Prove adding SV will lower the risk, given the same E(r)

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acegolfer
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Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Lately, I have seen many posts similar to

"adding SV and more bonds to market/bonds portfolio will increase the expected return at the same risk."

2 questions.

1. What do you mean by risk? Most of these posts don't explain what the risk means. Is it stdev? If not, can you provide a clear definition of risk? If too hard, no need to provide the measure of risk.

2. Can you prove the above statement using your risk definition in Q1?

Note 1: The above statement says "will increase" not "has increased."
Note 2: If your proof only involves simple statistics such average returns and sample stdev, then one can use the same argument to "adding Apple will increase the return and lower the stdev," which we don't agree. So you will have to prove using more than simple statistics.

edit: changed the title to "Prove adding SV will lower the risk, given the same E(r)" because everyone is explaining how SV lowers the risk.
Last edited by acegolfer on Thu Jul 31, 2014 1:54 pm, edited 2 times in total.
Rodc
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Re: Prove adding SV will increase E(r) given the same risk

Post by Rodc »

There is no proof of most anything in investing.

No proof SCV will help, should be expected to help, should be expected to hurt, or will hurt.

If you have a 40% estimate that your car shop is cheating you, do you find a new shop? What about 70%? Probably you won't change at 1% (heck it likely at least 1% at any shop!) and you will somewhere before 100% certainty.

Most of investing is like that. There is no proof, but you have to make decisions anyway, and you do.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: Prove adding SV will increase E(r) given the same risk

Post by Aptenodytes »

Google Swedroe Fat Tail
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Re: Prove adding SV will increase E(r) given the same risk

Post by acegolfer »

Aptenodytes wrote:Google Swedroe Fat Tail
TY. I googled it and read the first 10 search results.

1. I understand what fail tail risk means.
2. Most stated, Larry's portfolio will reduce the fat tail risk without affecting the expected return and the stdev.
3. Some stated, Larry's portfolio will cut off left tail more than right tail, which is what investors want.
3. They all stated the above as if it's a fact without any explanation or proof.

If it's a fat tail (left and right) risk, then it can be measured by skewness (3rd moment) and kurtosis (4th moment). Using these statistics, I wish someone can easily prove the OP statement. This proof will be more than just average return (1st moment) and stdev (2nd moment).

Specifically, can one show that Larry's portfolio (or adding SV to market) has
1. the same expected return
2. the same standard deviation
3. lower Prob(return < 0)
than the market portfolio?
Last edited by acegolfer on Thu Jul 31, 2014 12:50 pm, edited 1 time in total.
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Re: Prove adding SV will increase E(r) given the same risk

Post by larryswedroe »

acegolfer
First all we can do is demonstrate, not prove.

Second, if really interested read Reducing the Risk of Black Swans which presents the logic and evidence--but said simply you have higher expected return with SV than TSM. That allows you to lower beta, which is bigger risk than the premium itself. Also you gain diversification benefits as factors have low correlation. And most importantly when tail risk shows up your safe bond correlation which averages zero tends to go highly negative which is what cuts the tail risk.

Larry
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Re: Prove adding SV will increase E(r) given the same risk

Post by Rodc »

acegolfer wrote:
Aptenodytes wrote:Google Swedroe Fat Tail
TY. I googled it and read the first 10 search results.

1. I understand what fail tail risk means.
2. Most stated, Larry's portfolio will reduce the fat tail risk without affecting the expected return and the stdev.
3. Some stated, Larry's portfolio will cut off left tail more than right tail, which is what investors want.
3. They all stated the above as if it's a fact without any explanation or proof.

If it's a fat tail (left and right) risk, then it can be measured by skewness (3rd moment) and kurtosis (4th moment). Using these statistics, I wish someone can easily prove the OP statement. This proof will be more than just average return (1st moment) and stdev (2nd moment).
FWIW: computing 3rd and 4th moments from data is highly sensitive to noise in the data. It takes much more data than estimating the mean, and we don't have enough data to do a good job of estimating the expected mean.

There really is no "proof".
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: Prove adding SV will increase E(r) given the same risk

Post by pkcrafter »

What do you mean by risk?
The eternal question. SD? Well, no. Maximum drawdown? Hmm, not exactly. The chance you won't get what you expect? Depends.
Using these statistics, I wish someone can easily prove the OP statement.


Read Rodc's post(s) again.
When times are good, investors tend to forget about risk and focus on opportunity. When times are bad, investors tend to forget about opportunity and focus on risk.
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Re: Prove adding SV will increase E(r) given the same risk

Post by acegolfer »

Larry, once again, thanks for your prompt reply.

