Monday’s post about factor analysis was, I admit, too technical for most readers’ tastes. At least that’s the conclusion I drew when the two most enthusiastic comments came from a professor of statistics and an astrophysicist. But the brave few who managed to read to the end saw my promise to put all this in context. What can factor analysis teach us about where an ETF’s returns are really coming from?
Two decades of research has shown that the returns of a diversified equity portfolio can largely be explained by its exposure to three factors: the market premium, the value premium, and the size premium. A broad-market index fund like the iShares S&P/TSX Capped Composite (XIC), by definition, should be neutral in its exposure to the value and size premiums. And as we saw in my previous post, it is: the value and size coefficients for XIC are negligible. So, on to the next step.
Let’s now take a look at the iShares Dow Jones Canadian Value (XCV) and the iShares S&P/TSX Small Cap (XCS). We should obviously expect XCV to have extra exposure to the value factor, while XCS should capture the size premium. Here are the results of a factor analysis covering the five years from 2008 through 2012:
Turns out XCV does indeed show a significant value tilt, with a value coefficient of 0.3589. To put that in context, during a period when value stocks outperform growth stocks by 2%, this fund would be expected to outperform the market by about 0.72% (0.3589 x 2%).
On the other hand, the fund’s size coefficient is significantly negative. That’s not surprising considering the Big Five banks make up almost 40% of its holdings. During a period when small caps outperform large caps by 2% you would expect XCV to underperform the market by about 0.79% (–0.3930 x 2%).
Moving on to XCS, we see the fund has a predictably huge small-cap tilt, as shown by its size coefficient of 0.9260. The only surprise here is the fund’s negative alpha—and a pretty high one at that. Management fees will have some impact here, but they’re not enough to account for a drag of 0.4477% per month. Unfortunately, when a factor analysis shows negative alpha we know something is causing a drag on returns, but we can never be sure what that is.
An eye for value
OK, it’s time to look at some other popular Canadian ETFs and see what we can learn from factor analyses.
Over the last five years, dividend stocks have tended to outperform the market: for example, the iShares Dow Jones Canada Select Dividend (XDV) delivered an annualized 3.76% from 2008 through 2012, compared with 0.58% for XIC. Meanwhile, those who champion fundamental indexing have noted it too had good record over this period: the iShares Canadian Fundamental (CRQ) returned 2.46% annually. Let’s see what a factor analysis reveals:
What do you know? Both ETFs show an even larger value tilt than XCV. As Justin Bender argued on his blog last year, dividend ETFs can be thought of as “value ETFs in disguise.” (Larry Swedroe goes into more detail on this subject here.) Think of it like this: a stock’s yield is its dividend amount divided by its price. Many dividend junkies focus on the numerator in that fraction (the high dividend amount), but the real driver of the returns is the denominator: the lower price.
Fundamental indexing, too, is really just a methodology designed to get greater exposure to value stocks, something its critics have long noted. Research Affiliates, creators of the fundamental index, downplayed this for long time, but now they seem to acknowledge it freely.
During the five years ending in 2012, the iShares Dow Jones Canadian Value (XCV) returned 2.93% annually, falling between XDV and CRQ. That’s not a coincidence. All three funds are just different ways of tapping into the value premium, which was strongly positive during these five years. When the value premium is negative during other periods, you can probably expect these funds to struggle in similar ways.
Special FX
Now onto a fund that’s more of a head scratcher. The First Asset Morningstar Canada Value (FXM) has been the best-performing Canadian equity ETF during the last year: over the 12 months ending September 30 it returned almost 29%, while the broad market was up just 7% and the three value funds above managed “only” 16% or so. How did FXM pull off that remarkable performance? Have the folks at Morningstar found a way to harness the value premium in a way no one else has ever managed?
We can’t look at five years of fund performance, because FXM was launched in February 2012. However, First Asset kindly provided us with monthly index data to fill in the gaps back to the beginning of 2008. This time the factor analysis yielded some surprises:
Yes, there’s value tilt, but there’s also a huge—and statistically significant—size tilt as well. (Remember, in the three value funds we considered above, the size coefficients were negative.) There’s also a significant alpha, though the low t-stat indicates it may just be random noise. But however you slice it, FXM is more than just a value fund.
