nice short piece on the math of factor investing

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larryswedroe
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nice short piece on the math of factor investing

Post by larryswedroe » Thu Mar 30, 2017 12:42 pm

Some simple examples to show the power of diversification

A Skeptic's Guide to Factor Investing

Larry

[Link fixed by admin LadyGeek]

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Re: nice short piece on the math of factor investing

Post by Volkdancer » Thu Mar 30, 2017 12:46 pm

I had to copy and paste but that works and the article is succinct and interesting as an actionable logic.

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Re: nice short piece on the math of factor investing

Post by jalbert » Thu Mar 30, 2017 12:51 pm

From the article:
Let’s also assume three theoretical alternative factor premia, Factor 1 (F1), Factor 2 (F2) and Factor 3 (F3) exhibit an empirical Sharpe ratio of 1, on par with the market. Further assume that they are uncorrelated to the market and to each other. This is broadly consistent with the historical evidence on factor premia,
Seriously? The value and size factors are independent? Then why would it generally be considered that the value factor is stronger for small stocks, and the size factor effect is inverted for growth stocks? (Moreover, this undermines the correctness of the F-F linear model, not just this article).
Last edited by jalbert on Thu Mar 30, 2017 12:57 pm, edited 1 time in total.
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Re: nice short piece on the math of factor investing

Post by saltycaper » Thu Mar 30, 2017 12:54 pm

Further assume that [the factors] are uncorrelated to the market and to each other.
Haha. No.
Quod vitae sectabor iter?

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Just sayin...
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Re: nice short piece on the math of factor investing

Post by Just sayin... » Thu Mar 30, 2017 1:13 pm

Thanks Larry! Here's a more user-friendly link:

http://www.investresolve.com/blog/skept ... ead%20More

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Re: nice short piece on the math of factor investing

Post by patrick013 » Thu Mar 30, 2017 1:29 pm

There is a great deal of evidence supporting the existence of alternative sources of excess returns, such as value, momentum and low risk.
Sure, even here : Value versus Growth Stocks

Still running across "dividends" as a possibility for a few extra percent return.

I've paraphrased this to pick out the details.

This particular study covered December 31, 1951 to December 31, 2003.

The 50 highest dividend yielding stocks (excluding utilities)
from the multi-cap group returned 13.35 percent a year.

The 50 highest dividend yielding stocks (excluding utilities)
from the Large Stocks group returned 13.64 percent, better than
the 500’s return of 11.52 percent for the same period.

With Large Stocks the high-dividend strategy entailed less risk
than the group, and it beat the group 86 percent of the time over
rolling 10-year periods. That’s impressive.

(What Works on Wall Street by James O’Shaughnessy)
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Re: nice short piece on the math of factor investing

Post by lack_ey » Thu Mar 30, 2017 1:31 pm

saltycaper wrote:
Further assume that [the factors] are uncorrelated to the market and to each other.
Haha. No.
Also, the issue people have is in gauging benefit over additional frictions such as higher expenses, trading costs (internal to a fund), perhaps higher taxes, etc. And in the real world people are not mixing pure factor exposures, and calculating Sharpe under simplified assumptions doesn't directly apply if you can't borrow at the risk-free rate and conjure these factor exposures out of thin air.

All this overly simplified demonstration illustrates is that if you have multiple uncorrelated assets each with positive Sharpe ratio (one higher than the others), the best portfolio by Sharpe ratio is a mix of them. Doesn't everybody know that already? I don't really see this adding much of any understanding. There's too much information thrown away, simplified, and abstracted, all for a payoff that just proves something relatively trivial to begin with.

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Re: nice short piece on the math of factor investing

Post by larryswedroe » Thu Mar 30, 2017 4:54 pm

First, the size factor has low correlation with beta, about .4 and close to zero with value and value about 0 with beta, so they are clearly unique factors, both with premiums. Now that simple model is not perfect because of the small growth problem. So you can improve on that by screening out groups of the lottery tickets.

Lack_ey while you and I agree on this simple issue most Bogleads IMO don't or they would have more exposure to these other factors

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Re: nice short piece on the math of factor investing

Post by Random Walker » Thu Mar 30, 2017 6:34 pm

It's not discussed in the essay, but I think it's relevant. When a factor diversified portfolio underperforms, I'm pretty sure it's by a very small amount. When it outperforms, the outperformance tends to be very significant.

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Re: nice short piece on the math of factor investing

Post by Alchemist » Thu Mar 30, 2017 9:09 pm

I take serious exception to the continued definition contortions used by those selling factor strategies.

An increased concentration into a risky asset is the opposite of diversification.

If you want to promote factors because you think taking the risks that they will show up in the future and provide excess returns, then that is a fine argument to be had. But for the love of the dictionary, please stop trying to re-define basic investment terms. It is eroding your credibility and reeks of sales fluff.

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Re: nice short piece on the math of factor investing

Post by Random Walker » Thu Mar 30, 2017 10:38 pm

Not the opposite of diversification, just another way of looking at diversification: number of stocks versus sources of return

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Re: nice short piece on the math of factor investing

Post by in_reality » Thu Mar 30, 2017 11:14 pm

Random Walker wrote:Not the opposite of diversification, just another way of looking at diversification: number of stocks versus sources of return

Dave
No it's not. It is concentration by definition.

By concentrating on stocks/funds that give you value/momentum/low volatility/small exposure, you are excluding the stocks that give you exposure to the opposite.

