Shortfall Minimizing Portfolios
abstract

Many institutional and private investors seek for a long run excess
return relative to a reference strategy (e.g. money market, bond
index, etc.) which they want to attain under a minimal shortfall
probability. In this article it is shown that even in the long run
in order to attain a substantial excess retum a high shortfall
probability has to be accepted. In the model the prices of the
assets follow geometric Brownian motions. Two types of a shortfall
are distinguished. A shortfall of type I occurs, if at some point of
time the investment goal is missed by a given percentage. There is a
shortfall of type II, if the investment goal is missed at the end of
the planning horizon. To begin with, only constant portfolio weights
are admitted. For both types it can be shown that minimizing the
shortfall probability under a given excess return is equivalent to
the Merton problem. Under realistic parameter values moderate
shortfall probabilities are only compatible with very bw excess
returns. Finally, it is shown, that “Constant Proportion
Portfolio Insurance“ (CPPI) does not lead to a reduction of
the shortfall probability.



type

journal paper



keywords

Pension Finance, Shortfall, Portfolio Optimization, Excess Return, CPPI 


language

English

kind of paper

journal article

date of appearance

23122006

journal

SAV Bulletin

publisher

Stämpfli Verlag AG (Bern)

volume of journal

02

page(s)

125142

review

blind review



citation

Baumann, R., & Müller, H. (2006). Shortfall Minimizing Portfolios.
SAV Bulletin, 02, 125142.