We decided to dig a little deeper. Though it’s notoriously difficult to harness, there’s lots of evidence for a fourth factor: the momentum premium. Stocks that have recently risen or fallen in price tend to persist in the same direction for some time. So we ran a new regression with this fourth factor thrown into the mix:
This definitely helped: the higher R-squared value suggests the data fit this model better than our three-factor analysis. Momentum does indeed seem to contribute to the excess return. (In the Morningstar index tracked by FXM, one of the criteria is three-month earnings estimate revisions, which is a traditional momentum screen.) The value coefficient is higher now, too, but the size coefficient is still unexpectedly large.
Nathan Stretch—the reader who first encouraged us to look at FXM—ran his own regressions using different factor data and found even less evidence of value exposure and even more unexplained alpha. The truth is, it’s hard to know what’s going on here. FXM certainly has a very different sector mix: while the three value ETFs above are dominated by the Big Five banks, FXM includes exactly none of them. If the fund were actively managed, you might attribute some of its outperformance to stock-picking skill. Since it’s not, it may just be luck.
Bottom line, FXM bears no resemblance to the other value funds we’ve considered here. While its recent performance has been outstanding, it’s hard to know whether it will continue, since it’s not clear where those outsized returns are coming from.
Note: Once again, thanks to Justin Bender and Nathan Stretch for their help with these factor analyses. If you’re interested in learning how to “roll your own,” see Justin’s new blog post, How to Run a 3-Factor Regression Analysis.
For people who want to know more about statistics but would really rather leave the math behind, I found Naked Statistics by Charles Wheelan to be absolutely excellent. More useful than my two 200-level university courses in statistics, and quite a fun read.
I tend to be very skeptical of claims of investing skill, and factor analysis can help to debunk many such bogus claims, but it can be taken too far as we introduce more and more factors. If we take factor analysis to the extreme and make each stock its own factor, it’s obvious that there can be no stock-picking alpha because all returns are explained by the factors. If we presume for a moment that a given investor has genuine skill, his alpha as measured by factor analysis will shrink as we increase the number of factors. Perhaps 5 factors is a reasonable number, but if continue to add more it will start to look like we’re just desperate to prove that an expectation of positive alpha doesn’t exist. I’m content to say that some investors are just lucky and a very few others may have actual skill, but none of this matters because I don’t have skill and I can’t indetify others who have skill.
@Mike: I should be clear that the factors used in these analyses are not just arbitrary bits of data. It really doesn’t make sense to talk about “each stock being its own factor.” In this context, a risk factor is a specific characteristic that has been empirically shown to lead to excess returns above the risk-free rate. Once you get beyond the four factors discussed here, there really aren’t any other significant ones. (Though the gross profitability premium has been discussed recently.)
But it is certainly important to acknowledge that this is not an exact science. A lot of it depends on the data you use for each factor, i.e. how do you identify the value premium or the small-cap premium over a given period? Different researchers use different methodologies and while they all arrive at similar conclusions, differences will crop up. For example, Justin and Nathan use different techniques to run their regressions and got subtly different (though not contradictory) results. Expressing the coefficients to four decimal places does lend a false air of precision.
I really enjoyed these last couple posts. I am an engineer and the geek in me loves this type of analysis and discussion. I get all excited about correlation coefficients and t-Stats.
But the reformed investor in me knows better than treat any of this in any way other than “nice to know”. I was one of those guys that in the past had a 40-tab spreadsheet full of all kinds of calculations and stats on my portfolio, trying to balance cap weightings, sector allocations, geography, book values, etc.. Now I have 5 of the simplest, broad market, low cost ETFs I can find, and it’s liberating. This stuff is fun to read and great for education, but not something I believe I could be any better at than the masses in order to attempt to use to my advantage in anyway.
Thanks for the awesome posts, Dan. I admit, though, that I may not be your target audience (being a mathematician), although it seems as though a lot of your top commenters are what you would call bona fide “geeks” :)
As for the question of whether incorporating additional factors to a model makes sense, you can use the Akaike information criterion (http://en.wikipedia.org/wiki/Akaike_information_criterion) to help with model selection.
@Willy: Thanks for the comment. I hope it was clear the reason I introduced this idea: it’s not about trying to gain any advantage as an investor, except the advantages of insight and skepticism. When someone claims to have created an index or investment strategy that is new and innovative, it’s worth scratching the surface to find out what’s going on.