If value/momentum/low volatility/size exposure pay a premium (as many eventually expect), you will have outperformed the market. If it doesn't you will have underperformed.

You are by definition concentrating your stocks to those you expect to outperform.

Wait - stop the presses. Only holding the US is now considered to be diversification!!! If you don't overweight the US, you won't have US exposure.- per the alternative definition of factor investing that some wish to adopt

[of course you will have US exposure even if you weight by global market cap weighting, and of course you will have value/momentum/low volatility/small exposure if you weight by global market cap weighting. The alternative view that you won't have value/momentum/low volatility/small exposure unless you overweight them is inconsistent in that it doesn't also say you won't have US exposure unless you overweight it]

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Re: nice short piece on the math of factor investing

Post by larryswedroe » Fri Mar 31, 2017 7:37 am

In reality,
Sorry but your view is just your view,not fact.

By it's very definition TSM has all of its eggs in one factor among the number of them that explain differences in returns. And these are unique/independent factors which diversify risks as they are subject to different risks. And historically diversifying across these factors has produced more efficient portfolios, and has done so POST PUBLICATION, not just pre

Now it's true that you have perhaps fewer stocks, but you still have many thousands, more than sufficient to diversify away idiosyncratic risks.

Also the mistake people make by thinking TSM is the most diversified portfolio is that isn't even in the literature--it is THEORY that it's the most EFFICIENT, not most diversified. A more equal weighted portfolio would be more diversified, avoiding the concentration risk in the stocks with the most market cap, like S&P 500 is just 500 stocks out of say 4000 in US but has about 80% plus of the market cap. but that would be less efficient to run, with high trading costs in the smallest stocks

Larry

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Re: nice short piece on the math of factor investing

Post by in_reality » Fri Mar 31, 2017 7:55 am

larryswedroe wrote:In reality,
Sorry but your view is just your view,not fact.

By it's very definition TSM has all of its eggs in one factor among the number of them that explain differences in returns. And these are unique/independent factors which diversify risks as they are subject to different risks. And historically diversifying across these factors has produced more efficient portfolios, and has done so POST PUBLICATION, not just pre

Now it's true that you have perhaps fewer stocks, but you still have many thousands, more than sufficient to diversify away idiosyncratic risks.

Also the mistake people make by thinking TSM is the most diversified portfolio is that isn't even in the literature--it is THEORY that it's the most EFFICIENT, not most diversified. A more equal weighted portfolio would be more diversified, avoiding the concentration risk in the stocks with the most market cap, like S&P 500 is just 500 stocks out of say 4000 in US but has about 80% plus of the market cap. but that would be less efficient to run, with high trading costs in the smallest stocks

Larry
Hahaha. You are saying I don't have exposure to America by holding Vanguard Total world. You are saying I don't have exposure to value by holding Vanguard Total World.

Classic!

Wait, if I remove half the growth and large stocks from my holding of Vanguard Total World, then I am diversified.

Yeah, yeah, sure. Whatever.

Anyway, I like reading your stuff Larry. Keep it up!

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Re: nice short piece on the math of factor investing

Post by Random Walker » Fri Mar 31, 2017 9:59 am

In_reality,
Maybe remove the sarcasm from your thinking and writing, then you may learn something. Then at least, you'll have a better understanding of the tradeoffs involved in making your TSM decisions. It will add to the conviction you have in the plan you choose.

Dave

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Re: nice short piece on the math of factor investing

Post by in_reality » Fri Mar 31, 2017 10:14 am

Random Walker wrote:In_reality,
Maybe remove the sarcasm from your thinking and writing, then you may learn something. Then at least, you'll have a better understanding of the tradeoffs involved in making your TSM decisions. It will add to the conviction you have in the plan you choose.

Dave
Just saying people who have exposure to growth and value are diversified. More diversified than a portfolio of only value stocks even though it loads on value and beta while TSM only loads on beta.

Just saying that taking international out of the world market might outperform given the red-white-and-blue factor but to call it diversified begs for correction.

There's no sarcasm in my posts, it's more like astonishment at the level of absurdity in the claim, and some actual doubt in my mind if people are being serious.

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Re: nice short piece on the math of factor investing

Post by dbr » Fri Mar 31, 2017 10:31 am

I wish people would keep this discussion to just doing the math and showing the results rather than appealing to and arguing about labels, such as "diversified." I don't think the market history (retrospective and prospective) of investments knows a thing about how we are labeling those investments. You can calculate factors and you can tabulate returns and calculate statistics about those returns and you can relate all those results to each other. Just do that and move on.

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Re: nice short piece on the math of factor investing

Post by Da5id » Fri Mar 31, 2017 10:35 am

Random Walker wrote:In_reality,
Maybe remove the sarcasm from your thinking and writing, then you may learn something. Then at least, you'll have a better understanding of the tradeoffs involved in making your TSM decisions. It will add to the conviction you have in the plan you choose.
While I don't do factor investing myself, I don't dismiss it either.

That said, the word "diversification" is obviously subject to different definitions. Saying that concentrating in certain factors is MORE diversified than owning the broader market is only correct if you choose to define diversification in a certain way. I'd tend to believe that by the definition held by many diversification is generally achieved by owning the broader market rather than by concentrating in segments of it based on factors. I'd also believe that factors may improve risk adjusted returns over the long haul, but whether investing in factors is more "diversified" by the definition of diversification most investors actually hold is, well, an odd choice of words.

