CAPM & Asset pricing models

Question 1

CML

What Is the Capital Market Line (CML)?

Answer 1

The capital market line (CML) represents portfolios that optimally combine risk and return. It is a theoretical concept that represents all the portfolios that optimally combine the risk-free rate of return and the market portfolio of risky assets. Under the capital asset pricing model (CAPM), all investors will choose a position on the capital market line, in equilibrium, by borrowing or lending at the risk-free rate, since this maximizes return for a given level of risk.

Question 2

CML

What is the formula and Calculation of the Capital Market Line (CML)

Answer 2

Rp =portfolio r, rf=risk free rate, RT=market r, σT=std. dev of market r, σp =std. dev of portfolio r

Question 3

Briefly explain how the Capital Asset Pricing Model (CAPM) assumptions ensure that all assets lie on the Security Market Line (SML). How does this differ from the argumentation behind the Arbitrage Pricing Theory (APT) prediction that all assets lie on the arbitrage pricing line (or plane)?

Answer 3

In the CAPM world, any security that is mispriced would instantly be pushed back to the SML, as
all (continuously optimizing mean-variance) investors adjust their demand for the asset.
The key difference with the APT is that the CAPM requires all investors to invest in the same way
(mean-variance optimization) and to update their portfolios continuously. The APT ‘just’ requires
that there are sufficiently many (or wealthy) arbitrageurs out there that exploit mispricing fast
enough.

Question 4

What is alpha ?

Answer 4

Excess return that cannot be explained by the CAPM

Alpha (α) is a term used in investing to describe an investment strategy’s ability to beat the market, or its “edge.” Alpha is thus also often referred to as “excess return” or the “abnormal rate of return” in relation to a benchmark, when adjusted for risk.

It means youre above the SML

Question 5

Below are some statements about the assumptions and implications of the Capital Asset Pricing Model (CAPM). For each statement, indicate whether it is true or false. If the statement is false, briefly explain why. (7 points)
1. Investors are mean-variance optimizers.
2. All investors have the same estimates of expected risk and return (homogeneous expectations).
3. Estimated correlations between assets only differ if investors have different investment horizons.
4. Every asset, including privately traded assets, is part of the theoretical market portfolio.
5. The optimal investment portfolio is the same for every investor.
6. The only relevant risk premium is the market risk premium.
7. Investors diversify market risk by combining high beta assets with low beta assets.

Answer 5

True: 1, 2, 4, 6.
False: 3: Investors cannot have different investment horizons in the CAPM setting. 5: Investors have the same optimal risky portfolio but may differ in how much risk they take. 7: Market risk is systematic/undiversifiable.

Question 6

CAPM suggests you can calculate E(R) if you know 3 things

Answer 6

• riskfree rate (easy)
• Equity risk premium (hard)
• Beta, market portfolio as driving risk factor (hard)

Question 7

How do you calculate Alpha?

Answer 7

Alpha = eR - ( Rf - beta (Rm - Rf))

E (R) - RF = alpha + beta * Rf

Question 8

The CAPM model is widely used in practice. List two applications of the CAPM and briefly explain them.

Answer 8

1. Beta is regarded as an important risk measure.
2. CAPM is used as a performance benchmark for traders / portfolio managers. Does a specific trader over- or underperform relative to the market? (use Security Market Line and Jensen’s alpha).
3. Companies use CAPM to set up a benchmark hurdle rate (cost of equity capital) for internal investment decisions. In fact, majority of the US CFOs use CAPM for their cost of capital calculations.

Question 9

What are the assumptions of the CAPM?

Answer 9

Solving the equilibrium can only be done under a set of restrictive assumptions:
o Assumption 1: all agents are atomistic: agents are small relative to the markets, they are price takers
o 2: all agents have the same planning & decision horizon (no long or short term, all the same).
o 3: agents invest in publicly traded assets
o 4: there are no transaction or information costs
o 5: agents are mean-variance optimizers
o 6: agents are rational, agents use exactly the same information sets and have exactly the same estimates of E(r), sigma and ro (p)

Question 10

What are the two predictions of the CAPM?

Answer 10

1. The optimal risky portfolio R in mean-variance space, that was left unspecified in MPT, now in fact takes a very specific form: it is the market portfolio. Changing prices alter the efficient frontier in such a way that the market portfolio becomes the tangency portfolio.
2. Since all investors hold the market portfolio, the only type of risk they are exposed to is market risk.
   o That is, only relevant risk premium is the market risk premium.
   o A stock’s expected return should thus depend on a compensation for that stock’s exposure
   to market risk, which is measured by the security’s beta (co-variance with the market)

Question 11

How can you calculate a stocks beta?

Answer 11

Question 12

How do you use the market model to decompose a stock’s risk into systematic and stock-specified risk

Answer 12

BETA IS FOR systematic risk

R squared = variance due to market in regression

Question 13

Why do we use Cross-sectional asset pricing tests

And what are the two main types?

Answer 13

The key question in asset pricing: “Why do some securities have a higher expected return than others?”

