number of them and they are uniformly distributed throughout time, can yield radically
different portfolios even though the same universe of stocks is used. Portfolio size is also
an important factor (smaller portfolios use fewer data points, therefore the distribution
of possible outcomes will be more varied). If every possible starting point is used and
portfolio performance is computed, the following two observations are worth making.
On the one hand, the worst (or best) possible experience can be determined by simply
finding the portfolio with the worst (or best) return. We know what to expect if we are as
unlucky (or lucky) as possible from the point of view of timing. On the other hand,
portfolio performance can be averaged over all starting points in order to obtain a
somewhat more real-world expected return.
We begin by describing the mechanics of portfolio construction. The following
variables must be considered:
1.Portfolio size The maximum number of stocks owned in the portfolio.
2.Holding period The maximum amount of time any stock in the portfolio is held.
3.Entry point The number of trading days post event date to wait until each stock is
bought.
As mentioned above, the ability to run a fully invested portfolio of a given portfolio
size is very sensitive to the shape of the event distribution. It is easier to construct
portfolios from large universes where events occur regularly. Likewise, longer holding
periods help by decreasing the turnover rate. The effect of entry points is slightly more
subtle and shall be considered in detail later.
We simulate a fully invested, (initially) equally weighted, next available portfolioPas
follows. LetM 2 Ndenote the portfolio size ofP. Then there areMdistinct strains
running simultaneously that constituteP. Within each strain, a stock is bought, held for
the holding period, sold at expiration of the holding period, capital from the sale is re-
invested in the next available stock in the universe, and the process is repeated. Suppose,
then, that we wished to compute the performance ofPbetween the datesd 1 andd 2. Let
iMbe a natural number. Ifr 1 ;:::;rnare the partial period returns of theith strain ofP
betweend 1 andd 2 , as described above, define the performance of theith strain ofPto be
the linked return
Ri¼Ynj¼ 1ðrjþ 1 Þ 1 :Finally, the performance ofPbetweend 1 andd 2 is simply the equally weighted average
XMi¼ 1Ri=M:It is assumed, therefore, that ond 1 an equal amount of capital is invested in each strain
and grows according to the sequence of partial period returns. In other words, the
portfolio is initially equally weighted, but the position sizes change according to the
success or failure of the stocks.
One difficulty in defining portfolio simulations in this way is the potential for cash
drag. Say a stock is sold in one particular strain, and the next opportunity is not until
two months later. If, then, the market were to jump 20% in that 2-month interval, excess
returns of the portfolio would likely suffer. In order to address this potential problem,
240 News and abnormal returns