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 January 2009 Together We Fall Regardless of the Model, Correlations Converge in Down Markets
Quant models (and actively managed portfolios, for that matter) should ideally successfully switch back and forth between extremes to protect cumulative value. Conceptually, that's not a difficult idea, but it becomes much more so when one tries to translate it into the "real world". Most models tend to be more successful in one type of market or the other, but not necessarily both. There's one other thing to factor in, too -- the fact that all markets (and investments) tend to converge when markets fall. That's not to say any 50-point drop on the Dow automatically drags down gold, or bonds, or even small cap stocks. But correlations do tend to converge when there's a definite bear market such as the one that's now occurring. When even the most diversified portfolio suffers across the board, it's even more difficult for a single asset class-driven equity model to succeed.
That's precisely the environment our quant models are currently encountering. What we wanted to examine was how much the market itself affected them. This is actually the second bear market for Portfolios 3 and 4 as both were launched in mid-2000, just on the eve of the Tech blowup. They certainly joined all other equities during the ensuing decline, and haven't missed much of the 2008 decline, either. The question is: Did correlations rise as the market fell or are did they remain roughly the same? In general P3 and P4 have followed market trends throughout their out-of-sample lifetimes, but do correlations grow in down markets and decline when stocks head up? (For the record, Portfolios 5 and 6 are also quant models, but they didn't go out of sample until 2004. We didn't include them because they lacked the same the depth of data.)
What the Record Shows Correlation is a measure of how two different series -- in this case the models and the benchmark -- move relative to one another. Perfect positive correlation would have them moving in the same direction, either up or down, at the same time in the exact same magnitude. That's the goal of index funds.
Correlation is measured on a scale of -1 to +1, the latter being perfect positive correlation. Perfect negative correlation (-1) means the two series move in opposite directions with the same magnitude. This is the goal of so-called "inverse" funds that allow investors to profit when markets fall. The series and the benchmark can be positively correlated without moving to the exact same extent. That's the goal of the quant models. Hopefully they'll go up when the market does, but to a higher degree. They'll probably fall when the market declines, but hopefully to a lesser degree. Such behavior would still be a positive correlation (they're headed in the same general direction), just less than perfect. If this is the case, correlations would be somewhere between 0 and +1. That's precisely what we found. Looking over the entire out-of-sample period (July 1, 2000 through November 2008), correlation for P3 and the S&P 500 is 0.8420 while P4 and the S&P 500 is even higher, 0.9306. So far, so good. But what happens when market conditions change? Correlations aren't stagnant, they can change, too. You'd want them to be high when the market is going up, but lower when the market is going down. Unfortunately, that's not what we found for P3 and P4. You can't just look at one point to calculate a correlation -- it has to come from a number of observations, it has to be a series. There's no right or wrong time period to measure, but we decided to use 125-days which is roughly one-half year as measured in trading days. We created a new series for both the models and the benchmark based on 125-day rolling periods. The first was trading days 1-125, the next was days 2-126, then 3-127, etc, until we moved though the entire 101 month period. The results are graphed in Charts 1 and 2.
In both Charts, the model returns are measured on the left scale, and correlation on the right. The blue line represents the quant model returns, the green the index returns, and the red the correlation between the two, and is measured in the right scale. You've probably already realized, but it bears saying anyway: The correlation line doesn't begin until 125 days into the observation period because this defines the first rolling period. This results in a slight lag between the returns (which are running ahead) and the correlations (which are running behind). We didn't adjust the charts for this, yet the results are still fairly obvious. In both cases, as returns fell into 2002, correlations increased. As returns neared their bottom and the pace of declines increased in mid-2002, correlations rose at an increasing rate and peaked along with he market decline (remember the slight lag for correlations). This is especially evident on Chart 1. When the market again turned upward, from 2003 through 2007, correlations declined and held relatively steady until the market again turned in 2007. As the declines increased in 2008, the correlations again spiked up. This pattern is clearly visible in both charts. In this case, the old saw about correlations converging in a downdraft seems to hold true. For P3 and P4, correlations definitely are stronger with the benchmark when it's heading down.
