Subject: Re: A mechanical strategy
OK - scrap all the above - My basic assumption is that you will implement in Excel.

I thought thru it -and this is what it needs to have ( Of course on top of your Excel portfolio simulator)

(1) Add these columns to track
(a) Portfolio Value
(b) Cash Value
(c) Buy side
(d) Sell side

(e) Might help to track # of shares too

Also dont have the T-bill ie cash returns or set it to zero initially - because that would facilitate the SANITY CHECK

The simplistic constancy is on the buy/sell sides

Buy side = P[i-1]* (1- theta)*(1+alpha1)

where,
P[i-1] is last months portfolio value, Theta is the current actual monthly drop in Index, Alpha1 is the BTD threshold parameter
Trigger check Theta > =Alpha ( positive treatment, you can do the other side too)

As you can see that is the hyperbolic function

Sell side = P[i-1]*(1+theta)*(1-alpha2)
where,
P[i-1] is last months portfolio value, Theta is the current actual monthly rise in Index, Alpha2 is the STP threshold parameter
Trigger check Theta > =Alpha2 (again positive treatment)



So ENDING STATUS
BTD
P[i] = P[i-1]*(1-theta) + Buy Side
Cash[i]= Cash[i-1] - Buy Side

STP
P[i]= P[i-1]*(1+theta) - Sell Side
Cash[i]= Cash[i-1] + Sell Side

You add the T bill return to Cash in the end ie Cash[i] = Cash[i-1]* (1 + T-bill/12) for the first term

Hope this will aid in a smooth setup!