Feels a bit like a sales pitch. We all know diversification is good. Factors are diversification. You should therefore invest in factors. I don't like the ambiguity of meaning of diversification between steps 1 and 2 there myself.

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Re: nice short piece on the math of factor investing

Post by in_reality » Fri Mar 31, 2017 10:47 am

dbr wrote:I wish people would keep this discussion to just doing the math and showing the results rather than appealing to and arguing about labels, such as "diversified." I don't think the market history (retrospective and prospective) of investments knows a thing about how we are labeling those investments. You can calculate factors and you can tabulate returns and calculate statistics about those returns and you can relate all those results to each other. Just do that and move on.
I have tremendous respect for Larry Swedroe.

I will refrain from pointless bickering and do apologize. Can I come out of the corner please? I promise to be nice!

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Re: nice short piece on the math of factor investing

Post by rkhusky » Fri Mar 31, 2017 10:51 am

larryswedroe wrote: Now it's true that you have perhaps fewer stocks, but you still have many thousands, more than sufficient to diversify away idiosyncratic risks.
According to Morningstar, DFA Small Value has 1083 stocks (31% in Micro category) and Vanguard Small Value has 827 stocks (9% in Micro category). Total Stock Market has 3512 stocks (2.5% in Micro category).

I agree that Small Value funds are less diversified than Total Market funds. Factor adherents need to come up with a different word to describe their concentration into more risky stocks - perhaps factor-diversification (factor-diversified). Fund returns come from their stock returns. If your fund has fewer stocks, your fund has fewer sources of return.

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Re: nice short piece on the math of factor investing

Post by dbr » Fri Mar 31, 2017 11:02 am

in_reality wrote:
dbr wrote:I wish people would keep this discussion to just doing the math and showing the results rather than appealing to and arguing about labels, such as "diversified." I don't think the market history (retrospective and prospective) of investments knows a thing about how we are labeling those investments. You can calculate factors and you can tabulate returns and calculate statistics about those returns and you can relate all those results to each other. Just do that and move on.
I have tremendous respect for Larry Swedroe.

I will refrain from pointless bickering and do apologize. Can I come out of the corner please? I promise to be nice!
I didn't mean this to apply to any one person. I think there are a lot of "offenders" in this department.

My view on this is that "explication by terminology" creates confusion rather than clarity. I would say your points are probably more in agreement with my view than otherwise, but unfortunately these discussions never seem to arrive at more clarity.

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Re: nice short piece on the math of factor investing

Post by larryswedroe » Fri Mar 31, 2017 11:31 am

in reality,
Be helpful if you actually stated factual information, your responses only show lack of knowledge, not any wisdom.
I certainly would not say you don't have exposure to America, which of course you do. And while you have exposure to value stocks by owning TSM you have NO EXPOSURE to the value factor because the growth stocks you also own provide NEGATIVE exposure exactly offsetting the value exposure the value stocks provide. Now you would know that if you read the literature or my book. Your statements to random are just plain incorrect.

Again, there are more than one way to think about diversification. Can be by number of stocks, or by factors. And the facts are that portfolios diversified across factors have historically produced more efficient returns, better risk adjusted returns due to the diversification benefits. Again, those are facts, not opinions.

And of course there was sarcasm and the astonishment is only because you are IMO blind to thinking about the world through the one single lens you know, market beta, while there are other ways to think about diversification.

When I discuss the issue I am very specific about what I mean by diversification. In some ways a diversified by factor portfolio is more diversified by factors that explain returns, while sacrificing some diversification by number of stocks. But my "larry portfolio" which is globally diversified just as much as TSM global is, and still owns thousands of stocks, last I looked about 4k vs say 12k. But 4k is plenty enough to eliminate/minimize idiosyncratic risks, which is what diversifying across more stocks provides. So IMO it is a very good trade off and historically has provided MUCH more efficient returns, and not just in backtesting but in live portfolios we have been building for more than 20 years. So investors who agreed have benefited greatly.

Might be helpful if you had more of open mind, and not be so stuck in "past" way of thinking about things. Just my opinion.

Hope that is helpful
Larry

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Re: nice short piece on the math of factor investing

Post by in_reality » Fri Mar 31, 2017 11:47 am

larryswedroe wrote:Some simple examples to show the power of diversification
Here's a tip:

Some simple examples to show the power of factor-diversification.

Using "diversification" the way you do is about as good as "smart beta".

That's all.

Anyway, if price-to-retained earnings explains the value premium more than HmL, is a traditional value fund that first screens on HmL and then on other metrics the best approach?

Couldn't there be stocks on the growth side that also have favorable price-to-retained earnings ratios?

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Re: nice short piece on the math of factor investing

Post by patrick013 » Fri Mar 31, 2017 3:11 pm

in_reality wrote:
Hahaha. You are saying I don't have exposure to America by holding Vanguard Total world. You are saying I don't have exposure to value by holding Vanguard Total World.
I was looking for answer to this and found it I think. Can you say value stocks beat
growth stocks the majority of years observed ? I think so. Can you say the international
stocks beat the 500 the majority of years observed (last 20 years) ? I don't think so.
Can you say Intl is a "value trap" ? These value stocks don't seem to be a trap but
a welcome allocation when the 500 has it's dis-economies-of-scale.

