Resistant Regression

It is a fact that on most days, not much is going on in the stock market. When we estimate the relation of a stock with the market, or the “beta” of a stock, we use all available daily returns. This might not be wise as some days are not really typical and contaminate our estimate. For example, Steve Jobs past away recently, AAPL moved quite a bit as a result. However, this is a distinct event that does not reflect on the relation with the market, but is company specific. Our aim is to exclude such observations, taking into consideration that we don’t want to lose too much information, not all large swings are irrelevant.

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Price is right, part two – Trading strategy.

Having stock market in mind, in the previous post: “Price is right, part one.”,  I stated that we should not think in terms of “the price went up/down too much” but that “the current price level is wrong since…. and the market is not getting it because…”, bearing in mind that Mr. Market is not a weak player to say the least.

In this post I back this claim with the examination of a trading strategy that ignores economical arguments, thus is only based on relative price moves. Say you believe  my previous post is horseshit, wouldn’t it be nice to short the market if it’s “too high” and to long it when it “went down too much”? Fine!, let’s have a look at the performance of such a strategy.

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Pairs Trading Issues

A few words for those of you who are not familiar with the “pairs trading” concept. First you should understand that the movement of every stock is dominated not by the companies performance but by the general market movement. This is the origin of many “factor models”, the factor that drives the every stock is the market factor, which is approximated by the S&P index in most cases.

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OLS beta VS. Robust beta

In financial context,  \beta is suppose to reflect the relation between a stock and the general market. A broad based index such as the S&P 500 is often taken as proxy for the general market. The  \beta , without getting into too much detail, is estimated using the regression:

    \[stock_i = \beta_0+\beta_1market_i+e_i\]

A  \widehat{\beta_1} of say, 1.5 means that when the market goes up 1% the specific stock goes up 1.5%. (Ignoring all the biases at the moment!)

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Flash Crash

In his book, “A demon of our design”: Richard Bookstaber talks about the concept of coupled systems. These are systems where, once launched, are impossible to shut down. One such process is a plain take off. Once started, the pilot has no way back, he cannot stop after getting off the ground, so the only way is up. Well, in financial markets, up is generally considered good,

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Reducing Portfolio Fluctuation

THIS IS NOT INVESTMENT ADVICE.  ACTING BASED ON THIS POST MAY, AND IN ALL PROBABILITY WILL, CAUSE MONETARY LOSS.

Most of us are risk averse, so in our portfolio, we prefer to have stocks that will protect us to some extent from market deterioration. Simply put, when things go sour we want to own solid companies. This will reduce return fluctuation and will help our ulcer index against large downwards market swings. Large caps are such stocks. But which large caps should we chose? The squared returns are often taken as a proxy for the volatility so, keeping simplicity in mind, I use those.

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Intra-day Volatility Pattern

When we speak about volatility we generally refer to the relative movement of an instrument, say stock, from its center, say average. So high volatility instrument means high swings in its price process. In recent years, with the increase in “fire power”, both in computing and information flow, there has been a spike in analysis of intra-day data. Data that describes the price within the day, as oppose to the more conventional, “open” (open price of the stock for the day) and “close” quotes.

We take a look at the pattern of “swings” from stock prices within the day.

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