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There's a significant issue in what you say that I'll come, but I don't
believe it matters whether a stock trades today or not in terms of valuing
it. The last trade is the value. Why not think about value in accounting
terms and consider the NAV to be marked to market (but not the Andersen
paradigm). Simplistically, everything is (only) worth the last bid, not the
ask.
You mentioned that some of your stocks don't trade everyday, which is what's
giving rise to your daily valuation concern, if I understand you correctly.
Just for the record since you asked me to look at my stocks, I NEVER trade
or invest in a stock for which options aren't traded, let alone whether the
stock trades every day. Trading stocks that don't trade everyday is clearly
placing your capital at the poorest end the liquidity continuum, which is
implicitly a higher risk strategy, and that will impair the merit of using
the Sharpe ratio to measure performance. In other words, the lower the
liquidity, (probably) the greater the standard deviation, and thus a lower
Sharpe ratio, which ought to tell to exclude stocks from your portfolio that
don't trade everyday if a particular Sharpe ratio (number) is your benchmark
as it were.
==========
Implicitly all open positions are in my portfolio you say. Right, so they
are, and it is open positions we are talking about nothing else. But open
positions do not automatically get a close value on all dates. If there is
no close value on a certain date in the database for a certain stock traded
and included in the portfolio, what is the value of that stock? Check your
own stocks, you will find that there are stocks that are not traded all
dates. My question has to do with how to handle the calculations of sharpe
values for those dates and those stocks during backtesting.
> -----Original Message-----
> From: cwest [mailto:cwest@xxxxxxxxxxxx]
> Sent: den 10 augusti 2002 23:08
> To: Bengtsson, Mats; Bob Fulks
> Cc: omega-list@xxxxxxxxxx
> Subject: RE: A complicated (for me) question on protfolio calculations
>
>
> Whew! You're measuring the performance of your portfolio by
> the Sharpe Ratio, right. Implicitly all open positions are in
> your portfolio, so how can you miss anything as you seem to
> be saying? If a position is closed it's no longer in your
> portfolio, but that doesn't change the way you measure the
> performance of your portfolio. Externally, you can also
> measure the performance of individual stocks in which you're
> not perhaps temporarily holding a position, but that isn't
> relevant to the measurement of the portfolio.
>
> Colin West
>
>
> -----Original Message-----
> From: Bengtsson, Mats [mailto:mats.bengtsson@xxxxxxxx]
> Sent: Saturday, August 10, 2002 1:35 PM
> To: Bob Fulks
> Cc: omega-list@xxxxxxxxxx
> Subject: RE: A complicated (for me) question on
> protfolio calculations
>
> 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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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.
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