Geoff,

 I presume one must still come up with expected returns as well as correlations for each asset or asset class modeled. How exactly is this done?

 Steve

Steve and Chinwhisker:

You guys are getting ahead of me.  I want to lay out the uses of Monte Carlo in a fairly systematic way, but I will briefly address your points.  First, Monte Carlo is most useful when it is self-parameterizing, which means that it automatically generates forward-looking statistical parameters for expected return, risk, and correlations.  In the Ben Stein thread, we debated some issues around this--but this is a key feature.  QPP is self-parameterizing although users can adjust these parameters if they do not agree. 

We will eventually get down to the detailed issues of portfolio construction that Chin has raised, but I am inclined to start from the start...see the next post.

Steve and Chin: if you guys really want to jump ahead, you may want to start here:

Projecting Portfolio Risk and Return

Geoff

Monte Carlo methods have largely come to the awareness of individual investors and advisors as tools to estimate portfolio survival rates for income draws in retirement or to estimate the amounts of wealth that can be generated with a certain level of confidence.  A well-known specific application is by Bill Bernstein in his famous series of three articles article called The Retirement Calculator from Hell. (this is part III but it has links to I and II).  In these articles, Dr. Bernstein introduced a lot of investors to the curse of volatility and how it makes it even harder to fund retirement.  This type of analysis led to the now-famous "4% solution" which suggested that investors could safely draw 4% of their portfolio value in the first year of retirement, and then scale that amount with inflation in each future year and have a high confidence of funding a 30-year retirement. 

The 4% solution has entered the folklore of financial planning, even though it is based on some ridiculous simplifications.  I discussed these and how the dafe draw rate was related to these assumptions in this article called Beyond the 4% Solution.  The point of this article is that the safe draw rate is a function of how well the portfolio is built.  Mr. Bernstein and many other authors assumed a simple 60/40 portfolio (60% S&P500 and 40% bonds).  They mad reasonable assumptions about the expected returns on these two investments and left it at that.  The reality is that we can and should do better.  A portfolio with REIT's and commodities etc. will be better diversified than the old 60/40 and therefore can provide higher returns relative to risk, etc. 

The fundamental point is that your safe withdrawal rate depends on your specific portfolio--and this can be modeled.  FinancialEngines.com tried to solve this problem for investors, running Monte Carlo (MC) for actual portfolios of mutual funds using Style Analysis.  Style Analysis can work well for all-fund portfolios but does not do well for individual stocks or for asset classes that exist well outside the list of asset classes treated in the model.  For a review of Style Analysis by Dr. Bill Sharpe, this is a good one. 

I set out to build QPP because of the limitations of Style Analysis and because MC analysis on purely historical data does not generate good asset allocations.  If you are not aware of this, have a look at Bill Bernstein's classic The Intelligent Asset Allocator.  In this book, he makes it very clear how and why asset allocations based on historical data are a bad idea--you simply end up over-weight the assets that have out-performed in the historical period you use.  Frankly, classical mean-variance analysis and building the 'efficient frontier' is easy analytically.  The hard part is parameterizing the models.

Meanwhile, as investors were grasping the impacts of risk on their safe income draws, the financial industry was spending a lot of time on Monte Carlo applications for portfolio analysis.  This is the branch of study from which we get quotes like that of David Swensen at the start of this thread.  Institutional fund managers were looking for tools to do measure the forward-going risk and return of portfolios.  Modern applications of portfolio modeling for institutional investors are quite mature these days and perhaps the inconic provider is RiskMetrics--you can find some great technical articles on their site.  The point of efforts like this was to use quantitative tools to measure and set risk constraints and also to find ways to better tune a portfolio.  These models are what are referred to as forward-looking models--not as in a crystal ball--but rather that they combined market data with financial models to make estimates of future performance rather than just looking at trailing performance. 

For wealth manager and investors today, I think the ideal application is to combine the two efforts listed above--and this is what I focus on in my work. 

This all may sound pretty esoteric but this is standard stuff for institutional investors and, remarkably, many of the models agree pretty well.

For individual investors and wealth managers, there are three related questions:

1) figuring out the right risk level

2) figuring out the portfolio that gives the most return for that risk

3) matching savings plans to projected income levels

RiskMetrics, mentioned earlier has a very high end Monte Carlo tool called WealthBench for very wealthy investors.  If you poke around on their site, you will find some interesting stuff that agrees in the main with these points. 

One of my pet peeves in the financial analytics world is companies that put out tools without providing much (or any) validation that these tools are any good.  Sadly, this is often the case.  I have written an article on a set of standards that are reasonable.  This is especially relevent in the wake of the Pension Protection Act of 2006, which encourages the use of computer models.

First, and perhaps most obvious, a model that is supposed to incorporate volatility into portfolio planning should be benchmarked with respect to its projected volatility.  A standard approach in the pfofessional world is to compare projected Monte Carlo model volatility to the 'implied volatility' in options prices.  This is discussed in the article linked above and QPP has been benchmarked in this way. 

Out of sample tests of portfolio projections for a range of portfolios and market conditions are also obvious and necessary:

Projecting Portfolio Risk and Return

The lack benchmarking and documentation for some of the Monte Carlo models that are proposed for portfolio planning is worrisome to me. 

