January 2003
More Than Just Return
| "Appearances often are deceiving." |
| -- Aesop The Wolf in Sheep's Clothing |
VER SINCE WE LAUNCHED OUR quant portfolios (P3 and P4) in mid-2000, we've been monitoring their performance on a regular basis here at the Work in Progress page. Previous pages are all accessible in the Archives.
Up until now, most analysis has focused on return and correlation with benchmarks, but there are actually many other measures that are equally if not more important. Sure, return is what you ultimately take to the bank or spend at the grocery store, but it alone doesn't tell the whole story.
Why? Well consider this: If a model portfolio closely follows a benchmark that's down, it will be, too. That's what's happened to our quant portfolios that had the misfortune of being launched at the beginning of a bear market (see Realistic Expectations). Despite the absolute return, the close correlation may actually be a positive, not a negative.
Risk also plays an important role. If a model portfolio's return falls below that of its benchmark, it may also have an
lower level of risk. If so, that's not necessarily a negative, it's just a difference. Risk-adjusted return is the appropriate concept here.
With this in mind, let's take another look, not only at our quant portfolios (P3 and P4), but our bottom-up value portfolios (P1 and P2) as well.
We aren't considering our newest quant portfolio, P5, not because these concepts don't apply to it, but rather because it's too early to have any really meaningful data. While we backtested it from the early '90s (see Think Inside the Box), we didn't begin measuring its actual performance until January 2002. As time passes and more data becomes available, we'll revisit P5.
Portfolio 1:
The Long and Short of It
Portfolio 1 has the longest track record dating back to 1991. This is a large cap bottom-up value model. Like all of our portfolios, it's always fully invested in equities, regardless of market conditions.
As with the other portfolios, you can find P1's year-to-date performance on the Historical Performance page and its annual and quarterly performance Graphs. One thing we haven't considered is its performance over its entire history. While P1's struggled recently (what all-equity portfolio hasn't?), the longer history tells a better tale.
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Chart 1 P1 Performance from Inception June 30, 1991 - October 31, 2002 |
 Source: Ibbotson Associates/Quantview |
Chart 1 shows P1's cumulative performance from its inception. Over the entire period -- including this past year -- the portfolio is still ahead of it's primary benchmark, the S&P 500 as well as the S&P 500 Value Index, a measure of large cap value stocks. A long-term outlook has a way of making many things look better.
Long-term statistics do, too. Table 1 shows the arithmetic mean, standard deviation, and Sharpe ratio for P1 and its benchmarks over the 136 months from July 1991 to October 2002.
We used the arithmetic rather than the geometric mean since the former gives a better sense of what return you can expect in any given year. Over the total period, P1's average was about 3% better than that of its benchmarks.
To achieve that return, P1 took on additional risk. Standard deviation is a measure of risk, gauging the average divergence from the mean. Over the 136-month period, P1's standard deviation was just a little over 10% greater than the S&P 500 and the S&P 500 Value Index.
Risk, in and of itself, isn't necessarily a bad thing if it's rewarded with a more than equal amount of return. In other words, if you assume a greater amount of risk, you should expect an even greater amount of return.
| Table 1 Portfolio and Benchmark Statistics | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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The Sharpe ratio is a way to measure risk-adjusted return. As it's name implies, it's a simple ratio that compares excess return to risk. Excess return is calculated by subtracting the "risk-free rate" from a portfolio's actual return. The risk-free rate is what you would expect to earn by taking on little, if any risk. It's usually represented by the short-term Treasury Bill. Risk is measured by standard deviation.
In general, the greater the Sharpe ratio, the more "efficient" the portfolio from a risk/return standpoint. Like other ratios, the Sharpe ratio is most informative when compared that of a specific benchmark. When returns are negative -- as they have been for the past three years or so -- Sharpe ratios will be negative, too. The most best will be those closest to zero.
As you can see from Table 1, P1, the S&P 500, and the S&P 500 Value Index all had positive Sharpe ratios over the past 136 months. P1 trailed both benchmarks indicating that although it had a greater average return, it was still not as high as would be expected for the additional risk exposure.
You can see this rather clearly in Chart 2. Here all three are plotted with risk (standard deviation) on the horizontal axis and return on the vertical axis. P1 is represented by the red square while the S&P 500 is the pink circle roughly in the middle of the chart.
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Chart 2 P1 Risk and Return June 30, 1991 - October 31, 2002 |
 Source: Ibbotson Associates/Quantview |
P1 lies above the S&P 500 because of its higher average return. It also lies to the right because of its increased risk.