Ok, I'll agree that there's no proof. But here are my comments to your 2nd paragraph. Sorry, I don't have time to read your book and I hope someone who read the book can give a feed back to the following comments.
you have higher expected return with SV than TSM.
I buy this, assuming average return is the best predictor for the (future) expected return.
That allows you to lower beta, which is bigger risk than the premium itself.

This lowers the market risk (beta) but will increase other risks that SV carries. So it's a stretch to state that it's lowering the overall risk. And I don't know what you mean by the risk is bigger than the risk premium itself. Are you comparing beta with the market premium = E(Rm) - Rf?
Also you gain diversification benefits as factors have low correlation.
Isn't this another way of saying adding SV (with low correlation) to the market portfolio will reduce the risk? That's exactly what I asked you to explain in the first place and one can't use the result to explain the result. Or, perhaps I misinterpreted your "diversification benefits." Can one explain what the diversification benefit means in this context?
And most importantly when tail risk shows up your safe bond correlation which averages zero tends to go highly negative which is what cuts the tail risk.
I'm trying to understand this important statement. I interpreted this statement as in times of market crash (left tail), safe bonds are likely to have positive returns. If true, does this happen because SV are added to the market portfolio? And this will not happen, if SV are not added to the market portfolio?

Sorry for asking all these questions. I really want to understand the rationale behind tilting before I jump to SV. I rarely make decisions, if I don't understand what's going on. I hope anyone can answer my questions related to Larry's post. If you think these questions are outrageous, let me know. I won't ask any more to clarify the other's comments so that I can understand. Perhaps, I have a very bad comprehension skill.
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Re: Prove adding SV will increase E(r) given the same risk

Post by Aptenodytes »

If you don't want to take the time to read Larry's book, then I wonder how much you really care about the question.

If you are seriously contemplating adopting the fat-tail portfolio, surely you owe it to yourself to take the 30 minutes or so it would take to grasp the essentials.

If you aren't serious about the question but mildly curious at the 5-minute level, then there's no need to ask people to write book reports for you. In five minutes you can get all you need from reading the short articles on this question that Larry has linked here.
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Re: Prove adding SV will increase E(r) given the same risk

Post by YDNAL »

acegolfer wrote:Lately, I have seen many posts similar to

"adding SV and more bonds to market/bonds portfolio will increase the expected return at the same risk."
First, here's Jack Bogle's take (2012) on expected return:
http://www.morningstar.com/cover/videoc ... ?id=571370
Benz: So, let's start with your outlook for the market. Let's start with equities, and talk about what your expectations are and how you arrive at them?

Bogle: Well, I've been using this kind of system, if you will, ever since the early 1990s, when I forecasted returns for the 1990s, and it's very simple, and it is extremely helpful, because I divide market returns into two categories--investment return and speculative return.

Investment return is a dividend yield on the day you buy into the market, and to that is added earnings growth that follows. So, today, the dividend yield is around 2%, and I think we can look forward to 5% in earnings growth--nothing is guaranteed, but basically there is nominal growth, and the country is going to be growing like that rate, I think, nominally. And so that would be a 7% investment return or fundamental return.
Using Bogle's guessing forecasting process (above), would you "expect" more return (more risk) from Small and Value companies (SV) than from what your quote refers to as "market?"
  • 1. "Yes" answer: you could have lower investment in SV companies to match the expected return from the "market."
    2. "No" answer: you should own the market.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by larryswedroe »

ace
First, the book explains it all well I believe. And only about 2 hour read in total
Second, but while market can drop say 50%, when was last time you saw SV relative to TSM go down 50%? And also risks not highly correlated, that's important. So say in 2001 when TSM was down big SV was up.
third, adding SV doesn't reduce overall risks but provides exposure to different types of risks, low correlation, and it allows you to lower beta risk which is the key.
Finally you are mixing things up. Adding SV is what allows you to hold more safe bonds which go up in crashes, or tend to. IF you don't own more SV than you don't own more safe bonds, and hence have bigger losses.
So say in crash TSM goes down 50% and SV goes down 60%, but now you own say 30% equities, all SV, vs say 70% or more. And now you own 70% safe bonds which went up instead of say 30% or less.

It's the negative correlation in financial crises that helps cut the left tail risk while not necessarily cutting right tail as much because bonds don't tend to crash in bull stock markets.

