[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

RE: A complicated (for me) question on protfolio calculations



PureBytes Links

Trading Reference Links

A well, things were not as easy as I hoped for. I believe I can get the
calculations now including start capital right (I am rewriting a piece of
code I have earlier received). But I start to wonder if what I want to
measure is what I measure.

All calculations are done on portfolio level, day by day. My interest is on
how good the trading system is. When looking at the portfolio level, I now
compare equity from day to day, including total capital, take the mean, take
the standard deviation, annualise the value to get a comparable measure. But
I am looking only at protfolio level now. If I were to change the period to
monthly, that would mean I had a lot fewer measurements, and the standard
deviation would be based on only one equity value per month.

But what I have beneath the portfolio level is the trade by trade level. All
those trades would give a lot of values for each and every month, individual
means and standard deviations. To compare strategies where the strategy is
run on a whole set of stocks, thus creating a portfolio during backtesting,
is Portfolio level only a good measure? Do I need to in some way include the
details from all trades from every period to get to a more accurate measure
on the strategys Sharpe value?

> -----Original Message-----
> From: Bob Fulks [mailto:bfulks@xxxxxxxxxxxx] 
> Sent: den 11 augusti 2002 15:20
> To: Bengtsson, Mats
> Cc: omega-list@xxxxxxxxxx
> Subject: RE: A complicated (for me) question on protfolio calculations
> 
> 
> At 7:54 AM +0200 8/11/02, Bengtsson, Mats wrote:
> 
> >I am trying to measure the first alternative of your two 
> alternatives 
> >down below, performance of the account. But it is not a real 
> account it 
> >is a simulation of a system trading strategy on a number of 
> stocks, but 
> >that does not matter.
> 
> True.
> 
> >I am doing the calculations you describe, but a little different, 
> >instead of taking market to market change in account each day, I use 
> >the accumulated portfolio change in account each day. This 
> is what is 
> >causing the question, I view tha change each day as being the 
> >accumulated change to the account each day, not the sum of all 
> >individual market changes each day. Since I want to do the 
> calculation 
> >on the portfolio level, I get to days where not all stocks 
> involved in 
> >the account traded, and thus the question what is the market 
> value of 
> >that stock that day. Currently, since it is not traded, I give it no 
> >value but then the standard deviation becomes high.
> 
> You take the value of the total portfolio at the end of each 
> day. I was confused by the term "a stock didn't trade that day".
> 
>    > If you mean that your system didn't take a trade in that
>      stock that day, it doesn't matter. The portfolio still
>      has a value that day.
> 
>    > If you mean that there were no trades on any exchange for
>      that stock that day (so you do not know what its true
>      value is at the end of the day), then you could estimate
>      its values based upon how much a market index moved since
>      the last time it traded. You could also use the bid/ask
>      price as guidance. I cannot imagine why you would
>      need to be so precise, however.
> 
> 
> >If I would have done my calculations on a market to market basis, I 
> >believe I would sort of have tha same question, one day one of the 
> >stocks would not have been traded, the account is open, and 
> question is 
> >how to include that stock into the equation? Did it lose all 
> the money 
> >(high standard deviation)? Does it have the same value as the day 
> >before until proved otherwise? Should I in some way try to 
> guess what 
> >value it really has by for exampling saying the change of 
> the value is 
> >the same as for all other stocks in the portfolio traded that day?
> 
> The most accurate way to estimate the value is to use the 
> "single index" model for the stock price. The return (change 
> in value) for a day is approximated by:
> 
>     Return_stock = alpha + beta * Return_Index + error_term
> 
> The error_term is a random variable with zero mean so can be 
> disregarded when figuring the expected value. So you would 
> need to determine the alpha and beta of each stock using 
> linear regression analysis of recent days then use those 
> numbers in the above equation. Alpha will be a fraction of a 
> percent, plus or minus (for a daily
> change) and beta should be between about 0.5 and 1.5.
> 
> If you look closely, all stocks have this problem to some 
> degree since the last trade of the day may have been at, say, 
> 3:35PM eastern time and the market may have changed quite a 
> bit in the last hour of trading. Mutual funds have a similar 
> problem calculating the Net Asset Value (NAV) of the fund at 
> the end of a day.
> 
> I recently had experience with a similar issue. I am using 
> deep-in-the-money index put options to hedge a mutual fund 
> account for a friend. These are December 2002 or March 2003 
> options so they may not trade on some days. Thus, the last 
> trade value shown on the brokerage website each night may be 
> several days old. But the bid/ask price is correct as is a 
> calculated value based upon the value of the index. In this 
> case, the valuation is a big factor in the account value so 
> accuracy was important to determine how well the hedge was 
> tracking the portfolio.
> 
> Bob Fulks
> 
> 


This message contains information that may be privileged or confidential and is the property of the Cap Gemini Ernst & Young Group. It is intended only for the person to whom it is addressed. If you are not the intended recipient, you are not authorized to read, print, retain, copy, disseminate, distribute, or use this message or any part thereof. If you receive this message in error, please notify the sender immediately and delete all copies of this message.