# What do you do with low r-squared when calculating high-frequency beta

I am calculating a high-frequency beta. For example I have 90 days of data of the S&P and GOOGLE and I have 10-minute percent returns for each instrument. Each day has 34 10-minute percent returns so my data set is 2 vectors that are both 3060 in length (90 days x 34 10-miunute percent returns each day) = 3060 data points for the S&p and 3060 data points for GOOGLE.

Next in R I run a regression

reg= lm(google~snp) # both the google and snp vector have lenght = 3060
summary(reg)


My question is that sometimes I get low R-squared for the regression. Is this expected...should/can anything thing be done about it?

I know beta is usually done using daily data NOT 10-minute data but even with daily data sometimes the r-squared is low. What is the significance of beta with a low r-squared?

Thank you.

## 2 Answers

This simply suggests the linear model is a poor fit in high frequency. But is this that surprising, even before you crunch the numbers? I argue not, for the following reasons:

1. Even at low frequencies (i.e. monthly or annually), it is known that the classical CAPM (which is what you're running, albeit at a much higher frequency) does not fit well. It'd be a truly miracle that the CAPM model that performs poorly in low frequencies would even work any better in high frequencies.

2. It is also well known that high frequency financial econometrics exhibit a lot of behavior that are not found in their low frequency equivalents. Just a few to think about --- stochastic volatility, jumps, etc., and these properties of a single asset itself, without regard to how it co-moves with another asset (say S&P). All these imply that a simple linear model is expected to fail.

A high R-squared (1.0) means that you can explain the movements of one time series using the other. The lower your R-squared is, the worse your explanation is -- that includes the 'quality' of your beta.

You can try to improve your R-squared score using different regression types. Beware of overfitting.