The book shows you the historical evidence. You can then choose to use it or not.
Larry
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Re: Prove adding SV will increase E(r) given the same risk

Post by thx1138 »

acegolfer wrote:
And most importantly when tail risk shows up your safe bond correlation which averages zero tends to go highly negative which is what cuts the tail risk.
I'm trying to understand this important statement. I interpreted this statement as in times of market crash (left tail), safe bonds are likely to have positive returns. If true, does this happen because SV are added to the market portfolio? And this will not happen, if SV are not added to the market portfolio?

Sorry for asking all these questions. I really want to understand the rationale behind tilting before I jump to SV. I rarely make decisions, if I don't understand what's going on. I hope anyone can answer my questions related to Larry's post. If you think these questions are outrageous, let me know. I won't ask any more to clarify the other's comments so that I can understand. Perhaps, I have a very bad comprehension skill.
I think I can answer this part... Since SV has higher expected return than TSM when bad times come you will have more bonds in a portfolio built from SV than a portfolio built from TSM. Thus you will get more exposure to the favorably negatively correlated bonds simply because you own more of them.

And the premiss for negative correlation with safe bonds (e.g. Treasuries) is that in bad times they go up in value from a "flight to safety". Only the safest and highest rated bonds get this benefit. In 2008-2009 the flight to safety was extreme, even fairly highly rated corporate bonds were being priced as if their were going to be failure rates of large companies in like the 5% range. So if your bonds aren't rock solid they will go down along with the equities in bad times.

So it isn't that SV affects your bonds somehow it is that SV has higher return, and that higher return allows you to own *more* bonds. Similarly it allows you to own *safer* (that is lower yielding) bonds than if you were chasing yield in your bond portfolio. By making your equities "as risky as possible" in the sense of higher return and your bonds "as safe as possible" in the sense of lower yield you can create a portfolio with more favorable anti-correlation between the two asset classes.

EDIT: Whoops, looks like Larry posted while I was distracted mid-post here. Anyway, you got your answer straight from the horses mouth before I chimed in!
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Kevin M »

acegolfer wrote:Note 2: If your proof only involves simple statistics such average returns and sample stdev, then one can use the same argument to "adding Apple will increase the return and lower the stdev,"
Assuming that you're talking about historical results, I've already shown, in another thread, that although adding Apple to a Total US Stock fund did increase return, it also increased standard deviation of annual returns (by a lot!). Not only did I show that portfolio standard deviation increased, but I also showed why, using the Markowitz equation for the standard deviation of a portfolio of two risky assets.

Note that you also can find periods of time when adding small-cap value to a total US stock portfolio increased standard deviation of the portfolio. It so happens that if you look at the longest time period for which data for all three exists in the tool I used (using Vanguard funds), this is not the case (SCV actually had lower std dev than TSM!), but you can find other time periods where it is the case.

This reply is not intended to address any of your other points or take either side in the debate, just to address this one point.

Kevin
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Most stated that there's no proof.

I cannot prove that adding SV will lower the risk, given the same E(r). But I can prove that's adding another portfolio (possibly SV) can increase the E(r) but lower stdev at the same time. In other words, there's an academic explanation for why the market portfolio is not mean-variance efficient. I doubt most can understand the following and if you have any questions, I'll be happy to answer.

First, let's refresh the traditional portfolio theory, where only mean and variance matter. One implication of this theory is that the optimal portfolio for any investor is a portfolio of risk-free asset and the market portfolio, which is mean-variance efficient. How to allocate between these 2 assets depends on individual's risk aversion.

In the new multi-factor portfolio theory, which is an extension of the above theory, investors are concerned not only about mean and variance, but also other types of risk. It can be fat tail, financial distress risk or any risk that investors are concerned about.

With more dimensions of risk, the efficient frontier is no longer a 2 dimensional (mean-variance) graph. For example, if there's one additional risk factor, then the space will become 3-dimensional and the efficient frontier becomes a 3-dimension shape. Once the risk-free asset is added, then the efficient frontier becomes a cone shape. (Imagine you spin a straight line to make a cone in 3-dimension space.) This cone shape frontier is constructed with 3 assets: risk-free, market, and another risk factor portfolio. The latter 2 assets are called multi-factor efficient. How to allocate between the 3 assets depends on individual's aversions to each risk. Since the average investor is concerned about this other risk, the average portfolio will not be at the highest point on the cone for a given stdev, which means the expected return is not at the maximum for a given stdev. This explains why even if the market portfolio is multi-factor efficient, it's not mean-variance efficient. Simply speaking, the average investor (=market portfolio) will give up some return to reduce the other risk for a given amount of stdev.

