Multifactor Investing - A comprehensive tutorial

Asset allocation, risk, diversification and rebalancing. Pros/cons of hiring a financial advisor. Seeking advice on your portfolio?
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ClosetIndexer
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Multifactor Investing - A comprehensive tutorial

Post by ClosetIndexer »

Introduction

This post covers a comprehensive example of building a diversified equities portfolio using multifactor investing. I hope that it will help to demonstrate how one could go about applying the Fama-French 3-factor model in real life to create a portfolio matching their risk tolerance and personal requirements.

If you've never heard of the Fama-French model, or want a refresher, here's the Bogleheads wiki summary, and right from the horse's mouth, this 1992 paper by Fama and French. (It's actually quite readable, even for those of us without finance degrees.) I've included a few more links at the bottom of this post too.

I will discuss the analysis and thought process I went through while designing my portfolio from beginning to end, with reference to the various tools and resources I used to help make decisions. This was my own personal process, so I'm certainly not saying it's THE way for everyone, but again, I hope it will provide a useful example at least of the kinds of things one might want to think about.

I'm going to try to avoid getting deeply into the merits of multifactor investing itself, which are discussed elsewhere. (The links I've included at the bottom could be a good start.) There are certainly counter-arguments out there as well. Basically I believe that the size and value premiums seen historically are likely largely risk premiums. (Although there may be at least some behavioural component as well, particularly for value.) Regardless, it seems to me that the premiums are more likely than not to continue into the future. However, I personally do not feel it's prudent to rely on capturing the entire amount of the historical premiums going forward. So my general approach is to start with TSM (Total Stock Market), then tilt only if the historical premium that tilt would have achieved significantly outweighs the additional costs, both explicit and implicit, and the additional standard deviation of achieving the tilt - essentially leaving myself a sort of 'margin of safety'.

So, the plan for this post is to give an example of how one might rationally apply the Fama-French three-factor model to one's equity investing decisions, rather than to argue the merits of the model itself. What follows is, more or less, the actual process I went through. I'll present it as a tutorial since it's more convenient to write it that way, but I don't profess to be an expert and am certainly open to comment or criticism. (Especially if it helps me improve the efficiency of my portfolio!)


1. Determine Equity / Fixed Income Split

The first step is to determine a reasonable baseline split between equities and fixed income, based on personal risk tolerance. The most logical way I've seen to frame the question of risk tolerance is Larry Swedroe's "Willingness, Ability, and Need to take risk". His book, The Only Guide You'll Ever Need to the Right Financial Plan is a great primer, and an easy read. Canadian Couch Potato has a review here.

To keep things simple, we start by assuming that the equities portion of the portfolio will be in global market-cap weighted index funds - ie, total stock market - and the fixed income portion will be all short term government bonds - essentially zero term and credit risk. Then it's just a matter of determining what percentage of equities vs fixed income matches our personal risk tolerance and needs. Although there are many caveats to using historical data to project future returns, historical data can give us a good idea of future risk. In other words, a portfolio with 60% equities and 40% fixed income can be expected to have similar risk exposure in the future (be it standard deviation (volatility), maximum draw-down (loss), etc) as it did in the past. Given our starting assumption of short-term, high-quality fixed income, we can therefore estimate the risk of our portfolio by looking just at the equities side, which we can estimate using the historical risk of the global stock market. Short bonds do potentially provide a bit of diversification benefit, but most of their benefit is essentially 'dilution'; ie: scaling down the equity portion.

Based on data from Ken French's site, the annual standard deviation of the US stock market has been about 20% since 1927. Global data only goes back to 1990, but since 1990 the global standard deviation has not been significantly lower than the US over the same period, so we can use 20% as a rough guide to the long-term average SD of the global market. If our maximum tolerance is 10%, we would therefore want about a 50/50 equity/fixed income split. Of course, standard deviation is a somewhat meaningless, abstract number for most. Finiki has a good summary of the maximum expected losses of a portfolio based on various equity/fixed income splits, based on Bill Bernstein's excellent book, The Four Pillars of Investing. (Like us, Bernstein bases his numbers on short-term, high quality bonds.) An online risk tolerance survey might also be useful as a rough guide, like this one from Vanguard.

Anyway, getting off topic a bit. The idea is to choose a split that you're comfortable with and that meets your needs. Then, if you make changes to either side - either tilting equities away from TSM or adding term or credit/default risk to fixed income - you need to adjust the equity/fixed income split to keep your overall risk exposure the same (or less). More on this in Step 6.

My personal baseline was 75% equities, 25% fixed income.


2. Determine Reasonable Targets for Fama-French Factor Tilts

The next step is to get a feeling of what various levels of tilt really mean. We need to have a rough idea of what factor tilts we might want to target so that we know what funds to look for. As one looks at funds with greater degrees of tilt toward small or value companies, both the explicit (MER) and implicit (negative alpha) costs of those funds goes up. (Alpha is a measure of a fund's performance relative to the expectations of the 3-factor model. The best funds we expect to have alphas of near zero minus their MERs.) So the greater our tilt, the more we're relying on the expected factor premiums to outweigh these drags. Therefore the goal is to access as much of the expected premiums as possible, while still keeping the factor tilts as moderate as possible.

To help turn this rough (and contradictory) goal into actual numbers, we can look at some spreadsheets showing the historical risk (standard deviation) and return of various theoretical tilted portfolios. Links to the spreadsheets, results, and some analysis are here. They cover 81 portfolios, ranging in 0.1 increments from 0,0 to 0.8,0.8 weightings to SMB and HML. This shows us the theoretical benefit that was gained historically with various levels of tilt, not including any added costs or negative alphas in achieving that tilt. We can see that there has been diminishing marginal returns to greater degrees of tilt, particularly in the SMB factor. Personally, I decided that tilts of 0.1 to 0.3 to SMB and 0.3 to 0.5 to HML were 'close enough' to the efficient frontier, as a rough guideline. This is just one way to formulate the question, perhaps suited to visual thinkers. Here's another.

Note: It is also important to question whether, in your situation, it is appropriate to tilt at all! First of all, tilting involves using more funds, which increases trading expenses and portfolio complexity. For smaller portfolios, the hypothetical gains are likely not worth these added (guaranteed) costs. I would guess the break-even point is somewhere in the $60-100k range, as a rough estimate. Also, if the small and value premiums are indeed compensation for risk, logically they must not be appropriate for all investors. Some of my thoughts on these issues are here and here.


3. Choose Specific Funds for Each Region

There are four main geographical regions we're interested in as Canadian investors: US, Canada, EAFE (aka "International Developed"), and Emerging Markets. As a default starting point, we would split the equities portion of our portfolio into these four regions by market cap, so about 45% US, 5% Canada, 35% EAFE, and 15% Emerging, or thereabouts. In reality, we will over-weight some regions based on higher expected risk-adjusted returns: particularly Canada due to tax and currency effects, but possibly other regions depending on the results of our analysis of specific funds. Therefore, it makes sense to look at what investment vehicles are available in each region before deciding on firm percentages.

The correlations between the factors for various regions are relatively low, much lower than the overall market correlations. So while global diversification is useful in general, it is even more useful to diversify one's exposure to the small and value factors. So ideally one would target the same factor loadings everywhere. That said, it turns out they are much easier to achieve in some regions (US) than others (Canada, Emerging).

To compare between funds in a given region, we look at several factors: their expenses, their tracking errors, and most importantly, their 3-factor (3F) factor weightings and alpha. If investing in a taxable account (which I am), the tax consequences of the funds are important too; these are largely determined by their yields and turnover. Higher yield means more of the return expected by the 3F model is in the form of dividends instead of capital gains, which receive inferior tax treatment, (although much less so for the Canadian portion of the portfolio). Higher turnover can lead to capital gains distributions, especially for newer funds, whereas we would generally prefer to defer capital gains as much as possible. Higher turnover also leads to higher trading costs within the fund, but that will be seen in the tracking error and 3F alpha.

Management expenses (MER), tracking error, yield, and turnover can be found in the funds' prospectuses and/or annual reports, if not right on the fund companies' websites. (The reports are generally available on the companies' websites as well. If not, they can often be found through morningstar (.ca for Canadian, .com for US), or as a last resort, by using EDGAR for US funds, or SEDAR for Canadian. 99% of the info you'll want is available on the companies' websites though.)

For the 3F weights, we need to perform 'linear regressions'. The goal is to describe a portfolio of stocks (such as a mutual fund or ETF) as a linear combination of several factors: Market beta, HML, and SMB. Basically what that means is we look at a period of historical returns for a given fund, and use software like Excel, Calc, or R to mathematically compare them to the performance of the three Fama-French factors over the same period. If it turns out that the fund tends to go up when the HML (value) factor goes up, and vice-verse, it means that the fund has a positive loading of that factor. For more info on what the factors actually mean, see this 1992 paper by Fama and French, and/or the Bogleheads wiki summary.

