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FINANCIAL INVESTMENTS Faculty:Bernard DUMAS

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At equilibrium, the ... The portfolios are grouped into 10 size classes ... others are ('If you do not know who the fools' are, you are the fool ' ) so that : ... – PowerPoint PPT presentation

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Title: FINANCIAL INVESTMENTS Faculty:Bernard DUMAS


1
FINANCIAL INVESTMENTSFaculty Bernard
DUMAS The CAPM session 2-1
2
Overview
  • CAPM
  • Proof
  • Is the CAPM a true statement?
  • Deviations
  • The equilibrium approach to investment
  • Performance measurement
  • (This has been the main impact of the CAPM on the
    investment industry)

3
Proof of CAPM
4
Reminder on optimal diversification at individual
investor level condition of optimality
  • How can you tell whether a portfolio p is well
    diversified or efficient ?
  • For each security i, E(Ri) - r must be lined up
    with cov(Ri,Rp) or, equivalently, with
  • ?i/p cov(Ri,Rp)/var(Rp)

?i/p
5
Market level syllogism
  • All weighted averages of efficient portfolios
    are efficient
  • At equilibrium, the market portfolio, m, is an
    average of individually held portfolios, each of
    which is assumed to be efficient
  • Therefore, the market portfolio is efficient

6
Market equilibrium
  • For each security i, E(Ri) - r must be lined up
    with cov(Ri,Rm) or, equivalently, with ?i/m
    cov(Ri,Rm)/var(Rm)
  • CAPM can be extended to the case in which there
    exists no risk-less asset.

7
The CAPM logic
8
How do you test the CAPM?
9
Is the CAPM true?
  • Content cross-sectional relationship
  • when comparing securities to each other, linear,
    positive-slope relationship of mean excess return
    (risk premium) with beta
  • zero intercept
  • no variable, other than beta, matters as a
    measure of risk or has an influence on expected
    return differences

10
Is the CAPM true?
  • How can you tell?
  • Two-pass approach
  • First, for each security, measurement of mean
    excess return and beta using history of returns
    (time series)
  • Second, relate mean excess return to beta (cross
    section)
  • First pass has no economic meaning, just a
    measurement (a statistical model). Second pass is
    embodiment of CAPM (a pricing model).
  • Note, however, that, if CAPM is right, it follows
    from second pass that ? in the first pass should
    have been equal to zero.

11
Example
12
First pass Security A
13
Second pass CAPM line
Best fit Intercept 3.82Slope
5.21Adjusted R2 0.4 Theoretical
line Intercept 0 Slope 8.12
14
Discussion CAPM may not even be testable
  • 1. the market portfolio is not observable (Roll
    critique)
  • 2. should use time-varying version, based on the
    information set of the investors. The latter is
    not observable (Hansen and Richard critique).

E(Ri) - r
A
date 2
B
A
B
B
date 1
A
?i
15
Observed deviations from the CAPM
16
There are deviations from CAPM
  • Fama and French (1992) investigate 100 NYSE
    portfolios for the period 1963-1990
  • The portfolios are grouped into 10 size classes
    and 10 beta classes
  • They find that return differential (risk premium)
    on ? is negative (and non significant)
  • whereas return differential on size is large and
    significant.

17
beta is dead ?
18
Book/market also
19
Recent thinking
  • Question is Fama-French evidence reliable?
  • Returns not IID return differentials may come in
    waves.
  • Perhaps, CAPM is right at each point in time
  • But CAPM line moves about
  • When indicator variables are used to track
    these changes over time (such as variables we
    shall list in lecture on predictability), size
    and B/M no longer show up in CAPM
  • So, these variables were showing up in the
    Fama-French analysis, not because CAPM was wrong,
    but only because movements in the line had not
    been properly accounted for

20
Other criticisms of CAPM
  • No account of re-investment risk (multi-period
    aspects)
  • inter-temporal hedging
  • No account of investors non traded wealth
    (similar to Roll critique)
  • when human capital is included, the CAPM so
    revised holds up better

21
The equilibrium approach to investment
22
In equilibrium
  • If all investors were mean-variance investors and
    had identical expectations,
  • the CAPM would be right,
  • And every investor could just hold the market
    portfolio (index fund), adjusting the level of
    risk by mixing it with riskless asset.
  • If there are deviations from the CAPM,
  • Then, some investors are not mean-variance
    investors,
  • there may be room for tilted index funds,
  • a form of active portfolio management.
  • Generally, if you are an average investor, you
    should hold the market portfolio. You need a
    specific reason to deviate from the market
    portfolio

23
Equilibrium interplay us vs. them
  • If everyone is a rational investor but have
    different expectations,
  • People who are bullish on a security hold more of
    it
  • If you are rational and others are not,
  • For instance, others may display aversion to some
    type of securities (e.g., small firms)
  • They require higher return on these securities
  • In equilibrium, you profit from their aversion by
    holding more of these securities
  • And, of course, they hold less
  • It is very important to know what you are
    (presumably rational) and what others are (If
    you do not know who the fools are, you are the
    fool  ) so that
  • By being yourself rational, you can exploit
    behavioral traits of others
  • You are aware of the reason for which you are
    likely to make a gain
  • This is a great justification for an investment
    strategy
  • If irrational behavior is very prevalent, that is
    no reason to discard concept of optimizing
    behavior
  • To the opposite, that is a great reason for you
    to know what it means to be rational
  • And for you to be rational
  • Most crucial piece of information how do you
    differ from the average investor?

24
Performance measurement
25
Main impact of CAPM performance measurement
  • Jensens alpha of the fund p
  • Only sign (not value) of ? matters
  • Cannot rank funds by ?
  • Use instead
  • Appraisal (or information) ratio ?p/?(?p)

26
What is the source of ? ?
  • Positive ? (if benchmark market) arises from
  • Either CAPM is incorrect
  • E.g., some investors are not mean-variance
    investors
  • In that case, the ? of any security reflects
    ability of mean-variance investors to take
    advantage of these investors by tilting their
    portfolio permanently
  • Or CAPM is correct but the portfolio manager has
    more information than the market
  • he/she receives signals
  • conducts time-varying portfolio strategy/tactic
  • then, ? of fund is truly a measure of expertise
    precision of signals ? number of signals received
    and acted upon
  • For measure of expertise, benchmark can be
  • Either market portfolio (if known to be
    efficient)
  • Or efficient portfolio calculated ex post, but
    with constant weight
  • In which case, ? measures ability of time-varying
    portfolio policy based on signals to beat
    constant-weight policy

27
Performance results
  • The vast majority of active managers has
    difficulty beating the SP500

28
Appendix
29
Perf. measurement critique of Jensens ? when ?
is time varying
(Admati and Ross)
high beta strategy
Portfolio excess RoR
low beta strategy
? lt 0 !
Low
High
Market excess RoR
?Disenchantment with performance measures not
predicated on observation (or modeling) of policy
followed by the fund.
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