Title: FINANCIAL INVESTMENTS Faculty:Bernard DUMAS
1FINANCIAL INVESTMENTSFaculty Bernard
DUMAS The CAPM session 2-1
2Overview
- 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)
3Proof of CAPM
4Reminder 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
5Market 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
6Market 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.
7The CAPM logic
8How do you test the CAPM?
9Is 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
10Is 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.
11Example
12First pass Security A
13Second pass CAPM line
Best fit Intercept 3.82Slope
5.21Adjusted R2 0.4 Theoretical
line Intercept 0 Slope 8.12
14Discussion 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
15Observed deviations from the CAPM
16There 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.
17beta is dead ?
18Book/market also
19Recent 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
20Other 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
21The equilibrium approach to investment
22In 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
23Equilibrium 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?
24Performance measurement
25Main 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)
26What 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
27Performance results
- The vast majority of active managers has
difficulty beating the SP500
28Appendix
29Perf. 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.