When you're ready to actually try a regression on a given fund, check out this excellent tutorial by the Calculating Investor. It shows how to get the data and do regressions on US funds, so that's a good place to start. Here's my analysis of the available options in each of the four regions, beginning with the US:

US Choices

I performed regressions on a number of funds from Vanguard, Powershares (RAFI funds), DFA and others. (DFA funds can only be purchased through an adviser and the Canadian versions are different from the US ones, but they provide a good benchmark.) Particularly interesting was a deeper look at small value funds in this thread, where we found that you do indeed pay a significant cost for more concentrated, 'pure value' funds, as well as that the fourth factor, momentum, can provide useful insight in cases where alpha estimates are inconclusive. Later in that thread I also mention my thoughts on Margin of Safety in multifactor investing.
ClosetIndexer wrote: [The expected premium of our efficiently tilted example portfolio is] 1%, assuming factor premiums remain the same as they have been historically. Now, that's still worth doing in my opinion, but it's not exactly a massive margin for error. If you then go reaching for additional tilt using a less efficient product like RZV, you can see that remaining expected out-performance disappear very quickly. At least, that's how I look at it.

I believe in multifactor investing, but I want to give myself the best possible chance of achieving at least market returns over the long term. So if I don't see a strong enough chance that a portfolio will out-perform, long term, on a risk-adjusted basis, I would rather stick with TSM than roll the dice.
In the end I chose a 60/40 split of VBR and VTV, the small-cap value and large-cap value Vanguard ETFs based on MSCI indexes. This achieves estimated factor loadings of about 0.4 to HML and 0.3 to SMB. I expect that the S&P equivalents (VIOV and VOOV) or the Russel (VTWV and VONV) would have been fine too. The S&P have the advantage of slightly lower yield (hence less taxes), but have had slightly higher expenses (and tracking error), so that roughly cancels out. They have slightly less negative momentum than the MSCI, particularly on the small-cap side: about 0.05 less negative MOM exposure, which would be expected to make a difference of up to -0.5% per year, but at least historically that has been more than cancelled out by negative 4F alpha. Although, in regressions, the intercept (alpha) is the most difficult value to estimate precisely, so we are more confident in the momentum than the alpha. That said, the MSCI indexes are less concentrated than the S&P, which might result in (very slightly) less non-systematic risk. Since we're already cutting out about half of the total stock market with our value tilt, we prefer to be as diversified as possible. (Clearly it's a pretty close choice between MSCI and S&P.)

The Russel indexes are even slightly more diversified than the MSCI, and like the S&P they avoid the slight negative momentum seen in the MSCI small-cap. The small-value index also has greater HML (value) exposure, which historically has had a greater premium than SMB (small) and is more difficult to achieve without resorting to pure value funds. However, like the S&P funds, the Russel funds are slightly more expensive and have larger negative alphas than the MSCI (to an even greater extent). There is also a reason to expect these alphas might persist: the Russel indexes may be more prone to front running.

This Vanguard paper gives a good comparison of all the major indexes, with visual representations of their relative size bands, and some analysis.

I did consider adding a mid-cap value fund like VOE to the mix, since it would allow for the same factor weightings with a smoother ramp from small- to large-cap value, but ended up deciding against it. More specific reasoning behind the choice of VTV and excluding VOE is here, and regarding VBR is here. (Later in that thread (starting here) we also take a look at the RAFI US Small-value fund, PXSV, which looks potentially interesting but doesn't have enough history to know for sure. So for now we leave it for the more proven choice.) Oh, and general process is here, using Vanguard funds for example.

EAFE (International Developed) Choices

EAFE is both simpler than US because (unfortunately) there are far fewer value funds to choose from, and more complex because we do not have a ready-made set of factor returns to work with. In this thread I describe how to estimate EAFE factor returns, as well as the expected effects of the approximations, and results for several funds of interest.

Since this post is already turning into a novel, I've split off my EAFE analysis here. Basically, although there aren't many funds to choose from, there are a couple good options. It's especially good for taxable investors, since CIE (RAFI International Fundamental index) is Canadian-domiciled. As a result, we can build a decent tilted portfolio using CIE and SCZ for only 20bps more than an untilted one with VEA and SCZ (or VXUS). The resulting factor weights are about 0.1 SMB, 0.3 HML (roughly).

Emerging Markets Choices

Emerging markets is tricky because there really isn't any good Fama-French factor returns data to perform regressions with. Jason Hsu, now at Research Affiliates (of RAFI fame), does publish a set, but I've found they aren't particularly reliable. So on the EM side we're forced to use very rough estimates (meaning we need a larger margin of safety if we are going to pay a premium to tilt). I used two approaches. First, I looked at equivalent EAFE and Emerging indexes from the same index provider, and assumed the factor loadings might be very roughly the same. For example, VWO uses the MSCI Emerging Markets Standard index, so we expect it to be comparable to the MSCI EAFE Standard index (VEA), on which we can do a regression. Second, I give more attention to tracking errors. Theoretically, if it's well constructed, the best we can hope for is that an index will have 3F alpha of zero. So at the very least we know a given fund will have negative alpha equal to its tracking error. (Likely greater, perhaps much greater.) As it turns out, maintaining even mildly reasonable tracking error is a very high bar for most Emerging Markets funds, especially small-cap. On the value side, iShares Canada's CWO was interesting, as they just recently switched it over to track the RAFI Emerging Markets Fundamental Index. Unfortunately, it cheats by holding other ETFs and sampling/approximating its index, much like CIE used to, which resulted in horrifying tracking errors. I don't see any reason for CWO to do better. What's more, even the Powershares fund tracking that index, which doesn't cheat, has had average annual tracking error of more than -1.5% since its inception over 5 years ago. It's hard to imagine its slight value weighting making up that kind of handicap over the long term, especially since the index itself may well not be perfect either (ie: it may well have negative Fama-French alpha itself). DGS, the Wisdomtree Emerging Markets Dividend fund, is theoretically another option, but we expect it to have the same issues as its EAFE brother, DLS, as mentioned in the EAFE thread.

So, at the moment it looks like tilting in Emerging Markets is simply cost-prohibitive. You could roll the dice and get lucky, but that's not what we're looking for here. Personally, I actually wouldn't be surprised if the EM small and value premiums for this period end up being particularly large, precisely because they're difficult or impossible to capture. But that's just a guess, and I don't plan to bet on it. I will simply use VWO for Emerging Markets, even with its tilt toward large, and possibly reduce my overall EM exposure a bit, given its lower expectation. (More on this later.)

Canadian Choices

Finally, we have Canada. The first thing to note about Canada is that it actually already has a value and, especially, small tilt from a North American or global perspective. If we only held Canada in proportion to its global market cap, that wouldn't be an issue, as we would just be holding the market. But if we over-weight Canada (as we all do to some extent for tax and currency reasons), we should realize that we are adding exposure to the SMB and - to a lesser extent - HML factors implicitly. To avoid taking on unwanted risk, we will want to factor in that implicit tilt when choosing funds to meet our target factor weightings. (It's also important to take into account that over-weighting any country beyond its market cap weight brings in other idiosyncratic country risks, unrelated to size and value, so we have to weigh the costs and benefits when doing so. More on that here, and below.

For Canadian factors, I use essentially the same process I described for EAFE. More details on the source data used, along with results and analysis are here. (The OP of that thread presented initial analysis, but had a mistake in the SMB factors, so it was re-done in the post I linked to.) Unfortunately, I come to the conclusion that there simply aren't any Canadian small or value funds that could increase one's expectation sufficiently to overcome their increased costs, with a reasonable margin of safety. There are some that might break even, or if historical factor premiums hold out, perhaps outperform slightly. However, we have no guarantee that future small and value premiums will be as large as in the past, nor as large in Canada as in other markets. This is particularly true given then it looks like Canada already has an intrinsic small value tilt, and there is a decreasing marginal benefit to additional tilt, especially on the size factor (due to reduced diversification benefit). So until we have some better choices, in my opinion the best choice in Canada is to stick with a broad market fund: for now either XIC or VCE; once we can confirm its tracking error is satisfactory, ZCN.


