Definition of R-squared

In statistics, R-squared (R^{2}), or the coefficient of determination, is a widely used measure of a model (regression) performance against known observations. It is used in the asset management industry to measure the relationship between a portfolio and its benchmark. In the asset management world it is expressed as a percentage. R-squared does not, however, measure the performance of a portfolio, but it does measure the correlation of the portfolio's returns to the benchmark's returns. If an investor is seeking a portfolio or a fund that moves like the benchmark it would be wise to invest in a product or strategy with a high R-squared number.

A range of 70-100 per cent would indicate a high correlation between the portfolio's returns and the benchmark's returns.

A score of between 1 per cent and 40 per cent would show a low correlation between the portfolio's returns and the benchmark's returns.

Index funds and ETFs are likely to have an R-squared close to 100. R-squared is used to determine whether returns are generated by beta performance or alpha performance.

In March 2010 an FT columnist wrote about the true costs of investment funds, arguing that total expense ratios do not include the impact of direct and indirect transaction costs. In other words, the true cost of owning an actively managed fund can be higher than its TER suggests. One method of deriving an idea of true cost of a fund is to consider a fund's TER, its R-squared and the reported alpha (outperformance of its benchmark). The "true cost" can be derived if you take the difference in cost between the TER of any given fund and that of an appropriate low-cost index fund and apply this to the small proportion of the fund that the R-squared analysis suggests is the only genuinely actively managed component of the portfolio. The calculation reveals some spectacular overcharging.

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