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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
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