If one is a truly mean-variance investor, then he can tilt towards the top of the cone for a given stdev by adding the 3rd asset. (Imagine you slice the cone vertical to stdev axis and move to the highest point.)

To sum, it's theoretically possible to increase the expected return without changing stdev in a multi-factor world.

Next to prove that adding SV will increase E(r) and lower stdev, all we need to do is to show that SV has higher E(r), smaller stdev than MKT. Then if an individual adds SV to MKT, the E(r) will increase, stdev will decrease at the expense of higher beta (not CAPM beta).
Last edited by acegolfer on Sat Aug 02, 2014 6:42 am, edited 4 times in total.
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Re: Prove adding SV will increase E(r) given the same risk

Post by Kevin M »

acegolfer wrote: Sorry for asking all these questions. I really want to understand the rationale behind tilting before I jump to SV. I rarely make decisions, if I don't understand what's going on. I hope anyone can answer my questions related to Larry's post. If you think these questions are outrageous, let me know. I won't ask any more to clarify the other's comments so that I can understand. Perhaps, I have a very bad comprehension skill.
I think you are very wise to be cautious. Once you make the decision to tilt to SV, you must be prepared for long periods of tracking error (relative to say a portfolio of total market funds), and the associated regret. If tracking-error regret is likely to cause you to abandon your strategy, you probably should not tilt. Larry is very clear about this in his writings.

I think you should invest the small amount of money and time to read Larry's Black Swan book. My take is that he does a good job of showing how "The Larry Portfolio" would have generated similar returns as a more traditional 60/40 US stock/bond portfolio with lower standard deviation of returns and fewer poor outcomes (left tail risk) over the time periods he reviews. He also explains a theoretical foundation for this based on diversification among risk factors. He acknowledges that we can't predict that future returns will resemble past returns.

Although I gradually started tilting to small and value about 7-8 years ago, largely based on books by Larry, Bill Bernstein, and a few others), and plan to stick to my policy, I'm still not willing to go whole hog with the Larry portfolio. I think the biggest shortcoming of the book is a convincing case that the risk factors will persist into the future. I also think that the persistence of what appear to be risk factors is one of the big debates--certainly one we have here.

Kevin
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by JoMoney »

acegolfer wrote:...If one is a truly mean-variance investor, then he can tilt towards the top of the cone for a given stdev by adding the 3rd asset. (Imagine you slice the cone vertical to stdev dimension and move to the highest point.) To sum, it's theoretically possible to increase the expected return without changing stdev in a multi-factor world.
That's not "proof", it's a theory assuming other theories as if they were facts, despite some of those theories being empirically shown as bunk... but without an alternative model the theory goes on.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Rodc »

acegolfer wrote:Most stated that there's no proof.

But here's an academic proof why adding another portfolio (possibly SV) can increase the E(r) and stdev at the same time. In other words, there's an academic explanation for why the market portfolio is not mean-variance efficient. I doubt most can understand the following and if you have any questions, I'll be happy to answer.

First, let's refresh the traditional portfolio theory, where only mean and variance matter. One implication of this theory is that the optimal portfolio for any investor is a portfolio of risk-free asset and the market portfolio, which is mean-variance efficient. How to allocate between these 2 assets depends on individual's risk aversion.

In the new multi-factor portfolio theory, which is an extension of the above theory, investors are concerned not only about mean and variance, but also other types of risk. It can be fat tail, financial distress risk or any risk that investors are concerned about.

With more dimensions of risk, the efficient frontier is no longer a 2 dimensional (mean-variance) graph. For example, if there's one additional risk factor, then the space will become 3-dimensional and the efficient frontier becomes a 3-dimension shape. Once the risk-free asset is added, then the efficient frontier becomes a cone shape. (Imagine you spin a straight line to make a cone in 3-dimension space.) This cone shape frontier is constructed with 3 assets: risk-free, market, and another risk factor portfolio. The latter 2 assets are called multi-factor efficient. How to allocate between the 3 assets depends on individual's aversions to each risk. Since the average investor is concerned about this other risk, the average portfolio will not be at the highest point on the cone for a given stdev, which means the expected return is not at the maximum for a given stdev. This explains why even if the market portfolio is multi-factor efficient, it's not mean-variance efficient. Simply speaking, the average investor (=market portfolio) will give up some return to reduce the other risk for a given amount of stdev.

