How many baskets are your eggs in? Meucci diversity Attilio Meucci directly addresses the adage: Don’t put all your eggs in one basket. His idea is to think of your portfolio as a set of  subportfolios that are each uncorrelated with the rest.  If your portfolio can be configured ... [Read more...]

Not quite expected behavior of skewness and kurtosis. The question In each time period the returns of a universe of stocks will have some distribution — distributions as displayed in “Replacing market indices” and Figure 1. Figure 1: A cross-sectional distribution of simple returns of stocks. In particular they will have values for ... [Read more...]

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Guiding a ship, it takes more than your skill Spark David Rowe’s Risk column this month is about data leverage. The idea is that you are leveraging your data if you are using it to answer questions that are too demanding of information. The piece reminded me of a ... [Read more...]

How did the constraints affect portfolio betas, and how did the betas change over time? Previously “Low (and high) volatility strategy effects” created 6 sets of random portfolios — the so-called low vol cohorts — as of 2007 and showed their performance up to about a month ago. “Rebalancing the low vol cohorts” looked ... [Read more...]

If equity markets suddenly sprang into existence now, would we create market indices? I’m doubtful. Why an index? The Dow Jones Industrial Average was born in 1896.  This was when computers were humans with adding machines (but they did do parallel processing).  At that point boiling “the market” down to ... [Read more...]

The missing link between beta and volatility is correlation. Previously “4 and a half myths about beta in finance” attempted to dislodge several myths about beta, including that beta is about volatility. “Low (and high) volatility strategy effects” showed a plot of beta versus volatility for stocks in the S&P 500 ... [Read more...]

Does minimum variance act differently from low volatility?  Do either of them act like low beta?  What about high volatility versus high beta? Inspiration Falkenblog had a post investigating differences in results when using different strategies for low volatility investing.  Here we look not at a single portfolio of a ... [Read more...]

The subtitle is “Central banks, credit bubbles and the efficient market fallacy”. Executive summary This is much too important of a book to remain as obscure as it is.  Besides, it is quite a fun read. It talks about two subjects: Why markets for goods and services tend toward equilibrium ... [Read more...]

A bit of testing of the estimation of the variance matrix for S&P 500 stocks in 2011. Previously There was a plot in “Realized efficient frontiers” showing the realized volatility in 2011 versus a prediction of volatility at the beginning of the year for a set of random portfolios.  A reader commented ... [Read more...]

How wide is the darkness? Uses of models The main way models are used is to: shine light on the “truth” We create and use a model to learn how some part of the world works. But there is a another use of models that is unfortunately rare — a use ... [Read more...]

2011 was a good vintage for minimum variance, at least among stocks in the S&P 500. Previously The post “Realized efficient frontiers” included, of course, a minimum variance portfolio.  That portfolio seemed interesting enough to explore some more. “What does ‘passive investing’ really mean” suggests that minimum variance should be considered ... [Read more...]

A look at the distortion from predicted to realized. The idea The efficient frontier is a mainstay of academic quant.  I’ve made fun of it before.  This post explores the efficient frontier in a slightly less snarky fashion. Data The universe is 474 stocks in the S&P 500.  The predictions ... [Read more...]

We know the words but what do they mean? Some definitions Here are some definitions of “passive investment management”. Investopedia says: A style of management associated with mutual and exchange-traded funds (ETF) where a fund’s portfolio mirrors a market index. Wikipedia says: Passive management (also called passive investing) is ... [Read more...]

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How fat tailed are returns, and how does it change over time? Previously The sister post of this one is “A slice of S&P 500 skewness history”. Orientation The word “kurtosis” is a bit weird.  The original idea was of peakedness — how peaked is the distribution at the center.  That’... [Read more...]

The Super Bowl tells us so. The Super Bowl Indicator The championship of American football decides the direction of the US stock market for  the year.  If a “National” team wins, the market goes up; if an “American” team wins, the market goes down. Yesterday the Giants, a National team, ... [Read more...]

Why returns have a stable distribution As “A tale of two returns” points out, the log return of a long period of time is the sum of the log returns of the shorter periods within the long period. The log return over a year is the sum of the daily ... [Read more...]

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How symmetric are the returns of the S&P 500? How does the skewness change over time? Previously We looked at the predictability of kurtosis and skewness in S&P constituents.  We didn’t see any predictability of skewness among the constituents.  Here we look at skewness from a different angle. ... [Read more...]