4. Choose Global Asset Allocations

So, we now know what our best options are in each of the four regions. The next question is how to divide total equities between the four. There is no straightforward answer. It depends on one's personal situation, particularly in terms of taxes and risk exposures outside of investments. It also depends hugely on the assumptions and estimates made, which will be different for everyone. However, there is at least a logical way to look at the question:

We start with a straight market cap-weighted global portfolio. That would be approximately 46% US, 36% EAFE, 13% Emerging, and 5% Canada. Weighting by market cap gives maximum diversification, which should result in maximum risk-adjusted expected return, all else being equal. Then, we look at the things that make 'all else' not equal. In other words, aspects of each reason that cause us to expect a higher (or lower) than average return, or greater (or less) than average overall risk. If a given region has higher risk-adjusted return given our circumstances, we would increase its weighting, and vice-verse. So essentially we can start by adding up all the costs and benefits of each region, to give it a single annual % premium (or cost) compared to the global average. Here are the results I came up with for a personal (non-corporate), taxable investor:

Canada

The Canadian portion of our portfolio, using VCE, costs 0.1%. As a taxable investor, the most significant aspect of Canada is its dividend tax treatment. Earning $X in Canadian (eligible) dividends is approximately equivalent to earning $(1.3 * X) in foreign dividends (or other income).* Since yields average around 2-2.5%, this means about a 0.7% premium on our Canadian returns that is not tied to any corresponding risk. So net we have 0.7%-0.1% = 0.6% premium. Then we factor in the factor weightings (no pun intended...) VCE has an HML of about -0.1, which has a theoretical cost of around 0.2%, leaving us with +0.4%. Finally though, if we over-weight Canada significantly, we should also consider its intrinsic factor weightings on the portion that we're over-weight compared to market cap. This is where personal estimates come in. Based on historical data, Canada's 0.3,0.15 small,value loadings could mean an additional risk-adjusted premium of 1.2%, bringing the total to 1.6%. That part is obviously far less certain than the cost and tax differences though, so must be taken with perhaps an entire shaker of salt.

*to get a more precise number for your 'dividend equivalency factor' (that 1.3), go to taxtips.ca, choose your province, and take (100% - a) / (100% - b), where a is your marginal eligible dividend tax rate, and b is your marginal other income tax rate.

On the risk side, a larger Canada holding results in decreased currency risk, assuming we plan to spend $CAD in retirement. (At least, up to a point. Some international exposure will actually decrease currency risk, as well as the obvious diversification of country risk.) To get a rough idea of just how much this currency risk protection might be worth in terms of returns, I took a wild guess at what a reasonable worst-case currency fluctuation might be between my weighted average investment contributions and my retirement withdrawals. I chose 40%. So, if the CAD rose by 40%, how much performance difference between CAD and international equities does that equate to on an annualized basis over a 30 year time-frame? Something like 1.7% per year, depending on how you define the difference. Anyway, the idea is simply to get a ballpark. (Of course, the currency could easily go the other way, leaving your international holdings better off by that amount, but that would be extra, unneeded money. The currency risk benefit of Canadian holdings is in minimizing downside risk, measured in CAD.) That number is obviously entirely dependent on assumptions, but at least it gives a rough idea. The currency risk avoidance is probably worth something more than say 1%, and less than say 3% per year, assuming minimizing downside risk is the goal, as opposed to simply maximizing expected value.

On the other side of the risk equation we have country risk. Stock market returns in different developed countries vary a lot, over long periods of time. Based on data like this, I estimated that a reasonable worst case would be Canadian under-performance by 3% annualized over my investing horizon. (Of course it could just as easily out-perform, but the idea is to not put too many eggs in one basket.) Naturally every region has risks, but when we put a significant percentage of our portfolio in one country representing 5% of the global market cap, and heavily concentrated in just three sectors, we are taking on significantly more risk than by putting a large chunk in the US, for example, which has a much larger and more diversified economy, with far more global exposure and sector diversification.

The nice thing is, although the potential country risk is fairly large, it is canceled out well by the currency risk benefit along with the tax savings. Therefore it should be safe to considerably over-weight Canada, assuming there aren't even better opportunities elsewhere...

(...unsurprisingly there aren't, although the US comes close...)

United States

In the US, our 60/40 combination of VBR and VTV has an effective MER of 0.1%, after adjusting for acquired expenses. The portfolio has factor weightings of approximately 0.3 to SMB and 0.4 to HML, which historically had a risk-adjusted premium of about 1.5%, so net we have a 1.4% premium. (Of course, that considers only the explicit costs of the funds, not any additional negative alpha, and it assumes factor premiums in the future are the same as the past, so certainly no guarantees.)

Currency risk has already been considered a bonus on the Canadian side, so we won't double-count it here or elsewhere. The US is not entirely without country risk of its own, particularly if we're also over-weighting Canada, since the US and Canadian markets are highly correlated. However, the US market makes up half the global market, and is highly diversified, so its country risk should be relatively minimal.

International Developed

The effective costs of our international portfolio of 50% CIE and 50% SCZ is the sum of their MERs and the irrecoverable withholding taxes on SCZ's 3.1% yield, for a total of about 0.8%. We get factor weights of about 0.09 to SMB and 0.27 to HML, which historically, in the US, meant a premium of about 1.1% after adjusting for increased standard deviation. (I feel I should note again that these factor weights are rough estimates only. I use a couple decimal places to be accurate, but it certainly doesn't mean they have that level of precision. Also, even if they did, they are subject to drift.)

Put the two together and we get a net premium of 0.1%: effectively zero.

Emerging Markets

Finally we have Emerging Markets, which are simple since it's just one fund: VWO. The effective cost is the 0.2% MER plus the irrecoverable foreign withholding taxes, approximately 15% of the yield, or 0.34%. So 0.54% total. We estimate that VWO's size loading is the same as VEA's, about -0.3 SMB. As a very rough estimate using the US factors, that means a risk-adjusted premium of -0.7%. So in total we have a (negative) premium of -1.24%.

Emerging markets likely possess some unique risk factors, and so provide a diversifying effect independent of their small and value characteristics. It would not be prudent to eliminate them from the portfolio entirely. However, given their added costs and the fact that we can't cost effectively tilt them to small or value (or indeed, even achieve an untilted size), it does seem reasonable to reduce their weighting below market cap, particularly given we have better reasons to expect premiums in the US and, particularly, Canada.

Naturally, in retrospect, the decisions we end up making here won't be ideal. They may not even be close. But there's nothing we can do about that. All we can do is take into account all available information to give ourselves the best chances of maximizing return and minimizing risk, given what we do know, today.

5. Results

Note that my personal situation was slightly different from the above because my taxable investments are inside a CCPC, which in my case at least means that withholding taxes are only about 25% recoverable. So basically foreign stocks end up having an additional cost on the order of 20bps. So, based on the above analysis with that slight tweak - and a lot of guess work - here's what I came up with for regional allocations:

Canada: 30%
US: 38%
EAFE: 26%
Emerging: 6%

As an aside, if we consider North America as a whole, that works out to 68% domestic, 32% foreign.

Then, based on these factor weights for each region,

Canada: -0.1 SMB, 0 HML
US: 0.3 SMB, 0.4 HML
EAFE: 0.1 SMB, 0.3 HML
Emerging: -0.3 SMB, 0 HML,

as well as a bit extra for the over-weighting of Canada, which from a North American perspective has 0.3 SMB, 0.15 HML, we end up with estimated global factors of approximately

0.20 SMB, 0.27 HML

That's a bit lower than what we had hoped for, but close. HML in particular is low due to lack of good tilting options in Canada. Given the close relationship between Canada and the US, it seems reasonable at this point to see if we can get more HML tilt in the US to compensate. However, doing so requires the use of more concentrated 'pure value' funds, which we determined just aren't worth it. So, we stick with these allocations, confident that we're getting a mild to moderate tilt while not overspending or taking on unnecessary non-systematic risk. At worst, over the long term we expect to roughly pace the market, since we haven't added a great deal of additional cost. At best, our small and value tilts may result in 1-2% out-performance.

6. Re-adjusting Asset Allocation

The final step in our portfolio-building process (on the equities side at least) is to adjust our split between equities and fixed income to compensate for the tilt we've added, thus keeping our expected risk in line with the tolerance we established in Step 1. For that, we can go back to my handy spreadsheet. Our baseline untilted portfolio of 75% equities, 25% fixed income had a historical annual standard deviation of about 15.3%. To get that same level with our 0.2 SMB, 0.3 HML tilted portfolio (on the equities side), we need to reduce the equities portion of the total portfolio to about 68%. This is just a rough estimate since we're only using US historical data, but it should be in the right ballpark.

Alternatively, instead of aiming for a constant level of risk, we could aim to hold return constant while minimizing risk. This latter approach would be more appropriate if the split we came up with in Step 1 was based around the minimum annual return we expect to require in order to fund retirement. (Not an ideal way to go about it, but sometimes a necessary one.) In that case, instead of finding the equities percentage to hold risk constant while hopefully increasing return, we would find the percentage that holds return constant (given the expected after-cost premium we expect from our tilts), resulting in a lower level of standard deviation for the same expected return.