Hi Geoff,

Just wanted to chime in and say Thanks for posting this.  Your efforts are appreciated.  I am probably not knowledgable enough to contribute to the converstation other than to extend my gratitude.

I look forward to reading some of the links you provided as well as the thread as it progresses, but for now, I must remove the toothpicks from my eyelids and hit the sack!

Lurking and learning.

Thanks a $M

Brian

Here is the problem that I have with Monte Carlo simulations and specifically QPP.  The MCS is only as good as the input; GIGO.  In all cases the primary input is historical data – returns, volatility and correlations.  You distinguish between short-term and long-term historical data, but it is historical data nonetheless.  It is easy to say that historical data is all that we have, so we must go with it, but that is not the way to evaluate risk.  Perhaps QPP is better than all the alternatives using historical data, but that is merely a consideration of relative value. 

The danger of following this approach is illustrated in the Supercharge book.  The suggestion is that it is possible to establish a portfolio using stocks rather than bonds that is equally conservative.  Statistically this can be done, but it requires assumptions based on historical data involving equity returns, volatility and correlations that may prove substantially wrong in the future.  On the other hand, there is a much greater certainty regarding the future performance of bonds.

Consider the writings of Mandelbrot and Taleb, the history of outliers, and occurrences such as LTCM and Japan. 

Heath:

The points you raise were originally a little further down my list of topics, but your raising them moves them up the list.

I have written two articles that specifically address these issues in the same context that you use (Black Swans, LTCM, etc)--here is an overview article:

Black Swans, Portfolio Theory, and Market Timing

Forward-Looking models use history but are predicting that the future is just like the past.  You must read some of the validation and testing docs to understand this in depth--but the article above covers the high points.  QPP captured the risks of the decline of financials, the potential for a volatility shock, and a number of other key issues just in 2007.  QPP's tail risks also map well to Moody's market-driven default risk calcs and to their KMV model, which is very good.

Now, the Taleb enthusiasts always point to LTCM as an example of the failure of models.  This is incorrect--it was a failure of one model in particular.  LTCM used their models to make massive leveraged bets that the correlations between certain bonds would mean revert.  These bonds were highly illiquid.  If the bonds did not mean revert, they got hammered.  They got hammered.  This is not what I or David Swensen or the majority of rational people use portfolio models for--this is discussed in the article above, along with other cases. 

It is true that portfolio models do not predict world wars, famines, or market collapse at all.  They do capture the long term statistics reasonably well.  If you are highly leveraged (subject to margin), etc. and are going to be destroyed if you get a margin call, QPP and tools like it are not for you.

I am not suggesting that anyone simply start using models because I say so--people need to do their own due diligence to make sure that the models are decent and meet their needs. 

As to bonds--you are correct that something with less uncertainty is more predictable than something with less uncertainty (stocks).  History suggests that investors must assume uncertainty if they want higher returns than bonds can provide, however, so it behooves us to look for better tools. 

MC tools are NOT a crystal ball--they are designed to provide rational measures of risk and return to help in the process.  QPP provides a paradign that is generally consistent with a body of other research.  If QPP estimated that it was easy to beat Swensen's projections of risk and return for the Yale portfolio, I would be concerned.  If QPP did not like Buffett's portfolio, I would be similarly concerned.  etc.

Without a portfolio tool, investors cannot 'see' their total portfolios very well.  It is very hard to 'feel' or 'intuit' portfolio effects on a forward going basis.  The market does provide information and QPP processes that information and presents it with a consistent forward view.  Why do you think people like David Swensen rely on these tools?

You are of course correct that the world might change so substantially that all that we know about risk and return and correlation totally breaks down--total Black Swan meltdown.  It is equally likely (probably more likely) that we will see rampant double digit inflation---and then bonds are very risky because of their decline in purchasing power.

There are a number of people who specifically like this issue who always comment on my articles on SeekingAlpha. com--if you are interested in more on this.  My article linked here provides some of that context, too.

Regards,

Geoff

“As to bonds--you are correct that something with less uncertainty is more predictable than something with less uncertainty (stocks).  History suggests that investors must assume uncertainty if they want higher returns than bonds can provide, however, so it behooves us to look for better tools.”

Let’s assume that your model is the best possible model for predicting equity performance, so maybe my point is better directed at Phil DeMuth.  I have a problem with the analysis found in Supercharge where the relative risks of a portfolio containing both short-term fixed instruments and equities are measured against a portfolio of all equities.  As I understand it, the book purports to demonstrate that the risk can be equalized, but with greater rewards to the latter.  The analysis assumes that the certainty of the equity returns is the same as the certainty of the fixed returns.  I think you agree that that assumption is erroneous.

"The analysis assumes that the certainty of the equity returns is the same as the certainty of the fixed returns.  I think you agree that that assumption is erroneous."

The assumption you state (above) is erroneous but neither Phil and Ben nor QPP would have ever suggested such a thing.  The certainty of returns is reflected in the projected volatility (i.e. standard deviation in annual returns).  Phil and Ben and QPP do suggest that bonds can be a 'blunt instrument' for risk management.  Rob Arnott shares this perspective, by the way.  The point is that bonds diminish risk by s