Which sectors are coherent, and which aren’t? Previously The post “S&P 500 correlations up to date” looked at rolling mean correlations among stocks.  In particular it looked at rolling mean correlations of stocks within sectors. Of importance to this post is that the sectors used are taken from Wikipedia. ... [Read more...]

I haven’t heard much about correlation lately.  I was curious about what it’s been doing. Data The dataset is daily log returns on 464 large cap US stocks from the start of 2006 to 2012 October 5. The sector data were taken from Wikipedia. The correlation calculated here is the mean correlation ... [Read more...]

Portfolio diversity is a balancing act. Previously The post “Portfolio diversity” talked about the role of the correlation between assets and the portfolio.  The current post fills a hole in that post. The 2 dimensions asset-portfolio correlation Each asset in the universe has a correlation with the portfolio.  If there are ... [Read more...]

A look at a simplistic measure of stock-picking opportunity. Motivation The interquartile range (the spread of the middle half of the data) has recently been added to the market portrait plots.  Putting those numbers into historical context was the original impulse. However, this led to thinking about change in stock-picking ... [Read more...]

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...]

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...]

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...]

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...]

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...]

Do non-trading days explain the mystery of volatility estimation? Previously The post “The volatility mystery continues” showed that volatility estimated with daily data tends to be larger (in recent years) than when estimated with lower frequency returns. Time adjusting One of the comments — from Joseph Wilson — was that there is ... [Read more...]

How do volatility estimates based on monthly versus daily returns differ? Previously The post “The mystery of volatility estimates from daily versus monthly returns” and its offspring “Another look at autocorrelation in the S&P 500″ discussed what appears to be an anomaly in the estimation of volatility from daily versus ... [Read more...]

Casting doubt on the possibility of mean reversion in the S&P 500 lately. Previously A look at volatility estimates in “The mystery of volatility estimates from daily versus monthly returns” led to considering the possibility of autocorrelation in the returns.  I estimated an AR(1) model through time and added a ... [Read more...]

What drives the estimates apart? Previously A post by Investment Performance Guy prompted “Variability of volatility estimates from daily data”. In my comments to the original post I suggested that using daily data to estimate volatility would be equivalent to using monthly data except with less variability.  Dave, the Investment ... [Read more...]

Are there times of the year when returns are better or worse? Abnormal Returns prompted this question with “SAD and the Halloween indicator” in which it is claimed that the US market tends to outperform from about Halloween until April. Data The data consisted of 15,548 daily returns of the S&... [Read more...]

How much predictability is there for these higher moments? Data The data consist of daily returns from the start of 2007 through mid 2011 for almost all of the S&P 500 constituents. Estimates were made over each half year of data.  Hence there are 8 pairs of estimates where one estimate immediately follows ... [Read more...]

Some pictures to explore the reality of the theory that stocks with higher beta should have higher expected returns. Figure 2 of “The effect of beta equal 1″ shows the return-beta relationship as downward sloping.  That’s a sample of size 1.  In this post we add six more datapoints. Data The exact ... [Read more...]

The first 6 trading days of August have been bad for the major indices, but how variable is that across portfolios? To answer that, two sets of random portfolios were generated from the constituents of the S&P 500.  The trading days are 2011 August 1 — 5 and 8. The returns of the indices for … Continue ... [Read more...]