Dr. Jayanthi Sankaran
Well-Known Member
Hi David,
In the following Example 6.1
Suppose that lambda = 0.95 and that the estimate of the correlation between two variables X and Y on day n - 1 is 0.6. Suppose further that the estimates of the volatilities for X and Y on day n -1 are 1% and 2% respectively. From the relationship between correlation and covariance, the estimate of the covariance rate between X and Y on day n - 1 is
0.6 x 0.01 x 0.02 = 0.00012
Suppose that the percentage changes in X and Y on day n - 1 are 0.5% and 2.5% respectively. The variance rates and covariance rate for day n would be updated as follows:
(Sigma(x,n))^2 = 0.95 x 0.01 ^2 + 0.05 x 0.005^2 = 0.00009625
My question is that according to EWMA
Covn = lambda*Covn - 1 + (1 - lambda)xn - 1*Yn-1
Extending the above for variance
(Sigma(x,n))^2 = 0.95 x 0.01 ^2 + 0.05 x 0.005^2 = 0.00009625 - I don't understand how 0.005^2 comes into the picture. It is not a volatility but a percentage change.
I don't know if I have made myself clear. Can you please clarify this - I seem to be missing something?
Thanks
Jayanthi
In the following Example 6.1
Suppose that lambda = 0.95 and that the estimate of the correlation between two variables X and Y on day n - 1 is 0.6. Suppose further that the estimates of the volatilities for X and Y on day n -1 are 1% and 2% respectively. From the relationship between correlation and covariance, the estimate of the covariance rate between X and Y on day n - 1 is
0.6 x 0.01 x 0.02 = 0.00012
Suppose that the percentage changes in X and Y on day n - 1 are 0.5% and 2.5% respectively. The variance rates and covariance rate for day n would be updated as follows:
(Sigma(x,n))^2 = 0.95 x 0.01 ^2 + 0.05 x 0.005^2 = 0.00009625
My question is that according to EWMA
Covn = lambda*Covn - 1 + (1 - lambda)xn - 1*Yn-1
Extending the above for variance
(Sigma(x,n))^2 = 0.95 x 0.01 ^2 + 0.05 x 0.005^2 = 0.00009625 - I don't understand how 0.005^2 comes into the picture. It is not a volatility but a percentage change.
I don't know if I have made myself clear. Can you please clarify this - I seem to be missing something?
Thanks
Jayanthi