If one is a truly mean-variance investor, then he can tilt towards the top of the cone for a given stdev by adding the 3rd asset. (Imagine you slice the cone vertical to stdev axis and move to the highest point.)

To sum, it's theoretically possible to increase the expected return without changing stdev in a multi-factor world.
That is all fine and fairly well understood by many. It has been discussed here any number of times.

But that is hardly "proof" of anything in the real world which you seemed to desire. Yes, mathematically things can exist in the sense of being potentially true. Given such and such hypotheses such and such follows. But are these hypotheses true, or rather close enough to true to matter, in the real world?

Jury is out.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

JoMoney wrote:
acegolfer wrote:...If one is a truly mean-variance investor, then he can tilt towards the top of the cone for a given stdev by adding the 3rd asset. (Imagine you slice the cone vertical to stdev dimension and move to the highest point.) To sum, it's theoretically possible to increase the expected return without changing stdev in a multi-factor world.
That's not "proof", it's a theory assuming other theories as if they were facts, despite some of those theories being empirically shown as bunk... but without an alternative model the theory goes on.
The only assumption that the new theory requires is that there' are other risk dimensions in addition to the stdev. There's no other theory needed. In addition, this theory doesn't depend on any empirical facts or bunks.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Tamales »

acegolfer wrote:The only assumption that the new theory requires is that there' are other risk dimensions in addition to the stdev. There's no other theory needed. In addition, this theory doesn't depend on any empirical facts or bunks.
Here are a couple dozen different risk measures, with links describing details of each: http://www.styleadvisor.com/resources/statfacts
including some that you noted earlier. Some are used to judge how much to trust another statistic and are of no use on their own.
Standard deviation definitely has its issues as a sole risk measure. Trouble is, there aren't many sources for the others. However, if you believe the logic of going from a 1 factor to a 3 factor model (because the one factor leaves a lot out even if the 3 factor doesn't model 100%), you'd think the same logic would hold for a single factor risk measure with similar weaknesses.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Tamales wrote: Here are a couple dozen different risk measures, with links describing details of each: http://www.styleadvisor.com/resources/statfacts
including some that you noted earlier. Some are used to judge how much to trust another statistic and are of no use on their own.
Standard deviation definitely has its issues as a sole risk measure. Trouble is, there aren't many sources for the others. However, if you believe the logic of going from a 1 factor to a 3 factor model (because the one factor leaves a lot out even if the 3 factor doesn't model 100%), you'd think the same logic would hold for a single factor risk measure with similar weaknesses.
Completely agree with your statement but it doesn't negate the explanation.

The argument that I made doesn't rely on a specific 2-factor or 3-factor model. The real investor's world may have infinite risk dimensions. The whole point is as long as there's another dimension to the risk, market portfolio is no longer mean-variance efficient.

The part that the current theory lacks is to identify what the real risk factors and risk premiums are. CAPM has identified the market risk and market premium. But no one identified what the S and V risk factors and premiums are.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by JoMoney »

acegolfer wrote:...The whole point is as long as there's another dimension to the risk, market portfolio is no longer mean-variance efficient...
But it's nice to know that investing in a "Total Market" portfolio has reasoning based in facts and proof beyond academic theory
http://www.vanguard.com/bogle_site/sp20 ... Mrkts.html
http://johncbogle.com/wordpress/wp-cont ... %20one.pdf
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

JoMoney wrote:But it's nice to know that investing in a "Total Market" portfolio has reasoning based in facts and proof beyond academic theory
http://www.vanguard.com/bogle_site/sp20 ... Mrkts.html
http://johncbogle.com/wordpress/wp-cont ... %20one.pdf
Thanks for the article. In case you misinterpreted, the multi-factor model implies that the market portfolio is efficient. But it's not mean-variance efficient.

In addition, the theory doesn't say everyone should tilt. There's nothing wrong with being the average investor who holds the market portfolio, even in the multi-factor world.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by larryswedroe »

few things
First, Kevin, would take a whole book to discuss all the literature on why one should expect the premiums to persist---in fact huge debate even as to whether risk, behavioral or some of both (my personal view). But there is whole literature on the subject as I have posted many times. One has to decide for themselves if they believe the premiums are LIKELY to persist.

Ace, EMH is nice working framework and it assumes TSM is mean variance efficient. However, like all models it is wrong. We know TSM is not mean variance efficient, or at least has not been with many anomalies left unexplained, including all the lottery tickets. So one has to decide if you follow the model even though you know it's wrong, or go with what you believe is stronger evidence.

