Online portfolio management tool

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iqfront
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Online portfolio management tool

Post by iqfront » Tue Mar 02, 2010 6:44 am

This thread is about the online portfolio management tool at http://www.iqfront.com/portfoliotool.php

You can create professional portfolio reports, perform Markowitz type mean-variance portfolio optimization and conduct portfolio sensitivity analyses with it. The tool uses adjusted end-of-day closing prices to take into account stock splits and dividends. The security data is automatically being kept up to date. Most of the world’s significant stock markets are covered, including those in the US, Europe, Asia and Australia.

Note that I am not promoting anything or anyone. This tool is – genuinely – free of charge; you can do everything I state on this thread without spending a dime. I have agreed with the Bogleheads administration about starting this thread with the purpose to describe in detail what (and how) you can do with the tool, provide examples, sample applications and also answer questions. I’ll do my best to post daily to keep the discussion going on, but due to a rather demanding day job can’t make promises.

I had built something like this in MATLAB a long time ago for personal use and found it rather useful for keeping my long-term portfolio on track. Having recently familiarized myself with server side programming, I decided to put such a service available for the public. I hope you find it useful. I would also appreciate if you could report any bugs to me and provide feedback on what you think might be missing from the tool.

Note that the tool throttles portfolio queries to ensure that all users are being served equally.

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Re: Online portfolio management tool

Post by iqfront » Tue Mar 02, 2010 7:47 am

Before we start, let me point out that the portfolio management tool described in this thread is not a trading tool by any means. It will not give you “signals” to enter and exit trades. It will not tell you where the market is heading next. And, make no mistake about it, the tool is not guaranteed to make you any money.

We are talking about a tool for rigorous investment management. To me, this always boils down to managing the risk-return profile of a security portfolio according to a pre-specified plan. Now, there are many ways to do this. Some prefer the Graham-Dodd-Buffett way, others (including myself) prefer quantitative methods, yet still others prefer something else. While value investors look for fundamentally mispriced securities and “hidden potential”, many portfolio managers with a quantitative bias use modern mathematical methods to monitor the (expected) risk-return profile of a portfolio; their ultimate aim, of course, being to optimize it. This is what the tool I’m describing here is all about. Facilitating quantitative analysis and optimization of security portfolios without much knowledge of the underlying mathematics, it can be viewed as an easy-to-use alternative for Excel. Moreover, it should provide a hands-on illustration of the fact that managing a portfolio of securities is vastly different from managing individual securities. I don’t think this is evident at all when using the portfolio tools at MSN Money, Yahoo! Finance or Google Finance, although they do provide a lot of useful information about individual securities.

There are certain caveats at using mathematical methods for portfolio management. They are widely reported in the academic literature, and I certainly intend to describe (at least some of) them here, once we get there.

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First steps

Post by iqfront » Tue Mar 02, 2010 8:43 am

Ok, let’s get going. Assume for the moment that we have held the following security portfolio, consisting of some large cap stocks in the S&P 500 index and a couple of ETFs, since 1-Jan-2005:

Long 2000 shares Vanguard REIT Index ETF (ticker code VNQ)
Long 500 shares iShares Barclays TIPS Bond (ticker code TIP)
Long 100 shares Apple (ticker code AAPL)
Long 200 shares Exxon Mobil (ticker code XOM)
Long 300 shares Microsoft (ticker code MSFT)
Long 400 shares Procter Gamble (ticker code PG)
Long 500 shares Johnson & Johnson (ticker code JNJ)
Long 600 shares General Electric (ticker code GE)
Long 700 shares JPMorgan Chase (ticker code JPM)

This portfolio is entered into the iQfront tool as a string:

+2000*VNQ+500*TIP+100*AAPL+200*XOM+300*MSFT+400*PG+500*JNJ+600*GE+700*JPM

As a side note: The portfolio tool can handle considerably larger portfolios than this. I successfully completed a test run on a local server with a portfolio of over 300 securities. However, unless your portfolio actually is that large, please do not test it. My code is not particularly easy on the system resources.

Let’s create a report from 01-Jan-2005 to 01-Mar-2010, a period of over five years. An assumption we make here is that the risk-free rate of return is 4% per year. This may or may not be realistic, but we’ll stick to it for the sake of illustration.

I'll go through the report generated by the tool in the next posts.

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Report contents 1

Post by iqfront » Wed Mar 03, 2010 4:00 am

Image

The above rather self-explanatory items display the general characteristics of the sample portfolio +2000*VNQ+500*TIP+100*AAPL+200*XOM+300*MSFT+400*PG+500*JNJ+600*GE+700*JPM for the reporting period.

Note that reported above are expected quantities of the portfolio. They are estimated from historical data, and, had we applied weighting to emphasize the more recent data (or a different method altogether), the estimates would be different. We now arrive at the first caveat of mathematical portfolio management methods: These estimates are known to be relatively unstable in time. Past returns are not necessarily indicative of future returns (now how many times have you heard this before?). A nice thing about the iQfront portfolio tool is that you can easily test the stability of these estimates – just enter a different reporting period and assess the end result. As mentioned above, and as we’ll discuss later, the tool allows placing emphasis on the most recent observations. This is useful, for instance, after a significant structural break in the data processes – for example, the crash of Autumn 2008. You want the estimates to remember (faintly) what it was like before the event and yet (more significantly) resemble the presently prevailing market conditions.

To conclude, I’ll try to briefly explain the above report items in layman’s terms. Returns are differences of logarithmic daily closing prices. Volatility is, of course, the standard deviation of portfolio returns. Value at Risk is defined as the percentage of portfolio value that one should at least expect to lose at a given probability level. Hence, in this example, there is a 5% probability that the portfolio value drops at least 2.75% in any given day. In other words, in a very long period of trading days resembling those observed during the past 5 years, in 5 out of each 100 days the portfolio value can drop at least 2.75%. The Value at Risk estimates are based on Gaussian distributions, which are often (but not always) sufficient in practice - another caveat of mathematical portfolio management methods. The expected Sharpe ratio, or risk-adjusted efficiency, of the portfolio is negative because investing in the risk-free asset would (under our assumption of 4% p.a. riskless return) have yielded more than 3.08% per annum. Finally, I decided to compare the present portfolio to the S&P 500 index; the tool reports that the portfolio’s beta relative to S&P 500 is 0.92, indicating that we should expect its movements (while still random) resemble those of the reference index very closely.

