The data analysis conducted so far indicates a negative
persistence () of the log differences of pairs of voting and
non-voting stocks of a company. It should be possible to take
advantage of this knowledge. If we found a profitable trading
strategy, we would interpret this result as a further indication
for the reverting behavior of voting/non-voting log-differences.
The average relationship between voting and non-voting stocks in
the sample period may be expressed in the following way,
But how to know that a `turning point' is reached? What is a
signal for the reverse? Naturally, one could think, the longer a
negative difference persisted, the more likely the difference is
going to be positive. In our simulation, we calculate the maximum
and minimum difference of the preceding trading days (for
example
). If the current difference is more
negative than the minimum over the last
trading days, we
proceed from the assumption that a reverse is to come and that the
difference is going to be positive, thereby triggering a long
voting and short non-voting position. A difference greater than
the
day maximum releases the opposite position.
When we take a new position, we compute the cash flow from closing the old one. Finally,
we calculate the total cash flow, i.e. we sum up all cash flows without taking interests
into account. To account for transaction costs, we compute the total net cash flow. For
each share bought or sold, we calculate a hypothetical percentage, say , of the
share price and subtract the sum of all costs incurred from the total cash flow. In
order to compare the total net cash flows of our four pairs of stocks which have
different levels of stock prices, we normalize them by taking WMF stocks as a numeraire.
In Table 14.3 we show the total net cash flows and in
Table 14.4 the number of trade reverses are given. It
is clear that for increasing transaction costs the performance
deteriorates, a feature common for all pairs of stocks.
Moreover, it is quite obvious that the number of trade reverses
decreases with the number of days used to compute the signal. An
interesting point to note is that for RWE, which is in the German
DAX
, the total net cash flow is worse in all situations. A
possible explanation would be that since the Hurst coefficient is
the highest, the log-differences contain less `reversion'. Thus,
the strategy designed to exploit the reverting behavior should
perform rather poorly. WMF and KSB have a smaller Hurst coefficient than
RWE and the strategy performs better than for RWE. Furthermore,
the payoff pattern is very similar in all situations. Dyckerhoff
with a Hurst coefficient of
exhibits a payoff structure
that rather resembles the one of WMF/KSB.
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Regarding the
interpretation of the trading strategy, one has to be aware that neither the cash flows
are adjusted for risk nor did we account for interest rate effects although the analysis
spread over a period of time of about years.