In a recent article, I used Quantext Portfolio Planner [QPP], our Monte Carlo simulator, to test how well the predicted portfolio statistics did as a forecast of performance, and contrasted this to using historical performance as a guide. This sort of test is actually fairly easy to perform. In QPP, the user specifies a period of historical data to use in driving the Monte Carlo simulation. In an historical test, you start with a specific historical period (I tend to use three years of data), run the simulation forward, and then look at how the predicted statistics fare in the next three year period. With enough tests, you can start to nail down how the model performs. In the article above, I looked at a series of stocks over about thirty years. The results, easily checked by any user of the software, showed that the forward-looking Monte Carlo results were a far better prediction of portfolio risk and return than using historical performance.
This kind of testing is one important way for users of a quantitative portfolio tool to build confidence. To be honest, I am a little baffled that other providers of Monte Carlo and related asset allocation tools do not make this kind of analysis available to users. Monte Carlo is not a silver bullet, but it can substantially improve estimates of portfolio risk and return which will then enable better decisions---if the underlying analytics are solid.
As a follow up to the previous article, I decided to analyze another portfolio of stocks over an historical period, with a focus on dividend-yielding stocks. As the portfolio components, I chose an arbitrary selection of twenty stocks from S&P’s list of Dividend Aristocrats. The S&P Dividend Aristocrats (pdf file) are companies that have raised dividends every year for the past twenty five years, as well as being members of the S&P Composite 1500 index. These are not the highest yielding companies, but rather those that have a consistent history of raising dividends. I chose twenty stocks from this list and created a portfolio that is equally allocated between them (below).
This portfolio was taken from the top of the list of Dividend Aristocrats when they are sorted alphabetically---it really is arbitrary in terms of the companies, their sectors, and their past performance. The Dividend Aristocrats, as a group, have massively out-performed the S&P500 since 1990. The question, of course, is whether there was some way to know that these stocks would perform well prior to this out-performance. It is all well and good to look backwards and wish we had invested more in these companies, but it is not useful. I wanted to use QPP to generate predictions of performance in an historical period, and then see how these predictions fared.
To analyze what kind of forward-looking information could be derived from the historical performance of these stocks, I used QPP to generate outlooks for a series of three-year periods since 1990, up to the end of February 2007:
In the results above, for example, the period from 3/1/1992-2/28/1995 was used to drive the Monte Carlo to generate predictions for the subsequent three-year period (3/1/1995-2/28/1998). For the first three-year period, our portfolio generated annualized return of 12.7% per year. The Monte Carlo simulation, using only these years as input, predicted that the future expected annual return for this portfolio was 17.4%--and this is what is labeled Predicted above. The Monte Carlo simulation is not predicting for a specific window in time, but rather is saying that this portfolio will average 17.4%, for some unspecified period of time starting from 3/1/1995. As it happened, the average return over this next three year period (3/1/1995-2/28/1998) was very high, with annualized total returns of 35%. This was, of course, a boom period for the market as a whole, with the S&P500 having annualized returns of 26% before dividends. I have found in my historical tests that when the Monte Carlo simulation tells you that the expected future return on a portfolio is substantially higher than the trailing performance, this is a good indicator for the portfolio. QPP did not predict that the S&P500 would shoot up the way that it did during the 1995-1998 period, but it did indicate that this portfolio was expected to generate much higher returns than it had in the previous three years. This would have been a good indicator that this portfolio was worth riding for a while.
Now, let’s flip forward three years. On 2/28/1998, this portfolio had a trailing three-year annualized return of 35%. The market was in a state of boundless optimism. At that time, and just using the trailing three-year period, QPP predicted a future expected annualized return of 14.6%, less than half of what this portfolio has generated in trailing three years. Now, 14.6% is a high annual return, but the broader message is that QPP was saying that this portfolio had been vastly out-performing the expected annual return that could be rationally justified on the basis of portfolio risk. Over the next three years, our portfolio generated annualized returns of 9.5%, which beat the S&P500 but was still, as the model predicted, far below the recent performance. The Monte Carlo simulation generates expected future annualized return, not a ‘forecast’ for the next few years. When the simulation shows that the expected future annualized return is far below recent history, it is a good idea to be concerned.