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Report contents 2

Post by iqfront » Wed Mar 03, 2010 4:23 am

Time evolution of the sample portfolio +2000*VNQ+500*TIP+100*AAPL+200*XOM+300*MSFT+400*PG+500*JNJ+600*GE+700*JPM is also displayed for the reporting period:

Image

It is clear from the above that the crash of autumn 2008 was not particularly gentle on the portfolio. You might (correctly) come to think that this is largely because of significant exposure to the real estate market (VNQ) in the event of a dramatic subprime mortgage crisis. We’ll later conclude rigorously that this indeed is the case; by reducing exposure to VNQ we would - under the estimated return and risk figures - be better off in terms of both risk and return. It is important to bear in mind that we will be able to draw this conclusion without any knowledge of macroeconomics and causes of the crash.

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Report contents 3

Post by iqfront » Wed Mar 03, 2010 11:41 am

The next item on the report is the performance of individual portfolio components:

Image

The portfolio’s heavy exposure to the real estate market through VNQ is evident.

Let us next optimize this portfolio. Tick “Optimization” and “no short selling” and set “emphasis on recent data” to zero (0)…

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Post by walkinwood » Wed Mar 03, 2010 3:40 pm

Does it support mutual funds?

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Post by cvn74n2 » Wed Mar 03, 2010 4:06 pm

I have been playing around with the tool this morning. I find it easy to use, supports stocks, ETFs, and mutual funds. I build queries in Word and then copy into the program. You will shortly see a donation.

One thing I would like to see added is an an option to automatically rebalance the portfolio yearly to original proportions (as the white paper outlines). Right now I have to look up historical prices and reset the share count for each security to have the portfolio start in the same place for various periods to properly compare the effect of optimization.

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Post by iqfront » Thu Mar 04, 2010 3:53 am

cvn74n2 wrote: One thing I would like to see added is an an option to automatically rebalance the portfolio yearly to original proportions (as the white paper outlines). Right now I have to look up historical prices and reset the share count for each security to have the portfolio start in the same place for various periods to properly compare the effect of optimization.
I hear you. Let's agree (shall we) that I'll finish this thread and then gather all requests in one place, apply priorization if necessary and see that the updates are made.

Thanks for your feedback.

To everyone: Feel free to interrupt me at any time and comment.
Last edited by iqfront on Thu Mar 04, 2010 7:36 am, edited 2 times in total.

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General thoughts on portfolio optimization

Post by iqfront » Thu Mar 04, 2010 4:26 am

Before we arrive at what I consider the most insightful parts of the report, let us digress for a moment and discuss portfolio optimization on a more general level.

Portfolio optimization usually - and also in our case - refers to mean-variance optimization. This problem can be formulated and solved using standard techniques of convex quadratic programming. I built the iQfront portfolio optimization engine on an algorithm of Prof. William F. Sharpe (yes, that William Sharpe): “An algorithm for portfolio improvement” in Lawrence, K. D., Guerard, J. B. and Reeves, G. D. (eds): “Advances in Mathematical Programming and Financial Planning”. JAI Press, 1987. This algorithm facilitates such an approximate solution of the optimization problem which can be easily ported to the web environment.

The general mean-variance optimization problem has two mutually contradictory objectives: Maximization of (mean) return and minimization of portfolio risk (variance). Since these objectives are contradictory, the best you can hope for is to find a set of Pareto optimal solutions. A Pareto optimal solution of a multi-objective optimization problem is such that you cannot improve the solution relative to any one criterion without compromising the solution relative to some other criterion. In portfolio optimization, the set of Pareto optimal solutions is called the efficient frontier. It consists of such (optimal) portfolios whose return characteristics cannot be improved without taking additional risk and, conversely, risk cannot be reduced without reducing the portfolio’s expected return.

Your goal as an investor should therefore be – and remain – as close to the efficient frontier as possible: According to the theory, it is as good as it gets. Now which portfolio on the efficient frontier should your target be? That depends on your preference for risk! This is the essence of quantitative portfolio management. By fixing a risk tolerance you implicitly fix a return estimate for your portfolio, assuming that you are able to stay on the efficient frontier (not an easy task by any measure). I will later introduce a minimum-risk investing strategy as an application of the iQfront tool to illustrate this point.

It is important to remember that quantitative portfolio management methods, such as mean-variance optimization, are no black magic. At best they can enable the portfolio manager to remain solvent when the market does not, but this requires considerable intuition and experience of the methods. It is my hope that the iQfront tool can help you gain it and assess whether or not such methods could play a part in your strategy.

I will finish with a couple of remarks. Bear in mind that the efficient frontier with short selling allowed is different than the efficient frontier with short selling disallowed. This is because the search space in the former problem is larger. Also bear in mind that portfolio optimization is always carried out in a given universe of risky assets. In our case, the universe is fixed at the outset by the current portfolio you enter in the iQfront tool. This implies that the efficient frontier you obtain depends on the current portfolio. There really is no way around this, but you can always introduce “phantom” portfolio members with zero weights. For instance, try the portfolio +100*AAPL+0*XOM+0*M and see the result.