The dashed line in Chart 2 represents what's known in Modern Portfolio Theory as the Capital Market Line (CML). It's created by drawing a line from the risk-free rate through the diversified market portfolio, in this case the S&P 500. Simplifying this for our purpose here, any portfolio lying above the line is more efficient than the S&P 500 and any falling below is less efficient. The CML is, therefore, a simple graphical way to gauge portfolio efficiency.
As the Sharpe ratio suggested, P1 falls below the CML since it fails to provide sufficient additional return to compensate for its additional risk. Just eyeballing Chart 2, it would seem P1 would have needed to average around 16% or more for its given level of risk.
But there's one other thing to notice from Chart 2: Even though P1 lies below the CML it isn't far from it. Despite its struggles in the past 12 months, P1 is only slightly less efficient than its benchmarks, the S&P 500 and the S&P 500 Value Index. Indeed, as Chart 1 suggests, P1 has better relative performance in an up market, so it may not take a tremendous rally to get it back to the CML.
In this case, if you look past simple return -- especially short-term return -- the statistics clearly show P1 is working about as well as you can hope.
Portfolio 2:
In Search of a Benchmark
Portfolio 2 was created at the launch of this Website back in July of 1997. It was initially designed to complement P1 by holding small cap value stocks as opposed to P1's large caps. Like the older portfolio, P2 uses a bottom up approach.
As often happens with stocks, things quickly changed. Large cap Lowes bought P2's small cap, Eagle Hardware, Mega-cap Intel gobbled up Xircom, etc. We let our winners run, but at the same time, we no longer had a small cap portfolio.
After six trades in mid-November 2002 (see Historical Performance), P2 is now back to its small cap roots. That, of course, doesn't change the fact that it had previously been a "multi-cap" portfolio for the majority of its short life.
It also doesn't make it any easier to find an appropriate benchmark. Had it remained small cap, the S&P 600 or Russell 2000 would be good fits. We often compare it to the Nasdaq since that index is also multi-cap, yet that's not quite right, either, since the Nasdaq is so skewed towards technology. The S&P 1500 Super Composite is multicap, but it's capitalization weighted with an almost 90% large cap focus. Wilshire offers a number of broad market indexes, but all of our other benchmarks are S&P.
For consistency's sake, we finally decided to measure P2 against the originally intended benchmarks: the S&P 600 and the S&P 600 Small Value Index. Chart 3 shows cumulative return for all three for the period July 2000 - October 2002.
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Chart 3 P2 Performance vs. Small Cap Benchmarks June 30, 2000 - October 31, 2002 |
 Source: Ibbotson Associates/Quantview |
We should point out that Chart 3 doesn't cover P2 from its inception in July 1997 due to the fact that we originally only kept bi-monthly data for posting purposes. It wasn't until the creation of our first two quantitative portfolios (P3 and P4) in July 2000 that we started keeping daily figures.
Over the 28 months for which we have data, a $100 dollar investment in P2 would have shrunken to $75. Keep in mind this measurement period is essentially a bear market.
Over the same time frame, small cap stocks posted a mild loss while small cap value stocks were actually in the black. P2 doesn't look too good relative to the return on the small cap indexes.
It also doesn't stack up too well in regard to risk. Look back at Table 1 and you'll see that P2's risk, as measured by standard deviation, was almost 50% greater than that of the S&P 600 while less so relative to the S&P 600 Value Index.
This is easy to see on Chart 4 where P2 falls well to the right of both small cap benchmarks. It's return is also well below the indexes, not the results you'd hope to see.
Then again, P2 really wasn't a small cap portfolio throughout the time in question so perhaps it's appropriate to look at a broader context.
Consider this: For the 28 months from July 2000 to October 2002, P2, while in the red, still had the best return (least loss) of all of our portfolios. It's arithmetic mean of -10.44% was well ahead that of the S&P 500 (-16.57%) as well. It's Sharpe Ratio of -0.0909 was well ahead of the S&P 500's (-2.746) as well. Given this, it's not surprising P2 plots above the period's CML as shown on Chart 4.
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Chart 4 P2 Risk and Return June 30, 2000 - October 31, 2002 |
 Source: Ibbotson Associates/Quantview |
But just as it isn't entirely appropriate to compare P2 to the small cap indexes, it's equally misleading to rely solely on its relation to the S&P 500. Nevertheless, we would suggest that P2 falls right about where it should in Chart 4.
