Jules said: "…there are always at least two different aspects of risk, namely "probability of a loss" and "size of a loss". There are many ways to integrate them into a single risk measure. This is why I said that you can determine the risk only if you choose a formula first. "
Agreed.
Jules, is it possible to take the density distribution of some sort of stochastic simulation method (such as Monte Carlo), and then treat the information as Normally distributed (on the basis of an argument similar to Central Limit Theory)? In this case, one could reasonably select a value of drawdown loss and quickly establish the likelihood* of this loss occuring. Such a method would cover both "probability of a loss" and "size of a loss" in one result. True? Take for example: crudely speaking, can I gaze at the Monte Carlo graph and reasonably assert that the most likely value for annual profit is the one where the density of results is highest? Excuse my limited knowledge of stats.
Charles.
[*Accepting that for these kind of statistics to be valid there are: a) a sufficient number of data points, b) the external conditions (e.g. Market Fundamentals) under which the system is operating stay constant (! Yes, I know this is far-fetched, supposing if !)]
"is it possible to take the density distribution of some sort of stochastic simulation method (such as Monte Carlo), and then treat the information as Normally distributed (on the basis of an argument similar to Central Limit Theory)? In this case, one could reasonably select a value of drawdown loss and quickly establish the likelihood* of this loss occuring. Such a method would cover both "probability of a loss" and "size of a loss" in one result. True? Take for example: crudely speaking, can I gaze at the Monte Carlo graph and reasonably assert that the most likely value for annual profit is the one where the density of results is highest?"
Charles, the true answer to this is "no." Most systems are backtests. Tyring to push its predictions or past behaviors into future behaviour is not really going to give anything you can be confident in. It might help you to decide good stop losses or profit targets, but the market is a living, breathing organism. That is why it is required to say that "past performance is no guarantee of future performance" warning. It is quote true. The market does not perform to expectations like a well-trained circus lion. It is more like trying to control a huge school of piranhas with your bare hands. The strongest testimony to that, is the extremely high number of systems here that get sheared and shattered when they wander out onto the market superhighway here on C2.
No past drawdown or monte carlo or statistical analysis will guarantee you anything. Especially when you are new. There is a lot of "art of the trade" and "money management" and getting the pulse of the market here. But it takes a while to attain this. Again, trying to go leveraged while new is likely to leave you much poorer for the experience until you get your sea legs.
Charles,
Even if you know the entire distribution for sure, that wouldn’t solve the problem that I meant. This problem is that there is no “objective” definition of risk. Your definition would cover both aspects (size and probability), but it is not the only way to do that. VaR and ES also cover both. But perhaps I’m too philosophical now.
The real problem is that there is often not enough data for reliable estimates about tail events. Compare the estimation of future floods: If you have only three months of data, all coming from a dry season, it will be hard to estimate the size of a flood that happens once every 100 years…
The nonparametric versions of the risk estimates in the advanced statistics are based on the theorems of Extreme Value Theory, which are in many respects comparable to the Central Limit Theorem. But usually there are just not enough data to rely on the limit behavior. That’s why different estimates for the same thing can be so different.
you might find the following article interesting for a different view on risk: http://tinyurl.com/28ujd4
