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Mats,
I think you need to decide whether the Sharpe ratio is an acceptable measure
in your case. If it is, then you're addressing periods of measurement, not
the measurement itself. The Sharpe ratio may not be relevant if you're
concerned with micro comparisons, which I'd suggest is more or less a futile
pursuit.
<-- you wrote -->
I am more looking at selection of trading systems than portfolios. But since
I allow the system to scan amongst a lot of stocks, the evaluation of the
trading system is done on protfolio level. I do not consider the strategy
complete though, it will be added to for handling other types of market
situations. This is the reason I continue to look at what performance
measures to use to select strategy, not to evaluate portfolio.
My reason for the previous question, and the reason for my continuation in
questioning about this is that the Sharpe value as I use it (now evaluating
money needed and including that in the calculation as it should) gives me
what i believe is a too limited picture of a difference when the difference
is about the nature between the strategies compared.
First strategy: Buys a lot of times, gives a fairly good amount of return,
buys in both good and bad times. Gets a good Sharpe ratio, and a good return
on account as calculated, gives a fair Kelly Value
Second strategy: Buys mostly in good times, stays quite out in bad times.
Gets a very good Kelly value but a lot fewer trades than the above.
These can not be compared by just taking the money needed, looking at
portfolio level sharpes and then selecting the best Sharpe value. Well, that
would be too simple in all situations, but in this one it is so obvious,
Sharpe is not measuring what is to be measured, at least not as I use it
today.
The sharpe calculation for the second system is hindered since the second
system spans the same period as the first, but buys only on the good times
of that period. Thus annualised return on account becomes low. The money are
not calculated with as invested in other places when not used for trading
(this I think about adding, is there a standard for that?).
Really, the sharpe value for the second system should be calculated only for
those times where money is put at risk. Is there any reason not to look at
it in that way?
> -----Original Message-----
> From: Volker Knapp [mailto:vk@xxxxxxxxxxxx]
> Sent: den 22 augusti 2002 07:57
> To: Bob Fulks; Bengtsson, Mats
> Cc: omega-list@xxxxxxxxxx
> Subject: AW: A complicated (for me) question on protfolio calculations
>
>
> Bob.
> Absolutely right! Just look at the equity curve of you
> portfolio - it always tells me more then any number. Play
> with the starting dates, the parameters and the percenteges
> that you risk... and you get a very good feeling. Dont forget
> to testrun it on other markets too....
>
> Volker Knapp
> Wealth-Lab Inc.
> http://www.wealth-lab.com
> http://www.wealth-lab.de
>
> ++-----Ursprungliche Nachricht-----
> ++Von: Bob Fulks [mailto:bfulks@xxxxxxxxxxxx]
> ++Gesendet: Donnerstag, 22. August 2002 01:58
> ++An: Bengtsson, Mats
> ++Cc: omega-list@xxxxxxxxxx
> ++Betreff: RE: A complicated (for me) question on protfolio
> calculations
> ++
> ++
> ++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
> ++>>
> ++>>
> ++>
> ++>
> ++>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.
> ++
>
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.
<-- snip -->
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