I guess I'd rather have some value stocks than some Intl and in a different allocation
than the market allocation, to give them a chance to perform.

I still use Bogle's 5-fund portfolio.
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Re: nice short piece on the math of factor investing

Post by dbr » Fri Mar 31, 2017 3:18 pm

Is there somewhere in this discussion that someone has missed the definitions of factors? Factor exposure means relative to the allocation that is already in the total market That is, the total market is not said to not have certain asset classes. It is said to not have an excess or deficiency of certain asset classes relative to itself.

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Re: nice short piece on the math of factor investing

Post by LadyGeek » Fri Mar 31, 2017 3:37 pm

The wiki has some background info: Factors (finance)

If anyone has an update or correction, please let me know.
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Re: nice short piece on the math of factor investing

Post by kolea » Fri Mar 31, 2017 4:23 pm

larryswedroe wrote:But 4k is plenty enough to eliminate/minimize idiosyncratic risks, which is what diversifying across more stocks provides.
But it cannot just be the number of stocks which determines if the portfolio has the minimum amount of idiosyncratic risk, it is how those stocks are apportioned across all possible idiosyncratic risks. It seems that we cannot reasonably presume to be able to enumerate all idiosyncratic risks so all we can do is make sure we do not concentrate too much in any one industry, sector, size, quality, state of incorporation, age of company, age of CEO, whatever. Risks can come from anywhere. So a strategy that discriminates at all in its selection of stocks that go into a portfolio must be exposing itself to idiosyncratic risk. I just don't see any way around that.

Here is an example. Somewhere in this thread the comment was made that TSM does not expose itself to the value factor because it has growth exposure that offsets value. So let's say you compose a portfolio that is diversified across all factors, including value, with the idea that it has also minimized idiosyncratic risk. Now let's say Congress passes tax reform that really hits value companies hard. This is idiosyncratic risk against the value factor part of the portfolio. Now in TSM, that risk is offset because TSM also has growth exposure, but the only way the factor portfolio with the value factor can offset that idiosyncratic risk is through exposure to growth within the other factors (like the quality factor). But if it is able to offset that risk, it seems like it should also be negating the effect of the value premia, just as it is in TSM.

I hope this makes sense. It seems to me that the two are incompatible - minimizing idiosyncratic risk while at the same time isolating factors.

[edit] changed "small" to "value". Booboo.
Last edited by kolea on Fri Mar 31, 2017 5:42 pm, edited 1 time in total.
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Re: nice short piece on the math of factor investing

Post by Random Walker » Fri Mar 31, 2017 4:41 pm

Kolea,
I think idiosyncratic risk = single stock risk.

I think it's fair to say that a certain number of stocks is required to diversify away the risk inherent in any single stock. I think single stock risk is effectively diversified away anytime a fund has at least perhaps greater than 500 individual stocks.

Dave

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Re: nice short piece on the math of factor investing

Post by rkhusky » Fri Mar 31, 2017 4:48 pm

kolea wrote: Somewhere in this thread the comment was made that TSM does not expose itself to the value factor because it has growth exposure that offsets value.
There is no value (or growth) factor in the FF model. The model uses the difference in returns between a group of stocks that have a value characteristic minus the returns of a group of stocks that have a growth characteristic. This set of return differences is then correlated with the returns from a given fund to generate the HmL factor for that fund. It is possible, but perhaps not probable, that a group of growth stocks could have returns that provide a positive HmL factor. The wiki article above also uses factor in multiple ways.

The FF model provides no information on the future performance of funds with a high, zero or low HmL factor. That is a completely separate analysis.
Last edited by rkhusky on Fri Mar 31, 2017 5:23 pm, edited 1 time in total.

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"Factor Investing"

Post by Taylor Larimore » Fri Mar 31, 2017 4:56 pm

Bogleheads:

I expressed my own thoughts about factors in this post: Factor Investing

There is more than one road to Dublin.

Best wishes
Taylor
"Simplicity is the master key to financial success." -- Jack Bogle

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Re: nice short piece on the math of factor investing

Post by kolea » Fri Mar 31, 2017 5:41 pm

Random Walker wrote:Kolea,
I think idiosyncratic risk = single stock risk.

I think it's fair to say that a certain number of stocks is required to diversify away the risk inherent in any single stock. I think single stock risk is effectively diversified away anytime a fund has at least perhaps greater than 500 individual stocks.

Dave
Terminology is a bear, eh? Perhaps I should have said nonsystematic risk. For instance the energy sector as a whole has risks that are unique to that sector alone but spread across all the companies in the sector.
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Re: nice short piece on the math of factor investing

Post by kolea » Fri Mar 31, 2017 5:49 pm

rkhusky wrote:
kolea wrote: Somewhere in this thread the comment was made that TSM does not expose itself to the value factor because it has growth exposure that offsets value.
There is no value (or growth) factor in the FF model.
Yes I realize that. I did not say exposure to the growth factor, just to growth. I was leveraging the distinction Larry made in this post:
posting.php?mode=quote&f=10&p=3307034#pr3306453

In which he said:
And while you have exposure to value stocks by owning TSM you have NO EXPOSURE to the value factor because the growth stocks you also own provide NEGATIVE exposure exactly offsetting the value exposure the value stocks provide.
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Re: nice short piece on the math of factor investing

Post by Jiu Jitsu Fighter » Fri Mar 31, 2017 5:49 pm

Owning the total stock market does not mean you "own all of the factors". I'm not sure why the folks that do not understand diversifying a portfolio using factors have such a vociferous opinion about it.