So fundamental asset pricing test are cross-sectional in nature.

-They come in two basic types: Portfolio sorts and Fama-MacBeth (1973) research paper.
- Both of these test use (average) realized stock returns as a proxy for expected returns.

Question 14

What is the equity premium puzzle?

Answer 14

Realized equity premium much higher than what theory predicts, however there is survivalship bias

Question 15

What does CAPM say about Expected vs. realized alpha

Answer 15

Question 16

How do researchers usually check if the CAPM works?

How do you test the CAPM?

Answer 16

Empirical studies of the CAPM usually take the form of cross-sectional tests based on U.S. stock returns

“Do stocks with a higher beta yield higher returns on average?”

Fama and French (1992, “The Cross-Section of Expected Stock Returns,” Journal of Finance) is one of the most cited papers in this field.

Question 17

What is the size effect?

Answer 17

F&F show that stock returns are strongly negatively related to the size of the firm (measured by market equity or ME) -> the size effect in equity returns

“The size effect in finance literature refers to the observation that smaller firms have higher returns than larger firms”

The size effect is a market anomaly in asset pricing according to the market efficiency theory. According to the current body of research, market anomalies arise either because of inefficiencies in the market or the underlying pricing model must be flawed. Anomalies in the financial markets are typically discovered form empirical tests. These tests usually rely jointly on one null hypothesis H0= markets are efficient AND they perform according to a specified equilibrium model (usually CAPM).

Question 18

What is the value effect?

Answer 18

F&F show that the higher the book value of equity relative to the market value (the “book to market ratio” or BE/ME), the higher subsequent returns  the value effect

The value effect is the excess return that a portfolio of value stocks (stocks with a low market value relative to fundamentals) has, on average, earned over a portfolio of growth stocks (stocks with a high market value relative to fundamentals).

A recent theoretical framework is where a stock’s expected rate of return depends on its sensitivity to cash-flow and discount-rate news. It is argued that a rational investor cares more about falling expectations of future cash flows since this unambiguously reduces investor wealth. An increasing discount rate does the same, but is partly offset by the higher expected return that comes with an increasing discount rate. The outperformance of value stocks is interpreted as compensation for the observation that value stocks are more sensitive to changes in expectations of future cash flows.

A number of behavioural finance explanations argue that human cognitive biases may lead to asset mispricing. I.E. representativeness, conservatism and overconfidence, which all lead to investor over- and under-reaction and thereby the value effect.

Question 19

What are the problems with testing the CAPM?

Answer 19

• Betas are estimated with error
• True market portfolio cannot be measured (should also
  contain bonds, real estate, human capital, private firms)
• Betas change over time
• We can only observe realized returns, which may differ
  from expected returns (Elton, 1999, Journal of Finance)

Question 20

Answer 20

Question 21

Answer 21

Question 22

Portfolio 1 has an expected return of 30 percent and a St.dev of 35%

Portfolio 2 has an expected return of 40% and an st.dev of 25%

is this possible following the sipmle CAPM

Answer 22

Yes! If the CAPM is valid, the expected rate of return compensates only for systematic(market) risk, represented by beta, rather than for the standard deviation,which includes nonsystematic risk. Thus, Portfolio A’s lower rate of return canbe paired with a higher standard deviation, as long as A’s beta is less than B’s.

Question 23

Using these assumptions and the Capital Asset Pricing Model (CAPM) with the AEX as the market portfolio, what is your estimate of ASML’s market beta? What are the weaknesses of this approach? Briefly explain your answers. (3 points)

Inferred beta through graph of one year and algebra. Market portfolio is aex.

Dont do calc, why is estimating beta through this approach weak?

Answer 23

One can argue that historical data are not informative about the future. Also, it can be tricky to base the expected returns on only one year. Both the ASML and AEX have negative expected returns over this period, which is odd. It might be better to include a longer time period, but it is not trivial how far back the dataset should go. Distant past cash flow information might not be relevant anymore for the current situation or a longer time horizon might include events (such as market crashes) that influence the estimates. Besides, the theoretical market portfolio cannot be observed. The market index used here is surely not the ‘market portfolio’ of the CAPM. Also, the assumptions of the CAPM might not hold and the CAPM may not be the ‘correct’ asset pricing model.

Question 24

When a capm estimate is off, does it invalidade the model?

Answer 24

This difference between ex ante expected returns and ex post realized returns does not invalidate asset pricing models such as the CAPM. The CAPM says something about expected alphas (namely, that they should be zero), but does not say something about realized alphas (so they can deviate from zero). Realized alphas can be negative because of unexpected news (e.g., discount rate and/or cash flow news). Besides, even though the Yahoo’s estimate was a steady estimate, the estimate of the beta can also be off.

Question 26

What is beta in disguise?

Answer 26

an important caveat is the joint hypothesis problem: we do not know the correct asset pricing factor
so it cannot be ruled out that the alpha on the long-short portfolio is actually a compensation for
other sources of risk (“beta in disguise”).