On Conditional Distribution and Portfolio Optimization
Diversification is one of the central themes in modern portfolio
theory. Yet, mean-variance optimization, which plays a fundamental role
in the theory, often gives rise to portfolios that are overwhelmingly
concentrated in just a few assets. The reason for this is that
mean-variance optimization is notoriously sensitive to its inputs,
which are expected returns and covariance matrix.
The Black-Litterman method was developed to alleviate the input
sensitivity problem. It combines the market equilibrium expected
returns, which are obtained by solving an inverse problem, with
conditional distribution theory, which adjusts the mean vector to
reflect an investor's personal forecast of a few expected returns. In
this talk, we outline the background and approach behind their method.
We then present a new unified method that extends the results by
Black-Litterman. The motivation for the method is to obtain conditional
mean vector as well as conditional covariance matrix given an
investor's view, which embraces forecasts not only of expected returns
but also of volatilities and correlations. Our method is based on a
simple application of conditional distribution but it does not requires
a Bayesian approach as in the Black-Litterman method. Finally, we
discuss its application to asset allocation problems and certain risk
management issues.
Sat 10 a.m., 200 LOV (lecture and assignments)
Tues 3:40 p.m., 200 LOV
Thurs 3:40 p.m., 200 LOV
Feb 22, 3:40 p.m., 220 LOV
Paul Beaumont, FSU Economics
Stripping the Yield Curve I
Feb 24, 3:40 p.m., 200 LOV
Scott Mixon, Warburg Dillon Read
Factors Explaining Movements in the Implied Volatility Surface
This talk explores the relationship of changes in the index implied
volatility surface to economic state variables. Three latent variables are
sufficient to explain 90% of the variation in the surface, but observable
variables have explanatory ability confined largely to options with less
than 1 year to expiration. Index returns, both domestic and foreign,
significantly affect option volatility at all maturities, as do changes in
short rates. Changes in the slope of the yield curve affect options with
less than 1 year to maturity.
A revolution is taking place in money management with the creation of
index funds and the benchmarking of active managers. I will look at the
implications to the industry and speculate that manager skill (the ability
to add value to a benchmark) will become a traded derivative.
In carrying out a large portfolio transaction, a trader must balance the
liquidity
premium he must pay to trade rapidly, against the uncertainty of future
prices to which he is exposed by trading slowly. Using a simple model for
how trading moves prices, and using a simple utility function formulation
for balancing risk against known costs, we apply the calculus of
variations to determine an optimal trading strategy in terms of a few
market parameters. We argue that these solutions are a realistic
mathematical formulation of traders' intuition about optimal trading. We
examine actual US stock market data to estimate the parameters in our
model, and show that the time scales characterizing optimal liquidation
strategies vary by several orders of magnitude across the market. Our papers are available on our Web page at
http://finmath.uchicago.edu/~almgren/optliq/
Sat:
Scott Mixon, Warburg Dillon Read
Quantitative Jobs in Finance
Advice to job searchers from a relatively recent job searcher. The
discussion covers the various types of jobs available and strategies for
learning about job opportunities in the private sector. Emphasis is placed
on details that quantitative job searchers often overlook.
