioned, the
skewness preference. The co -skewness CAPM directly
addresses that lottery. effect. It acknowledges
that human desire for the rare massive payout.
Exactly. This extension includes a term for co
-skewness as a priced factor. It adds higher
order statistical moments to the equation, which
is a fancy way of saying it incorporates the
idea that investors are willing to accept a statistically
inferior return if the distribution of those
returns is positively skewed, offering that lottery
like chance. So it's trying to model the irrationality
that the standard CAPM just dismissed. That's
a great way to put it. And that other major theoretical
extensions address the limitations CAPM imposed
regarding investor time horizons and even the
very definition of utility. Robert Merton's intertemporal
CAPM or ICAPM is key here, isn't it? It generalizes
the model beyond just a single period. The original
CAPM was inherently a static single period model.
Yeah. It was optimized for a short timeframe.
IGCM acknowledges that investors don't just optimize
their portfolio today. They save over decades
and need to manage risk over multiple periods,
allowing for repeated portfolio rebalancing.
It seems so obvious. The intertemporal aspect
just means that investors care about the uncertainty
of future investment opportunities as well as
their current wealth. So ICPM simply acknowledges
that we don't buy a house and then sell it tomorrow,
we say for 40 years, and that long time horizon
fundamentally changes our view of risk. That's
the practical implication. And the consumption
CAPM or CCAPM takes the redefinition of utility
even further. Instead of optimizing your final
wealth, CCPM argues that investors really seek
to maximize their consumption utility. So they
don't care about their portfolio value fluctuating
as much as they care about their ability to afford
goods and services in the future, their lifestyle.
Precisely. CCPM suggests that an asset's required
return should be based on how its returns covery
with aggregate consumption, not just market wealth.
Assets that perform poorly when overall consumption
is low, like during recessions when people are
struggling, are considered much riskier because
they fail you when you need them most. And therefore,
they have to offer a higher return. They must
offer a higher required return to compensate
for that risk. And finally, we noted the issue
of horizon misalignment when it comes to the
risk -free rate. This is a really practical point.
For long -term investors, the choice of the appropriate
risk -free rate, Shia Peer, really changes. If
you are saving for retirement, decades from now,
a short term Treasury bill rate isn't the most
relevant benchmark. So what should you use? Well,
long term investors might optimally choose assets
like inflation linked bonds as their true risk
free asset because their primary goal is to maintain
purchasing power over a very long time horizon.
This means the intercept of the SML isn't fixed.
It depends entirely on the investor's individual
timeline and objectives. It seems like the more
we learn, the more we realize that every single
simple component of that original elegant CAPM
formula had to be complicated, adjusted, or completely
replaced just to try and align the theory with
the real world. So what does this all mean for
you, the learner? We've completed our deep dive
into the capital asset pricing model, moving
from its magnificent theoretical structure all
the way to its systematic empirical breakdown.
Its core purpose to define required return based
solely on systematic risk or beta changed finance
forever. And despite all those powerful critiques,
the low volatility anomaly, the size and value
effects discovered by Fama and French, and Roll's
powerful argument that the true market portfolio
is unobservable, CAPM remains the essential foundation.
It provides the intellectual framework, the vocabulary,
and the starting point for nearly all modern
valuation. Its failure was constructive in a
way. It was incredibly constructive. It led directly
to the creation of the multi -factor models that
we use today. It is the lingua franca evaluation
used daily across corporate finance to justify
discount rates and asset allocations. It's the
simple, beautiful, but ultimately incomplete
map that forced us to acknowledge the vastly
more complicated terrain of real financial markets.
And that leads to a final provocative thought
for you to consider. The elegance of the original
CAPM required us to assume that every single
investor is a perfectly rational, utility -maximizing
machine, given that the greatest contribution
of CAPM wasn't its accuracy and prediction, but
rather the fact that its failure forced us to
define, measure, and then ultimately break the
rules of rationality by discovering behavioral
anomalies. What does that imply about the human
element that we will always fail to fully model
in our search for the perfect investment? That's
a profound thought. The human brain, not the
beta, might just be the final unpriced factor.
Thank you for joining us on the Deep Dive.