Finite State Return Analysis
For the last several years, I’ve been developing the concept of finite state stock return analysis. There are a bunch of excellent ways to implement this type of methodology. I’ve been specifically looking at dividing the market day into two finite states:
- Close to Open, or CO
- Open to Close, or OC
The entire market day is defined as CC, or Close to Close.
Stock returns are most widely calculated by dividing the current market price by the buy price. This simple operation gives the present value of each dollar invested.
The effect of dividends and splits on return is automatically addressed by using historical prices adjusted for dividends and splits.
Logarithmic Returns and Return Analysis
Logarithmic returns are additive over time making them convenient for computerized finite state analysis.
The Excel VBA code for calculating daily finite state log returns goes:
With Application.WorksheetFunction CC = .Ln(Arg1:=CloseX / LastCloseX) CO = .Ln(Arg1:=OpenX / LastCloseX) OC = .Ln(Arg1:=CloseX / OpenX) End With
With logarithmic returns: CC = CO + OC
Converting Log Returns Into Present Value
The excel Exp formula is used to convert log returns into present value of $1:
eCC = Exp(CC) eCO = Exp(CO) eOC = Exp(OC)
With Present Value returns: eCC = eCO * eOC