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It gets down to what you are trying to measure and why.
If you are trying to measure the performance of the total account vs.
time, (which is what an investor would normally be concerned with),
then just take the marked-to-market change in the account value each
day (week, month, etc.) and divide it by the previous end-of-day
value. This is the percent return in the day. Then calculate the
average annualized return and standard deviation of returns and
calculate the Sharpe Ratio. From that perspective, you don't care if
one or all stocks traded - just how the overall account is doing.
>From your description, I cannot figure out what you are trying to measure.
If you are trying to figure out how effective your system is trading
stock B as part of a portfolio of stocks, you could isolate all the
days that Stock B traded and do the calculation using only those
days. If Stock B traded on days 1, 3, ...., you could calculate the
percent return on the amount invested on each day and include only
those days in the calculation, I suppose.
Bob Fulks
At 9:35 PM +0200 8/10/02, Bengtsson, Mats wrote:
>Ok, yes I am convinced, I need to put the capital into the picture. I will
>do that. But my main question remains the question on the best way to handle
>stocks not represented on a certain day, when there are other stocks in the
>portfolio represented that day.
>
>> In your case, you should calculate the return each day on the
>> amount at risk each day and you will find that you will get
>> the right answers.
>
>To me, the above is the tricky part. I try to do what is stated above, but
>ask the question on how to do when I do not always have all trades
>represented each day for the stocks included in my portfolio (and I do
>calculations on portfolio level). To calculate standard deviation, I need to
>look at each and every days summed equity at close. Some days have more
>stocks in trade than others. But, the ones not being traded are still at
>risk. Those are the ones I need help on how to handle, what should I use in
>the calculations as that days equity on them? How do I handle the lack of
>knowledge the best?
>
>Example: Stock A trades day 1,2 and 3 so it is included in the portfolio for
>all portfolio days. Stock B trades only day 1 and 3. So when looking at
>calculating a Sharpe value for two stocks traded three days, I have to
>decide on how to handle stock B day 2 because I have no knowledge of its
>value. Thus I have to decide on calculation method as my alternatives below
>states, and this is here I am lost.
>
>Alternative 1: I could guess that the value of Stock B day 2 was same as day
>1, and then calculate portfolio changes based on two stocks, with equity at
>close known for all three days and using those days when calculating average
>and standard deviation. This is doing a calculation based on one possible
>assumption on stock value for stock B. Not good, but better than my current
>method which is alternativ 2 below.
>
>Alternative 2: I could say that stock B was not represented day 2, meaning
>that there was no value explicitly stated for it as an equity at close,
>meaning that it had value zero since no one bought it that day. My standard
>deviation on that portfolio will be quite high, since one stock is
>recognised as worthless day 2. This is what I do today, but looking at the
>results, this does not seem to give fair values, good trading systems
>sometimes get high standard deviations without good cause.
>
>Alternative 3: I could say that I know nothing about stock B for day 2 and
>that it should thus not be affecting the calculation more than the other
>stocks that day (sort of saying if they go up, it goes up, if they go down,
>it goes down). In the calculation I could do that by saying that day 1, the
>others had an equity on average of... Day 2 they had an average of ... The
>difference in those averages are then assumed to be the difference in equity
>also for stock 2. And the portfolio value day 2 is thus value of stock A day
>2 plus the assumed value of stock B day2. Once again taking a guess at value
>of stock B which affects calculations by an assumption, but it seems better
>than basing it on the assumption of stock B becomig worthless now and then
>(since all trades are closed out eventually, stock B where never really
>worthless).
>
>Alternative 4: Well, the only alternative I know of that is left is using
>the averages of equity for all stocks represented each day. This will
>represent stock B for day 2 with the value of stock A (Portfolio equity day
>1 is average of stock A and stock B times two, Portfolio value of day 2 is
>value of stock 1 times 2). This was my first guess on what alternative would
>be better than alternative 2, but I now see it is not good.
>
>Is there a better alternative? If not, which of the 4 above is the best?
>Clearly alternative 2 is taking the least assumptions but also paying
>unneccessary high tributes to days when a certain stock is not traded.
>
>
>> -----Original Message-----
>> From: Bob Fulks [mailto:bfulks@xxxxxxxxxxxx]
>> Sent: den 10 augusti 2002 20:45
>> To: Bengtsson, Mats
>> Cc: omega-list@xxxxxxxxxx
>> Subject: Re: A complicated (for me) question on protfolio calculations
>>
>>
>> You are not accounting for all the factors in your calculation.
>>
>> Consider that you have a $200,000 account.
>>
>>
>> Case 1 - Invest $20,000
>>
>> In this case you invest only $20,000 of the account and
>> achieve a 20% return on that investment = $4,000. Assume that
>> the standard deviation of those returns is 15% or $3,000.
