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I think you are worrying far too much about precision. Any reasonable
method will give about the same result.
Remember that even if you knew the exact Sharpe Ratio to 3 decimal
places, the future market will never be exactly like the past so such
precision is of little value in making decisions. What matter is
whether the number is 1 or 2 or 3, not whether it is 2.1 or 2.2.
Bob Fulks
At 8:46 AM +0200 8/21/02, Bengtsson, Mats wrote:
>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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