Finally, keep in mind that these standard deviation estimates are assuming fixed income is all in risk-free assets. Adding term or credit risk on the fixed income side will also require the equities/fixed income split to be shifted more toward fixed income to maintain the same level of risk. That's another topic though. :)

7. Maintenance

Once the portfolio is worked out, we have to maintain it. For me that means every year (on a set date) I will
  • Check the latest annual reports for each of my funds (ETFs). Particularly, look for any changes to the index methodology, or for larger than expected tracking error.
  • Rebalance funds toward chosen allocations. (I say toward because it's not necessary to get things exact, particularly if that means paying extra commissions, spreads, or taxes.) As far as what's "close enough", here are some good guidelines. Regardless, the goal is simply to keep things in line with your risk tolerance. It is possible that rebalancing will give a slight boost in returns due to mean-reversion, but don't expect it. Topic for another day.
Every 4 years (on leap years, 'cause it's convenient), or more frequently if I feel like it or am concerned with a fund's tracking error or other aspects of its annual report:
  • Redo regressions of all funds over the past 5 years; look for inconsistencies in factors or changes in alpha. Over shorter regressions than 5 years, the factors tend to vary quite a bit, so you need to look at at least 5 years to filter out the noise. Much longer than that though and it's tough to get an idea of how the factors might be drifting. So personally I've found 5 years appears to be a good compromise; YMMV. I will also run longer- and shorter-term regressions for supporting evidence though.
  • If factors have drifted considerably, evaluate whether allocations to each fund should be tweaked to better achieve overall desired factor exposures.
  • Also re-evaluate any funds that have had consistently high negative alpha or negative momentum. However, be aware that alpha, especially, is very difficult to estimate accurately. Be sure to check the confidence of the estimate based on its t-value or standard error. And don't make any decisions based solely on alpha without at least a few years' evidence.
  • Also look into products that were previously passed over, but appeared worthy of future re-evaluation, as well as any new small or value funds (or low-cost broad market funds like ZCN!) introduced since the previous check.
  • Document any changes made and the reasoning behind them, and note anything that should be reevaluated next time.
(There are also to-do items on the fixed income side, but I'll save that for a future topic.)


Summary

And there you have it! As I said at the beginning, I'm certainly no expert. This is the method I used, based on my own research and experimentation. I'm sure others will have other opinions. I do certainly believe the approach of simply holding globally diversified total stock market funds for the lowest cost possible is entirely valid. Tilting intelligently (obviously) takes a fair bit of effort. If one is comfortable managing their own 'couch potato' portfolio, but would not feel comfortable going through a process like the above without an adviser, it is almost certainly better to stick with the more straightforward approach. That said, if you are willing to put in a bit of time - or are like me (and I suspect many other FWF'ers) and actually enjoy this kind of thing - then you may want to consider multifactor investing.

I would love to hear any specific comments or criticisms. Also happy to answer any questions or to supply more background info if I missed anything in all the links.

So, I hope you found this interesting! Here are some resources if you're looking for more:


Resources:

IFA Primer on multifactor passive investing - IFA is a financial advice firm that focuses on multifactor (Fama-French) investing. Their '12-step' program is a great comprehensive primer for someone who's relatively (or completely) new to the concept of multifactor investing (or 'tilting'). Or even to passive investing in general. Just ignore the stuff about their proprietary portfolios. ;)

This post by Robert T over at Bogleheads catalogs a ton of related info. Should answer just about every question you could think to ask about multifactor investing.

When you're ready to try your own regressions, you can get started in just a few minutes using this great video tutorial by the Calculating Investor. I find his method is far faster and easier than using Excel, and only uses free software. I've got a slightly modified version of his script here. Works the same as in the example, but prints out the results in a nicely formatted matter at the end; handy for copying into your notes or, say, forum posts. :) It also pops up a graph to get a visual idea of how good the fit is.

Finally, there's a work in progress at the bogleheads wiki, which should eventually be a comprehensive resource for Fama-French regression analysis.
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Re: Multifactor Investing - A comprehensive tutorial

Post by adrian2 »

Wow, lots to chew upon.
ClosetIndexer wrote:As a taxable investor, the most significant aspect of Canada is its dividend tax treatment. Earning $X in Canadian (eligible) dividends is approximately equivalent to earning $(1.45 * X) in foreign dividends (or other income).
The comparative advantage of dividends has been reduced from 1.45 to about 1.3, although the trend seems to be reversing. Mr. Hymas has been using the 1.3 equivalency factor instead of 1.4 for a while.
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Re: Multifactor Investing - A comprehensive tutorial

Post by Arby »

Excellent post ClosetIndexer. It very closely follows my thought processes when I started my DIY portfolio about 12 years ago. I came to much the same conclusions as you did. DIY'ing would have been a much less painful process if I had been able to read your post back then.

One additional factor I used to select funds in a specific region is the average daily trading volume. I found the lower volume funds tended to have wider buy-sell price spreads, so I usually selected funds with the high trading volume.
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Re: Multifactor Investing - A comprehensive tutorial

Post by ClosetIndexer »

adrian2 wrote: The comparative advantage of dividends has been reduced from 1.45 to about 1.3, although the trend seems to be reversing. Mr. Hymas has been using the 1.3 equivalency factor instead of 1.4 for a while.
Ah, you're right. I was just assuming perfect integration would be the best estimate for most, which clearly isn't the case. Will correct the OP.
Arby wrote:Excellent post ClosetIndexer. It very closely follows my thought processes when I started my DIY portfolio about 12 years ago. I came to much the same conclusions as you did. DIY'ing would have been a much less painful process if I had been able to read your post back then.

One additional factor I used to select funds in a specific region is the average daily trading volume. I found the lower volume funds tended to have wider buy-sell price spreads, so I usually selected funds with the high trading volume.
Thanks! And yes, that's something to consider too. I give it a lower priority than the factors I listed though, since it's a one-time cost that would be overwhelmed by a small difference in annual costs (and/or returns) as long as the time-frame is long enough.
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Re: Multifactor Investing - A comprehensive tutorial

Post by Park »

ClosetIndexer, once again an excellent post. The following are only meant to be comments, not criticisms.

The problem that I have with tilting to small and value is does it work in a taxable account? As one's marginal tax rate increases, a total stock market approach (and maybe even a growth strategy) becomes more attractive relative to a small and value tilt strategy. In the top Ontario bracket, about 23% of one's capital gains and 46% of one's foreign dividends goes to the CRA. And with foreign dividends, one may lose withholding taxes, which can be 15%. So foreign dividends might be effectively taxed at 54%. A strategy which emphasizes return in the form of unrealized capital gains becomes more compelling. Unrealized capital gains are the only way to get your effective tax rate below 23%.

William Bernstein recommends tilting only in tax advantaged accounts.

In your post, you state that a small and value tilt strategy can result in 1-2% outperformance at best. I have asked the following question on the Bogleheads forum, and never got an answer to my question. Assume margin interest is tax deductible, which it is in Canada. Assume it is a taxable account. Which of the following strategies would outperform: a small and value tilt strategy or levering a total stock market index strategy with a ratio of 1.3?

As your post mentions, the investment vehicles for a Canadian investor to implement a small and value tilt strategy make it difficult to implement. Your post indicates that for Canadian and emerging stock markets, it's impossible to implement, except for a DFA investor. But DFA investing is associated with increased costs. With a leverage strategy, the investment vehicles are readily available to implement the strategy in a cost and tax efficient manner.

I am not advocating a leverage strategy. Leverage is a reasonable option for some investors to consider. But the gains from a small and value tilt strategy are not large (although over 30 years they might be), the strategy becomes more debatable in a taxable account and the vehicles available to implement the strategy make it problematic. IMO, if one wants to pursue a small and value tilt strategy, other options should be considered, including a leverage strategy.

What's more important than the strategy one follows (small and value tilt, total stock market, leverage) is the amount one saves, equity/bond split and how long one is investing for.

I actually do tilt to small and value, but only in my tax advantaged accounts. As my tax advantaged accounts are small compared to my taxable accounts, I want as extreme a small and value tilt as possible. Otherwise, I doubt that tilting to small and value would have any effect of significance on my portfolio. So I use RZV, and that exposes me to negative momentum.
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Re: Multifactor Investing - A comprehensive tutorial

Post by ClosetIndexer »

Park,

Thanks, interesting comments. Here are my thoughts, for what they're worth.

First of all, the goals of leverage and tilt are not necessarily the same. Leverage is pretty simple, really; you take on additional risk to get additional return. In theory, there is no difference between the decision to move from 80% to 100% equities or the decision to move from 100% to 120%. All just depends on your risk tolerance. In practice that's not quite true, for a couple reasons. First, leverage isn't free, meaning that the interest you pay for margin is generally higher than the 'risk-free rate'. So there's a bit of negative alpha baked in there. Second, the more one leverages, the more one risks a margin call. So even if your personal risk tolerance is theoretically high enough to withstand a given level of draw-down, if you are levered too far, you could be forced to sell. (Likely doesn't apply to only moderate leverage though.)

Multifactor tilt is a different animal, because you have more than one variable to work with. Rather than just linearly increasing risk and return, you have multiple risks that can be adjusted, so you can vary portfolio return and volatility separately, to some extent. Indeed, the approach I describe above aims to keep one of the two constant (in my case volatility), while changing the other (increasing return or decreasing volatility). Now if you are a believer in efficient markets, obviously something rings false about that, and to some extent I agree. As I mentioned in the OP, I suspect there is a bit of a behavioral element in the value premium, and while Fama and French don't necessarily agree, they did write a paper showing why if that were the case, it wouldn't necessarily be arbitraged away. However, there are risk explanations too, because volatility is not the only measure of risk. Different risks matter to different people, so given one's situation, value tilt may allow you to exchange a risk you do care about (portfolio volatility) for one that may not affect you as much (portfolio safety in a poor economy). (See here and here for more on that.)