Is it Just the Quant Models? Charts 3 and 4 show the results. P1 appears on Chart 3 and being a large cap model, it is also compared to the S&P 500. P2 is a small cap model, so is compared to its benchmark, the Russell 2000, on Chart 4. As before, returns are measured on the left scale and correlations on the right. The blue line is the benchmark, the green the model, and the red their 125-day correlation. In both cases, the results are quite similar to those for P3 and P4. Again correlations rise and peak with market declines, then fall off when the market rises only to rise again when the market sells off in 2008. Notice that both the returns and correlations are much more volatile for P2, the small cap model. This is exactly what you'd expect. Chart 5 summarizes the results for each of the models on an annual basis. (As noted on the chart, the 2000 values are for the final six months of the year while the 2008 are for the first eleven months.)
The same patterns are again evident. Correlations for all series peak in both 2002 and 2008, just as markets are falling to their lowest levels. (That last statement is somewhat hopeful regarding 2008.) Correlations decline during the middle of the period when the market is climbing. It's also interesting to notice how the relative correlations remain roughly the same whether rising or falling. In other words, the order for any given year in declining order of strength is P4, P1, P3, and P2. This suggests (but certainly doesn't prove) that all four of the models have a "normal" correlation with their benchmark (possibly around their total period correlation) and it's then adjusted to roughly the same degree for all by changing market conditions. That would further suggest, this phenomenon is not affected by the models' selection process or style. The fact that P2, the small cap model, also displays the same correlation pattern as the large cap models indicates that at least in this case diversification across capitalizations offers no protection in a declining market. That's precisely the time when one would hope for the benefits of diversification, yet here that's undermined by converging correlations regardless of capitalization.
Do Style, Capitalization, and Selection Methodology Matter at All? For instance, the relatively consistent levels of correlation indicate that the correlation with the S&P 500 will always tend to be higher for P4 than P3. This was the case for every year in the observation period. In constructing a portfolio, one would choose P4 for greater overall correlation with the benchmark and P3 for lesser. In most instances lesser correlations would be preferred in a declining market which would favor P3 over P4. But the choice isn't so clear in up markets. While higher correlations will stick closer to the rising market, lower correlations may actually have the opportunity to outperform. On the other hand, lower correlation models may also be prone to fall behind. This is often the case for many mutual funds in rising markets. Regardless, the choice of a higher or lower correlation model will still have a long-term impact on overall performance. In addition, diversification across capitalizations isn't totally meaningless, either. Although correlations increase for all four of our models in falling markets, small cap P2 is always the lowest. Even in the worst years with the highest market correlations (2002 and 2008 on Chart 5), P2 is typically the lowest. In these cases, including P2 with a large cap model (or models) may help limit losses. This, of course, is based on the critical assumption that the small cap and large cap benchmarks decline at roughly the same rates. The benefit of diversification could be significantly reduced if the Russell 2000 falls at a higher pace than the S&P 500. In actual portfolio construction, this is something that should be monitored, particularly in down markets. Obviously looking at four of our model portfolios can't conclusively prove anything regarding overall correlations in either up or down markets. However it strongly suggests that these four models experience higher correlations with their respective benchmarks in declining markets. This, along with their relative correlations, can be helpful when using them to construct portfolios although they don't seem to offer greater downside protection than the market benchmarks themselves. This, unfortunately, is probably true for most portfolios. Search this site! Just enter you key word or words: Get current quotes or follow your own custom portfolio,
courtesy of E-Line Financials:
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T'S LOTS EASIER TO FIND investments that will meet objectives under certain specific conditions than to find ones that work well under all conditions. For example, it's not too hard to find high beta stocks that will do well in raging bull markets, or defensive stocks that will hold up well when the bear comes around. But it's considerably more difficult to find shares that outperform in both circumstances.
