As discussed in the next post we are actually interested in how randomly selected portfolio ’s out- or underperformance deviates from the benchmark. This is a measure of the amount by which a randomly selected stock’s out- or underperformance deviates from the benchmark, on average. The market cap-weighted benchmark return is calculated asīenchmark return \(= \sum _ \). Th e stock weights and benchmarks returns for a measurement period are given in the graphs below: In the context of the CFA exam, standard deviation and variance are typically utilized to measure the variability of risk and return for investments. Afterwards I have to take an average of 3 years for each firm (e.g Firm 1, I need to obtain the Average Std for year 2005-2008,2006-2009 and so on). Stock C and D have market caps of 10% and 5% respectively of the total market. The standard deviation and the variance represent statistical measures used to calculate the dispersion or variability around a central tendency. I have to calculate the standard deviation for each year and for each firm. Stock A and Stock B have market caps equal to 45% and 35% respectively of the market’s total capitalisation. We consider a simplified stock market which consists of two large-capitalisations (cap) and two small-cap stocks. The analysis is also applicable when we compare managers against their peers. However, as preparation, we first consider market dispersion from a stock perspective.Īs before, performance is measured against the unbiased market-capitalisation (market-cap) weighted benchmark. If we want to examine how market dispersion affects manager outperformance we have to measure the dispersion of active portfolio returns instead. This measure describes the dispersion in individual stock returns. Here we explain the methodology for calculating an asset-weighted standard deviation of share returns, often also referred to as the cross-sectional standard deviation. Opportunities for successful security selection abounds when market dispersion is high, as discussed before. Market dispersion refers to the variation in returns of the market’s underlying securities.