OK, so those are both side issues. The main question is, is SV feasible in a taxable account. From what I have seen, the argument that it isn't is largely false. Look at the EAFE analysis I linked to above, particularly my follow-up below the main post. For EAFE, one simple untilted option would be to just use Vanguard's VEA. (Actually it has a bit of a large tilt.) Well, VEA's ttm yield was 5.31%! :shock: On the other hand, PDN had a ttm yield of 2.06%. So with an effective tax rate on foreign dividends of 54%, PDN is ahead by 1.76%, and that's not even considering the theoretical benefit of its small and value tilts.

In the US, we don't see this extreme advantage, but we still have yield of 1.87% for VTI and 1.95% for VBR. SO SV isn't way ahead, but it's not really behind either.

Now it's true that narrower ETFs may be more likely to distribute capital gains, and that may indeed factor into the analysis. Personally I haven't looked into it too closely because in my unique situation (investing within a CCPC with active business income), capital gains are actually good. But from what I've seen, this isn't a major concern. For example, here are VBR's distributions since 2008. Total capital gains distributions: zero.

So basically, I'm just not seeing these large tax disadvantages to tilted portfolios. In the EAFE case in fact, there currently appears to be a massive tax advantage. That's just my own analysis though. I have also certainly heard the claim that tilted portfolios are much less tax-efficient, so please do share any counter-evidence.

You've already read them in that other thread, but for the benefit of others, my thoughts on RZV (S&P 600 (small) pure value) are here. Personally if it were my only choice to tilt I think I would just stick with TSM, as I decided in Canada. As you mentioned, it has pretty significant negative momentum, which looks to me like it could wipe out much of the expected benefit of the tilt (or all of it on a risk-adjusted basis).
Park wrote:What's more important than the strategy one follows (small and value tilt, total stock market, leverage) is the amount one saves, equity/bond split and how long one is investing for.
On this I couldn't agree more, and I also agree that it needs to be pointed out occasionally when getting way into the little details like this.
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Re: Multifactor Investing - A comprehensive tutorial

Post by LadyGeek »

This tutorial is now in finiki: Multifactor investing - a comprehensive tutorial - finiki, the Canadian financial Wiki

The "External links" section hopefully catches all of the FWF and Bogleheads forum threads.

Corrections / suggestions should be posted here. Finiki editors are welcome to update the article directly.
Last edited by LadyGeek on 07 Oct 2012 10:49, edited 1 time in total.
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Re: Multifactor Investing - A comprehensive tutorial

Post by ig17 »

Park wrote:What's more important than the strategy one follows (small and value tilt, total stock market, leverage) is the amount one saves, equity/bond split and how long one is investing for.
Another factor to keep in mind, one has to stick to one strategy (SV tilt or total market) for a long time. As the graph below shows, either of the strategies can underperform for prolonged periods.

Put yourself in the shoes of a tilted investor who started investing around 1983. You would have needed almost religious level of belief in SV premium in order to stay faithful to the strategy til the end of 90s. Many investors would have bailed out along the way (effectively selling low after incurring higher costs).

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Russell 2000: small-cap value
Russell 3000: total market

The graph comes from Vanguard article: Small-Cap Value premium: Fact or fiction?
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Re: Multifactor Investing - A comprehensive tutorial

Post by ClosetIndexer »

Another excellent point. Similarly to taking on too much equity exposure then bailing when the market drops, the worst thing one can do is tilt toward SV then quit after it under-performs for an extended period. That's one of the reasons why IMO it's so important to really understand the fundamentals of the strategy before implementing it, rather than just picking funds with "small" and "value" in the names, or looking at the Morningstar style boxes or whatever, as so many seem to do. Otherwise, how can you know whether under-performance is just random market fluctuation, which as you point out can last a long time, or negative alpha coming from costs or inefficiencies of your funds or overall implementation?
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Re: Multifactor Investing - A comprehensive tutorial

Post by Park »

I'm taking this thread on a tangent, but nevertheless, I think it is an important tangent.

http://www.mebanefaber.com/wp-content/u ... kowitz.pdf

Above is a link to a paper published by two people from AQR and Booth School of Business. It looks at the tax efficiency of value and momentum investing. So far, I've just taken a cursory glance at it. I've never seen this paper quoted on the Bogleheads forum, although that may be because I haven't looked hard enough.

Based on an internet search, 2012 US tax rates for dividends are 15%, for short term capital gains 35% and for long term capital gains 15%. The above paper shows that since 1979, the taxes for those respective sources of income have been as high as 70%, 70% and 28% in the USA. The top Ontario rates are presently around 29% for Canadian dividends, 46% for foreign dividends and 23% for capital gains. I just point this out that tax rates vary. As a consequence, the importance of tax efficiency varies. Unfortunately, it's difficult to predict where tax rates will be 25 years from now.

The following comes from Table 1. For each index, I will give the annualized before tax return from 1979 to 2009; then I will give the annualized after tax return from 1979 to 2009 using historical tax rates at the time. Finally, I will give the annualized after tax return from 1979 to 2009 using 2009 tax rates. Those 2009 tax rates are the same as the present 2012 tax rates.

Code: Select all

Russell 1000 (large/mid cap)         11.18% 9.61% 10.41%
Russell 1000 Value                   11.81% 8.96% 10.24%
Russell 1000 Growth                  10.16% 8.88% 9.49%

Russell 2000 (small cap)             10.24% 7.69% 8.62%
Russell 2000 Value                   12.43% 8.86% 10.08%
Russell 2000 Growth                  7.49%  5.60% 6.32%
As you can see, for large and mid caps, you didn't come out ahead using a value strategy on an aftertax basis. For small caps, the value strategy comes out 1.17% greater than the blend strategy on an aftertax basis using historical taxes. If one uses 2009 taxes, the extra return is 1.46%

If the above American data is relevant to other stock markets, I would be disinclined to tilt to value only anywhere in the world in a taxable account. Even when one uses 2009 tax rates, value tilting in US large/mid caps didn't outperform the blended approach. And 2009 US tax rates are considerably lower than those of Canadians in the top tax bracket. (Edited to include the following: Canadian investors also tend to lose the ability to recoup foreign withholding taxes more than American investors do)

That does leave the possibility of tilting to small and value together in a taxable account. Outside the US stock market, the investment vehicles to tilt to small and value together don't exist, other than DFA. Even if they did, transaction costs tend to be higher outside the US stock market; that would decrease the small cap value premium. However, the small and value premium might be greater outside the USA.

That leaves tilting to small cap value in the US stock market. In a taxable account, that might result in 1.2% greater return.

But that 1.2% ignores transaction costs, which might be greater for a value strategy than a blend strategy. I wouldn't be surprised if tracking error is larger for a value index than a blended index.

Also, for the good majority of this period, small cap value tilting received little or no publicity. Investor awareness of small cap value tilting has increased considerably in the last few years. It wouldn't surprise me if this increased awareness decreases the small cap value premium, as more investors pursue this strategy. It's not much of an exaggeration to say that DFA is based on tilting to small and value; their asset base is not small.

Finally, remember that 1.2% greater return is based on US taxes. If I had to hazard a guess, taxes will be somewhat higher in Canada than the USA in the future, at least if you're in the top tax bracket.

So the prediction of 1.2% greater return may be on the high side.

My plan is to tilt to small and value together, but only in my tax advantaged accounts. As I don't invest with DFA, that means tilting to SCV only in the US market. As to whether I should stick to RZV for that purpose, I'm not sure :? .

One comparison that this paper didn't make is that of the Russell 3000 (total US stock market index) return on an aftertax basis to the Russell 1000 value, the Russell 2000 value and the Russell 3000 value.
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Re: Multifactor Investing - A comprehensive tutorial

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OK, I get that once you have unrealized capital gains you won't necessarily be able to efficiently switch funds (except for new contributions), so it makes sense to plan for what might change in the future. That said, it doesn't really make sense to me to base your strategy on the average tax treatment of the Russell indexes, since the 1970s, in the United States, rather than your actual situation given the funds you plan to use and your own tax consequences in Canada today. Both tax rates and yields were considerably higher over that period. (Long-term S&P 500 dividend yield.) If you expect one or both are more likely to be higher than lower in the future, then by all means include that in your analysis, but ISTM that our best guess for the future, imperfect as it is, would be the situation at present. You could say dividends should revert to historical levels, or you could say that the trend has been persistently downward and likely to continue. Taxes may be higher in the future due to an aging population, or whatever reason, but who knows when or how much.

What's more, even in that historical situation, you showed that the SV index still outperformed. So if higher future taxes are a concern, you could simply get a more moderate tilt by adding SV to TSM or to LB instead of using a LV component as well. It just doesn't make sense to me to use an index (S&P 600 PV) that we have every reason to expect to underperform due to its negative momentum, in order to avoid using ones that might, potentially, have lower (but still likely positive) premiums in the future if both taxes and dividends increase.