Larry
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

larryswedroe wrote: Ace, EMH is nice working framework and it assumes TSM is mean variance efficient. However, like all models it is wrong. We know TSM is not mean variance efficient, or at least has not been with many anomalies left unexplained, including all the lottery tickets. So one has to decide if you follow the model even though you know it's wrong, or go with what you believe is stronger evidence.

Larry
EMH doesn't assume TSM is mean variance efficient. And I have no idea why you are making that argument as if I said that. In fact, my whole argument was market is NOT mean-variance efficient. I guess you didn't read my post.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by larryswedroe »

aCe
EMH does assume TSM is the efficient portfolio.
That's why I mentioned it.
Larry
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

larryswedroe wrote:aCe
EMH does assume TSM is the efficient portfolio.
That's why I mentioned it.
Larry
But you stated as if I implied TSM is mean variance efficient, which I said is false.

In addition, I think you got the assumption the opposite way.

TSM being efficient assumes EMH not the other way around.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Kevin M »

larryswedroe wrote: First, Kevin, would take a whole book to discuss all the literature on why one should expect the premiums to persist---in fact huge debate even as to whether risk, behavioral or some of both (my personal view). But there is whole literature on the subject as I have posted many times.
Yes, understood--I almost added something to that effect to my earlier post. This would be a great book for you to write!
larryswedroe wrote:One has to decide for themselves if they believe the premiums are LIKELY to persist.
Yes, this is the tough one. It's hard for us amateurs to decide about this without a comprehensible summary of the literature that provides the supporting evidence. Ideally this would summarize papers that are critical of the model (including likely persistence of the factors); a point/counterpoint presentation, as in many of your articles.

Kevin
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by larryswedroe »

Kevin
there is a very good paper on at least two of them

Clifford Asness, Tobias Moskowitz, and Lasse Pedersen, authors of “Value and Momentum Everywhere,” which appears in the June 2013 issue of the Journal of Finance (the most prestigious of finance journals), add to the literature by studying these factors across eight different markets and asset classes (individual stocks in the U.S. the U.K., continental Europe, and Japan, as well as country equity index futures, government bonds, currencies, and commodity futures). The following is a summary of their findings:
• There are significant return premia to value and momentum in every asset class. The value premium was persistent in every stock market, with the strongest performance in Japan. The momentum premium was also positive in every market, especially in Europe, though statistically insignificant in Japan.
• Value strategies are positively correlated with other value strategies across otherwise unrelated markets and momentum strategies are positively correlated with other momentum strategies globally. This persistence assuages data mining concerns.
• Value and momentum are negatively correlated with each other within and across asset classes. The negative correlation between value and momentum within each asset class is consistent and averages –0.49. For stocks the correlation averaged -0.60. Their negative correlation and high positive expected returns implies that a simple combination of the two is much closer to the efficient frontier than either strategy alone — combining strategies results in improved Sharpe ratios.
• There’s significant evidence that liquidity risk is negatively related to value and positively related to momentum globally across asset classes. The implication is that part of the negative correlation between value and momentum is driven by opposite signed exposure to liquidity risk. However, liquidity risk can only explain a small fraction of the value and momentum return premia and comovement.
The authors offered this explanation for why momentum loads positively on liquidity risk and value loads negatively: “A simple and natural story might be that momentum represents the most popular trades, as investors chase returns and flock to the assets whose prices appreciated most recently. Value, on the other hand, represents a contrarian view. When a liquidity shock occurs, investors engaged in liquidating sell-offs (due to cash needs and risk management) will put more price pressure on the most popular and crowded trades, such as high momentum securities, as everyone runs for the exit at the same time, while the less crowded contrarian/value trades will be less affected.”