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Report contents 4

Post by iqfront » Thu Mar 04, 2010 9:34 am

The iQfront tool reports three optimal portfolios based on the given “current” portfolio: The minimum risk portfolio, the maximum return portfolio and the maximum Sharpe ratio portfolio. The minimum risk portfolio is the least risky portfolio with return characteristics similar to those of the current portfolio. The maximum return portfolio is the highest yielding portfolio with risk characteristics similar to those of the current portfolio. The maximum Sharpe ratio portfolio is that optimal portfolio with the highest Sharpe ratio under the assumed risk-free rate of return. While there is an infinite number of optimal portfolios on the efficient frontier, these three optimal portfolios should point you to a right direction whether your goal is to reduce the risk or increase the expected return of your portfolio.

The three optimal portfolios calculated by the tool are displayed in the report. In our example (see the previous posts) they are as follows:

Image

The optimization algorithm finds the percentage of capital to be allocated to the individual securities based on the estimates for expected return and covariance. The above portfolio weights are then obtained by converting these optimal percentages back to numbers-of-shares. The initial portfolio weights and average historical asset prices, with a possible emphasis on recent data, are used to achieve this.

When you study the table displaying the performance of the individual portfolio components - see again one of my previous posts - compositions of the above optimal portfolios should come to you as no surprise. The case of maximum return portfolio is evident in my opinion. Similarly, the risk-reducing effect of increasing exposure to TIP in the minimum risk portfolio should be clear. Indeed, mathematical portfolio management is just rigorous common sense. Needless to say, though: With larger portfolios it is usually not at all clear at the outset what the optimal allocations might be.

Note that by varying the assumption of risk-free rate of return, you can traverse all points on the approximation of the efficient frontier. Try a risk-free rate of 10% and see the corresponding Maximum Sharpe portfolio, for example. You might also want to test optimizing this test portfolio with short selling allowed; you could guess that GE might suddenly enter the optimal portfolios in spite of its poor 5-year performance…

As a final remark, remember that mean-variance optimization attempts to produce a maximum return at the least assumed risk. These two goals alone have nothing to do with sufficient diversification - another caveat of quantitative portfolio management methods.

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Post by ddb » Thu Mar 04, 2010 10:01 am

Since when are commercial posts and/or links to one's own website allowed on this forum?
"We have to encourage a return to traditional moral values. Most importantly, we have to promote general social concern, and less materialism in young people." - PB

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Post by EyeDee » Thu Mar 04, 2010 10:11 am

ddb wrote:Since when are commercial posts and/or links to one's own website allowed on this forum?
.
Iqfront got permission from Alex for one thread inviting people to try out their MVO tool since it might be useful to someone on the board, explaining it, and answering any questions that may arise.
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Post by Random Musings » Thu Mar 04, 2010 10:12 am

Note that I am not promoting anything or anyone. This tool is – genuinely – free of charge; you can do everything I state on this thread without spending a dime. I have agreed with the Bogleheads administration about starting this thread with the purpose to describe in detail what (and how) you can do with the tool, provide examples, sample applications and also answer questions.
Looks like OP got permission - and product is free. If it becomes commercial and a price is charged, I would assume that moderators would pull this thread from the board.

RM

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Post by ddb » Thu Mar 04, 2010 10:16 am

Random Musings wrote:
Note that I am not promoting anything or anyone. This tool is – genuinely – free of charge; you can do everything I state on this thread without spending a dime. I have agreed with the Bogleheads administration about starting this thread with the purpose to describe in detail what (and how) you can do with the tool, provide examples, sample applications and also answer questions.
Looks like OP got permission - and product is free. If it becomes commercial and a price is charged, I would assume that moderators would pull this thread from the board.
Free, yes, but the OP still benefits from the proliferation of this tool, plus there are banner ads all over the linked website. Oh well, not for me to decide...

- DDB
"We have to encourage a return to traditional moral values. Most importantly, we have to promote general social concern, and less materialism in young people." - PB

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Report contents 5

Post by iqfront » Thu Mar 04, 2010 11:58 am

The next item on the portfolio report is a graphical view of the efficient frontier along with the three optimal portfolios (discussed earlier) on it. The relative location of the current portfolio in terms of risk (x-axis) and return (y-axis) is also shown. And yes, our sample portfolio is rather far away from the efficient frontier:

Image

This figure also displays the result of a sensitivity analysis with respect to VNQ (tick “Sensitivity analysis” and enter the desired ticker symbol in the tool). A sensitivity analysis here refers to assessing the effect - in terms of risk and return - of a 50% change in a position. In our example, the two portfolios to be compared to the current portfolio are thus:

-50% change in exposure to VNQ: +1000*VNQ+500*TIP+100*AAPL+200*XOM+300*MSFT+400*PG+500*JNJ+600*GE+700*JPM

+50% change in exposure to VNQ: +3000*VNQ+500*TIP+100*AAPL+200*XOM+300*MSFT+400*PG+500*JNJ+600*GE+700*JPM

The sample result, displayed above, shows that given the current portfolio and its past performance, by reducing exposure to VNQ we could simultaneously reduce the portfolio’s risk and enhance its expected return.

EDIT: last -> next
Last edited by iqfront on Fri Mar 05, 2010 12:02 am, edited 1 time in total.

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Re: Report contents 5

Post by ddb » Thu Mar 04, 2010 12:00 pm

iqfront wrote:The sample result, displayed above, shows that given the current portfolio and its past performance, by reducing exposure to VNQ we could simultaneously reduce the portfolio’s risk and enhance its expected return.
So, should one make portfolio adjustments based on backtested results?

- DDB
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Post by Random Musings » Thu Mar 04, 2010 12:09 pm

Of course, the standard caveats to optimization and hitting the efficient frontier are that past returns that feed these results are backward looking - moving forward is where the crystal ball comes into play.

This tool may help a bit for people who invest in diversified passive class funds/ETF's with respect to how diversification typically helps us get closer to the efficient frontier - but playing with individual equities using these techniques seems more of a "if I only would have". I guess if you use a lot of equities in the sample size, at that point, you are looking at your own "mutual fund" in retrospect.

edit: beat me to the punch ddb

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Re: Report contents 5

Post by iqfront » Thu Mar 04, 2010 1:15 pm

ddb wrote: So, should one make portfolio adjustments based on backtested results?
Good trick question :). I guess we both know that the answer is yes and no.