For EAFE, what's wrong with PDN for small value? As I mentioned in my first reply and the linked EAFE thread, it has a ttm yield of 2.06% compared to over 5% for VEA, for a tax savings of almost 2% at today's rates, let alone any SV premiums.

Will the premiums be smaller in the short term due to increased popularity? I suppose it's possible. If so though, they will soon become unpopular again, and the premiums will increase. As mentioned above, you do need to commit for the long term, because there certainly will be long periods of under-performance. On the other hand, if you take a look at Vanguard's style index funds for example, you'll see that the growth funds are all significantly larger than their value counterparts. So I'm not convinced this value popularity is all that prevalent outside of these forums.

Anyway, just my opinions. Obviously everyone should do what they think best given their own situation and expectations. There are never any guarantees; all we can do is try to give ourselves the best chance of a favourable result, while minimizing risk.
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Re: Multifactor Investing - A comprehensive tutorial

Post by Park »

"According to Burton Malkiel, author of A Random Walk Down Wall Street, "it may not be possible to exploit the small-firm effect using real money." (Malkiel, 2004)"

The above quote is from https://global.vanguard.com/internation ... lcapEN.htm

On a pretax basis, small cap value outperforms large/midcap blend (small cap value is 1.25% more than large/midcap blend). This is from 1979 to 2009. The Vanguard link provides average annual American stock market returns from 1927 to 2004; small cap value outperformance compared to large blend was 4.6%.

On a posttax basis (1979-2009 data), small cap value does not outperform large/midcap blend, whether one uses historical tax rates (0.75% less) or the lower 2009 tax rates (0.33% less). As mentioned previously, one could make the case that 2009 US tax rates are overall lower than the present Canadian rates for those in the top bracket.

So in a taxable account, a reasonable conclusion is that large/midcap blend is no worse than small cap value.

In a tax advantaged account, small cap value will outperform large/midcap blend. I wouldn't be surprised if the difference was a little smaller, if one compared small cap value to the total stock market (Russell 3000, large/mid/small). Also, the outperformance of small cap value does not include the drag of possible greater tracking error (increased costs) associated with small cap value.

And once again, the increased popularity lately of small cap value tilting may decrease future outperformance. The difference in outperformance between the 1927-2004 and 1979-2009 periods would suggest that the small cap value premium has decreased with time. Will this trend continue? From the Vanguard link,

"The last issue to ponder is whether the small-cap value premium, if it truly exists, will continue. In an efficient market, is it reasonable to believe that investors would not seek to exploit the small-cap value premium, bidding up prices of these stocks in the process? Some researchers have suggested that if the premium existed, it has since dissipated after the wide circulation of historical small-cap value returns. (Schwert, 2001)"
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Re: Multifactor Investing - A comprehensive tutorial

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Park wrote: On a posttax basis (1979-2009 data), small cap value does not outperform large/midcap blend, whether one uses historical tax rates (0.75% less) or the lower 2009 tax rates (0.33% less). As mentioned previously, one could make the case that 2009 US tax rates are overall lower than the present Canadian rates for those in the top bracket.

So in a taxable account, a reasonable conclusion is that large/midcap blend is no worse than small cap value.
I still see no evidence of this. Yields were higher through the 80s than they are today. I still don't think that the performance of the Russell indexes in the 1980s is a good indication of the tax efficiency of small value indexes today. That we can tell for ourselves by actually looking at their yields (equal or lower than the market) and their funds' capital gains distributions (pretty close to nil, as far as I can see). Do you see something I'm missing here?

Park wrote:Also, the outperformance of small cap value does not include the drag of possible greater tracking error (increased costs) associated with small cap value.
Check out my OP. I take into account the alphas and tracking errors of each fund. Over its entire history since 2004, VBR and VTV (my personal US value choices) have consistently had tracking errors lower than their MERs (likely due to securities lending). PDN's tracking error has only been 0.2% greater than its MER since inception, and it's a RAFI fund, hence considerable turnover. Again, I'm just not seeing these hypothetical increased costs in real life, certainly not to the extent that they would overwhelm even conservative premium expectations.
Park wrote:"The last issue to ponder is whether the small-cap value premium, if it truly exists, will continue. In an efficient market, is it reasonable to believe that investors would not seek to exploit the small-cap value premium, bidding up prices of these stocks in the process? Some researchers have suggested that if the premium existed, it has since dissipated after the wide circulation of historical small-cap value returns. (Schwert, 2001)"
If it is a risk premium, it will continue in the long-term, even if it IS dissipated in the short term due to increased popularity (a big "if"). Even if it is a behavioural effect, as long as the underlying behaviour continues, so will the premium; it should not be arbitraged away. (Personally I believe the truth is somewhere in-between, but closer to the risk story.) Is it guaranteed to continue? Of course not. Neither is the ERP for that matter. Is it more likely than not? I think so.
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Re: Multifactor Investing - A comprehensive tutorial

Post by Park »

About the future of the small cap value premium, it will persist. The small cap premium is a risk premium (liquidity risk etc). As for the value premium, even if it's not a risk premium, I am confident that it will continue. Bubbles have always existed, and always will. That means growth stocks become overpriced periodically, which means they underperform relative to value stocks. So value stocks will outperform the market, as the rest of the market includes growth stocks.

About tracking error, your point is well taken. If one goes to the Vanguard website, the average annual difference between the index and the NAV of the following ETFs for the last 5 years is -0.06% annually for VBR (small cap value, minus means NAV less than index) and +0.02% annually for VTI (total stock market index, + means NAV greater than index). So the difference is 0.08%, which is very small.

About higher dividends in the 1980s, that is true. But when the authors ran the results using 2009 tax rates, large/mid cap value or small cap value did not outperform large/mid cap blend. And the 2009 tax rate for dividends was 15%. For a Canadian in the top tax rate, their 2012 tax rate on foreign dividends is around 45%, which assumes they can recoup any foreign dividend withholding taxes.

I would believe that small cap value ETFs have dividends that are at least no greater than a total stock market index ETF. There is less tendency for small cap stocks to pay dividends compared to large cap stocks. But I wouldn't say the same for large cap value stocks.

For 1979-2009 from the paper I cite, Russell 1000 index (large/midcap blend) had an annualized turnover of 7% and a dividend yield of 2.5%. The Russell 1000 Value (large/midcap value) had respective numbers of 17% and 3.4%. The Russell 2000 Value (small cap value) had respective numbers of 36% and 2.3%.

So even though the Russell 2000 Value had a lower dividend yield than the Russell 1000 index from 1979-2009, it still failed to beat the Russell 1000 index, whether historical tax rates or 2009 tax rates were used. And those 1979-2009 dividend yields aren't greatly different than present dividend yields. As for VBR (Vanguard small cap value) not having any capital gains distributions since 2008, I predict that won't continue indefinitely.

I still stand by my contention, that in a taxable account, large/midcap blend is no worse than small cap value.

The study would suggest that one might get an extra 1.25% pretax return for small cap value over large/midcap blend. As for large cap value, one might get an extra pretax 0.63% return over large/midcap blend. So a case can be made for tilting to small and value in a tax advantaged account.

But the point I'm making is that the small cap value premium may decline in the future. The Vanguard link suggests that the small cap value premium was considerably higher prior to 1979. Edited to change the following: there will be a small and value premium in the future, but how much lower than 1.25% or 0.63% may it go?
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Re: Multifactor Investing - A comprehensive tutorial

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A brief return to the tutorial: Multifactor investing - a comprehensive tutorial - finiki (and above). I don't understand how to put the final portfolio together. I'm tracking your exact steps from start to finish and lost track at the fund selection step.
  • Determine equity / fixed income split: 75% equity / 25% fixed
  • Determine Reasonable Targets for Fama-French Factor Tilts: 0.1 to 0.3 to SMB and 0.3 to 0.5 to HML were 'close enough'
  • Choose Specific Funds for Each Region: I went with (?)
  • Choose Global Asset Allocations --> Results: 0.20 SMB, 0.27 HML
  • Re-adjusting Asset Allocation: Using 0.2 SMB, 0.3 HML (round-off), arrive at 68% equity / 25% fixed
finiki wrote: Re-adjusting Asset Allocation

The final step in our portfolio-building process (on the equities side at least) is to adjust our split between equities and fixed income to compensate for the tilt we've added, thus keeping our expected risk in line with the tolerance we established in Step 1. For that, we can go back to my handy spreadsheet. Our baseline untilted portfolio of 75% equities, 25% fixed income had a historical annual standard deviation of about 15.3%. To get that same level with our 0.2 SMB, 0.3 HML tilted portfolio (on the equities side), we need to reduce the equities portion of the total portfolio to about 68%. This is just a rough estimate since we're only using US historical data, but it should be in the right ballpark.
In your spreadsheet, I entered 75% equities in "Charts" and find the SD of 15.32% at (0,0). Then, enter 15.32% as a constant SD in Charts2. Using the bottom chart, I find the 0.2 SMB, 0.3 HML point aligns with 67.82% (9.34% annual return). So I now have a 68% equities, 32% fixed income asset allocation.

