Pascal,Originally Posted by Pascal
Do you have any significant indication yet about which allocation is providing the best long term risk-adjusted returns between 100% of the time only in TNA/TZA (option 1) and a combination of TWM/RWM + GDX (option2)?
Billy
Not yet, but when you have an instrument with such strong returns as TNA/TZA, switching 50% out of that instrument into an instrument that produces only half of the return cannot help the performance (drawdowns/risks put aside). Also, the definition of a good risk/reward balance is different for each investor.
So, as I wrote, new research results bring more questions, which lead to more research and so on.
I plan to wrap what I did up to now, write a report and then do more work on the pending issues.
Pascal
Yet another option may be to try achieving better returns w/ the GDX robot by using the leveraged ETFs NUGT and DUST. That said, GDX is already quite jumpy, so the result may be too volatile for most investors. Also, they haven't been around much, so any backtest is going to be hard. Thanks,
Max
Last edited by Maxime A.; 06-20-2011 at 07:14 AM.
Just my oppinion but I think it is best to initially take leveraged ETF's out of the equation when searching for the optimal use for a given amount of capital.
Otherwise the test will probably indicate it's best go with TNA/TZA only for maximum gain.
The problem I see with that is that this is based on historical data. The maximum drawdown of any system lies in the future and is unknown.
Risk of ruin is probably quite high going all in on TNA/TZA even tough historical tests show it maximizes profit.
Instead of trying to maximize gain it might be better to maximze the MAR ratio. (MAR = CAGR / Max DD) This way, risk is taken into account.
My guess is diversification in systems leads to a higher MAR ratio and to a smoother equity curve. I believe that it is safer to use leverage on a diverse portfolio of systems (either by margin or leveraged ETF's) than it is to do so on a single system, no matter how great historical backtest says that system is.
GGT Forum Manager
Completely concur with Ray's comment. If I may add some color ...
Risk adjusted positioning increases the work we must put into our trading activities. It basically throws out the concept of "I'll own a maximum of 10 positions and my portfolio is Y, so each position is Y/10". While this approach certainly works, it is far less than optimum as the number of positions gets less and less. As M&K, O'Neil, et al. advise, fewer positions is best. If you believe this, then the impact of MDD is crucial as the drawdown contains more of your capital. Unfortunately, most individuals who counsel a low number of holdings rarely address risk-adjusted position sizing, because it's not a Finance 101 concept.
The obvious question is how to correctly position size. The not-so-obvious answer is dependent upon:
1) the expected gain of the securities in the entire portfolio
2) the correlation of the securities in the entire portfolio
3) the variance of the individual securities in the entire portfolio
4) the standard deviation of the prices of the individual securities
5) the allocation of capital between the different components of the individual securities
A very good starting point on understanding these concepts can be found in the following PowerPoint presentation. I've zipped it because ".ppt" is not an available upload option.
mathematicsofDiversification-ch05.zip
The key concept here, which directly supports Ray's assertions, are that we start the optimization process by constructing a portfolio with a minimization of variance in mind. Here, variance is equated to drawdown. Hence, for a given set of equities with quantified gains as well as standard deviation of the price series, we can form a portfolio which reduces variance while increasing gain.
The PowerPoint shows how to do it for a two-security portfolio -- doing it for more (which obviously is practical) requires more work and further requires that you know how to use Excel. The outline of how to do this for N-portfolios is also in the PowerPoint, and relies heavily on the work of Simon Benninga. The book has a disk with macros and worksheets ready to go, but of course, you have to understand some of the basic concepts shown in the PowerPoint in order to get anything meaningful out of the book.
Further supporting Ray's assertion that we should not use leveraged instruments in our optimization process is this paper:
1st_Place_Tony_Cooper_abstract.pdf
This is a heavier read, but pay attention to Figures 1 and 2, which give you some framework around the "optimum" leverage levels for the general market over various periods in the past. This paper is relevant because leveraged instruments multiply BOTH volatility as well as gains, resulting in the same behavior as their non-leveraged counterparts during the optimization process (I ignore the impact of the daily rebalancing of leveraged daily ETFs, which is adverse over the longer term).
Finally, the approach in the book and the included paper above do not address in a concise manner that volatility changes with the time frame being measured; they use standard lookback periods and take the volatility as equal-weighted over the lookback period. This is not a good approach in real life, so this last paper is a (heavy) introduction on using a moving average concept to have a better volatility estimate:
TD4ePt_2-StatisticsOfFinancialMarketReturns.pdf
Riskmetrics pioneered research on risk management, and I've not found a better reference.
If you've made it this far and you have a basic understanding of the concepts of volatility, jump to chapter 5, specifically Table 5.7 onward, to get a view on how the exponentially weighted moving average (EWMA) model is used in the forecast of returns and variances.
==================
Disclaimer: This is all a work in progress, and I'm still learning, learning, learning. Portfolio/position sizing is HARD, which is why most people (including me) simply do the Y/10 per position and are done with it. The concept of minimal-variance portfolio construction is hard to achieve, yet maintain in a practical fashion, but this shouldn't make you throw your hands up and say "it's not worth it". It's clear it *is* worth it, especially if you are happy with your holdings and have the knowledge that you're closer to maximum efficiency in gains and reduction in drawdown than you'd ever be with a Y/10 approach.
Paul,
This is a terrific wealth of resources on the topic! It shows your commitment to search for constant improvement.
Before digging into all the details, I have a conceptual hesitation.
It seems all the models are based on individual securities or stocks.
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?
Billy
Thanks for the material Paul. This is a topic that interests me vey much. It goes beyond simply being a trader. It's about learning how to manage money ... large sums of money. No doubt that all the billionaire funds know these concepts all too well.
Billy, I think one can diversify in multiple ways. Using IWM is a great starting point, being diversified in 2000 different stocks. But it doesn't have to end there. One can add another layer of diversifiction by employing multiple systems using different markets/strategies/timeframes. It doesn't have to be 1000 systems, I think 3 (IWM,GDX,XLE) is a nice number that is still managable.
Here's a few more links from the excellent automated trading system blog :
http://www.automated-trading-system....on-free-lunch/ (I like the coffee cup analogy)
http://www.automated-trading-system....uce-drawdowns/
I would consider to:
1. start by constructing a portfolio of the IWM Robot and GDX Robot that has produced the lowest intraday drawdown, not considering leverage.
2. next construct a portfolio of the IWM Robot and GDX Robot that has produced the lowest end-of-day drawdown, not considering leverage.
3. next construct a portfolio of the IWM Robot and GDX Robot that produces the lowest annualized volatility, not considering leverage.
After performing the above steps, a clear answer as to the appropriate allocation between the two robots may emerge (at least based on historical results) for the maximization of volatility-adjusted return. If not, further investigation will be required.
GGT Forum Manager
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:
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:
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:
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:
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).
=================
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:
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.
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.
=======================
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:
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:
73% IWM
27% GDX
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), that a minimum-risk portfolio exists with IWM and GDX in the allocations above.
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%.
===============
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:
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. 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
IWM: 69%
GDX: 23%
XLE: 8%
==================
So, in summary,
- 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
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).
Last edited by grems8544; 06-21-2011 at 07:15 PM.
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