I'a' Course Description Course Management

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Rm
m
Slope Rm - Rf
.
Rf
Ri Rf bi (Rm - Rf)
1.0
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Technical, theoretical conclusions of the CAPM as
a description of market equilibrium

• model prices cash flows CAPM is a pricing
  model (equation) in that is specifies how each
  cash flow should be priced in the market -- if
  FCF5 is the cash flow expected in year 5, then,
  via the capm, the market price of that cash
  flow should be
• FCF5/(1rfbetaiE(rm)-rf)5
• only beta matters only characteristic of the
  security that is priced is beta
• E(ri) is linear in beta security market line
  (SML) is a straight line

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• beta is relative risk average beta is normalized
  to 1.0, and beta can be interpreted as a cardinal
  number
• E(rm)-rf is the equity premium the current
  market price of a unit of risk
• ex ante description of the relation between risk
  and return no direct observation of either the
  right or left hand side is available (except for
  a riskless security) -- all values are
  expectations of in-the-future quantities, e.g..
  as firms and the market evolve so do betas and
  E(r)s
• assumption free conclusions if the assumptions
  fail (e.g.. no risk free asset, very
  heterogeneous expectations of returns, variances
  and covariances) the form of the model doesnt
  change much -- unless the assumption that fails
  is investor rationality or major impediments to
  competition -- such as a low degree of liquidity.

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Practical, applied implications and conclusions
of the CAPM

• risk and return should be aligned betas and your
  intuitive notion of risk should be related
• estimating parameters since the parameters beta
  and E(rm)-rf may change over time we need methods
  to estimate them and to find their current
  values
• estimating the equity premium estimates from
  past data (see following graph)
• estimates of beta with the market model (MM) an
  empirical, ex post form of the CAPM that
  employees the regression of ex post values of ri
  on rIndex, where rIndex is the return on a broad
  based financial market index

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• beta, according to the MM beta hat is an
  estimate of the true beta, or non-diversifiable
  risk, at least on average, over the period used
  in the regression
• alpha, according to the capm alpha should be
  zero in the first equation or should be
  rf(1-beta) in the second -- thus alpha can be
  used as an ex post measure of performance (Hows
  your alpha?)
• abnormal returns if, during the interval used in
  the estimation, the line of best fit was higher
  the security offered above normal returns, on
  average during the interval -- thus it was above
  the security market line

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• problems with beta hat as an estimate of true
  beta
• its stale -- doesnt capture change in financial
  or operating leverage
• it varies with the length of the interval used in
  the estimation
• it varies with the use of daily, weekly, or
  monthly returns
• it varies with the use of a different market
  index
• it varies depending on trading activity in the
  security
• smaller, less thinly traded firms have downward
  biased beta hats
• portfolio betas are more accurate
• therefore, though the model is valid, it may be
  subject to errors in usage and application

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Controversy are there other more sensible models
of demanded returns?

• investors base their decisions on consumption
  needs the m in E(rm.) is more complex -- c for
  consumption and includes housing and expected
  future salary as well as financial market returns
  
• investors spot many different risk components
  (arbitraging the many different risks, such as
  production risk or bond default risk or interest
  rate risk) there is more than one beta for each
  i
• illiquidity in some securities is a problem
  there would be an additional add-on to E(ri)

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Observations about the validity of the capm and
its alternatives

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can we test the empirical validity of the CAPM
(SML)?

• tests would focus on the relationship between
  returns and betas
• are returns linear in beta
• does only beta matter (not sigma, not book value,
  not size of firm or liquidity of firms
  securities, not dividend yield, etc)
• is the intercept the risk free rate
• problems with such tests
• we cant observe beta, only beta hat
• we cant observe E(ri), only ri
• we cant observe E(rm) only rI

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how to look at the numbers

• get a cross-section of firms or portfolios with
  different betas and see if the ex post returns
  on those firms are related to those estimated
  betas
• see if they are unrelated to anything else, i.e.
  run regression (an expost form of the SML)
  explaining returns with with beta and other
  potential explanatory variables

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• according to theory
• all coefficients (including the intercept) should
  be zero except lambda1
• lambda1 should be the equity premium or risk
  premium (between 4 and 8 hopefully)
• equation should explain a significant portion
  of all returns (the error term should be small,
  or a tight fit of all securities around the SML
  (although it is necessary to remember that we
  are using expost (realized) returns to proxy for
  ex ante (expected equilibrium) returns

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• according to the results
• using historical betas and historical returns the
  results provide questionable support for the
  relationship
• size is frequently important to explaining
  returns
• size is more strongly related to returns than is
  beta hat
• book value to market value, and price/earnings
  sometimes show up as being important to
  explaining returns
• using better estimates of beta (dynamic or
  changing betas)
• size and other variables become less important

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CAPM conclusions

• model does an adequate job of describing demanded
  returns when the beta reflects current risk --
  i.e. its useful paradigm, but does not describe
  everything about security returns, and must be
  used with care and analysis to arrive at proper
  beta value, proper risk premium, and proper risk
  free rate
• can be used as a basis for valuation of uncertain
  future cash flows
• other things possibly influencing expected or
  equilibrium returns include
• transactions costs stemming from less than
  perfect liquidity
• taxes
• maybe size
• maybe peculiar other market risk factors

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CAPM its pros and cons

• pro --
• simple and straightforward, easy to apply
• derived directly from portfolio choice with few
  added restrictions
• not very assumption dependent
• con --
• does not allow for complex risks
• evidence suggests something is wrong -- large
  predictive errors. Especially that size, book
  value, and P/E ratios seem to be related to risk
  adjusted returns
• attribution of the predictive error of the model
  is still a controversy
• due to inadequacy of the model (throw it out)
• due to difficulty of estimating risk (keep it)