Factor Premiums as Statistically Significant As Equity Premiums

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runnerguy
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Factor Premiums as Statistically Significant As Equity Premiums

Post by runnerguy »

I once seen some research that concluded something to the effect of: the factor premiums (some of them at least) are as or more statistically significant as the equity premium. Anyone familiar with this research?
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JoMoney
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by JoMoney »

It's something Larry Swedroe has commented about, but it probably depends specifically on which "factor" you're talking about.
One of the many things to keep in mind with these things though, is people go looking in the historical data for things that show "statistical significance" retroactively in portfolios formed from a research databases that may not represent portfolios you could actually invest in.
Finding significant "premiums" in real world mutual funds is a different story.
"To achieve satisfactory investment results is easier than most people realize; to achieve superior results is harder than it looks." - Benjamin Graham
lack_ey
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by lack_ey »

Taking the French data library and doing the most simple things possible, taking a look at raw factor returns (which are obviously gross of costs)...

For monthly return data from 1927 to present on US stocks:

Code: Select all

Factor   Mean StdDev  t-stat
Mkt-Rf  0.646  5.391   3.93
SMB     0.216  3.219   2.20
HML     0.388  3.505   3.63
MOM     0.671  4.740   4.64
Mkt-Rf is total stock market return minus the risk-free rate as represented by T-bills; SMB is size (small minus big); HML is value (high book-to-market minus low); MOM is momentum; all data taken from "Fama/French 3 Factors" except the momentum

Again, per month. Annualized figures would be roughly 12 times the monthly mean and sqrt(12) times the monthly standard deviation. i.e. with plenty of assumptions that are wrong, we calculate that these are statistically significantly not zero. So in theory the significance in some sense of value is similar to the market. Momentum even stronger. In practice, net of costs, things would look different, particularly for momentum. The costs on trading small caps used to be huge.

All the usual caveats apply. This is based on raw returns data. This represents backfilled data that people collected after noticing these things in the first place.
Northern Flicker
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by Northern Flicker »

And the t-stat is only a valid measure of statistical significance for random samples.
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Taylor Larimore
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by Taylor Larimore »

runnerguy wrote:I once seen some research that concluded something to the effect of: the factor premiums (some of them at least) are as or more statistically significant as the equity premium. Anyone familiar with this research?
runnerguy:

We have a long-discussion of "factor investing" here:

Factor Investing

Best wishes
Taylor
"Simplicity is the master key to financial success." -- Jack Bogle
larryswedroe
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by larryswedroe »

Lack_ey

As I have pointed out many times here I would be careful about drawing conclusions with the small cap premium being less significant and smaller than value. It's a topic discussed thoroughly in my new book. The reason is small is defined very differently than value. If small was defined in same way (top and bottom 30%, not 50%) the size of the premium would be much larger and so would it's statistical significance. Another good reason to own very small stocks if you are going to own small.

I would add that the same type of data, with similar premiums and similar statistical significance is found ALL around the globe, in virtually every country, addressing the issue of data mining that jalbert points out.

I would add that the evidence on Time Series MOM is premium of about 6% with TSTAT of more than 5. (that's annual basis)

Best wishes
Larry
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GreatOdinsRaven
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by GreatOdinsRaven »

One of my favorite AQR papers: Size Matters If You Control Your Junk.

Happy reading.
GOR

http://papers.ssrn.com/sol3/papers.cfm? ... id=2553889
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larryswedroe
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by larryswedroe »

Great
Yes that paper gets to the heart of the lottery tickets that are small growth stocks with high investment and low profitability (Not all small growth is overpriced)
It also matters how you measure size. If you measure it like value (top and bottom 30% instead of 50%) the premium becomes quite a bit larger and statistically more significant. And then of course if you control for junk it looks even better. Note we show the differences in how the metric (30% vs. 50%) matters, and how the premium would be larger if measured like value. This is something I would bet very few investors know.
Larry
lack_ey
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by lack_ey »

Defining size by top/bottom 30 rather than 50/50 and especially controlling for junk are both ex-post corrections, though, justifying the past as we see it now. You can always play that game now.

Of course even long-run historically you do see a fairly monotonic relationship between size decile and return so that also gives more credence to the idea than simply one statistic computed as above (if the whole effect were caused by outperformance in deciles 6-8 with 3 being the worst, you would have to wonder about it). This is one of the reasons why you shouldn't just look at one statistic blindly. The t-stats listed above were not given to be comprehensive but just illustrative of the kind of analysis some do. As stated repeatedly here and elsewhere, you also test in other countries, among other things, and analyze the data in different ways.

It's also worth noting that you can get more size exposure at a lower cost than most other factors. Assuming there is a relationship, it shouldn't be hard to exploit. You can easily tilt heavily to size, in part because of how it was defined.

On the other hand you can just as well adjust size for liquidity and find the resulting evidence is smaller, also as mentioned repeatedly here and elsewhere. You might also beta adjust size. But for what it's worth, the original Fama-French size factor as defined since about 1992 (out of sample) still showed an annualized return over 2%. This happened despite the relatively low trading costs of the era.
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Robert T
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by Robert T »

.
On the small cap premium, we can test changes in definition using the Ken French data.

Here are some results: 7/1926 – 7/2016

Monthly size premium/t-stat

Smallest 50 percent/largest 50 percent = 0.21 / 2.15
Smallest 20 percent/largest 20 percent = 0.39 / 2.18

The monthly premium almost doubles, but so does volatility leaving little change to the t-stat. The [20:20] size premium is the same as the standard Fama-French value premium over this period, both 0.39.

However, if we change the definition of SmB (to use 20:20 small:large sorts) then for consistency we need to also change the definition of HML (as it uses the 50:50 small:large sorts). If we change HML to also use the 20:20 split, we get:

7/1926 – 7/2016

Monthly value premium/t-stat

HML [using 50:50 small:large sort] = 0.39 / 3.64
HML [using 20:20 small:large sort] = 0.56 / 3.98

Using this changed definition, the resulting monthly value premium estimate also increases (from 0.39 to 0.56). While the relative gap between the size and value premium is smaller (0.21/0.39 to 0.39/0.56), the t-stat on the value premium is about double that of the size premium (with little change on this over the two definitions of the size premium: 2.15 vs. 2.18).

Robert
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larryswedroe
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Re: Factor Premiums as Statistically Significant As Equity Premiums

Post by larryswedroe »

Lackey
I don't agree with that view of changing the definition being an ex post change. It's simply using the SAME methodology to define the premiums. I could have said change HML to 50-50. You want to measure things in same way and all the other factors besides size are measured 30/40/30 so why is small 50/50> That never made any sense to me.

I would add that because size is 50/50 and not 30/30 it's much easier to load heavily on the size factor. So while you rarely see more than about .5 or .6 loading on value, you can easily find funds that load close to 1 on size, so you capture more of that smaller size premium (:-))

As simple example if you look at value premium as say 4% and get .5 you get 2% capture and if size is only 2% but capture 100% as you load 1 you get the same 1% capture. So that's important to understand as well.

Larry
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