L6 - The Capital Asset Pricing Model Flashcards

1
Q

What are the 6 assumptions underlying the CAPM?

A

A1) Investors are price takers.

  • Personal wealth is small compared to the entire economy. Investors act as though security prices are unaffected by their own trades.

•(A2) Investors have an identical one-period investment horizon

  • .–Investors ignore everything that might happen after the end of the single-period

•(A3) Investors face the same opportunity set - exactly the same portfolio frontier

  • .–They can only trade publicly available assets.\
  • –They can borrow and lend without constraints at the risk-free rate rf
  • (A4) No taxes and transaction costs - frictionless economy
  • (A5) Investors are rational mean-variance optimizers.
  • –Investors all follow the Markowitz framework.

•(A6) Investors have homogeneous expectations.

  • –Information is costless and available to all investors.
  • –Given a set of security prices and rf , all investors use the same expected returns and covariance matrix of security returns to generate the efficient frontier.
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2
Q

What is the market portfolio?

A

–If all investors use identical Markowitz analysis (A5) applied to the same universe of securities (A3) for the same time horizon (A2) and use the same information (A6), they all must arrive at the same composition of the optimal risky portfolio.

  • all investors under the CAPM assumptions will hold the same portfolio of risky assets

The market portfolio contains all risky securities. The weight for each security is its market value as a percentage of the total market value (wi = MVi/MVm)

where the market value of a security is the sum of the holdings each individual has in the stock (the sum of this gives the total market cap.)

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3
Q

How do you construct the Capital market line?

A
  • , we know the market portfolio is on the efficient frontier and is the optimal risky portfolio.
  • The line from the risk-free rate through the market portfolio is called the Capital Market Line (CML).

–CML is one of the CALs ( a special case of the CAL).

–CML is the best attainable CAL.

  • can draw an infinite number of CALs as there are numerous different risky portfolios but as there is only one market portfolio there is only one CML
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4
Q

What must all lending and borrowing sum to in the market?

A

0 - the sum of all assets put into riskless bonds must be equal to zero and the market needs to clear

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5
Q

What happens when certain stock is not included in the market portfolio?

A
  • No demand for the stock
  • price falls
  • Become an attractive choice
  • People start buying it
  • Gets included in the market portfolio
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6
Q

How do you calculate the contribution of asset S to the variance of a market portfolio?

A
  • the reason we bring the summation into the covariance is that the second term has a special interpretation –> is it the weighted average of all returns which is the markets returns
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7
Q

How do you calculate assets S contribution to the reward-to-risk ratio of the market portfolio?

A
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8
Q

What is beta?

A
  • a zero beta does not indicate 0 risk
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9
Q

What is the full CAPM equation?

A
  • beta is also referred to as the quantity of risk - how much risk you are bearing
  • the market risk premium is also called the price of risk —> how much reward you will receive when you bear one unit of systematic risk
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10
Q

What does the Security Market Line look like?

A
  • Slope is the market risk premium
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11
Q

What is the differences between the CML and SML?

A
  • p is any risky portfolio
  • cant be drawn on the same graph
  • CAL doesn’t need many assumptions but SML does
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12
Q

How do you calculate the portfolio beta?

A

the weighted average of all betas of each asset in the portfolio

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13
Q

What does it mean when an asset’s realised return lies above the SML?

A
  • it generates returns higher than that predicted by CAPM
  • it’s current price is too low (r = P1/P0 -1)
  • it is underpriced

Conversely, ovepriced seucrities lie below the SML

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14
Q

Why would you choose a low beta stock vs. a risk-free asset?

A
  • including a low beta high idosyncratic risk stock expands the portfolio frontier whereas the risk-free asset does not
  • When the market is bad the stock may have high excess rturns offset losses from other securities (risk-free asset cannot do this as excess return is always zero by definition)
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15
Q

What is alpha?

A
  • The vertical distance between the security and the SML is known as the alpha of that security. It is a measure of the abnormal return.
  • •Security analysis is the process of buying securities with positive alpha or shorting securities with negative alpha.
  • •Investment is difficult because it is not about finding out the good firms. It is about finding out the mispriced firms
  • .•The (SML) can be used to identify mispricing
    • –overpriced: negative alpha (current price too high - below SML)
    • –underpriced: positive alpha (current price too low - above SML)
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16
Q

How do CAPM hold up in the real world?

A

CAPM remains a reasonable model to explain the expected returns of risky assets. This implies:

  • –α is mostly zero.
  • –Positive and negative alphas are revealed only by superior security analysis.

•Grossman and Stiglitz (1981):

  • –Zero alpha equilibrium may be one that real economy can approach, but not necessarily reach.
  • –The actions of security analysts are the forces that drive security prices to “proper” levels at which alpha is zero. But if all alphas were identically zero, there would be no incentive to engage in such security analysis.
17
Q

What are the limitations of CAPM?

A
  • CAPM deals with the expected returns. It does not predict the actual returns.
    • –We can’t really calculate E(r) and standard deviation due to lack of population information.
  • •CAPM relies on the existence of a risk-free asset and a hypothetical market portfolio that includes all assets.
    • –They do not really exist
    • –We usually use index portfolio (e.g. S&P 500) as a proxy for the market portfolio.
    • –We usually use T-bills or T-bonds as the risk-free asset
  • •Estimating beta remains difficult
18
Q

How do you estimate beta?

A
  • high frequency trader estimate beta every 3/5 mins

the big problem with estimating beta is we do not know what sample period or data is the right ones to use!