I find it interesting that dividend investing, for example, is primarily a form of value investing, though it is not often discussed in those terms. Same thing with fundamental indexing: there’s definitely something going on there, though many people have argued for a long time that it’s simply a form of value investing. While it’s not much of an issue in Canada, in the US you could argue that one can tap into that value premium in much cheaper ways, such as through Vanguard’s value ETFs.
@CCP: Risk factors come from a combination of data mining, future testing, and a plausible story. It is possible to invent a practically unlimited number of ways to choose a subset of stocks in the stock market. Trillions of these subsets will show excess returns. If we then test them on future returns, millions will continue to show excess returns. What distinguishes small cap, value, and other recognized factors is their simplicity and the fact that they come with a plausible story for why it makes sense for them to give excess returns.
In general, I’m a fan of factor analysis, but it is more arbitrary than we want to admit. If we lower our standards for what counts as a factor, we could say that Microsoft is its own factor because it “has been empirically shown to lead to excess returns.” I’m not suggesting that this is desirable — after all, we can’t expect to find another stock exactly the same as a young Microsoft. My discussion of taking the number of factors to the extreme of making each stock its own factor was intended to illustrate the fact that measured alpha will tend to shrink as the number of factors increases, and goes to zero at the extreme. This shrinking of measured alpha with the number of factors would happen even if the alpha was the result of genuine skill.
I’m not sure how mysterious FXM’s alpha is. The t-stat on alpha is pretty low, so there is plenty of room for ‘noise’ (or ‘luck’ if you prefer). FXM could have a monthly alpha of 0.4 (annual of ~5%) and still only have a t-stat of 2ish, which is barely statistically significant. Without a lot more data to push the statistical uncertainty, it’s pretty hard to claim that FXM’s alpha is anything other than luck.
In most sciences we don’t even bat an eyelash at an unexpected measurement unless the t-stat is over 2, and a measurement is only ‘confirmed’ if the stat is something like 4 or 5.
Fantastic post!
“Two decades of research has shown that the returns of a diversified equity portfolio can largely be explained by its exposure to three factors: the market premium, the value premium, and the size premium.”
So why not just invest in small value stock in canadian, us and international and bypass the broadband market since the theory said we are pay premium to hold them?
@Francis: I was waiting for someone to ask that question! The value and small-cap premiums are real, but accessing them is not as straightforward as it may seem.
As we’ve seen in this post, there are many different ways to access the value premium: you can sort stocks by P/E ratio, book value, dividend yield, some combination of all of these, or you can take an approach like the Morningstar index and throw in other criteria as well. What’s the best way to do it? I don’t think anyone can answer that question.
Capturing the size premium is also a challenge, because small-cap stocks tend to be less liquid, and in the case of the Canadian market, they are poorly diversified (about 50% energy and mining stocks), so you introduce other costs and risks as well.
Let’s remember, too, that there will always be long periods were value stocks and small cap stocks underperform, and it takes a lot of discipline to stick to a long-term strategy when it appears not to be working. So there are behavioral issues as well.
Bottom line, there is a huge gap between theory and practice. For most investors, I think it makes more sense to stick to plain vanilla, low cost, simple portfolios. If you have access to low-cost products that offer these tilts (such as Dimensional Funds or Vanguard ETFs in the US), then you can definitely consider going that route, as long as you are prepared to pay higher costs and endure periods of tracking error compared with the broad market.
I think CCP’s last comment is just paraphrasing Yogi Berra: “In theory there is no difference between theory and practice. In practice there is.” :P
@Raman: Is that a real quote? As Yogi once said, “I didn’t say half the things I said.” :)
Thanks CCP, I’m neither a statistician nor an astrophysicist but I thoroughly enjoy your posts… especially the geeky ones!
For ETF’s with small and value tilts like VBR, what would the factor analysis look like? I’m assuming these are not mutually exclusive traits but does the fund only represent companies with plenty of both? If so, is it fair to say VBR gives the same value exposure as say VTV?
FXM is more of a mid-cap value fund (Morningstar.com). The ave mkt cap is 4.3 bil.
