Hardcopy versions of both The R Inferno and S Poetry are now available for sale. Physical economy Buy The R Inferno (the version dated 2011 April 30)   Buy S Poetry Discount The publisher, Lulu, has a coupon for a 25% discount off purchases (up to a maximum of $50) that is good until the … ... [Read more...]

Equal risk contribution of assets determines the asset weights given the variance matrix.  How sensitive are those weights to the variance estimate? Previously The post “Risk parity” gave an overview of the idea. In particular it distinguished the cases: the assets have equal risk contribution groups of assets have equal ... [Read more...]

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A review of market predictions and results for 2011, and a calibration for 2012 predictions (of 19 equity indices plus oil). Previously One year ago the post “Revised market prediction distributions” presented plots showing the variability of various markets assuming no market-moving forces. The follow-up post “Some market predictions enhanced some of those ... [Read more...]

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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...]

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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...]

How does the effect of our expected returns change over time?  This is not academic  curiosity, we want to know in the context of our portfolio if we can.  And we can — we visualize the effect of expected returns in situ. First step The idea is to look at the ... [Read more...]

Be careful if you have global daily data. The issue Markets around the world are open at different times.  November 21 for the Tokyo stock market is different from November 21 for the London stock market.  The New York stock market has yet a different November 21. The effect The major effect is ... [Read more...]

The return of a hypothetical fund was 17.9% in 2010.  We want to know if that is good or bad. The benchmark method The assets in the portfolio are constituents of the S&P 500, so we can compare our fund return to the return of the index. Figure 1: 2010 returns of: the fund ... [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...]

Investment Performance Guy has a post “Periodicity of risk statistcs (and other measures)” in which it is wondered how valid volatility estimates are from a month of daily returns. Here is a quick look.  Figure 1 shows the variability (and a 95% confidence interval) of volatility estimates for the S&P 500 index ... [Read more...]

Some thoughts and resources regarding a popular fund management buzzword. The idea Given asset categories (like stocks, bonds and commodities) create a portfolio where each category contributes equally to the portfolio variance. Two operations There are two cases in creating a risk parity portfolio: the universe is the asset categories ... [Read more...]

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For those who naturally compute portfolio returns correctly here are some lessons in how to do it wrong. The data Random portfolios were generated from constituents of the S&P 500 with constraints: long-only exactly 20 assets in the portfolio no more than 10% weight for any asset (just for fun) the sum ... [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...]

fMRI data from 90 locations in the brain look somewhat like daily closing prices on 116 stocks if you squint just right. Marginal Revolution was nice enough to point to “Topological isomorphisms of human brain and financial market networks”. I’ve only just glanced through the paper.  I find it interesting, but ... [Read more...]