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Re: nice short piece on the math of factor investing

Post by rkhusky » Fri Mar 31, 2017 6:01 pm

Jiu Jitsu Fighter wrote:Owning the total stock market does not mean you "own all of the factors". I'm not sure why the folks that do not understand diversifying a portfolio using factors have such a vociferous opinion about it.
It is not a question of not understanding, but in the continued use of a well established word "diversification," which has always meant adding additional types of investments to a portfolio, for something else that involves reducing the number of investments. Use a different term. I suggest factor-diversification, if the word diversification has to be part of it.

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Re: nice short piece on the math of factor investing

Post by Da5id » Fri Mar 31, 2017 6:01 pm

Jiu Jitsu Fighter wrote:Owning the total stock market does not mean you "own all of the factors". I'm not sure why the folks that do not understand diversifying a portfolio using factors have such a vociferous opinion about it.
I think the bigger question is definition of "diversifying".

To give an example, suppose there are 26 stocks in the universe, corresponding to the letters A-Z. By the definition I believe most intuitively have of "diversification" owning all 26 stocks in some proportions (market weight? whatever) would be the most diversified. But there are the factors, the even factor and the vowel factor. Stocks corresponding to even numbers (B,D,F,...Z) and vowels (data on Y is a bit controversial here) have superior risk adjusted returns. So by that logic, owning those 18 (19?) stocks is "more diversified" than owning the 26 because you invested solely in the factors rather than Beta (the whole alphabet). It might be a better strategy, but it feels like a torturing of the word diversification. To me. Yes this example is a bit contrived. It is just an example of why I feel like the use of the word diversification is being, well, stretched here.
Last edited by Da5id on Fri Mar 31, 2017 6:23 pm, edited 2 times in total.

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Re: nice short piece on the math of factor investing

Post by Jiu Jitsu Fighter » Fri Mar 31, 2017 6:11 pm

rkhusky wrote:
Jiu Jitsu Fighter wrote:Owning the total stock market does not mean you "own all of the factors". I'm not sure why the folks that do not understand diversifying a portfolio using factors have such a vociferous opinion about it.
It is not a question of not understanding, but in the continued use of a well established word "diversification," which has always meant adding additional types of investments to a portfolio, for something else that involves reducing the number of investments. Use a different term. I suggest factor-diversification, if the word diversification has to be part of it.
It's all the same - diversification of risk. There is no need to differentiate. People who more than one stock in an asset class diversify their risk just as they would when they own more than one asset class. The same applies to factors.

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Re: nice short piece on the math of factor investing

Post by Random Walker » Fri Mar 31, 2017 7:13 pm

Diversification just means not putting all your eggs in one basket. The most classic equity diversification is to invest in the universe of stocks. But TSM or S&P 500 is dominated by one factor, the market factor. All the investor's eggs are in one single market beta basket. If one expands or redefines the basket to include sources of return, then one can definitely diversify beyond the one factor. He can create a basket full of different drivers of returns: market beta, size, value, Momentum, profitability, credit, term.

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Re: nice short piece on the math of factor investing

Post by rkhusky » Fri Mar 31, 2017 7:27 pm

Random Walker wrote:Diversification just means not putting all your eggs in one basket. The most classic equity diversification is to invest in the universe of stocks. But TSM or S&P 500 is dominated by one factor, the market factor. All the investor's eggs are in one single market beta basket. If one expands or redefines the basket to include sources of return, then one can definitely diversify beyond the one factor. He can create a basket full of different drivers of returns: market beta, size, value, Momentum, profitability, credit, term.

Dave
Stocks and bonds are sources of return. Market beta, size, value, Momentum, profitability, credit, term are just characteristics of stocks and bonds.

Factor investing concentrates risk by filtering out stocks that do not have desirable characteristics. Increased risk has been associated with higher expected return and higher volatility.

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Re: nice short piece on the math of factor investing

Post by in_reality » Fri Mar 31, 2017 7:42 pm

Jiu Jitsu Fighter wrote:
rkhusky wrote:
Jiu Jitsu Fighter wrote:Owning the total stock market does not mean you "own all of the factors". I'm not sure why the folks that do not understand diversifying a portfolio using factors have such a vociferous opinion about it.
It is not a question of not understanding, but in the continued use of a well established word "diversification," which has always meant adding additional types of investments to a portfolio, for something else that involves reducing the number of investments. Use a different term. I suggest factor-diversification, if the word diversification has to be part of it.
It's all the same - diversification of risk. There is no need to differentiate. People who more than one stock in an asset class diversify their risk just as they would when they own more than one asset class. The same applies to factors.
No.

People will propose a "Larry" portfolio with small cap emerging and US small cap value. From a factor perspective, yes it's more diversified in that it will load on "size" and "value" and "beta".

Using VT (Vanguard Total world) which only loads on "beta" but includes US large caps, developed. It also includes the very same stocks that are give access to "size" and "value" and "beta" in the aformentioned factor-diversified porfolio.

I would say that a small cap emerging and US small cap value is more factor-diversified, but I would not say it's diversified.

The risk of the alternative view of "diversified" is that people will end up with portfolios that are "factor-diversified" but too concentrated. We see it on the forum.

