  In stochastic finance, one traditionally considers the return as a
competitive measure of an asset, {\it i.e.}, the profit generated by that asset
after some fixed time span $\Delta t$, say one week or one year. This measures
how well (or how bad) the asset performs over that given period of time. It has
been established that the distribution of returns exhibits ``fat tails''
indicating that large returns occur more frequently than what is expected from
standard Gaussian stochastic processes (Mandelbrot-1967,Stanley1,Doyne).
Instead of estimating this ``fat tail'' distribution of returns, we propose
here an alternative approach, which is outlined by addressing the following
question: What is the smallest time interval needed for an asset to cross a
fixed return level of say 10%? For a particular asset, we refer to this time as
the {\it investment horizon} and the corresponding distribution as the {\it
investment horizon distribution}. This latter distribution complements that of
returns and provides new and possibly crucial information for portfolio design
and risk-management, as well as for pricing of more exotic options. By
considering historical financial data, exemplified by the Dow Jones Industrial
Average, we obtain a novel set of probability distributions for the investment
horizons which can be used to estimate the optimal investment horizon for a
stock or a future contract.