Standing on 2/28/2001, you have generated 9.5% per year (annualized) for the most recent three years, but this would not have been a welcome outcome if you had been hoping for something like the 35% per year that this portfolio generated in the three years before that! This is a key point: if you are planning for a certain level of return and get much less, you are quite likely to have to change your plans. Having just gone through three years with 9.5% per year, what do you think about the future? On 2/28/2001, QPP projects an expected annual return of 14.9% going forward. This is more like it! QPP is showing that the 9.5% over the most recent three years was simply part of market swings and that the forward-looking expected performance is considerably higher. This means that the portfolio has under-performed its expected level of performance and the simulation is saying that is it likely that the portfolio will ‘revert to the mean.’ The portfolio actually generated 12.1% per year over the next three years (3/1/2001-2/28/2004). Looking forward from 2/28/2004, QPP’s simulation generated an expected future annual return for the portfolio of 10.8%, and the portfolio subsequently generated 12% (on average) over this period. The QPP forecast of 10.8% per year after a period when the S&P500 had returned only 1% annualized over the past three years (before dividends) is a fairly aggressive forecast that bore out, but this is really more about the fact that QPP is predicting based on expectations (i.e. long-term averages).
These last two periods are about as close an agreement between an expected performance and observed performance as you will ever expect to see. Remember, QPP is predicting averages over an un-specified future and we are comparing observed performance over a specific three-year period. This is analogous to predicting the height of a random person in your office when you know only the average height of all of these people. If you predict for enough people, you will do okay. For an individual person, you can be substantially in error. The same is true for Monte Carlo simulation.
Let’s consider a measure of how accurate the QPP expected return is as a forecast vs. using the previous three years. The Mean Average Error [MAE] in annualized return using the QPP-generated average return as our prediction over this period is 6.7%. If we use the trailing three years as our prediction, the MAE is 12.6%. For a detailed description of using this statistic, see this article (the same one linked earlier). The MAE is a good measure of the average error in annualized return that we can expect from the predicted value. I found that using QPP’s estimates for expected return as our prediction, we have an error in annualized returns over the next three years that is half what you get if you use the trailing three years as your guidance (which is a remarkably similar result to two other studies on totally different portfolios). Unfortunately, many people do choose their investments using trailing performance as their guide—and they pay a high price, with estimates that this behavior costs individual investors at least 2% per year, and often more. Using a forward-looking estimate from QPP provides a far more realistic outlook on future performance—and will lead to better decisions.
When we used three years of data through 2/28/1995 to drive the simulation, and QPP predicted an average annual return of 17.4%, that prediction is the model estimate for a long-term forecast. If we look at the entire subsequent period (3/1/1995-2/28/2007) the actual annualized return is 17.2%. If we benchmark QPP’s outlooks in this way—using the QPP expected future return as a forecast for the entire period from the day immediately after the three years used to drive QPP through 2/28/2007, the MAE of the outcomes are dramatically better—with MAE of 1.92%. This is a small sample, so I am not advocating putting a lot of weight on this but it is a nice qualitative demonstration of the QPP outlooks—we expect the actual average return to get closer to the forecasts with longer periods of time.
Now, let’s examine an issue of immediate interest. Going forward from 2/28/07, QPP is projecting an average annual return for this portfolio of 16.3% (shown in the table above). QPP is also projecting annualized standard deviation in return of 13.7%, much higher than the trailing three year standard deviation (5.5%). This is a high projected average annual return, as well as a fairly high volatility, albeit lower volatility than QPP is projecting forward for the S&P500 (15%). This outlook bodes well for this portfolio—and, more broadly, for this kind of strategy. This portfolio, with a trailing dividend yield of about 2.5%, has some very nice features. QPP calculates a current diversification metric of 66%, which is on the high end of what you typically see for an all-stock portfolio.
If you wanted to take this sample portfolio further—and actually consider this kind of strategy—you would want to narrow the list of Dividend Aristocrats by looking for companies that you actually want to own—I do not advocate a purchasing any company’s stock without knowing enough to want to own it. There are a couple of firms in the broader list of Dividend Aristocrats that I already own (JNJ, BAC) and you will find quite a number in Berkshire Hathaway’s main equity holdings — including Coke (KO), Anheuser Busch (BUD), Johnson and Johnson (JNJ), Procter and Gamble (PG), Bank of America (BAC), Wal Mart (WMT), and others. Once you have selected the companies that you like, generating an historical test of the projected performance vs. observed performance such as I have demonstrated here is also a good idea if there is enough data history. This provides stress tests of a portfolio in various market conditions.
Note: all runs of QPP used in this article used the default settings.