Of course, with these methods one should be looking for estimate stability in order to be able to project past into the future. If ex ante backtests showed a decent, anticipated performance across market regimes - an indication of stability - then the answer would be yes, in my opinion. You are free to disagree. The point of the post, however, was to describe the functionality of the tool by a rather fictive example, and that we aim to move the portfolio towards the efficient frontier by rebalancing.

I have repeatedly tried to emphasize that these methods are not bomb proof. But, then again, neither is buy-and-hold. When you estimate returns and covariances from historical data, you implicitly assume that the past somehow repeats itself in the future. But if you think about it, also the more sophisticated factor model estimates (and the like) can be subject to the very same assumption in rather subtle forms. As an analogy: It may be better to use correlation with all its known deficiencies than rely on some obscure robust correlation measure which may fail you when you least expect it.

Again, thanks for the deep question.

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Post by walkinwood » Thu Mar 04, 2010 2:15 pm

Vanguard's Prime Money Market ticker VMMXX is generating an error.

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Post by iqfront » Fri Mar 05, 2010 12:12 am

walkinwood wrote:Vanguard's Prime Money Market ticker VMMXX is generating an error.
It seems that there is no historical data available for this fund. Actually I could not find any historical security data for this ticker anywhere on the web! I checked Yahoo!, Google and MSN Money. Is there a location on the web where you can view historical data for this fund (and perhaps others)? If yes, then please let me know and I'll investigate possibilities to integrate the databases.

Thanks for the bug report.

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Post by iqfront » Fri Mar 05, 2010 12:35 am

As a continuation to the issue reported by walkinwood:

When analyzing a portfolio of funds, be careful to check that all the funds have existed during the entire reporting period. At present, the tool does not warn on missing data, unless no data is found at all. On the contrary, the tool attempts to interpolate missing data to create a uniform data set for the entire reporting period. This will yield incorrect results if, say, the first two years are missing for a certain ticker.

Actually the same warning goes for stocks, too. For example, if there has been a merger related to a given stock in the recent past, it is worthwhile to check data availability. You can do this by creating a report for a portfolio with only this stock in it.

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Discussion on the results

Post by iqfront » Fri Mar 05, 2010 5:16 am

In a previous post we concluded, based on a rigorous mathematical analysis, that by reducing the exposure of the current portfolio to VNQ – a REIT index fund – we could move the sample portfolio closer to the efficient frontier. In fact, we could simultaneously reduce the portfolio’s risk and enhance its expected return slightly. Not bad at all. Now, will this choice yield good results in the future? Maybe. We have been taught that the risk-return level of real estate is somewhere between government bonds and common stock. The past couple of years have cast this assumption in a new light, and the results of the previous sensitivity analysis merely reflect this fact. Although these results are more or less self-evident considering what has happened in the US economy during the past few years, it is remarkable that we did not need this knowledge anywhere in the analysis. Indeed, one of the virtues of quantitative portfolio management is the ability to draw such conclusions based on numerical data alone. In my opinion this is a huge benefit when the number of risky assets in the portfolio grows, as macroeconomic cause-effect analysis on the portfolio then becomes vague, potentially subjective and difficult to quantify (hand-waving in mathematicians’ parlance).

Now, you may question the legitimacy of using a purely model-based analysis. Such criticism is valid, there is absolutely no question of that, because models are never perfect. But consider this: Assuming that the theory behind the models holds, you know where you should be (the efficient frontier) and you have the tools to get there (optimization and sensitivity analysis). There is no hand-waving involved in this process. In addition to this, you can – and you definitely should – test for model consistency across different time periods. In a sense, by using quantitative methods for portfolio management you trade market risk for model risk. Whether this trade should be taken depends on your investment philosophy alone.

There is one obvious question that looms behind this discussion: What would the end result of our analysis have been at the turn of 2006-2007 when the outlook of the real estate market was overwhelmingly rosy? The answer depends on the initial portfolio, i.e. the universe of possibilities to invest in, and the preference for risk. Although there is not very much historical data to support the conclusion, thanks to the remarkably good performance of VNQ at that period, the sample portfolio discussed in the earlier posts would have been very close to the efficient frontier in February 2007 at the market peak. A major warning sign, however, would have been the lack of diversification in the sample portfolio: VNQ represented about 44% of the entire portfolio value back then! Going forward, the end result of the sensitivity analysis would eventually have been the same at the turn of 2007-2008: Reduce exposure to VNQ to move closer to the efficient frontier.

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Report contents 6

Post by iqfront » Fri Mar 05, 2010 5:27 am

To conclude the report description, here is a graphical comparison of the cumulative returns of the portfolios described in the previous posts. You can view it at the end of the report page.

Image

This figure clearly illustrates the previously made observation that the returns of the current portfolio resemble those of the S&P 500 index (ticker code ^GSPC). Recall that we had calculated an index beta of 0.92. The above figure also explains the terminology related to the optimal portfolios. In particular, it should be clear why “Minimum risk portfolio” and “Maximum return portfolio” are labeled like that.

Notice that these cumulative return series are based on realized data, not estimates.

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Post by walkinwood » Fri Mar 05, 2010 1:09 pm

iqfront wrote:
walkinwood wrote:Vanguard's Prime Money Market ticker VMMXX is generating an error.
It seems that there is no historical data available for this fund. Actually I could not find any historical security data for this ticker anywhere on the web! I checked Yahoo!, Google and MSN Money. Is there a location on the web where you can view historical data for this fund (and perhaps others)? If yes, then please let me know and I'll investigate possibilities to integrate the databases.

Thanks for the bug report.
I couldn't find any. I wonder if that is because it is a money market fund.

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Post by iqfront » Sat Mar 06, 2010 8:55 am

walkinwood wrote: I couldn't find any. I wonder if that is because it is a money market fund.
Oh, yep, I think that would be the reason. Fortunately, there are probably plenty of such securities whose risk-return characteristics are very similar to it.

