I am reading Marcos de Prado's Advances in Financial Machine Learning. In a section titled "the ETF Trick", he explains how to calculate periodic price and volume samples for a basket of securities. I have a number of questions about his methodology.
First, he defines the number of units held for instrument
i at time
Kt is the AUM of the basket,
w_it is the weight of instrument
o_t is the open price, and
phi_t is the close price of
i in USD.
B is referred to as "bars", which as I understand is a time period sampled according to a fixed frequency defined in the units of
t. This brings me to my first question: why is
h_it defined as a function of the open price, if
t is a subset of
Second question is likely related to the first. He further defines the change in market value of instrument
p_it is the close price. Why, again, the change in market value is a function of the open price, when
t-1 is a subset of
Then, he defines the nominal price of the basket of securities, as:
d(t) is the dividend at a time
t. This equation generally makes sense to me. I am just quoting it here for context.
Last, he defines volume traded for the basket of securities as determined by the "least active member" in the basket:
Here, I have two questions. (1) Why the least active member? (2) Why normalize by the number of units held for that security, i.e. what is the purpose of the denominator
|h_i,t-1|? Thank you!