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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
>
>
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