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Non-US securities

Post by iqfront » Sun Mar 07, 2010 7:28 am

The iQfront tool also supports non-US securities. For them an exchange specific suffix code is required in the tickers. Some sample portfolios from the world stock markets are listed below.

London (ticker symbols require suffix .L): +100*ATST.L+200*ANTO.L+300*AV.L+400*BA.L

Paris (ticker symbols require suffix .PA): +100*ACA.PA+100*TEC.PA+100*ALO.PA+100*BNP.PA

Frankfurt (ticker symbols require suffix .DE): +100*ADS.DE+100*ALV.DE+100*BAS.DE

Stockholm (ticker symbols require suffix .ST): +100*ALFA.ST+100*BOL.ST+100*SAND.ST+100*TLSN.ST+100*LUPE.ST+100*ERIC/B.ST

Milan (ticker symbols require suffix .MI): +100*BMPS.MI+100*BP.MI+100*CIR.MI+100*F.MI

Sydney (ticker symbols require suffix .AX): +100*AMP.AX+100*ANZ.AX+100*BHP.AX+100*BXB.AX+100*CBA.AX+100*CSL.AX

Toronto (ticker symbols require suffix .TO): +100*ABX.TO+200*AEM.TO+300*BBD/B.TO+100*CAE.TO+100*CLM.TO

Madrid (ticker symbols require suffix .MC): +100*SAN.MC+100*ABE.MC+100*EVA.MC+100*ITX.MC

India (ticker symbols require suffix .NS for NSE and .BO for BSE):

NSE:+100*UNITECH.NS+100*IFCI.NS+100*GVKPIL.NS+100*SUZLON.NS
BSE: +100*SANJIVIN.BO+100*SICAL.BO+100*BATA.BO

If there is a particular market not listed above that you’d like to have included, and you know that there is free (or ultra-low-cost) data available online, then let me know. I will check the possibilities to integrate the databases.

By the way, when analyzing securities from different exchanges, be very sure that their values are reported in the same currency. The tool itself does not verify this.

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Still to come

Post by iqfront » Sun Mar 07, 2010 8:02 am

There are three more topics that I intend to discuss in this thread:

1. Optimal capital allocation across different asset classes using ETFs
2. Stability of optimal portfolios – empirical evidence from over 3 years of data
3. A low-risk semi-passive equity investment strategy based on portfolio optimization

I will still need to prepare some material for 1 and 2. In the mean time, you are invited to provide feedback on features that could potentially improve the tool.

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Optimal capital allocation across different asset classes

Post by iqfront » Mon Mar 08, 2010 1:51 pm

This post describes a simple capital allocation method, or, more specifically, a portfolio improvement technique, using mean-variance optimization. Suppose that we are given the following (very much non-exhaustive) list of category ETFs to invest in:

DIA – Large capitalization US stocks
EEM – Diversified emerging market stocks
VNQ – Real estate REITs
TLT – Long term government bonds
SHY – Short term government bonds
GLD – Gold
IYM – Basic materials

Which ones should we buy, and in what proportions?

We will use over five years of historical data to estimate the expected returns and covariances and to optimize the portfolios: From January 1st 2005 to March 5th 2010. As there has been a significant change of market conditions – or a structural break – during this period, we will want to put more emphasis on the most recent data. In particular, we choose to weigh the most recent observation with a factor of ten (10) relative to the oldest observation. All other observations are given proportional weights through an exponential fit.

Suppose that the reference portfolio we would like to improve on March 5th 2010 consisted of equal dollar positions in each of the above ETFs. Under this “current portfolio”, the following optimization results are obtained with short selling disallowed and with riskless rate set at 3% per annum:

- Current portfolio: +946*DIA+2442*EEM+2154*VNQ+1108*TLT+1198*SHY+902*GLD+1594*IYM

- Minimum risk portfolio: +490*EEM+5425*SHY+2289*GLD

- Maximum return portfolio: +643*EEM+2164*SHY+5295*GLD

- Maximum Sharpe portfolio: +105*DIA+217*EEM+7844*SHY+1*GLD

The efficient frontier and a sensitivity analysis with respect to DIA are displayed below. You can readily see that reducing exposure to diamonds (DIA) takes the current equal-weight portfolio towards the efficient frontier in this model.

Image

Image

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Re: Optimal capital allocation across different asset classe

Post by iqfront » Mon Mar 08, 2010 2:01 pm

It is instructive to carry out the asset allocation example of the previous post with data endpoint at 5-Mar-2009. How similar are the optimal portfolios estimated one year ago? Note that you have to compare optimal portfolios with similar risk/return estimates in order to assess whether or not the weights change in time. In the posts to follow I intend to carry out a detailed analysis of this type.

Pay particular attention to the global minimum risk portfolio, by the way. It is theoretically the most stable in time. We'll discuss this feature later more.

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Post by Rich_in_Tampa » Mon Mar 08, 2010 2:33 pm

I would rather see a single post here linking to his website, with admin permission.

The long and specific discussion amounts to an on-line manual for a product which, if not for profit right now, has a commercial nuance to it.

I think the author's intentions are good, but don't like the precedent we are setting with this.

Put me on the "post with a link only" group for what it's worth. Just my opinion.
Rich

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Post by ddb » Mon Mar 08, 2010 3:00 pm

Rich_in_Tampa wrote:I would rather see a single post here linking to his website, with admin permission.

The long and specific discussion amounts to an on-line manual for a product which, if not for profit right now, has a commercial nuance to it.

I think the author's intentions are good, but don't like the precedent we are setting with this.

Put me on the "post with a link only" group for what it's worth. Just my opinion.
Me too. We are now on day 7 of the OP adding a new post to bump his thread to the top of the thread list. Very obvious manipulation of the exception that he was for some reason granted.

