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[QUOTE=Billy;13752]Since IWM is already including a +/- 2,000 stocks diversification and GDX is including a 32 stocks diversification, shouldn't you take into account the exisiting diversification implied in ETF holdings? In other words, can we be sure that the models are not misleading for our robot allocation needs?[/QUOTE]
Sorry for the delay in posting. I've been away since the subsequent conversation ensued.
Billy, I wrestle with this concept often. Is holding one security at 100% in my portfolio, such as the IWM or the SPY, "diversified", or does proper diversification require multiple holdings? I think this is what you are asking. I don't know the answer as I bang this out but allow me to think through it as I write...
When we talk about diversification, indirectly I think we're talking about a reduction in risk. Ideally, we're also looking for maintaining/increasing potential returns while reducing risk, but at the end of the day, I think the goal is to minimize risk while maintaining some constant (predictable) level of potential gains. I add this latter part because the "risk free return" (RFR) reference used in many calculations is a 3 month T-bill, which is assumed to have 0 volatility at some nominal return.
"Diversification Benefit" is something that the financial types talk about when going from a portfolio containing n=1 security to a portfolio containing n=m (m=many ~>15, 20, 50, etc.). The "benefit" portion comes from a reduction in risk as we add stocks. Offsetting this benefit are transactional costs, e.g., it's far cheaper to manage 1 security than to mange 50. So, returns are enhanced as n ---> 1, but risk increases as n ---> 1.
IWM is the market, for all intensive purposes. In support of this statement here is the correlation of IWM with other markets:
[ATTACH=CONFIG]8947[/ATTACH]
The correlation with the Dow is 0.87, with the S&P500 0.92, and the NASDAQ 0.95. Being the "market", we can assume that it is diversified, e.g., addition of any further stocks to IWM will not result in a significant change in the correlation with other broad markets. Put another way, we can assume that the addition of another security to IWM will not change the volatility of IWM in a significant manner.
Correspondingly, holding a single position that is 100% in IWM certainly represents a portfolio that contains the market. For the portfolio to be diversified, we need to successfully show that additional positions in the portfolio do not reduce volatility and return. Put another way, for a given level of estimated return, can we find a security that has greater or equivalent estimated return but lower volatility?
First of all, it's REALLY hard to find a company, or companies, that fit this bill. With my processing power, I can process about 55 stocks at a time, and I went through over 600 stocks in 10 batches and didn't find one that had higher return at the same or less volatility than IWM. Here's a representative chart:
[ATTACH=CONFIG]8942[/ATTACH]
I've circled IWM -- you can see that there are no stocks with higher return and lower volatility -- so it's the combination of all of these stocks, with their relative correlations, that give IWM higher return but lower volatility.
Take a look at this next figure:
[ATTACH=CONFIG]8943[/ATTACH]
Look at the left -- you can see IWM, and you can see a purple diamond just below IWM. The blue line represents all the possible combinations of these 54 stocks in terms of weighting, and the one "closest" to the IWM is chosen. The purple diamond shows that this portfolio of 54 stocks can be made to look like IWM with specific weightings, which is what managers of big funds attempt to accomplish.
Hence, I think we can conclude that:
[B]1) Holding 100% IWM is to be considered fully diversified within your portfolio, e.g., you're not going to improve your Diversification Benefit from n = 1 (because transaction costs are minimized, which maximizes takehome gain), and
2) out of the universe of 1800+ small-cap stocks, there are NO stocks that give an expected return higher than IWM at an equivalent or lower volatility (although I only checked ~600 of them).
[/B]
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IWM was the hard nut, GDX is easier.
Answering the question of whether a portfolio holding 100% GDX is diversified portfolio follows along the same lines as above. If we can show that the addition of a security improves/maintains the portfolio return while reducing volatility, then we can say GDX is not a diversified holding.
Take a look at the following chart, which is the expected returns/volatility of the components of GDX, sans LIHR:
[ATTACH=CONFIG]8944[/ATTACH]
I've circled GDX to make it stand out on the chart. As you can see, there are INDEXES (^RUT, ^IXIC, and ^GSPC) that have lower volatility at equivalent or higher gain. Furthermore, because ^RUT has the highest expected return but is lower in volatility, then the IWM proxy should be considered as the additional security so that we can maximize return yet realize a lower volatility than GDX alone.
[B]From the chart above we can conclude that owning a portfolio that was comprised of 100% GDX is not diversified -- there are additional securities that can be added which reduce risk (volatility) while improving gain.
[/B]
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Extra Credit ( I'm on a roll now and am learning a few things ... )
The next question in my mind is "what allocation of IWM and GDX minimizes volatility?". This is the same as asking what combination minimizes my pain to drawdown?
