Trading Catechism

nitro said:
All momentum traders wish that their PDF looked like this:


View attachment 159465

This is the famous Arcsine distribution. Do you notice something? The probabilities edge upwards instead of downwards. But the strangest thing is that this distribution is talking about a Random Walk!! How can this be?

The classic arcsine law says that a random walk will spend most of its time on one side of the axis with probabilities closer to either 1 or 0, than to be near 0.5. The result defies intuition because you would expect that the proportion of time the walk spends on one side of the axis would be 1/2. In fact thats the least probable.

We can use our usual coin toss to explain this. If Heads, A wins 1 unit and if the coin comes up Tails, B wins 1unit . After twenty iterations, the probability that either player A or player B has been in the lead for each and all of the twenty rounds is about 32% !! In other words, the probability that a player is being behind for each and all twenty rounds. In contrast, the probability that one of the players was in the lead ten of the twenty rounds is only like 10%.

This explains a great deal of momentum returns, and therefore one has to be very careful with "hot hands" - they are totally within the realm of randomness.

It is useful to know that the arcsin distribution is a special case of the beta distribution, which in turn is a Conjugate prior for the Bernoulli, binomial, negative binomial and geometric distributions.
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This is a great post. Do you trade for a living or work in an advanced field?
 
More concepts. Don't worry that it all seems disconnected.

A time series that displays a tendency to revert to its historical mean value is critical to the type of trading recommended in this thread. Note that a time series could be {a set of} cointegrated instruments. In fact, very few trading instruments on their own are mean-reverting on the time frames that won't make us go broke. Mathematically, such a (continuous) time series is referred to as an Ornstein-Uhlenbeck process. This is in contrast to a random walk (Brownian motion)which has no "memory" of where it has been at each particular instance of time.

One thing you need to do before embarking on statistical mean reversion is to test for it. In particular, it is important to understand the concept of stationarity. In the next few posts we see how this is done.
 
eurusdzn said:
Nitro,

How little known a synthetic spread do you feel is reasonable.? Software can scale volatility or detrend a spread so that it is MR. Does it make sense to do this? In another case , Matching 3 or 4 assets can lead to a MReverting spread but who is to say how much sense , for example, gold,yen and treasuries viewed as a single position makes at the time.
Also, say you do see something such as a level respected a few times recently. An example may be a spread of Brent and Emerging markets. I have seen this turn like clockwork yet i cannot reason this event by the fumdamentals and PA of the seperate legs and attribute it to a coincidence of the arithmetic.
Maybe it is a tradeoff. That there is a lot of the above going on that belongs the bucket, but , maybe one or two that dont. Telling the difference seems to be the rub.
Great thread.
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Brent vs Canadian and Russian indexes?
Brent vs a basket of middle east equity indexes?
You know what...looking at commodities and resource dependent economies opens up a lot of opportunities....
Gold vs South African indexes?
 
nitro said:
More concepts. Don't worry that it all seems disconnected.

A time series that displays a tendency to revert to its historical mean value is critical to the type of trading recommended in this thread. Note that a time series could be {a set of} cointegrated instruments. In fact, very few trading instruments on their own are mean-reverting on the time frames that won't make us go broke. Mathematically, such a (continuous) time series is referred to as an Ornstein-Uhlenbeck process. This is in contrast to a random walk (Brownian motion)which has no "memory" of where it has been at each particular instance of time.

One thing you need to do before embarking on statistical mean reversion is to test for it. In particular, it is important to understand the concept of stationarity. In the next few posts we see how this is done.
More...
Your statement kind of begs the question. Is there a consistent way to test which kind of process we're evaluating? How do you test whether a time series is brownian or Ornstein-Uhlenbeck?
 
Seems we try to do intuitiely , when math challenged , what should be done mathematically. Probably removes a lot of bias, opinion and irrational beliefs.
The Kalman filter ...well what a great new concept to me. It would be nice to be able to model, measure, test, then correct multivariate inputs.
I guess everyone is attempting cause and effect and then , correct and repeat. Some better than others. Young men take notice of this thread but of course that is just my opinion.

Ps, indeed Gambit, lots of opportunity if one makes those connections.
 
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