Here's why: From July 2000 - October 2002, small caps handily outperformed large caps. Just prior to that, stocks of big companies were highly overvalued and when their correction began in 2000, small company stocks held up much better. Chart 4 bears this out. Yet P2 wasn't either large cap or small cap, it was somewhere in between. That's precisely where it lands in Chart 4.
P2's eclectic nature has made it not only hard to classify, but difficult to measure as well. This analysis is definitely the least satisfying of all four portfolios, not because of P2's performance, but because of the lack of a clear benchmark. Statistics don't lie but in this case, they're only as accurate as the benchmarks are appropriate.
Portfolio 3:
Maybe Not What It Seems
You often hear pundits say, "It's a stockpicker's market." Presumably what they mean is no one sector or capitalization is going to outperform so you need to carefully select stocks from across the broad market that are uniquely positioned to do well. This is often referred to as a "bottom up" approach.
Portfolio 3 is a quantitative bottom up portfolio since its regression was based on the performance of the entire S&P 500 without regard to size or sector. The model attempts to isolate those fundamental features that led to the best performance in the sample period.
The "sample period" is a key concept here, since it was essentially the decade of the 1990s when growth handily defeated value. Throughout its short history, P3 has always been heavily skewed toward growth -- precisely right when growth fell out of favor.
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Chart 5 P3 & P4 From Inception June 30, 2000 - October 31, 2002 |
 Source: Ibbotson Associates/Quantview |
So how bad has it been? Just take a look at Chart 5 -- P3 is the blue line at the bottom. One hundred dollars invested in this portfolio back in July of 2000 would be worth $30 on October 31, 2002. As Table 1 shows, it's averaged an annual loss of over 35%.
Just looking at the returns, P3 would seem like a lost cause. But consider Chart 6, risk and return. Once again over the measurement period, the CML is downward sloping due to the S&P 500's negative returns. P3 is riskier than the S&P 500 and the S&P 500 Growth Index since it falls to the right them. P3's return is also less than that of the indexes.
But look where it falls in proximity to the CML -- it's virtually on it. This is a positive and meaningful factor when the measurement period is put into context.
July 2000 through October 2002 covers a severe bear market, that's why the CML aims downward. In this environment, you aren't rewarded for taking on more risk, you're penalized. As Chart 6 and the standard deviations in Table 1 attest, P3 did just that. Nevertheless, P3 is more efficient than the S&P 500 Growth Index.
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Chart 6 P3 and P4 Risk and Return June 30, 2000 - October 31, 2002 |
 Source: Ibbotson Associates/Quantview |
That's right, it's more efficient. You can see this from Chart 6 because it's closer to the CML than the Growth Index. You can see this from Table 1 because P3's Sharpe ratio (-0.3072) is greater than the Growth Index's (-0.3535).
What this also means is that in an up market -- something P3 has never experienced in its short life -- P3 should provide a higher return than the S&P 500 Growth Index. "Should" is the operative word here since this is based on the assumption that the Sharpe ratios of the series won't change.
Regardless, P3 is a good example why there's more to portfolio measurement than just return.
Portfolio 4:
Down but Up
Unlike P3, Portfolio 4 is sector weighted. Also unlike P3, it's only rebalanced once a year in mid-June. As a result, it's
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Like P3, P4 has a growth orientation so its return, in absolute terms, has suffered from inception. On the other hand, what growth stock -- or any all-equity portfolio -- hasn't suffered a similar fate?
Anyway, the point is if you just look at P4's absolute return over its short life, you might quickly write it off as a dog. But you might not do that if you take a closer look.
Chart 5 shows it's done a good job tracking the S&P Growth Index. No, it wasn't designed to do this, but as discussed above, its quantitative underpinnings drew from a sample that was biased towards growth.
The other thing to notice from Chart 5 is that P4's return isn't all that far from that of the S&P 500. Still, you might not think too highly of it since it does trail the index.
But look again at Chart 6. P4 is riskier than the index (~25% standard deviation vs. ~18% for the index), but plots above the CML. As Modern Portfolio Theory teaches, more risk means more return, whether positive or negative. Unfortunately, the last 28 months have been negative.
Given P4 resides above the CML, should the market turn, it should lead both the S&P 500 and the S&P 500 Growth Index. In light of the fact that stocks rise in far more years than they decline, this portfolio truly does have potential for the long term -- even though you wouldn't know it by looking at return alone.
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