Take a look at this chart:
[ATTACH=CONFIG]8945[/ATTACH]
The unlabeled yellow diamond in the middle of the picture is the result of 100 shares being allocated to GDX, and 100 shares being allocated to IWM. The blue line should extend down there but for some reason it does not. I'll look into that later.
It's clear from the blue line that there is yet another combination that has higher gain but minimum volatility. That allocation ends up being:
[B]73% IWM
27% GDX[/B]
This is telling me that all things being equal, using the price data that has a ~ 100d moving average applied (see RiskMetrics document provided earlier),[I][U] that a minimum-risk portfolio exists with IWM and GDX in the allocations above.[/U][/I]
Of course, maximizing expected return means placing all your eggs in IWM, since it has the highest return yet the lower volatility of the two, or IWM = 100% and GDX = 0%.
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Extra Extra Credit ...
Since Pascal is working on XLE, let's see what the allocations for a IWM-GDX-XLE triplet should be in order to minimize risk in the portfolio, again using data through 6/20/11:
[ATTACH=CONFIG]8946[/ATTACH]
So, we see that XLE lies halfway between IWM and GDX in terms of volatility as well as expected return. The unlabled yellow diamond is a 100-share contribution in each security. [I][U]The end of the blue line just above the unlabled diamond is the place where risk (volatility) is minimized -- and this corresponds to an allocation of [/U][/I]
[B]
IWM: 69%
GDX: 23%
XLE: 8%[/B]
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So, in summary,
[B][LIST][*]trading 100% in IWM maximizes your expected return and can be considered a fully diversified holding[*]trading 100% in GDX reduces your potential gain as well as introduces additional volatility to your portfolio[*]trading 73% in IWM and 27% in GDX minimizes your portfolio volatility, at the cost of some expected return[/LIST][/B]
I hope this has been helpful -- I've learned a few things, especially that intuition isn't always correct (my assumptions about GDX standing alone).
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[QUOTE]
So, in summary,
[B][LIST][*]trading 100% in IWM maximizes your expected return and can be considered a fully diversified holding[*]trading 100% in GDX reduces your potential gain as well as introduces additional volatility to your portfolio[*]trading 73% in IWM and 27% in GDX minimizes your portfolio volatility, at the cost of some expected return[/LIST][/B]
[/QUOTE]
That may be accurate if you replace 'trading' with the word 'holding'. Holding the different portfolios over time, you may end up with such risk-return characteristics. But when it comes to 'trading', none of that matters. None of those parameters come into material effect during the very short trading horizon of the Robots. Short term trading yields portfolios with totally altered risk-return characteristics.
What is efficient for a buy and hold index portfolio, is not necessary true for an actively traded portfolio. You cannot compare apple and oranges, eventhough they are both fruits and delicious.
Trying to pinpoint an optimal mix of Robot based trading in IWM/GLD is an exercise in futility. There will be periods when one specific mix is optimal. And that optimal mix is optimal for that particular period, in direct relation to the market movement in IWM and GLD during that particular time. And naturally, that will simply fluctuate over time.
I see a lot of effort is expended on slicing and dicing the Robot signals to get the most out of it. From my limited experience in the business, I would venture to guess that there is inherent risk in over optimizing within a very small data set. The nature of the market is change, eventhough very often, and ironically, the more things change, the more they stay the same. There is an inherent risk that what works perfectly for the last three years, may not work as well in the next three years. The key is the robustness of the algorithm.
It appears that the ROBOT methology of combining a trend following component with a mean reversion component is a very robust method that will withstood the test of different market conditions, with minor retuning over time. If people over optimize it for a very narrow trading period, the result may be counter productive.
As always, best of luck to everyone.
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Paul,
This is very good research. As we all know, correlations can change mightily during times of market stress, and usually not for the good (i.e., they rise) right when you need their benefit. It would be interesting to see how correlations worked during such times.
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@Adam: completely agree that correlations move with time.
A good side experiment would be for me to check these IWM/GDX correlations on the weekend, and see if they move much. I'll post the results here in the Algo forum and we can keep track; I'll start a new thread. My intuition tells me that they won't, but now that I've written those words, they will most likely change dramatically and all bets are off :)
I should have also stated in the note that the snapshots provided in the figures are just that -- snapshots. Expected returns will change daily/weekly/whatever, as will volatility. Time frame for lookback is very important, but with the EWMA method I use, I'm smoothing a lookback over about 100 days and since it's exponential, the data between 100 days ago and 93 days ago isn't that relevant compared to all of the other data...
Time will tell...
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Paul,
Interesting reseach. That said, I agree with Kenneth in that the suggested IWM/GDX allocations are usefull only when one uses 'buy and hold' of these securities. But that's not the case with the robots.