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Re: nice short piece on the math of factor investing

Post by Random Walker » Fri Mar 31, 2017 7:59 pm

Rkhusky,
Size, value, Momentum each have some explanatory power for equity's returns separate and independent from market beta. A TSM portfolio is a bet on a single factor, market beta. A tilted portfolio is spread across several different and independent factors. Whether we are talking asset classes, styles, or factors, the issue is how investments with different expected returns, volatilities, correlations, costs mix in a single portfolio. Diversifying across sources of return improves the portfolio's efficiency.
Two portfolios can have the same expected return. One may be a 60/40 TSM/TBM portfolio. The other may be a factor tilted 40/60 portfolio. One is more diversified across factors and has narrower dispersion of returns yet maintains same expected return.
When TSM tanks 50%, it will need to gain 100% to break even. A tilted portfolio, diversified across factors, with same expected return and bigger dose of bonds, may well not get walloped in the same way.

Dave

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Re: nice short piece on the math of factor investing

Post by Random Walker » Fri Mar 31, 2017 8:03 pm

In_reality,
If a factor diversified portfolio has say 500-1500 stocks in each of its individual asset classes, isn't that enough to diversify away the idiosyncratic single stock risk? Do you really need to add on the extra couple or few thousand stocks of the Wiltshire 5000 to adequately diversify away single stock risk?

Dave

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Re: nice short piece on the math of factor investing

Post by in_reality » Fri Mar 31, 2017 8:49 pm

Random Walker wrote:In_reality,
If a factor diversified portfolio has say 500-1500 stocks in each of its individual asset classes, isn't that enough to diversify away the idiosyncratic single stock risk? Do you really need to add on the extra couple or few thousand stocks of the Wiltshire 5000 to adequately diversify away single stock risk?

Dave
Yes, surely that is adequate to diversify idiosyncratic single stock risk. That's never been my point.

If you have a portfolio of 500 stocks that all load on value (so you have factor exposure to "value" and "beta"), are you more diversified by adding 500 more with the same characteristics, or by adding 500 that don't load on value?

Is 1000 value stocks really more diversified that 500 value and 500 growth?

You assume there is no idiosyncratic style risk. You assume there is no risk to holding only value. I think that in an investors horizon (remember not everyone is investing for the decades that value might take to prove it's worth), that the idiosyncratic style risk may show up.

So it's not the number of stocks. By definition you are not diversified across style by holding only value stocks. Yet paradoxically the claim is made that doing so will increase your "diversification". It's a confusing claim.

So "style diversification" and "factor diversification" are two different things. Obviously TSM has "style-diversification" and obviously a factor tilted portfolio doesn't and can't have "style diversification" by definition.

So Larry's use of "diversification" is unnecessarily confusing:
larryswedroe wrote:Some simple examples to show the power of diversification
If you mean "factor-diversification" please say so. It's different than "style diversification" or "size diversification" that most investors associate with "diversification".

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Re: nice short piece on the math of factor investing

Post by rkhusky » Fri Mar 31, 2017 8:49 pm

Random Walker wrote:Rkhusky,
Size, value, Momentum each have some explanatory power for equity's returns separate and independent from market beta. A TSM portfolio is a bet on a single factor, market beta. A tilted portfolio is spread across several different and independent factors. Whether we are talking asset classes, styles, or factors, the issue is how investments with different expected returns, volatilities, correlations, costs mix in a single portfolio. Diversifying across sources of return improves the portfolio's efficiency.
Two portfolios can have the same expected return. One may be a 60/40 TSM/TBM portfolio. The other may be a factor tilted 40/60 portfolio. One is more diversified across factors and has narrower dispersion of returns yet maintains same expected return.
When TSM tanks 50%, it will need to gain 100% to break even. A tilted portfolio, diversified across factors, with same expected return and bigger dose of bonds, may well not get walloped in the same way.

Dave
Factors are not independent.
Factors are not sources of return.
The FF model is much too coarse to say anything about how the correlations between individual stocks will affect portfolio returns.
If investing in a TSM fund is a bet, the same is true of factor investing.
Expected return rarely equals realized return.
I do agree that if one is concentrating risk and making a bet on deep value micro stocks that one should hold significantly more bonds.

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Re: nice short piece on the math of factor investing

Post by Da5id » Fri Mar 31, 2017 9:06 pm

in_reality wrote: So Larry's use of "diversification" is unnecessarily confusing:
I totally agree, regardless of the merits of factors.

Another example that to me is comparable:
My baseball card collection is more diversified than owning all the cards. It consists strictly of left handed American league pitchers. Three factors (left handed, American league, pitchers), more diversified than the "beta" of owning all the cards.

I object to twisting the meaning of diversification that most people attach to it that is needed to term factor investing as more diversified than TSM. It feels rather tendentious to me. And again, that is without arguing for or against the idea that factor investing is the way to go.

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Re: nice short piece on the math of factor investing

Post by Angst » Fri Mar 31, 2017 9:56 pm

Abstract. There's another verb we could throw into the mix. Above and beyond the reduction of idiosyncrasy achieved by diversification through the holding of high numbers of companies in a portfolio, I prefer a well-diversified portfolio that is also abstracted towards the factors of value and small cap.

Growth is a "factor", is it not? If so, would not 50/50 Growth/Value be more "diversified" than 100% Value? We're talking about tilting more than diversifying, or perhaps diversifying the factors we choose to tilt towards, to the exclusion of others. This all seems kinda silly, actually.

