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calculating the high frequency return

2 messages · Mark Leeds, Rob Steele

#
Suppose I have the bid and ask data for a stock XXX, at every minute ( 
best bid and best ask ). Then, say I want to calculate the
return to

A) going long that stock at 10:10 for 10 minutes.

B) going short that stock at 10:10 for 10 minutes.

I realize that , since I have only quote data, the whole thing is 
approximate anyway because the actual prices that one transacts in
are unknown ( or in the transaction price data which I'd rather avoid 
dealing with ) but my understanding is that  the best approximation is

lgoing ong return =   (bid at 10:20 - ask at 10:10)/ask at 10:10

going short return = ( ask at 10:20 - bid at 10:10)/bid at 10:10

Since I'm taking the spread into account in the formula ( rather than 
using ( midpoint at 10:20 - midpoint at 10:10)/midpoint at 10:10 ),
  then these are not the negative of each other, as they would be if one 
used the midpoint.  but I would think that above gives a better measure 
than using the midpoint because it implicity takes into account the 
transaction cost due to the spread which actually could be different 
depending on whether one is going long or short.

Any comments or corrections are appreciated. There's also interest 
rebates when one shorts but I'm assuming they are small enough
to ignore.  it also assumes that you can close the transaction EXACTLY 
when you want to which is not particularly realistic either. Still, if 
there's something wrong with above or a better way to calculate these 
things or a known standard source that explains it, enlightenment is 
appreciated.


 
Mark
On Sun, Jan 4, 2009 at 9:59 PM, Josh Ulrich wrote:

            
3 days later
#
Doing what you propose makes sense but be aware that it assumes there's
enough depth at the quote to fill your order and that your order has no
lasting impact on the market.  Both assumptions are valid if your order
is small enough and the stock is liquid enough but you'd have to get
much fancier to model large orders realistically.
markleeds at verizon.net wrote: