P1.T4. Valuation and Risk Models - Linda Allen, Chapter 2 Study Notes, page 19

[Dr. Jayanthi Sankaran]

Hi David,

In the above referenced, what is the generalized formula for calculating hybrid weights? Could you please clarify! Does one need to memorize this formula for the exam?

Thanks
Jayanthi

 

[David Harper CFA FRM]

Hi @Jayanthi Sankaran

Given lambda (λ) persistence (smoothing parameter) the weight of the (n)th observation is given by (1-λ)*λ^(n-1). I don't think this really requires memorization: the most recent weight is (1-λ) which is multiplied by successive lambdas (recall that lambda is, by definition, the ratio of successive weights).

Page 19 reflects the readings adjustment, which is to not assume an infinite series but rather a series with (T) observations; if there are only (T) observations, the above weights won't sum to 100%, so they are each "levered up" by 1/(1-λ)^T. So, for a finite horizon, we have weights that sum to 100%, yet retain constant proportion lambda, where weights are given by: (1-λ)*λ^(n-1)* 1/(1-λ)^T = (1-λ)*λ^(n-1)/(1-λ)^T. I hope that explains,

 

[Dr. Jayanthi Sankaran]

Thanks David, appreciate it!

Best
Jayanthi