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Re: nice short piece on the math of factor investing

Post by stlutz » Fri Mar 31, 2017 11:52 pm

Let's step away from the words like "factor" (which isn't in reality the investing approach being advocated in the first place). Let's also not confuse sufficient diversification with maximum diversification. Finally, don't confuse diversification with portfolio efficiency.

Suppose I've identified 4 types of stocks that have beaten the market historically on Sharpe ratio basis. For the purposes of illustration I'll arbitrarily refer to them as "smallcaps", "value", "momentum", and "low volatility".

As the article supposes, I may think that there is only a 50% chance that each of them will beat the market in any significant way going forward. If that is the case, it is very much worth my while to diversify among them and own some combination of a) smallcap stocks, b) value stocks, c) high momentum stocks, and d) low volatility stocks. By owning all of these types of stocks, I can become more confident that I will exceed the market return by some degree. That is, by betting on all 4 types of stocks, my odds of beating the market are significantly higher than 50%, which would be my odds if I only invested in, say, value stocks. Moreover, a portfolio with a variety of different types of stocks is diversified by any measure.

So far, so good.

The question becomes whether I want to expand that diversification to add in high volatility, low momentum, about to go bankrupt money losers as well, or maybe some high flying big cap biotech stocks. Doing so would make my portfolio even more diversified. Would it make it better? Arguably no. "More diversified" does not always mean "better".

Now, owning all of the stocks is generally considered the most diversified portfolio (although there can be plenty of debate as to what weighting scheme actually diversifies the best). Subtracting out bunches of bad stocks will make the portfolio less diversified; however, doing so may make it more efficient/better etc.

The article illustrates that up to a point, diversifying will make your portfolio more efficient. Beyond a certain point, however, more diversification (i.e. adding in "bad" stocks) can lead to less efficiency.

The one concern I'd point out about the article is that it excludes any possibility of these types of trades being overcrowded and thus leading one to expect negative return premiums in the future. If you allow for a 25% chance of beating the market, a 25% of underperforming, and a 50% of equalling the market, well then it makes sense to go for the most diversified, own-all-of-the-stocks type of portfolio. In this scenario, the most diversified portfolio is also the most efficient one. To an extent, the article rigged the outcome by only considering the positive and neutral cases while excluding the negative possibility.

It is in Taylor Larimore's world of equities where most diversified=most efficient. In Larry's world, there is a trade off beyond a certain point.

Nothing I've said to this point should be remotely controversial on this board.

Full disclosure: I personally think that the tradeoffs required by Larry's model better approximate reality simply because that's how everything else is in life.

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Re: nice short piece on the math of factor investing

Post by nedsaid » Sat Apr 01, 2017 9:12 am

stlutz wrote:Let's step away from the words like "factor" (which isn't in reality the investing approach being advocated in the first place). Let's also not confuse sufficient diversification with maximum diversification. Finally, don't confuse diversification with portfolio efficiency.

Suppose I've identified 4 types of stocks that have beaten the market historically on Sharpe ratio basis. For the purposes of illustration I'll arbitrarily refer to them as "smallcaps", "value", "momentum", and "low volatility".

Nedsaid: I think you have picked four of the best. Momentum seems to be the largest performance premium and the most consistent and yet also seems to be the hardest to capture. Hard to capture because of turnover costs and also because it is very difficult if not impossible to capture in smaller stocks. Momentum as practiced in real life seems to be a large cap game as you have larger trading volume and it is much easier to trade and trade very quickly.

Low Volatility seems to be a crowed trade right now. Just look at the prices of consumer products stocks.

I have often wondered if Small Value is getting crowded but 2016 was a big year. So far, so good.


As the article supposes, I may think that there is only a 50% chance that each of them will beat the market in any significant way going forward. If that is the case, it is very much worth my while to diversify among them and own some combination of a) smallcap stocks, b) value stocks, c) high momentum stocks, and d) low volatility stocks. By owning all of these types of stocks, I can become more confident that I will exceed the market return by some degree. That is, by betting on all 4 types of stocks, my odds of beating the market are significantly higher than 50%, which would be my odds if I only invested in, say, value stocks. Moreover, a portfolio with a variety of different types of stocks is diversified by any measure.

So far, so good.

The question becomes whether I want to expand that diversification to add in high volatility, low momentum, about to go bankrupt money losers as well, or maybe some high flying big cap biotech stocks. Doing so would make my portfolio even more diversified. Would it make it better? Arguably no. "More diversified" does not always mean "better".

Nedsaid: There gets to be a "cancelling out" effect as you invest in more and more factors. It seems most efficient if you invest in two or three factors beyond market. Personally, I invest in market, size, value, and momentum. My concerns are two-fold: first that value and momentum might cancel each other out and secondly the fee drag on whatever excess performance I might get from the factors.

Now, owning all of the stocks is generally considered the most diversified portfolio (although there can be plenty of debate as to what weighting scheme actually diversifies the best). Subtracting out bunches of bad stocks will make the portfolio less diversified; however, doing so may make it more efficient/better etc.

Nedsaid: This doesn't always work, I own a couple of Quant or "Index Optimization" funds that seek to mimic the S&P 500 with equal sector weightings to the index but with lower risk stocks and with about 200 stocks rather than the 500 in the index. Also the market cap in the Quant funds are lower than the index. One such fund is value oriented and invests for higher dividend yield than the index and the other is growth oriented. The Value oriented fund has trailed the S&P 500 in recent years (not surprising as Value has trailed the S&P 500) and even a Value fund in the same fund group. The growth oriented fund has about tracked the S&P 500.

