In statistics, linear regression is often used to model the linear relationship between a scalar response and one or a few variables. It is usually represented by the following.
Y = A + BX
(where Y represents the scalar response, A represents the Y-intercept and B represents the gradient/slope and X represents the variable. If there are more than one variable, you will then have X1, X2 etc)
In the area of investments, linear regression could be used to predict housing prices or understand the performance of a particular investment strategy. I have written about the use of linear regression in several articles in my blog, particular pertaining to housing prices.
There are many different kinds of theories used in quantitative finance which are representations of linear regression. Examples will be Capital Asset Pricing Model (CAPM) and Fama and French Three Factor models. The inherent need for us to be able to understand or even predict the performance of an investment strategy leads to the creation of these linear regression models. Being humans, we just find that there is a need for us to be able to explain everything (you get the drift).
One important component of a linear regression model is the metric, R-Squared. R-Squared measures how closely the linear regression model fits the data. A R-Squared value of 1 means that all the data points lie nicely on the line of best fit. When used in the area of quantitative finance, a R-Squared value of 1 will mean that the linear regression model fits the data perfectly and is often used to represent the market index. Hence, the R-Squared value is then used to assess the percentage of a portfolio's performance as a result of the benchmark (market index). If your portfolio has a high R-Squared value of 0.9 and above, your portfolio performance is very largely attributed to the market index. To put it bluntly, there is nothing special in your portfolio. You are better off buying the market index.
While having a very high R-Squared value is probably not something you like to have if you are not looking at replicating the market index, a very low R-Squared value is not something which you will want to have too if you want to compare against the market index. If the R-Squared value is below 0.5, you can't actually make reliable comparisons between your portfolio and the market index as your portfolio and the market index are too uncorrelated. To give a quick example, the ARKK (Ark Innovation ETF) has a R-Squared value of 0.625 since inception (since January 2015). This is probably a good value to be having as it's a value which represents sufficient correlation yet still far off from exact duplication of the market index.
So isn't R-Squared value just about correlation? What's the big deal about it? You might be thinking.
If you are just comparing portfolios or assets by a single R-Squared value, it probably won't make too much sense. Like all data, you need to have several metrics in place to make full sense of the story. In portfolio comparisons, you will usually also factor in important metrics such as alpha and beta to have a fuller picture of the portfolio's performances (more on this will be covered in future blog posts). The reason why I pointed out specifically R-Squared value in this blog post is because I think it's an underrated yet powerful value which allows you to know the performance of your portfolio managers. It represents the active management element of the portfolio manager which differentiates his/her portfolio from a typical benchmark index, and is probably what you are paying for. You often hear people talk about alpha or beta. But rarely do you hear about the R2 value, which can be equally important.
Again, with the use of various platforms nowadays, it's no longer difficult for you to find the R2 value of your portfolio. Simply go to portfoliovisualizer.com and do a backtest. Under metrics, you can find a whole array of values (including R2 value) for your portfolio.
For the frequent readers, you all should have noticed I'm starting to track the performance of my portfolio and will be providing regular monthly updates in this blog. If you are wondering what's the R2 value of my portfolio, it's 0.704 in the same time period as above (since January 2015 till now) which is a value I'm happy with. If you are curious about the full metrics of my portfolio (which I will share on Patreon) and what the constituents in this portfolio are, do sign up as a patron!
Till the next time.
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