There are also these papers showing risk explanations for value and size premiums, which means you should expect them to persist
1.Baruch Lev and Theodore Sougiannis, “Penetrating the Book-to-Market Black Box,” Journal of Business Finance and Accounting (April/May 1999).
2.Robert F. Peterkort and James F. Neilsen, “Is the Book-to-Market Ratio a Measure of Risk?” Journal of Financial Research (Winter 2005).
3.Maria Vassalou and Yuhang Xing, “Default Risk in Equity Returns,” Journal of Finance (April 2004).
4.Xinting Fan and Ming Liu, “Understanding Size and the Book-to-Market Ratio: An Empirical Exploration of Berk’s Critique,” Journal of Financial Research (Winter 2005).
5.Howard W. Chan and Robert W. Faff, “Asset Pricing and the Illiquidity Premium,” The Financial Review (November 2005).
6.Charles Lee and Bhaskaran Swaminathan, “Price Momentum and Trading Volume,” Journal of Finance (October 2000).
7.Ralitsa Petkova, “Do the Fama-French Factors Proxy for Innovations in Predictive Variables?” Journal of Finance (April 2006).
8. Aydin Akgun and Rajna Gibson, “ Recovery Risk in Stock Returns,” Journal of Portfolio Management, Winter 2001.
9. Gerald R. Jensen and Jeffrey M. Mercer, “Monetary Policy and the Cross-Section of Expected Returns,” Journal of Financial Research, Spring 2002.
10.Gabriel Perez-Quiros and Allan Timmerman, “Firm Size and Cyclical Variations in Stock Returns,” July 1999.
11.Lu Zhang, “The Value Premium.” January 2002, http://papers.ssrn.com/sol3/papers.cfm? ... _id=351060
12.Joao Gomes, Leonid Kogan, and Lu Zhang, “ Equilibrium Cross-Section of Returns, March 2001. http://assets.wharton.upenn.edu/~zhanglu/
13. Moon K. Kim and David A Burnie, “The Firm Size Effect and the Economic Cycle,” Journal of Financial Research, Spring 2002.
14.Nai-fu Chen and Feng Zhang, Journal of Business, “Risk and Return of Value Stocks,” October 1998.
15. Clifford S. Asness, Tobias J. Moskowitz, and Lasse H. Pedersen∗Value and Momentum Everywhere, February 2009.
16. Joachim Grammig, “Creative Destruction and Asset Prices,” March 2011.
17. Jia Wang, Gulser Meric, Zugang Liu, and Ilhan Meric, “The Determinants of Stock Returns in the October 9, 2007-March 9, 2009 Bear Market,” The Journal of Investing (Fall 2011).
18. Nishad Kapadia, “Tracking Down Distress Risk,” May 2010
19. Angela J. Black, Bin Mao and David G. McMillan, “The Value Premium and Economic Activity: Long-run Evidence from the United States,” December, 2009.
20. Nicolae Garleanu, Leonid Koganz, and Stavros Panageas, “Displacement Risk and Asset Returns,” July 2008.
21. Lorenzo Garlappiy and Hong Yanz, “Financial Distress and the Cross Section of Equity Returns,” September 2007

Just partial list of course
hope that helps
Larry
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Epsilon Delta »

acegolfer wrote: In addition, the theory doesn't say everyone should tilt. There's nothing wrong with being the average investor who holds the market portfolio, even in the multi-factor world.
The theory doesn't say anybody should tilt. As you mention the trade off between risks is a personal choose. However choosing to optimize mean-variance in world with multiple risks is choosing to ignore those other risks. This seems a little precipitous if you don't know what those other risks are.

The market portfolio at least considers the average investors tolerance to those risks. If somebody should tilt one way, then there must be somebody else who should tilt the other way. Without deeper understanding you can't say which direction you should tilt.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by cowboysFan »

I think the Fama-French data set from 1927-1956 shows almost no risk adjusted, after cost premium to small value in the US, if you use standard deviation as your measure of risk. Using their 5x5 data set, I get a geometric mean of 15% and standard deviation of 53.58% for the smallest, most value oriented stocks, while for the largest and most growth oriented stocks, I get an annualized return of 9.43% and a standard deviation of 23.66. So from one perspective, SV yields about 60% more annual return, but has over double the risk. Then, I looked at what AA for a SV/cash(0 volatility asset) portfolio would yield the same standard deviation as a 100% LG portfolio. A AA of 44.2% SV/55.8% cash yielded the same standard deviation as 100% LG. Assuming cash returned the rate of inflation 1.5%, then the SV/cash portfolio returned 10.02%. That's an extra risk-adjusted return of 0.59%, but if you pay DFA an extra 0.47% in ER, then your risk adjusted return is 12 basis points more with SV. Adjust for more frequent trading in a segment of the market with higher bid-ask spreads, and your after cost, risk adjusted SV premium is 0 or close enough to 0 to be considered noise.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Epsilon Delta wrote: The theory doesn't say anybody should tilt. As you mention the trade off between risks is a personal choose. However choosing to optimize mean-variance in world with multiple risks is choosing to ignore those other risks. This seems a little precipitous if you don't know what those other risks are.

