Working Papers
Tony
Berrada
Beta arbitrage strategies, when do they
work and why? (January 2012) with R. Messikh, G. Oderda and O. Pictet
Abstract: Contrary to what traditional
asset pricing would imply, a strategy that bets against beta, i.e. long in low
beta stocks and short in high beta stocks, tends to out-perform the market.
This puzzling empirical fact can be explained through the concept of relative
arbitrage. Considering a market in which diversity is maintained, i.e. no
single stock can dominate the entire market, we show that beta-arbitrage
strategies out-perform the market portfolio with unit probability in nite time.
We use the theoretical decomposition of beta-arbitrage excess return to provide
empirical support to our explanation on equity country indices, equity sectors
and individual stocks. Finally we show how to construct optimal beta-arbitrage
strategies that maximize the expected return relative to a given benchmark.
Incomplete information,
idiosyncratic volatility and stock returns (December 2011) with J.
Hugonnier
Abstract: when investors have
incomplete information, expected returns, as measured by an econometrician,
deviate from those predicted by standard asset pricing models by including a
term that is the product of the stock’s idiosyncratic volatility and the
investors’ aggregated forecast errors. If investors are biased this term
generates a relation between idiosyncratic volatility and stock returns.
Relying on forecast revisions from IBES we construct a new variable that
proxies for this term and show that it explains a significant part of the
empirical relation between idiosyncratic volatility and stock returns.
On Some Approximations of
Dynamic Optimal Portfolios Policies (March
2011) with J. Hugonnier and K. Kousse
Abstract: We
present a Taylor-expansion based methodology for deriving approximate closed
form solutions of dynamic optimal portfolio allocation problems. We illustrate
this methodology with two settings. First, as an illustrative example, we
consider a non-gaussian stochastic short interest rate and a stochastic market
price of risk as state variables and derive an approximate optimal strategy in
this setting. Comparative statics revealed some interesting facts regarding the
optimal portfolio. Simula- tions help to compare the approximation with the
solutions obtained by the Monte-Carlo simulation methodology introduced by
Detemple, Garcia and Rindibascher (2003). Using the simulations to compute the
certainty equivalents of the different strategies, we look at the costs induced
by the suboptimality of the approximation and they are relatively small.
Second, we model the term struc- ture of interest rates in a HJM framework and
the market price of risk as a stochastic state variable. We derive approximate
closed form formulae for the dynamic optimal portfolio policy in this setting.
These approximate closed form formulae have the advantage of easing
implementation of large-scale dynamic asset allocation problems. To illustrate
this, we implement this strategy on a dataset of S&P500 universe of stocks.
Our approximate strategy outperformed the myopic portfolio out-of- sample,
which suggests that hedging demands against the different sources of risk
create value for the investor.
Optimal Investment with Adjustment Costs (in preparation)
with J. Hugonnier
Abstract : This paper provides a general solution to the
neoclassical model of invest- ment with adjustment cost, when the exogenous
price process follows an arbitrary nonnegative semi-martingale, under the
assumption of constant return to scale technology. The main theorem is
illustrated by three exam- ples: (i) a model with shifts in regime (ii) a model
with shifts in regime and incomplete information (iii) a model with fixed costs
of adjustment. In these three examples we provide closed-form expressions of
the optimal in- vestment strategy, the marginal value of capital and the firm
value.