The article illustrates that up to a point, diversifying will make your portfolio more efficient. Beyond a certain point, however, more diversification (i.e. adding in "bad" stocks) can lead to less efficiency.

Nedsaid: The "cancelling out" effect I talked about earlier. My feeling is that you probably don't have to add the "bad" stocks, just keep adding factors. My guess is that if you go beyond market, size, value, and momentum you get diminishing benefits if not outright diminishing returns. There gets to be a point where too much diversification isn't diversification at all.

The one concern I'd point out about the article is that it excludes any possibility of these types of trades being overcrowded and thus leading one to expect negative return premiums in the future. If you allow for a 25% chance of beating the market, a 25% of underperforming, and a 50% of equalling the market, well then it makes sense to go for the most diversified, own-all-of-the-stocks type of portfolio. In this scenario, the most diversified portfolio is also the most efficient one. To an extent, the article rigged the outcome by only considering the positive and neutral cases while excluding the negative possibility.

Nedsaid: I do think factors get overcrowded and at times generate negative return premiums. But this effect is temporary as at some point animal spirits kick in and human nature and human behavior takes over. The old fear and greed thing. The problem is that human beings are not 100% rational beings. People, including market professionals, do some pretty silly things. This is why the factors persist.

It is in Taylor Larimore's world of equities where most diversified=most efficient. In Larry's world, there is a trade off beyond a certain point.

Nothing I've said to this point should be remotely controversial on this board.

Nedsaid: I don't know. If I said that the grass is green and that the sky is blue, the quants would be all over me for using anecdotal evidence and not understanding the concepts and for not understanding the math. That's what I thought too but now I know better. Sometimes just breathing can be controversial.

Full disclosure: I personally think that the tradeoffs required by Larry's model better approximate reality simply because that's how everything else is in life.
A fool and his money are good for business.

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Re: nice short piece on the math of factor investing

Post by larryswedroe » Sat Apr 01, 2017 1:19 pm

In reality
Using "diversification" the way you do is about as good as "smart beta".

That's all.

Anyway, if price-to-retained earnings explains the value premium more than HmL, is a traditional value fund that first screens on HmL and then on other metrics the best approach?

Couldn't there be stocks on the growth side that also have favorable price-to-retained earnings ratios?
These statements show a lack of understanding of terms, it's really that simple.
Smart beta is an oxymoron in most cases because it is just beta, just not market beta . With that there are examples of smart beta such as patient trading, not forced trading when stocks leave indices, or screening out stocks with traits the research shows have poor risk adjusted returns, like lottery stocks.

As to growth stocks having favorable P/E ratios, what does that even mean? Either you have low or high P/E ratios and by definition growth stocks have relatively high P/E, by standard definition top 30%.

Now there are various metrics that result in a value premium, and it's not that one is better than the other. In fact the research tends to support the use of multiple metrics, diversifying them, because some work better in some industries and there are periods when each of them outperform, so diversifying by using multiple metrics improves or smooths returns.

What's sad to me is your inability to look at world in any other way than you are doing. There are MANY different ways to think about diversification and certainly TSM is NOT the most diversified, not even in theory. It's just that it's the most efficient, in theory (but not supported by facts because there are groups of stocks whose exclusions would result in more efficient portfolios).

Larry

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Re: nice short piece on the math of factor investing

Post by larryswedroe » Sat Apr 01, 2017 1:21 pm

There is no value (or growth) factor in the FF model.
Gee this would be news to Fama and French since it is called the Fama-French three factor model, with the factors being size, value and market beta.
According to Morningstar, DFA Small Value has 1083 stocks (31% in Micro category) and Vanguard Small Value has 827 stocks (9% in Micro category). Total Stock Market has 3512 stocks (2.5% in Micro category).
Now everyone would agree that from a perspective of number of stocks SV is clearly less diversified. But it certainly has enough stocks to virtually eliminate any idiosyncratic risks. And a globally diversfied SV portfolio would own agbout 4x as many stocks so it too would be just as diversified in terms of geopolitical risks and geographical risks as a global TSM portfolio. And it would also be well diversified by industry/sector and countries. And it would have much less individual stock concentration!
Now with that said it also has exposure to three factors instead of just one, and that diversfies risks. And if used to lower beta you get more safe bonds and that dramatically reduces the concentration of risk of a PORTFOLIO, lower market beta, the largest risk, while increasing it to other factors including TERM, which also has basically no correlation to the market beta.
So from all perspectives but one a globally diversified "larry portfolio" can be said to be more diversified than a global TSM portfolio, but that one case it is less diversfied--but it's clearly less risky at same time (just look at the historical evidence).
Larry

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Re: nice short piece on the math of factor investing

Post by larryswedroe » Sat Apr 01, 2017 1:31 pm

Angst,
Growth certainly could be said to be a factor (though it's usually not because of the NEGATIVE expected return). But remember the TSM has no exposure to the growth factor any more than it has exposure to the value factor because the growth stocks it owns which give it positive exposure to the growth factor exactly offsets the negative exposure to the growth factor that the value stocks TSM owns provides. So no exposure to any factor, by definition, except market beta.
Larry

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