- DDB
"We have to encourage a return to traditional moral values. Most importantly, we have to promote general social concern, and less materialism in young people." - PB

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Post by iqfront » Tue Mar 09, 2010 6:56 am

ddb wrote:
Rich_in_Tampa wrote:I would rather see a single post here linking to his website, with admin permission.

The long and specific discussion amounts to an on-line manual for a product which, if not for profit right now, has a commercial nuance to it.

I think the author's intentions are good, but don't like the precedent we are setting with this.

Put me on the "post with a link only" group for what it's worth. Just my opinion.
Me too. We are now on day 7 of the OP adding a new post to bump his thread to the top of the thread list. Very obvious manipulation of the exception that he was for some reason granted.

- DDB
I do appreciate your effort to keep up the forum's high quality, but accusing me of manipulation is a bit out of line. I have tried to make the posts as information-packed as possible, which is why they need some preparation. My intention has been to describe in sufficient detail what one can do with the tool and what are its caveats. I seriously believe that this information is benefical to those thinking about integrating MPT to their investment strategy.

I have already indicated the topics left to post on, and my intention is to post them as promised. There are not many of them, so please bear with me, I will try to make haste.

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How stable are optimal portfolios?

Post by iqfront » Tue Mar 09, 2010 7:12 am

Optimal portfolios in the sense of Modern Portfolio Theory are constructed using estimates of expected returns and covariances. The estimation process can rely on the analyst’s view of the future events, or it can be based on realized historical data. A drawback of the former approach is that it is subjective - most analysts do not have access to a crystal ball – although one can make rather informed estimates based on the literature (see e.g. http://papers.ssrn.com/sol3/papers.cfm? ... id=1368689). The iQfront tool takes the latter approach; the obvious weak point being the assumption that the past would repeat itself in the future. Now how much does this actually happen in practice? Or, more importantly: How similar are optimal portfolios calculated at different instants of time?

It is important to realize that there is no one single correct answer to this question. Indeed, the answer depends on many factors: The universe of assets (initial portfolio), the number of data samples used for estimation, emphasis on recent data, preference for risk and so on. Nonetheless, getting a gut feeling of the problem is important, because, ultimately, we want the optimal portfolios to have predictive power: The optimal portfolios of the past should remain close to optimal for a while (at least until we rebalance).

For the sake of illustration, I conducted a test based on the previous asset class allocation example, with the universe of assets being DIA, EEM, VNQ, TLT, SHY, GLD, IYM. This is a very small universe of assets, but sufficient for our purposes nonetheless. I used 500 observations, corresponding to about 2 years of data, for the estimation of returns and covariances. There was no emphasis on recent data. The optimization was carried out roughly once per month. For consistency, I required that the expected portfolio return would be as close to 7.5% per annum as possible on every optimization instance. Why 7.5%? Because it turned out that it was impossible to obtain consistently larger expected p.a. portfolio returns than about 7.7% out of this universe of assets without leverage. Under these circumstances, requiring a return of 10% would then have introduced additional instability to the optimal portfolios because of varying optimization targets. This is hindsight, but apparently necessary to isolate the source of uncertainty.

The calculated optimal allocations, i.e. percentage of capital, without short selling are displayed in the below table. All row values from DIA (left) to IYM (right) sum to 100%, representing the total portfolio composition.

Image

What observations can we make from this table? First of all, the optimal portfolios are clearly time dependent. However, apart from the slight oscillation between TLT and SHY – two similar low-risk assets (maybe one would be enough for this case) – the weights of the optimal portfolios appear to change relatively smoothly in time. It is not surprising that the most unstable period was the late 2008: The optimal portfolios providing a 7.5% p.a. expected return varied considerably between every optimization instance at that time. Do you recall fund managers complaining about the malfunctioning of standard market models during those days? I do. Finally, you might wonder why gold has been highly preferred by the optimization algorithm since mid-2009. Just compare the performance of the assets since early 2008 and you’ll see the reason.

Note that nowhere in this post have we studied whether or not it is optimal to rebalance at the above frequency.

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Post by kcyahoo » Tue Mar 09, 2010 9:04 am

This thread does not feel right for this forum. I appreciate the effort and the potential usefulness to some in this forum. Make this a "link to" user guide.
Retired @ 57, now 75 | was 50/45/5, then 42/54/04, now 35/60/5 | KC

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Post by duhmel1 » Wed Mar 10, 2010 2:58 am

kcyahoo wrote:This thread does not feel right for this forum. I appreciate the effort and the potential usefulness to some in this forum. Make this a "link to" user guide.
Maybe we can have a poll, otherwise this rambling may go on and on and on

Analystic
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Post by Analystic » Wed Mar 10, 2010 6:36 am

Thanks for sharing this tool!

I tried it on my last funds purchase:

[Feb 23, 2009 March 9, 2010]

Optimization results and sensitivity analysis

- Current portfolio:
+5000*AOD+5000*IAF+5000*JEQ+2500*SWZ+2000*TDF

- Minimum risk portfolio:
+11631*AOD+4201*IAF+3210*JEQ+1758*TDF

- Maximum return portfolio:
+9541*AOD+1735*IAF+11288*JEQ+1749*TDF

- Maximum Sharpe portfolio:
+3347*AOD+17808*JEQ+6156*SWZ+297*TDF

Overall portfolio characteristics

- Initial value: 117555 $

- Final value: 213780 $

- Profit/loss: 81.86 %

- Expected return: 0.23 %/day (or 58.73 % annualized)

- Expected volatility: 1.75 %/day (or 27.72 % annualized)

- Expected Value at Risk (5%): 2.87 %/day (or 45.6 % annualized)

- Expected Value at Risk (1%): 4.07 %/day (or 64.59 % annualized)

- Expected Sharpe ratio: 2.1

- Expected index beta: 0.71

I see that SWZ is not included in either the minimum risk portfolio or the maximum return portfolio. I have been considering selling the SWZ but I have just been holding off because I don't like to trade very often. This analysis has given me the courage to dump the SWZ. Now ... it would be very easy to just glance at the portfolio and see SWZ as the obvious runt of the litter - but - hey, it's a computer analysis!

