Risk control is a complex subject,
and an area where simple and robust guides are
particularly valuable. Few concepts are simpler
and more intuitive than the stoploss, and it has
taken a vicelike grip on some investors' approach
to the subject. During investor meetings, I have
even been asked: "Let us talk about risk
control... what kind of stoploss do you use?"
Unfortunately, despite its appeal
the stoploss is no panacea. In fact, it is not
even a good system for the vast majority of portfolio
investors, as a simple simulation will illustrate.
The stoploss rule I will consider is that any
position is automatically closed when it loses
more than a certain fixed percentage from the
initial price at which the trade was made.
Before looking at why this may
not work in portfolios, it is worth considering
a situation in which it can work very well. Imagine
a commodity trading adviser (CTA), trading concentrated
positions in one or a handful of liquid assets,
and making money following trends in the market.
If the CTA loses money on a position then it has
misjudged the existence of a trend and it should
get out, bide its time, and again jump in the
next time it thinks a trend has started.
It can easily be shown that for
positivelyautocorrelated (or trending) series,
stoplosses can help because when the stop is hit
your expectation is that further losses would
have followed. This suggests that stoplosses can
make money as well as reducing downside, but how
realistic a model is this imaginary CTA of what
most alternative investors do?
Most investors construct a diversified
portfolio of assets. At any time a portfolio might
have between 10 and 100 positions contributing
significantly to the overall risk profile. In
this situation the worst losses for the portfolio
are likely to be caused by common movements in
related groups of positions rather than by events
that affect only a single position, and stoploss
is quite blind to this portfolio aspect of risk.
Some alternative investors follow
trades that are mean reverting, so that returns
are negatively autocorrelated. Examples might
include value investors betting that disliked
companies will move back into the mainstream,
or arbitrage and relative value traders betting
that assets will move towards some economic relationship.
On meanreverting trades, stoplosses systematically
take you out of your best positions.
Many alternative investors trade
in relatively illiquid assets, in which case slippage
 the difference between the level at which you
place the stop and your average trade price 
will cost you a significant amount every time
your stop is hit.
Those are three serious problems,
but obviously they do not apply to all investors
all the time. However, there are two problems
that are much more fundamental because they do
almost always apply. Provided that hitting the
stop does not change our expectation of future
return or future volatility, it is easy to show
that stoplosses will increase trading cost and
portfolio risk, and this should concern any investor
who cares about their Sharpe ratio.
Figure 1
The blue bell curve in fig 1
represents a trade, with return on the X axis
and likelihood on the Y. We may hope that the
mean return is somewhere positive, but what we
know for certain is that as soon as we put money
on the table there is uncertainty, or risk. Now
let's simulate a stoploss trading rule, shown
in the red curve on fig 1. We can choose how tight
to make the stop; the tighter it is, the more
we restrict the worst loss we can take, but also
the more likely that we are "stopped out"
and exit the trade, and fig 2 shows a family of
stoplosses that result from setting the stop at
different levels. In all these curves, I have
ignored frictional costs so that the average return
of the trade is not changed by the addition of
the stoploss.
Figure 2
Table 1
Stop 
Position Volatility 
Leverage

Portfolio
Volatility 
0% 
20.0% 
100% 
20.0% 
4% 
19.9% 
104% 
20.8% 
6% 
19.8% 
107% 
21.2% 
12% 
19.7% 
113% 
22.2% 
17% 
19.4% 
120% 
23.3% 
26% 
18.9% 
136% 
25.7% 
36% 
18.2% 
156% 
28.3% 
Table 1 illustrates why, even
in this favourable simulation, the stoploss hurts
performance. The first two columns of the table
show the likelihood the stop is hit and the standard
deviation (volatility) of the trade that results.
I've assumed the pure trade had a standard deviation
of 20%, and you can see a modest reduction in
volatility due to the stoploss, because the elimination
of largest negative results tends to outweigh
the matching reduction in results near zero. However,
even for a stop that is hit 36% of the time, the
reduction is only from 20% to 18%. This may seem
somewhat disappointing, but it gets much worse
when we consider the effect on the portfolio as
a whole.
The third column looks at the
impact on leverage that is required if we wish
to retain the same average exposure to the trade.
If there is a 36% chance we are stopped out, we
need to make bets 1 / (1  0.36) = 1.56x as large
just to maintain the same average exposure.
We pay the price for focussing
on the position and ignoring the portfolio by
being forced to use additional leverage. At the
portfolio level this has two horrible effects:
1. It increases our volatility,
in this case to 18.2% x 1.56 = 28.3%.
2. It increases our transaction costs, in this
case by something like 1.56x and so reduces our
expected return.
Both sides of Sharpe ratio have
been damaged, a disastrous result for "risk
control".
Though the table shows results
for volatility, the same basic argument applies
to all other risk measures. Stoploss takes us
out of some of the available trades, so we are
making inefficient use of diversification, so
we are running more risk than we should.
For Table 2, I have picked a
measure chosen to flatter stoploss, the worst
simulated result for a single position. This is
exactly what stoploss is designed to reduce. However,
when adjusted for the required increase in average
position size it is clear that stoplosses cease
to improve this statistic if the stop is being
hit more than a small percentage of the time.
Even in terms of its own objectives, stoploss
fails.
Table 2
Stop 
Worst Position 
Leverage 
Worst Portfolio 
0% 
51% 
100% 
51% 
4% 
30% 
104% 
31% 
6% 
27% 
107% 
29% 
12% 
25% 
113% 
28% 
17% 
22% 
120% 
26% 
26% 
19% 
136% 
26% 
36% 
17% 
156% 
26% 
For a portfolio investor in nontrending
trades, stoploss is a bad approach. It looks in
the wrong place, leads to unprofitable turnover,
increases transaction costs, decreases expected
returns and increases volatility. Just say no.
This article
originally appeared in the April 2005 issue of
the AIMA Journal and is republished with their
permission.