CRQ = 22.3 bil; XCV = 25.6 bil ; XDV = 11.9 bil and XCS is only 694 mil. FXM is almost an ”equal weight” fund. The returns are on par with some actively managed funds in the small/mid cap category. RBC O’Shaughnessy All Cdn Equity Sr A is similar in terms of size and value with a YTD return of 25.5 %..
@Jon: Tough question to answer. Things get complicated when the factors overlap, but I think it’s fair to say that, no, VBR and VTV do not have the same value exposure. It would be reasonable to hold both funds in a portfolio to get a steep value and size tilt. I agree it would be interesting to run a regression on these ETFs and see what turns up.
This is a timely post for me–I just bought some FXM last week!
I am in the midst in setting up what’s essentially my own take on the Uber Tuber portfolio, and I thought that I would split my Canadian equities between all-market and value (as opposed to the all-market/small cap split in the Uber Tuber). I considered XCV, but when I looked at its details I discovered that nearly 30% of its holdings are in Royal Bank, TD Bank and Bank of Nova Scotia…and I’m already getting lots and lots of bank exposure in my all-market holdings (e-Series and some HXT). FXM, on the other hand, seems to hold some companies that could certainly be considered value stocks.
My biggest challenge was getting the stock ticker right…I kept trying to buy XFM instead of FXM.
(I’ll also mention that I chose to split my US holdings between VTI, VTV and VB, and for international I chose a split between VXUS, EFV and VSS.)
@Kiyo: I totally agree. There’s significant evidence out there that while it is possible to mitigate negative momentum, capturing positive momentum is extremely difficult if not impossible. So the explanation for that is likely luck, as is most likely explanation for the positive alpha (especially given that the fund only holds 30 stocks). Personally I prefer to find funds that consistently have alpha close to zero, as that is more likely to be sustainable. It seems to me that a fund with large positive alpha one year could just as easily have large negative alpha another year. That said, it looks like FXM is the only true Canadian small-value fund thus far, so it will likely find a market, especially given its stellar performance thus far.
@Francis: The thing is, the outperformance of small and value isn’t free. Yes, they sometimes underperform, but the other issue is when they tend to do so. Historically it has tended to be during times of economic turmoil. (Which is not necessarily the same as bad times for the stock market, in fact, it’s often the opposite.) However, poor economic times are times when a person would be more likely to rely on their savings, so there is added risk to a portfolio that tends to drop in value at those times. Since there’s added risk, there should be added return on average, over the long term.
At least, that’s the “risk story” explanation. There are also economists who believe that the small and especially value factor are more a behavioral issue — basically that value stocks do better because investors as a whole behave irrationally in overvaluing growth stocks. In that case, it really is a “free lunch”.
Whichever explanation you subscribe to, it is important to understand that a weighting to small and value is expected to increase the overall volatility of your portfolio, so it’s a good idea if you do tilt to SV to also decrease the total percentage of your portfolio in equities. By doing so, you can end up with a portfolio that has the same expected volatility but higher expected return, or the same expected return but lower expected volatility. (Of course, reality does not always follow expectations. Just like the stock market is expected to outperform bonds, but that doesn’t always turn out to be the case.)
And of course, as CCP says, costs are also very important. I personally tilt to small and value in the US and international portions of my portfolio, but not in the Canadian portion, because I didn’t find that any funds available in Canada provided a sufficient expected premium to make up for the increased cost and risk.
@Jon: Last year I looked at various US small cap funds, including VBR, here: http://www.bogleheads.org/forum/viewtopic.php?p=1499630#p1499630. Also small cap funds, including VTV, here: http://www.bogleheads.org/forum/viewtopic.php?f=10&t=103351. You can see the factor loadings I came up with at the time in those posts.
If you’d like to try updated regressions yourself, there’s a new website where you can do that by just typing in the ticker symbol: http://www.fundfactors.com. (No affiliation; the creator is also a member at bogleheads.org and sent me a PM about it.) You can try setting various start and end dates to see how the factor loadings vary over time.
Fascinating stuff. Just out of curiosity, do any of the factors (value, size, momentum, etc.) exhibit significant negative correlation with each other? If so, wouldn’t holding negatively correlated tilts damp out volatility? For example, if the value factor was negatively correlated with the size factor and your portfolio was tilted towards both factors then when value underperforms, it would be compensated for by the outperformance of size and vice versa.