I'm going to play with this some more.
Last edited by Analystic on Wed Mar 10, 2010 9:19 am, edited 2 times in total.
Disclaimer: I am making all of this up.

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Post by iqfront » Wed Mar 10, 2010 8:47 am

Analystic wrote:Thanks for sharing this tool!

I'm going to play with this some more.
Glad to hear you like it.

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Post by iqfront » Wed Mar 10, 2010 8:50 am

What kind of return would the previous “7.5% expected return” optimal ETF strategy rebalanced roughly once every month have yielded? Without taking into account transaction costs and taxes, one dollar invested in the portfolio at the beginning of 2007 would have evolved as follows:

Image

This corresponds to a return of about 6-7% per annum, depending on how the return series is interpolated.

It is important to note that we have not studied stability of the return series with respect to the time to rebalance. In particular, the portfolio returns are likely to be sensitive to whether you rebalance every 20 days or every 200 days.

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Global minimum variance portfolio

Post by iqfront » Wed Mar 10, 2010 8:52 am

We have seen that optimal portfolios are not constant over time. This is not surprising. What might be surprising, however, is that there is one particular optimal portfolio on the efficient frontier which is known to be relatively stable over time both in theory and in practice: The global minimum variance (volatility) portfolio. It is that optimal portfolio which is obtained by minimizing variance while ignoring the return estimates altogether. In our case it is the bottom-left point on the efficient frontier.

Why is the global minimum variance portfolio likely to be relatively constant over time? First of all, since the expected returns are ignored in the portfolio optimization task altogether, uncertainty regarding these estimates does not affect the optimization results. Second, volatility - of equity indexes in particular - is known to have significant autocorrelation. In other words, periods of low volatility are likely to be followed by periods of low volatility, and vice versa for periods of high volatility. It follows that an investment strategy which attempts to track the global minimum variance portfolio in a sufficiently large universe of assets is the most unlikely to ever be significantly exposed to bubbles and the subsequent crashes – i.e. sources of significant volatility.

A practical application of the above idea is the low-risk equity investment strategy described here: http://www.iqfront.com/whitepapers.html. This strategy is based on the well-known empirical observation that asset class selection - stocks in the present case - accounts for majority of the returns. This being the case, one might be better off trying to minimize risk than chasing returns. Indeed, during the testing period 2003-2009 the strategy achieved consistently lower risk than the S&P 500 index (in 2004 the volatilities were equal), with a realized average annual return of 7.6%.

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Post by metalman » Wed Mar 10, 2010 9:00 am

You mean people would pay for this junk?

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Post by iqfront » Wed Mar 10, 2010 9:04 am

duhmel1 wrote:
kcyahoo wrote:This thread does not feel right for this forum. I appreciate the effort and the potential usefulness to some in this forum. Make this a "link to" user guide.
Maybe we can have a poll, otherwise this rambling may go on and on and on
Let's make this easy for everyone: I will no longer continue posting general information on the tool, as some of you find it inappropriate for the forum.

I would like to have this thread left open for possible bug reports, though.

Thank you for your patience, I came in peace ;-). Please remember that many of my remarks apply generally, i.e. irrespective of what software or tool is used for optimizing portfolios.

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Post by Analystic » Wed Mar 10, 2010 9:12 am

OK.

Here is the fly in the ointment. I ran the analysis again using the year PRIOR to my purchase. That is what would happen if I used this tool to help me make decisions about what to buy prospectively.

Optimization results and sensitivity analysis

[Feb 23, 2008 to Feb 23, 2009]


- Current portfolio:
+5000*AOD+5000*IAF+5000*JEQ+2500*SWZ+2000*TDF

- Minimum risk portfolio:
+15288*JEQ+8097*SWZ

- Maximum return portfolio:
+10554*JEQ+10322*SWZ

- Maximum Sharpe portfolio:
+15288*JEQ+8097*SWZ

Overall portfolio characteristics

- Initial value: 243545 $

- Final value: 117555 $

- Profit/loss: -51.73 %

- Expected return: -0.29 %/day (or -73.65 % annualized)

- Expected volatility: 3.26 %/day (or 51.83 % annualized)

- Expected Value at Risk (5%): 5.37 %/day (or 85.25 % annualized)

- Expected Value at Risk (1%): 7.61 %/day (or 120.76 % annualized)

- Expected Sharpe ratio: -1.44

- Expected index beta: 0.72

Hey! SWZ is the star of the show! The program just told me it was a dog!
Last edited by Analystic on Wed Mar 10, 2010 9:48 am, edited 1 time in total.
Disclaimer: I am making all of this up.

Analystic
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Post by Analystic » Wed Mar 10, 2010 9:26 am

It looks like if I had used the tool to help me decide whether or not to purchase the portfolio I actually did that it would have advised me to to make this investment instead:

+10554*JEQ+10322*SWZ

with these results instead:

Overall portfolio characteristics


- Initial value: 126408.72 $

- Final value: 179695.84 $

- Profit/loss: 42.15 %

- Expected return: 0.13 %/day (or 33.96 % annualized)

- Expected volatility: 1.52 %/day (or 24.14 % annualized)

- Expected Value at Risk (5%): 2.5 %/day (or 39.71 % annualized)

- Expected Value at Risk (1%): 3.54 %/day (or 56.24 % annualized)

- Expected Sharpe ratio: 1.41

- Expected index beta: 0.8
Last edited by Analystic on Wed Mar 10, 2010 9:47 am, edited 1 time in total.
Disclaimer: I am making all of this up.

Analystic
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Post by Analystic » Wed Mar 10, 2010 9:29 am

My choices: Profit/loss: 81.86 %
iFront optimized: Profit/loss: 42.15 %

Ouch!!!

Not a subtle difference here.

