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Articles

Nuts & Bolts: Survivorship Bias

Survivorship Bias (SB) is a plague to most trading system developers.  Pick any basket of stocks to trade and you’ve just introduced it into your results, especially if that basket is a collection of index components (like the S&P500, Nasdaq 100, etc).

So what exactly is this bane of all algo traders?  Here’s the textbook definition:

In finance, survivorship bias is the tendency for failed companies to be excluded from performance studies because they no longer exist. It often causes the results of studies to skew higher because only companies which were successful enough to survive until the end of the period are included

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Nuts & Bolts: The Law of Large Numbers

Trading is a stochastic process;  i.e, the outcome of each trade is not deterministic and has a distinctly random bias.  Sometimes you win, sometimes you lose.  Sometimes you win big, sometimes you take it in the pants.  Often your winning or losing trades will cluster together in a row;  Other times, they’ll alternate in a more noisy fashion.

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Nuts & Bolts: Expectation

When I first started trading nearly 100% of my focus was on the percentage of my trades that were winners (win probability).  After all, winning feels good and I wanted to maximize that much as possible.  But over time I learned that the win probability of a system is largely irrelevant (regardless of how good it makes you feel);   Instead of worrying so much about winning I really should have been focusing on my system’s expectation.

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Nuts & Bolts: Risk Reduction vs Portfolio Size

I was just re-reading a chapter on risk in a trading book I bought a few years ago, and came across an interesting observation:

The reduction in risk of a portfolio is proportional to the number of stocks in that portfolio.

Not exactly page one news for most traders/investors.  But here’s the more interesting part:

Portfolio Risk has a non linear relationship to Portfolio Size roughly equivalent to 1/sqrt(N).

According to the book, if you start with one stock in your portfolio and add one additional stock, your risk drops by 30%, a very significant change. With a portfolio of 3 stocks, it drops by 43%, and with 4 stocks, by 50%. But you start to get diminishing returns above 4 stocks, as can be seen by this table from the book:

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Nuts & Bolts: The Calmar Ratio

Over the years I’ve experimented with a slew of optimization metrics, from the simple to the exotic and almost everything in between.  But the metric that has become my “Go To” ranking criteria is the humble Calmar Ratio (sometimes called the MAR, RAR, or the Sterling Ratio).

The Calmar Ratio is simply the annualized return divided by the maximum peak-to-trough equity curve drawdown during the time period in question.  It is effectively the risk-adjusted (or risk-normalized) return of a system.

So what’s so magic about the Calmar?   In short, it captures the essence of what separates a “good” equity curve from a “bad” one in a very simple and compact equation.

Which begs the question:  “What exactly makes a good equity curve?”.

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