>>
>> Assume you invest the remaining $180,000 at the risk-free
>> rate of 3% for a $5,400 return with zero standard deviation.
>> Thus, the Sharpe Ratio of the portfolio is:
>>
>> Sharpe = (Return - Risk_free_return) / Standard_deviation
>> = (4000 + 5400 - 3% of 200000) / 3000
>> = 3400 / 3000 = 1.13
>>
>>
>> Case 2 - Invest $200,000
>>
>> In this case you invest all $200,000 in the same investment
>> and achieve the same 20% return on that investment = $40,000.
>> Assume that the standard deviation of those returns is again
>> 15% or $30,000.
>>
>> Sharpe = (Return - Risk_free_return) / Standard_deviation
>> = (40000 - 3% of 200000) / 3000
>> = 34000 / 30000 = 1.13
>>
>> So we see that the Sharpe Ratio of the overall portfolio is
>> THE SAME IN EITHER CASE!
>>
>> That is one of the advantages of using the Sharpe Ratio - it
>> measures the return-to-risk ratio. In both of the above
>> cases, the excess return (return in excess of the risk-free
>> rate) was proportional to the risk, so the Sharpe Ratio of
>> the resulting portfolio is independent of what percentage of
>> the portfolio you invest.
>>
>> It measures the Sharpe Ratio of the investment itself and is
>> independent of how much money you invest in it.
>>
>> If the investment is a trading system, for example, the
>> Sharpe Ratio measures the performance of the trading system,
>> independent of the trade-size. (Caveat: if trade size gets
>> very large - near the so-called "Vince optimal_F point" - the
>> relationship ceases to be linear and the Sharpe Ratio begins
>> to decrease as the trade size increases, [but only an idiot
>> would use trades that large...])
>>
>> In your case, you should calculate the return each day on the
>> amount at risk each day and you will find that you will get
>> the right answers.
>>
>> Bob Fulks
>>
>>
>> At 3:02 PM +0200 8/10/02, Bengtsson, Mats wrote:
>>
>> >From this list I have learned to trust the Sharpe-value. The
>> >calculation behind it seems fair, but yet, when looking at
>> the results
>> >I get usig it compared to Kelly value and other figures, I realise I
>> >have to change the portfolio calculation.
>> >
>> >The problem seems to lie in the assumptions behind my own portfolio
>> >calculations, and thus I need advise on how to adjust the
>> calculations.
>> >If i do the calculations on only one stock everything is
>> fine. What is
>> >happening is that on some shorter days there are a lot less
>> trade than
>> >on longer days, and on some days by pure chance some less
> > traded stocks
>> >are not traded at all. The portfolio calculation translates
>> this to a
>> >risk using the Sharpe value, which is fair, but looking at it I see
>> >that the risk is overestimated in strategies using fewer buys than
>> >strategies using many buys.
>> >
>> >My guess is that this can be remedied by using equity per stock for
>> >each day in the calculation instead of just equity as is
>> done now. My
>> >question is if I am right, and if not what else to do.
>> >
>> >Below is an explanation of the calculation at what I consider as the
>> >wring assumption.
>> >
>> >Date Equity Number of stocks Equity per stock
>> >990119 280000 303 924
>> >990121 260000 281 925
>> >990122 283000 305 928
>> >990123 261000 281 929
>> >
>> >As can se above, when calculating Sharpe ration based on
>> equity change
>> >from day to day, the value will go up and down (-20000 first day,
> > >+23000 next day, minus 21000 thirs day, ...). This is how the
>> >calculation is done today, giving a low sharpe ratio in the
>> end. If I
>> >instead would calculate the risk based on changes in equity
>> per stock
>> >included in the measure, I would get a much smoother curve.
>> >
>> >It can be argued that the risk is higher since the trades include
>> >stocks that by some reason do not trade each and every day, thus the
>> >Sharpe ratio shall swing more. I can accept that as the truth, but I
>> >prefer to view that as a micro-level calculation which is to be
>> >considered and remedied when creating the trading systems
>> and trading
>> >them, not a macro level assumption that shall result in such
>> swings in
>> >the portfolio Sharpe calculation as it does. Instinctively I
>> feel that
>> >using the equity per stock should be a much fairer result
>> than equity
>> >that is travelling up and down just because some stocks do not trade
>> >same days as others (this will always be the case when trading
>> >international markets, some markets will have holidays when
>> others do
>> >not).
>> >
>> >I would very much appreciate any help and input on this
>> subjet. It is
>> >from this list I have learned to trust the Sharpe ratio, now I would
>> >like to have a little help in applying it better to Portfolio level
>> >calculations than I do today.
>> >
>> >--- Mats ---
>> >
>> >
>> >
>>
>
>
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