What do you think? I will PM my email if you don't feel comfortable answering but hopefully those who don't like this thread will never come back so you should be OK and others may be interested in seeing your reply.

For the rest of you I am renting out my crystal ball portfolio selector. It has a proven 81.86% rate of return!
Disclaimer: I am making all of this up.

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RE: Online portfolio management tool

Post by codeotter » Thu Mar 11, 2010 6:31 pm

I haven't used your tool, but what do you think of http://www.portfoliomonkey.com/ ?

Analystic
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Re: RE: Online portfolio management tool

Post by Analystic » Thu Mar 11, 2010 9:30 pm

codeotter wrote:I haven't used your tool, but what do you think of http://www.portfoliomonkey.com/ ?
It looks interesting. Here's how it looks at SWZ:


Analyze:
plus-on
SWZ: $11.62
The Swiss Helvetia Fund, Inc.

Portfolio Monkey Estimate
Long-Term Short-Term
Info This chart plots SWZ’s historical return distribution against a theoretical normal (bell curve). The closer the fit, the more likely its returns can be described by its Expected Return (mean) and Volatility (standard deviation).

* Info Expected ReturnThis is Portfolio Monkey's estimate of how much SWZ is expected to return on an annualized basis over a long-term investment horizon. Learn more about how Portfolio Monkey calculates this.Expected Return: -0.6%
* Info Volatility This is how much the security is likely to deviate from the expected return. The higher the volatility, the riskier it is. Learn moreExpected Volatility: 20.1%

* → SWZ is more volatile than 53% of the securities in our database
* → SWZ has a higher return potential than 27% of the securities in our database.



The expected return is -0.6% - That doesn't look good!

But it is still better than 27% of securities in their database. - That doesn't look good either!
Disclaimer: I am making all of this up.

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Post by iqfront » Tue Mar 16, 2010 9:49 am

Analystic wrote:My choices: Profit/loss: 81.86 %
iFront optimized: Profit/loss: 42.15 %

Ouch!!!

Not a subtle difference here.

What do you think? I will PM my email if you don't feel comfortable answering but hopefully those who don't like this thread will never come back so you should be OK and others may be interested in seeing your reply.
Thanks for your example.

Having considered it for a while now, I have decided to reply in public because this is an important topic and because there is apparently room for misinterpretation of the report contents. Your example is a magnificent illustration of the old cliché: Past returns are not indicative of future returns. From the point of view of realized risk and return, 2008 was somehow the mirror image of 2009, as seen in your results.

You have used just one year of historical data for creating the return/covariance estimates, and, thus, the optimal portfolios. While this approach may be perfectly valid (depending on your overall strategy) you have implicitly accepted the fact that there is considerable variance in the optimal portfolio weights across the optimization runs. Indeed, the optimal portfolios would probably have been pretty different if you did the optimization just one month later or earlier. You could test if the end result is still the same with a rebalancing taking place once per month. I should, however, point out that in order to assess the overall profitability of a strategy based on portfolio optimization, one year of data is hardly sufficient; you should compare the performance of the two strategies (your crystal ball vs. the maximum return one) across many years.

Just to make it explicit, the correct way of interpreting the optimization results generated by the iQfront tool is this: Assuming that the past returns and covariances estimated during the reporting period are indicative of the future (up to the next point of portfolio rebalancing), the current portfolio could be improved to the points X, Y and Z. Note that the word "improved" can be interpreted in three distinct ways depending on your goal. Also note that I have personally advocated going for the minimum risk portfolio because the above assumption is best fulfilled for that particular portfolio (see the white paper link in my previous post for an illustration). If you choose to go for maximum return, be prepared to accept more model risk, because return estimates on one year of historical data are generally rather noisy.

In your case I would suggest to include a longer period of historical data to estimate the returns and covariances for portfolio optimization. If I were you I would also include "phantom" portfolio members (with coefficient zero, e.g. +0*EEM) to the initial portfolio to ensure that the universe of assets for the optimization is large enough so that none of your optimal portfolios would consist of just 1-2 assets. The less components in an optimal portfolio, the more convinced you have to be of the correctness of the risk/return estimates behind it.

Edit: Analystic - please post further questions (if any) regarding this particular problem in private.

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Post by ddb » Tue Mar 16, 2010 10:28 am

iqfront wrote:Past returns are not indicative of future returns.
I think we'll all agree with that! Of course, you contradict yourself in this next part:
Assuming that the past returns and covariances estimated during the reporting period are indicative of the future (up to the next point of portfolio rebalancing), the current portfolio could be improved to the points X, Y and Z.
Surely you see the problem with this entire project. It seems like every few months we get someone on this board looking to develop some sort of optimization platform (basically a search for the Holy Grail of increased returns and/or reduced volatility), but the same problem always exists: the output is a function of either past performance or on expectations of future performance, neither of which are likely to represent what will happen in reality.

I mean, seriously, what do you expect people to do with a tool like this?

(all of the above is rhetorical, I don't really need a response)

- DDB
"We have to encourage a return to traditional moral values. Most importantly, we have to promote general social concern, and less materialism in young people." - PB

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Post by Analystic » Tue Mar 16, 2010 8:21 pm

Without quoting iqfront's reply but assuming that I did:

This was not a theoretical purchase. That is what I did purchase on the date shown. Running the analysis one month before or after is just not part of the equation.

You suggested that one year was not a good time frame for the analysis. Since I included the actual funds, dates, and amounts purchased it would be helpful if you would go ahead and rerun the data in the manner that you feel is optimum and post the results.

I am very much in favor of using computers to beat the dealer. I'm sure there are ways to do it. Goldman Sachs is just not sharing!

Anyway ... since your program seems to be a black-box for us at this point (Data in - data out. We have no idea what is going on inside the box) we will need a little more guidance about how best to make it useful.

If utility ultimately depends on trends continuing as they have in the past .... well .... unfortunately things just don't work that way.
Disclaimer: I am making all of this up.

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