To get the real picture one needs to do these 'buy and hold' tests on the equity curves of the robots instead of the ETF's directly. I'd be very interested in the results of such a test. But this is something only Pascal and Billy can do as it would require the actual historical trades of the robots. Actually thinking about it, we don't need the historical trades. Pascal could supply the equity curve data instead.
It's true that there is a limited 'data set' but that's not necessarily a problem as this post shows with 'walk forward allocation'.
One could use a sliding window of past 3 years of data to keep the allocation % dynamically up to date.
[url]http://www.automated-trading-system.com/practical-leverage-space-model-more-realistic/[/url]
PS, anyone know the answer to the 'summer puzzle' ?
[url]http://www.automated-trading-system.com/off-the-grid/[/url]
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[QUOTE=Rembert;13839]
To get the real picture one needs to do these 'buy and hold' tests on the equity curves of the robots instead of the ETF's directly.
I'd be very interested in the results of such a test. But this is something only Pascal and Billy can do as it would require the actual historical trades of the robots.
[/QUOTE]
Thank yoy Paul for the extraordinary depth of your research.
Thank you Kenneth and Rembert for your very constructive remarks.
In all friendliness, let me say that it is very easy to say "what to do", but it is another thing to get everything done!
Pascal is working very hard on this, but a new software development is required first for complete results.
The study is progressing on trading only the 20 DMF signals without the risk management from the robots.
Some drawdowns look frightful so the added value from the robots' risk management element will be instructive also once the new software development is finished.
Billy
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Hi Billy,
That's very true. But also remember we're just having a conversation here. Exchange of idea's etc.
I'm not asking Pascal or you to drop what you are doing to do some tests. No need to feel pressure from the forums to do things.
In due time I think it would be good tough to have a look into position allocation tests for the robots. But it's not a priority. When the time arrives I'll be glad to help if you guys can then provide eiter historical trades or equity curve data of the robots.
Again, really appreciate the work you guys are doing.
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2 Attachment(s)
[QUOTE=Kenneth K;13832]That may be accurate if you replace 'trading' with the word 'holding'. Holding the different portfolios over time, you may end up with such risk-return characteristics. But when it comes to 'trading', none of that matters. None of those parameters come into material effect during the very short trading horizon of the Robots. Short term trading yields portfolios with totally altered risk-return characteristics.
What is efficient for a buy and hold index portfolio, is not necessary true for an actively traded portfolio. You cannot compare apple and oranges, eventhough they are both fruits and delicious.
Trying to pinpoint an optimal mix of Robot based trading in IWM/GLD is an exercise in futility. There will be periods when one specific mix is optimal. And that optimal mix is optimal for that particular period, in direct relation to the market movement in IWM and GLD during that particular time. And naturally, that will simply fluctuate over time.
I see a lot of effort is expended on slicing and dicing the Robot signals to get the most out of it. From my limited experience in the business, I would venture to guess that there is inherent risk in over optimizing within a very small data set. The nature of the market is change, eventhough very often, and ironically, the more things change, the more they stay the same. There is an inherent risk that what works perfectly for the last three years, may not work as well in the next three years. The key is the robustness of the algorithm.
It appears that the ROBOT methology of combining a trend following component with a mean reversion component is a very robust method that will withstood the test of different market conditions, with minor retuning over time. If people over optimize it for a very narrow trading period, the result may be counter productive.
As always, best of luck to everyone.[/QUOTE]
I agree with you Kenneth.
What Paul's excellent work implies is that IWM B/H makes sure that you move with everybody else and at the same speed. This means that if everybody else jumps off the cliff, you are sure to be with them. This means that the implied drawdowns for both IWM and GDX are pretty bad in buy and hold situations (shown below). This means that market diversification will not prevent bankrupcy when the whole market sinks.
The only way to avoid that is to start trading them. Then, the implied IWM/GDX balance will have more to do about the type of trading strategy we use on each instrument and on their combination.
For example, the IWM/GDX combination would be different when trading the robots than when trading a 50/200MA crossover strategy.
Pascal
[ATTACH=CONFIG]8950[/ATTACH]
[ATTACH=CONFIG]8951[/ATTACH]
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IWM/GDX Portfolio
Below is a link to the IWM/GDX portfolio analysis.
[url]http://www.effectivevolume.eu/content/Reports/IWM_GDX_Portfolio_Analysis.pdf[/url]
Pascal
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[QUOTE=Pascal;13852]Below is a link to the IWM/GDX portfolio analysis.
[url]http://www.effectivevolume.eu/content/Reports/IWM_GDX_Portfolio_Analysis.pdf[/url]l[/QUOTE]
Thank you Pascal. Great documentation, as always.
With an IWM historical MDD of -10.5%, is it safe to conclude that using the leveraged triple ETF would result in a MDD in excess of -31.5%?
Regards,
pgd