*Originally posted on* *the* *Cliff’s Perspective blog at AQR.com*

My colleagues have produced a paper on something we call, perhaps pretentiously though we can’t come up with a better word for it, “craftsmanship” — what we believe to be a necessary part in creating successful factor portfolios. What factors (value, momentum, small, quality, others?) you believe in, or dismiss, gets much of the attention. That’s understandable and appropriate. But we think there are many smaller decisions that each can matter some, and collectively can matter a lot. I won’t repeat the analysis and examples from the paper here (please read it!). But, I will use this essay as an excuse to discuss, in brief, two separate topics that I’d been planning to write about for a while (I still might expound upon these more in the future).

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__Fees__

The first one is factor investing fees. Yes, I’m now the fox writing an essay on how much to pay the henhouse guards. That’s your last warning — the rest will be my honest opinion, but it’s obviously impossible for me to be completely unbiased. Of course, if “craftsmanship” (again, read the paper!) ex-ante matters and if it varies across managers, then it is rational to have variation in fees across managers even if they espouse the same factors and philosophy. Thus, you can accurately take away from the craftsmanship paper that you should rationally be willing to pay factor managers who have better craftsmanship slightly more than others. One may also take away the implicit and self-aggrandizing belief that we fall into that category.

Still, I want to make an even more obvious point about fees, one that I think surprisingly gets lost sometimes. Magnitude matters, and fees for factor based investing are, in general, already much lower than traditional active management. Basically, a move from fees like 150 basis points (e.g., traditional active management) to fees like 30 basis points (e.g., factor tilted long-only portfolios) is pretty huge.^{1} By contrast, a move from 30 to 20 basis points, not so much.^{2},^{3} Make no mistake, all-else-equal, lower fees are better! But the plausibility of all-else-not-being-equal gets substantially higher when the absolute differences in fees get much lower. For example, on 500 basis points of active risk the reduction in fees from 150 to 30 basis points is equivalent to a Sharpe/information ratio pickup of 0.24 (a 120 basis point reduction divided by 500).^{4} That may seem low to those used to the Sharpe ratios so many managers claim, but it’s a reasonably big number. It’s a non-trivial fraction of the Sharpe ratio of the whole stock market over modern history. So, in that sense it’s a very big savings. Now, an additional fee reduction from 30 to 20 basis points is worth 0.02 Sharpe ratio “points.” This 0.02 may seem trivial, but if you think there’s any non-trivial difference in craftsmanship among implementers it’s far more plausible that it’s worth 0.02 rather than 0.24 Sharpe points. This means if you think the manager charging 30 basis points has a better than 0.02 Sharpe advantage you’d happily take them over the manager charging 20 basis points. Yes, this is all kind of obvious, and all I’ve proven here is that big numbers matter more than small numbers. But in a world where we have seen major fee reductions for some types of management over the last, say, decade, I think this perspective indeed gets lost sometimes as the numbers have indeed all gotten smaller.

__The Tyranny of Small Decisions__

Even if (if!) you’re making a large collection of small decisions correctly there can be long periods in which these decisions hurt instead of help you. This is true collectively, looking at the net of all these choices, and even more so when each decision is viewed standalone. Getting your time horizon lined up with some rational expectations is always a huge issue in investing. But, it’s perhaps more of an issue here as the edge to “small decisions” is almost by definition smaller. And, there are often a lot of them to make. One important subtlety is that one cannot avoid at least attempting some form of craftsmanship as choices have to be made.^{5}

Let’s just make up an example. Imagine there are ten independent (uncorrelated) sources of “craftsmanship alpha” and that each adds 2 basis points of expected return at the cost of 20 basis points of tracking error from each (against some idea of a super simple “non-crafted” alternative.)^{6} Each is thus a 0.10 Sharpe ratio viewed alone. Together they are expected to add 20 basis points to the overall factor implementation inducing 63 basis points of tracking error (20 basis points times the square-root of ten). That’s a Sharpe ratio of 0.32 from the collective craftsmanship (in addition to the basic factor returns).

This is not a bad deal particularly, say, continuing the example posited above where this craftsmanship costs an extra 10 basis points in fees.

But, as many have noted in other contexts, a Sharpe ratio like 0.32 can be hard to live with. Its chance of subtracting from your performance in a given year is about 37%. Its chance of subtracting over five years is about 24%. And, wait for it… over twenty years the chance it subtracts is still about 8%. That’s right. There’s a non-trivial chance your craftsmanship is every bit as good as you think, and it subtracts over two full decades, perhaps the lion’s share of your career. Such is the unforgiving, uncaring math.^{7}

Now, if you think those stats are bracing for the full set of ten unrelated additive pieces of craftsmanship, each with a 0.10 Sharpe ratio, then you are entering a special kind of hell if you are evaluating each on their own. Sharpe advantages of 0.10 have a 33% chance of losing over twenty-year periods. That means an individual minor improvement you believe in, and you are right about, could quite easily let you down over your career.

Of course, a remaining question is how one can ever be confident in each individual piece of craftsmanship if they are 0.10 Sharpe ratios viewed standalone. There is no magic answer (and please remember that you do have to choose!), and it is similar to getting comfortable with any strategy. We consider basic economic sense (“diversify across equally intuitive ways to measure a factor”, “don’t take unintended risks”, “trade as cheaply as you can”), and we look at evidence from very long periods, importantly and hopefully obtained in many places (geographies and assets classes). Despite them all being small advantages when viewed alone, we are confident enough, for instance, in the examples highlighted in the craftsmanship paper to make these many small decisions and to believe our strategies may