Finance 2: Investors and Markets
The plan for Wednesday May 27, 2009
•
Mixed bag of remarks
•
Sharpe’s Ch. 8. Many words, concepts
and thoughts; no cases.
Remarks
The course evaluation form should show up soon.
We have A104 (too) for next week’s exam.
I forgot the ”self-fulfilling prophecy” Merton remark
on Mon. (Yes, I drag that out every time.)
Next Wed we also do multi-period portfolio choice
from Mossin to Munk. We need to see some
equations.
Chapter 8: Words & Terms
Positive (what people actually do) vs. normative
(what people show do) economics. We’ve been
”largely positive”, although the distintics is less
than clear.
Advisors. (Beware: Salesmen too.)
Life-cycle decisions: Education, work, retirement.
Pensions: Defined benefit vs. defined contribution.
Asymmetric information: Adverse selection and
moral hazard.
Chapter 8: Past and future returns
Densities of 25Y yearly mean and
standard deviation estimators
15
st. dev.
10
mean
0
5
Density
Expected returns are hard
to predict. Even past
ones! Standard
deviations are more
accurately estmated.
(Last week’s exercises.)
The graph on the right is my
version of Sharpe’s
exepriment in Sec. 8.4.
Increasing sampling
frequency makes this
even more pronounced.
-0.1
0.0
0.1
Estimate
0.2
0.3
Sharpe’s Figure 8.4 shows that portfolios
based on estimates are all over the place.
(The welfare loss, though, is not clear.)
Portfolio choice based on historically
estimated returns typically gives a lot less
diversification that ”we would like”,
Three words: Equity premium puzzle.
Sharpe suggests (Sec. 8.8.1) reverse
optimization/engineering: Estimate
(co)variances and use (say) CAPM
backwards to estimate expected returns.
I’m not sure I 100% understand his
experimental design on p. 203-4. (Nonzero correlation between something nonrandom and … what?). Hand-In #2.
Espec. w/ Black-Litterman thrown in too.
Correlation caveat
100 companies ~5,000 covariances to
estimate. 500 companies ~ 125,000
Probably more than the #observations you
have. Clearly, simple estimation is
unstable.
Popular sol’n: Put some structure on; the
single index model, for instance:
r_i =a+ b * r_M + eps_i
(CAPM if a=0)
May work well for stocks and portfolio
choice. And looks very stable.
However, correlation is not a suitable
measure for dependence in extreme
cases.
Thus, a ”single index approach” does not
work well for credit risk modelling.
But that was exactly what people did –
under the fancier heading of ”the Gaussian
copula model”. The rest is history.
Factor models
CAPM type regression of individual stock returns
on the market (index) have ”patterns in
residuals”.
Fama/French say that variations are well explained
by 2 extra factors:
”small minus big” returns
and
”growth minus value” returns.
Fits right into regression framework. Enourmous
literature. (One note: Arbitrage pricing theory in
Sec. 8.6.2 isn’t what you’d think.)
Sec 8.7-8: Investing or Betting?
Investing: Take clients’ preferences and positions
into account to comprise portfolios.
Betting: Try to beat the market based on better
predictions. (Picking stocks, strategic asset
allocation.)
Again, the distinction is fuzzy in reality.
Macro consistency is a test: If you advised
everybody, would markets clear? If not, you’re
betting.
Sec. 8.11: More Advice From Sharpe
Diversify.
Economize. Costs matter.
Personalize.
Contextualize. (Too bad - Sharpe did almost the
whole book without such ”management speak”!)
Asset prices are not set in a vacuum”
And May I Add: We Have Seen ...
Inductive rather than deductive approach.
Run experiments, analyze results.
When we let agents trade ’till equilibrium,
there is a strong tendency for the market
to end up in a situation where CAPM’ish
results give a good description of prices.
That despite assumption voilations.
Portfolios, though, can differ a lot.
It’s not a zero-sum game:
• There are gains from trades – even from
structured products.
• There are losses from ”poor structures”
(Case 11.)
But remain sceptical:
• Not everybody can beat the market.
• There are probably very few free lunches.