What happens next? It's a simple multiplication - of what? I couldn't find how to complete this last and most important step in the process - translating the results back into a portfolio. You give an example over in the Bogleheads forum, but I'm missing something basic and can't connect it with your tutorial.

Subject: How to choose FF Factor Weightings
ClosetIndexer wrote:.....To look at a whole portfolio, you simply take the weighted average of its constituents' factor loadings. So if your equities are 75% TSM and 25% VBR, you multiply TSM's factor weightings (which are RM-RF=1, SMB=0, HML=0) times 0.75, plus VBR's factor weightings times 0.25. That gives you the factor weightings of your entire equity portfolio. Using the spreadsheet, you can then plug in your total percentage of equities (38.6% I assume), to see the historical risk/return performance of those factor weightings...
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Re: Multifactor Investing - A comprehensive tutorial

Post by ClosetIndexer »

@LadyGeek:

I think you've got things out of order a bit. In step 3 you already chose the funds in your portfolio. There are a number of factors that come into play, which is why I have linked to several external threads that get into details, but basically you're trying to match your desired factor loadings while optimizing other factors like costs, (negative) alpha, diversification, taxes, etc. Your overall factor loadings for any given region are simply the weighted averages of the loadings of the funds you choose. So for example in the US I chose 60% VBR and 40% VTV. If we say, for simplicity, that VBR's loadings are 0.6 to SMB, 0.4 to HML, and 1 to RM-RF, and VTV's are -0.2 to SMB, 0.3 to HML, and 1 to RM-RF, our overall loadings for the US are 0.6*VBR + 0.4*VTV, or about 0.28 to SMB, 0.36 to HML, and 1 to RM-RF.

Then, in step 4, you decide on how much of your equities will be allocated to each region: Canada, US, EAFE, and Emerging. So once that's done, in Step 5, you can multiply the factors you got for each region by that region's percent weight to get the overall factor loadings for your equities. I also added a bit due to the fact that we're over-weighting Canada compared to its global market cap, and it has a tilt compared to the North American portfolio. What I did was take the amount of Canada that we're holding beyond its global percentage of market cap, and multiplied its tilt by that. (In this case, 30%-5% = 25%.) My logic was that the global market-cap weighted portfolio by definition has no tilt. So the portion of Canada that matches its market cap weighting is untilted. It is only by increasing it that the tilted nature of Canada compared to North America as a whole becomes a factor. This isn't an exact science, and I am sure there are other ways to look at it. That was simply the approach that made sense to me. Honestly there are so many sources of uncertainty here, I don't think we should worry too much about precision. Our Emerging factors are complete estimates, and the factors we use in our regressions in the three other regions should be similar, but aren't directly comparable. The goal is just to have a rough idea of our overall tilt. In this example, my best guess using the approach above was about 0.2,0.27 to SMB,HML. (All the funds I used had RM-RF that wasn't statistically different from 1, so I just assumed they were all 1 and focused on SMB and HML.)

Anyway, that little Canada quirk aside, the short answer is that the factor weightings of your portfolio are the weighted averages of the factor weightings of all the funds in your portfolio.
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Re: Multifactor Investing - A comprehensive tutorial

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Park wrote:For 1979-2009 from the paper I cite, Russell 1000 index (large/midcap blend) had an annualized turnover of 7% and a dividend yield of 2.5%. The Russell 1000 Value (large/midcap value) had respective numbers of 17% and 3.4%. The Russell 2000 Value (small cap value) had respective numbers of 36% and 2.3%.

So even though the Russell 2000 Value had a lower dividend yield than the Russell 1000 index from 1979-2009, it still failed to beat the Russell 1000 index, whether historical tax rates or 2009 tax rates were used. And those 1979-2009 dividend yields aren't greatly different than present dividend yields. As for VBR (Vanguard small cap value) not having any capital gains distributions since 2008, I predict that won't continue indefinitely.

I still stand by my contention, that in a taxable account, large/midcap blend is no worse than small cap value.

The study would suggest that one might get an extra 1.25% pretax return for small cap value over large/midcap blend. As for large cap value, one might get an extra pretax 0.63% return over large/midcap blend. So a case can be made for tilting to small and value in a tax advantaged account.

But the point I'm making is that the small cap value premium may decline in the future. The Vanguard link suggests that the small cap value premium was considerably higher prior to 1979. Edited to change the following: there will be a small and value premium in the future, but how much lower than 1.25% or 0.63% may it go?
One thing to keep in mind is that the Russel indexes only recently (a couple years ago I believe) instituted buffer zones between their style and size slices. These were previously used by all the other major index providers, and serve to reduce turnover. The switch to CRSP indexes should result in a further incremental improvement. That said, the numbers using MSCI haven't been too much lower than the 33% you quoted for the small value index. I dug back through some annual reports to see turnover and capital gains distributions for Vanguard's small value fund:

Code: Select all

    Turnover  Capital Gains*
2000   82     4.93%
2001   59     5.03%
2002   57     3.13%
2003** 100    0.00%
2004   30     0.00%
2005   28     0.00%
2006   25     0.00%
2007   34     0.00%
2008   30     0.00%
2009   33     0.00%
2010   25     0.00%
2011   30     0.00%

*As a percentage of pre-distribution end of year NAV
**Switched indexes from S&P to MSCI - high turnover this year due to index switch
So, zero capital gains distributions since the switch. (The main reason for switching was to reduce turnover.) In the 3 years I had data for before the switch, turnover was much higher, and about 4.5% per year in capital gains distributions.

So... what to expect for the future? I agree with you that zero capital gains distributions forever is unrealistic. That said, I don't see a reason to expect a return to the levels of S&P or Russel indexes in the past. For one thing, the prevalence of ETFs now reduces the need for distributing capital gains. The popularity of Vanguard and its funds also allows it to do much of its turnover with inflows and outflows as I understand it.

That said, your point is well taken. If funds like this were to revert to paying several percent per year in capital gains distributions, that would very quickly eliminate any potential advantage in a taxable account. (Particularly for foreigners like us who have to pay full income taxes on foreign income, regardless of type.) So it is something to watch out for at the very least. I wonder what 'the experts' predict for realistic levels of capital gains distributions going forward...

Edit: See this great answer/resource over at bogleheads: http://www.bogleheads.org/forum/viewtop ... 1#p1508641
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Re: Multifactor Investing - A comprehensive tutorial

Post by Park »

Due to other commitments today, I am going to respond in more than 1 post.

For 1979 to 2009, Russell 1000 had a pretax return of 11.18%; Russell 1000 Value had a pretax return of 11.81%. So a large value tilt gave you an extra 0.63% in pretax return.

For the same time period, the Russell 1000 had a 2.5% dividend yield; the Russell 1000 Value had a 3.4% dividend yield.

So the extra 0.63% pretax return can be explained by the increased dividend yield. If one assumes 45% tax on dividends, that results in a extra 0.3465% posttax return.

That assumes that the remaining 11.18% of the Russell 1000 Value return has the same tax efficiency as the Russell 1000 return. However, 0.27% of the remaining Russell 1000 Value return is dividends. If one assumes 45% tax on dividends, that pretax 0.27% is a posttax 0.1485%. The corresponding 0.27% in the Russell 1000 is deferred capital gains. Assume the tax on the deferred capital gains is anywhere from 0% to 22.5%. So in the Russell 1000, that pretax 0.27% is anywhere from 0.20925% to 0.27% on a postax basis.

So the extra 0.3465% posttax return is down to an extra 0.225%-0.279% posttax return.

Based on morningstar data going back to 2008, both VTV(Vanguard large cap value) and VTI (Vanguard total stock market) haven't had any capital gains distributions.

For the last 5 years, VTV had the same tracking error as VTI.

The extra 0.63% pretax return will be subtracted slightly by currency exchange costs. As for the other 0.27%, you can defer currency exchange costs with deferred capital gains, but you can't do that with dividends.

One can make the case that tilting to large value in a taxable account for a Canadian in the top tax bracket is not worth it. And in a CCPC, where you're going to lose about 74% of the 15% withholding tax on American dividends, it's even less worth it.
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Re: Multifactor Investing - A comprehensive tutorial

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Park wrote: The extra 0.63% pretax return will be subtracted slightly by currency exchange costs. As for the other 0.27%, you can defer currency exchange costs with deferred capital gains, but you can't do that with dividends.
Sure you can. Just reinvest the dividends. No currency exchange.

