Under the covers of strange bedfellows. Previously The idea of implied alpha was introduced in “Implied alpha — almost wordless”. In a comment to that post Jeff noticed that the optimal portfolio given for the example is ever so close to the minimum variance portfolio.  That is because there is a ... [Read more...]

Torturing portfolios to give different volatilities between a factor model and Ledoit-Wolf shrinkage. Previously There have been posts on: “What the hell is a variance matrix?” factor models Ledoit-Wolf shrinkage Question Two of the several ways to produce an estimate of the variance matrix of asset returns is a statistical ... [Read more...]

What’s that thing about arithmetic and geometric returns and the variance? Previously An introduction to the difference between simple and log returns is: A tale of two returns Issue Suppose you are predicting the mean annual return of an asset for some number of years.  To simplify the discussion, ... [Read more...]

When investment skill is simulated, it is often presented as if it is obvious how to do it.  Maybe I’m wrong, but I don’t think it’s obvious. Previously In “Simple tests of predicted returns” we saw that prediction quality need not look like what you would find ... [Read more...]

Using garch to learn a little about the distribution of returns. Previously There are posts on garch — in particular: A practical introduction to garch modeling The components garch model in the rugarch package garch and long tails There has also been discussion of the distribution of returns, including a satire ... [Read more...]

How good is the current opportunity to pick stocks relative to the past? Idea The more stocks act differently from each other relative to how volatile they are, the more opportunity there is to benefit by selecting stocks.  This post looks at a particular way of investigating that idea. Data ... [Read more...]

How has the distribution of correlations changed over the last several years? Previously Posts about correlation boxplots explained Data Daily returns of 443 large cap US stocks from 2004 through 2012 were used.  The sample correlations — almost 98,000 of them — during each year were created. If we were actually using the correlations, then … Continue ... [Read more...]

How variable are garch predictions? Previously There have been several posts on garch, in particular: A practical introduction to garch modeling The components garch model in the rugarch package Both of these posts speak about the two common prediction targets: prediction (of volatility) at the individual times (usually days) term ... [Read more...]

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What effect do predicted correlations have when optimizing trades? Background A concern about optimization that is not one of “The top 7 portfolio optimization problems” is that correlations spike during a crisis which is when you most want optimization to work. This post looks at a small piece of that question.  ... [Read more...]

Exploring the quality of predictions using random portfolios and optimization. Previously “Simple tests of predicted returns” showed a few ways to look at expected returns at the asset level.  Here we move to the portfolio level. The previous post focused on correlation.  Win Vector Blog points out that gauging prediction ... [Read more...]

Some ways to explore how good a method of predicting returns is. Data and model The universe is 443 large cap US stocks that have data back to the beginning of 2004.  The daily (adjusted) close was used. The model that is used as an example is the default signal from the ... [Read more...]

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A prediction of a portfolio’s volatility is an estimate — how variable is that estimate? Data The universe is 453 large cap US stocks. The variance matrices are estimated with the daily returns in 2012. Variance estimation was done with Ledoit-Wolf shrinkage (shrinking towards equal correlation). Two sets of random portfolios were ... [Read more...]

More risk does not necessarily mean bigger Value at Risk. Previously “The incoherence of risk coherence” suggested that the failure of Value at Risk (VaR) to be coherent is of little practical importance. Here we look at an attribute that is not a part of the definition of coherence yet ... [Read more...]

How to fit and use the components model. Previously Related posts are: A practical introduction to garch modeling Variability of garch estimates garch estimation on impossibly long series Variance targeting in garch estimation The model The components model (created by Engle and Lee) generally works better than the more common ... [Read more...]

An exploration of the usefulness of sectors. Previously This subject was discussed in “S&P 500 sector strengths”. Idea Stocks are put into groups based on the sector that the company is considered to be in.  Cluster analysis is a statistical technique that finds groups.  If sectors really move together, then ... [Read more...]

Calibrations of 2013 predictions for 18 equity indices — plus some publicly available predictions. Orientation The distributions are an attempt to see the variability if there were no market-driving news for the whole year. Another way of thinking: mentally moving the distribution to center on a prediction gives a sense of the variability ... [Read more...]

An explanation of quartiles, quintiles deciles, and boxplots. Previously “Again with variability of long-short decile tests” and its predecessor discusses using deciles but doesn’t say what they are. The *iles These are concepts that have to do with approximately equally sized groups created from sorted data. There are 4 groups ... [Read more...]

Historical Value at Risk (VaR) is very popular because it is easy and intuitive: use the empirical distribution of some specific number of past returns for the portfolio. Previously “The estimation of Value at Risk and Expected Shortfall” included an R function to estimate historical VaR. Generating portfolios A useful ... [Read more...]