CODEWITHSUNDEEP
rcovariance
kris
kris

Reputation: 37

How to calculate the covariance matrix for the log return series, using both the returns and returns squared

The example data is provided below.

data <- data.frame(normal_return = c(0.02012, 0.03488, 0.00418, 0.01780, 0.00563, -0.00187),
                   log_return = c(0.01992, 0.03429, 0.00418, 0.01764, 0.00562, -0.00187))

How could I calculate the covariance matrix for the log return series, using both the returns and returns squared

Is that just simply using cov() function?

Upvotes: 0

Views: 824

Answers (1)

Dion Groothof
Dion Groothof

Reputation: 1456

Making a call to cov() is the appropriate way to obtain the variance-covariance matrix. The variances are on the diagonal and the covariances are represented by the off-diagonal elements.

my_cov <- cov(data)
> my_cov
              normal_return   log_return
normal_return  0.0001808887 0.0001779709
log_return     0.0001779709 0.0001751051

If you want to obtain the sd, you should use the square root of the diagonal of this matrix.

> sqrt(diag(my_cov))
normal_return    log_return 
   0.01344949    0.01323273

Edit

If you would like to also include the square of normal_return in the covariance matrix, the easiest way to go about is creating a new column, which includes these values.

# new column: square of normal_return
data$sq_return <- data$normal_return^2
my_cov <- cov(data)
> my_cov
              normal_return   log_return    sq_return
normal_return  1.808887e-04 0.0001779709 5.934746e-06
log_return     1.779709e-04 0.0001751051 5.828500e-06
sq_return      5.934746e-06 0.0000058285 2.170196e-07

If you would like to have the output in fixed instead of exponential/scientific notation, you can run options(scipen = 999).

One final note, if you would like to convert the covariance matrix into a correlation matrix, you may call to the cov2cor() function and use a covariance matrix as its argument.

my_corr <- cov2cor(my_cov)
> my_corr
              normal_return log_return sq_return
normal_return     1.0000000  0.9999858 0.9472112
log_return        0.9999858  1.0000000 0.9454920
sq_return         0.9472112  0.9454920 1.0000000

## cov2cor() scales a covariance matrix by its diagonal
##           to become the correlation matrix.

Upvotes: 1

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