Rather than comparing the yields of the Russell indexes, why not compare the yields of the indexes you plan to use? VTV has a ttm yield of 2.6%. VV (large cap blend) is 1.91%. So at 45%, that added yield costs about 0.31%. Here are the factor loadings for both funds since inception:

Code: Select all

                                RM-RF     SMB     HML    Alpha (annual)
    VV (Large blend)             0.97   -0.09    0.02    -0.18%
       Std. Error                0.01    0.02    0.02     0.47%   R^2 = 0.993

    VTV (Large value)            0.93   -0.21    0.33    -0.40%
       Std. Error                0.02    0.04    0.03     0.96%   R^2 = 0.972
Now, obviously those should be considered as part of an overall portfolio. But if we just compare them directly to get a rough idea, you get about 0.9% in risk-adjusted premium for VTV, historically. Personally I use the longest period available to estimate the premiums, but then try to give myself a reasonable margin of error. Using a more conservative recent number sounds logical to me too. However, if we just look at the period since 1979, the difference is actually larger. A portfolio with the loadings of VV had about 12.3% annualized return and 16.2% standard deviation over that period. A portfolio matching VV had about 11% annualized return and 17.2% SD.

You can't just look at the returns of given indexes over time to estimate the premiums, since a lot of the reason their premiums have come down is because their factor loadings have also come down. Also, while the value premium has been lower over that period, the value factor has also been less correlated with the market, so adding value has actually increased return and decreased standard deviation, rather than the standard trend of increasing it.

This kind of thing is why I suggest finding the actual factor loadings of the funds you're interested in, then basing your expectations on them, rather than through comparisons to other indexes or funds. To easily see the premiums (and risks) associated with various ideal tilted portfolios over various periods, you could use my spreadsheet here.

Anyway, it appears to me that the benefit outweighs the cost with a sufficient margin of safety, at least given my tolerance level. That does assume continuing low capital gains distributions however.
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Re: Multifactor Investing - A comprehensive tutorial

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ClosetIndexer wrote:@LadyGeek:

I think you've got things out of order a bit. In step 3 you already chose the funds in your portfolio. There are a number of factors that come into play, which is why I have linked to several external threads that get into details, but basically you're trying to match your desired factor loadings while optimizing other factors like costs, (negative) alpha, diversification, taxes, etc. Your overall factor loadings for any given region are simply the weighted averages of the loadings of the funds you choose. So for example in the US I chose 60% VBR and 40% VTV. If we say, for simplicity, that VBR's loadings are 0.6 to SMB, 0.4 to HML, and 1 to RM-RF, and VTV's are -0.2 to SMB, 0.3 to HML, and 1 to RM-RF, our overall loadings for the US are 0.6*VBR + 0.4*VTV, or about 0.28 to SMB, 0.36 to HML, and 1 to RM-RF.

Then, in step 4, you decide on how much of your equities will be allocated to each region: Canada, US, EAFE, and Emerging. So once that's done, in Step 5, you can multiply the factors you got for each region by that region's percent weight to get the overall factor loadings for your equities. I also added a bit due to the fact that we're over-weighting Canada compared to its global market cap, and it has a tilt compared to the North American portfolio. What I did was take the amount of Canada that we're holding beyond its global percentage of market cap, and multiplied its tilt by that. (In this case, 30%-5% = 25%.) My logic was that the global market-cap weighted portfolio by definition has no tilt. So the portion of Canada that matches its market cap weighting is untilted. It is only by increasing it that the tilted nature of Canada compared to North America as a whole becomes a factor. This isn't an exact science, and I am sure there are other ways to look at it. That was simply the approach that made sense to me. Honestly there are so many sources of uncertainty here, I don't think we should worry too much about precision. Our Emerging factors are complete estimates, and the factors we use in our regressions in the three other regions should be similar, but aren't directly comparable. The goal is just to have a rough idea of our overall tilt. In this example, my best guess using the approach above was about 0.2,0.27 to SMB,HML. (All the funds I used had RM-RF that wasn't statistically different from 1, so I just assumed they were all 1 and focused on SMB and HML.)

Anyway, that little Canada quirk aside, the short answer is that the factor weightings of your portfolio are the weighted averages of the factor weightings of all the funds in your portfolio.
Thanks, I understand the factor weightings now. I missed the global weighting totally. The significance of your global sector correlations in the detail threads was lost to me, as it's never discussed in the Bogleheads forum in this context (not needed in a diversified US market?). I could have missed it, though.

Suggestion: Change step 4, Choose Global Asset Allocations to "Choose Global Asset Weightings" as this section weights (multiplies) the global coefficients with the SMB, HML factors. This is more clear to me.

With your help, I've managed to work through the entire process. I think all that's needed in Fama-French three-factor model analysis - Bogleheads is a short summary (replicated in the finiki version) and just point to the tutorial. Then, I can finally focus on expanding the regression analysis.

====================
Why are the global weights different? In Choose Specific Funds for Each Region:
finiki wrote:As a default starting point, we would split the equities portion of our portfolio into these four regions by market cap, so about 45% US, 5% Canada, 35% EAFE, and 15% Emerging, or thereabouts.
But in Choose Global Asset Allocations:
We start with a straight market cap-weighted global portfolio. That would be approximately 46% US, 36% EAFE, 13% Emerging, and 5% Canada.
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Re: Multifactor Investing - A comprehensive tutorial

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LadyGeek wrote: Thanks, I understand the factor weightings now. I missed the global weighting totally. The significance of your global sector correlations in the detail threads was lost to me, as it's never discussed in the Bogleheads forum in this context (not needed in a diversified US market?). I could have missed it, though.

Suggestion: Change step 4, Choose Global Asset Allocations to "Choose Global Asset Weightings" as this section weights (multiplies) the global coefficients with the SMB, HML factors. This is more clear to me.
Well, what we're doing in that step is deciding what percentage of our equities should go to each region. That's generally referred to as asset allocation. A number of factors go into the decision (which I list), including factor the factor weightings we achieved for each region, costs, and tax efficiency. Once we decide on the allocations to each region, we are able to calculate the weighted average global factor weightings.
LadyGeek wrote: Why are the global weights different? In Choose Specific Funds for Each Region:
finiki wrote:As a default starting point, we would split the equities portion of our portfolio into these four regions by market cap, so about 45% US, 5% Canada, 35% EAFE, and 15% Emerging, or thereabouts.
But in Choose Global Asset Allocations:
We start with a straight market cap-weighted global portfolio. That would be approximately 46% US, 36% EAFE, 13% Emerging, and 5% Canada.
Ha, I guess in one case I decided to round to 5%s, and in the other to the nearest %. Regional market caps are always shifting, so the idea is just to have a rough starting point. That said, I probably should use the same numbers everywhere. I suggest the 5%s to emphasize the fact that they're a rough guide.
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Re: Multifactor Investing - A comprehensive tutorial

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I agree with 5%, as that's also the recommended band for simple portfolios (new investors). IOW, decide on an asset allocation to the nearest 5%.

For perspective, 5% is a different way of expressing 0.05 increments on a scale of 0 to 1. Compare to moving 0.1 steps for the SMB and HML factors, which is also on a scale of +/-(0 to 1).

For a tutorial, consistency is important. As you can see, I stop when they don't match.
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Re: Multifactor Investing - A comprehensive tutorial

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LadyGeek wrote:I agree with 5%, as that's also the recommended band for simple portfolios (new investors). IOW, decide on an asset allocation to the nearest 5%.

For perspective, 5% is a different way of expressing 0.05 increments on a scale of 0 to 1. Compare to moving 0.1 steps for the SMB and HML factors, which is also on a scale of +/-(0 to 1).

For a tutorial, consistency is important. As you can see, I stop when they don't match.
OK, updated the wiki.

Actually, the factors can have a range of +/- infinity. However, with realistic long-only portfolios, it is difficult to achieve levels much higher than 0.8 or so, particularly for HML exposure.
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Re: Multifactor Investing - A comprehensive tutorial

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Is there a sweet spot for portfolio size and age of investor. With a small portfolio is it worthwhile to tilt? If it's a large portfolio already producing $4500-6000 a month income (max utlity?) is it worth while. For a 60 to 65 year old they may be dead before the tilt effect adds value?
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Re: Multifactor Investing - A comprehensive tutorial

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BRIAN5000 wrote:Is there a sweet spot for portfolio size and age of investor. With a small portfolio is it worthwhile to tilt? If it's a large portfolio already producing $4500-6000 a month income (max utlity?) is it worth while. For a 60 to 65 year old they may be dead before the tilt effect adds value?
Hmm.. well, just like the ERP, the small or value premiums may not show up for some time. However, if you're reducing your overall equity exposure for retirement, small and value exposures will be reduced as well. In fact, small and value can be used to maintain the same expected return while cutting the left tail, so they could be considered better for retirees in that way. Also, one of the main arguments for the risk story behind value is that its risk tends to show up (in the form of increased correlation with the market factor) in poor economic times, when job security may be an issue. For (near-)retirees, that's not really an issue.

So, yes the premiums may not show up in time. Same with the equity risk premium. IMO answer in both cases is the same: increase fixed income. If anything ISTM that tilts make more sense as you approach retirement, all else being equal. (The primary goal being to reduce volatility risk by allowing for a larger fixed income allocation with the same expected return, rather than to boost expected return.)

Of course, there are always other factors to consider as well - taxes being a big one, as discussed by Park.
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