The market portfolio at least considers the average investors tolerance to those risks. If somebody should tilt one way, then there must be somebody else who should tilt the other way. Without deeper understanding you can't say which direction you should tilt.
The multi-factor theory does say some (not all) should tilt because stdev is not the only measure of risk. If stdev is the only risk, then we are back to the traditional 1-factor theory and nobody should tilt because it's impossible to lower the risk and increase E(r) at the same time.
Correct, in a multi-factor world, if one optimizes the mean-variance, he's ignoring other risks. However, I bet most investors know that they are exposed to other risks not just stdev. For example, if one's human capital is positively correlated with an industry, then those industry stocks will add another risk to him in addition to the market risk. Naturally, isn't it better for him to hold less of these industry stocks? Or is it better not to tilt and just hold the market portfolio?

I agree 100% that some investors tilt one way and others will tilt the opposite way. I didn't mention this because this thread is not about where to tilt. But I did mention that the average investor will always hold the market portfolio and I also explain that this market portfolio is multi-factor efficient but not mean-variance efficient, which is the topic of this thread.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Epsilon Delta »

acegolfer wrote: The multi-factor theory does say some (not all) should tilt because stdev is not the only measure of risk.
If you have multiple measures of risk but everybody makes the same trade off you get a situation where nobody tilts, even though tilted portfolios are on the efficient frontier. It's a degenerate solution, but it's not the same as having only one risk dimension.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Kevin M »

acegolfer wrote:I didn't mention this because this thread is not about where to tilt.
But the title of the thread mentions "adding SV", which is what we mean by tilting to SV. If this thread is not about tilting to SV, then what is it about?

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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Epsilon Delta wrote:
acegolfer wrote: The multi-factor theory does say some (not all) should tilt because stdev is not the only measure of risk.
If you have multiple measures of risk but everybody makes the same trade off you get a situation where nobody tilts, even though tilted portfolios are on the efficient frontier. It's a degenerate solution, but it's not the same as having only one risk dimension.
Not really. Note that even if an individual's optimal portfolio in mean-variance world is a combination of risk-free asset and tangency portfolio depending on one's risk aversion, the market portfolio doesn't include risk-free asset.

In the multi-factor world, even if every individual will choose a different combination of risk-free asset, market portfolio and the other factor portfolios (tilt), at the aggregate, the market portfolio at the aggregate will not include risk-free asset and other factor portfolios.

As stated in another post, not everyone tilts to the same direction because everyone has a different risk aversion.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Kevin M wrote:
acegolfer wrote:I didn't mention this because this thread is not about where to tilt.
But the title of the thread mentions "adding SV", which is what we mean by tilting to SV. If this thread is not about tilting to SV, then what is it about?

Kevin
Thanks for pointing out that I didn't address "adding SV"

I thought this thread is more about lowering the risk, given the same E(r). So I provided a theoretical proof for why that is possible. However, I can't prove adding SV will always achieve that effect.

OTOH, there are many threads discussing why one should tilt to SV. That's why I didn't consider this thread to be about tilting to SV.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Epsilon Delta »

acegolfer wrote:In the multi-factor world, even if every individual will choose a different combination of risk-free asset, market portfolio and the other factor portfolios (tilt), at the aggregate, the market portfolio at the aggregate will not include risk-free asset and other factor portfolios.

As stated in another post, not everyone tilts to the same direction because everyone has a different risk aversion.
This is an assumption, but it is not needed by the theory. It is entirely possible for everybody to have a portfolio that consists only of the risk free asset and the market portfolio. Because of the nature of the market portfolio and the risk free asset the average exposure to the "tilt" portfolio must be zero. Zero tilt portfolio for everybody is a consistent solution.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Rodc wrote:
That is all fine and fairly well understood by many. It has been discussed here any number of times.

But that is hardly "proof" of anything in the real world which you seemed to desire. Yes, mathematically things can exist in the sense of being potentially true. Given such and such hypotheses such and such follows. But are these hypotheses true, or rather close enough to true to matter, in the real world?

Jury is out.
1. I have not seen the theoretical justification using multi-factor efficient frontier was discussed here any number of times. Perhaps, I missed it.
2. My post was not trying to prove anything in the real world and I never desired so. It's only a mathematical justification for why it's possible for one to increase the E(r) and lower stdev by tilting from the market. I started my post stating this.

I hope that clarifies my real intent.

In addition, I never intended to prove why one should tilt to SV. And I can't prove adding SV will always increase E(r) and decrease risk.
Last edited by acegolfer on Thu Jul 31, 2014 10:39 pm, edited 2 times in total.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Epsilon Delta wrote: This is an assumption, but it is not needed by the theory. It is entirely possible for everybody to have a portfolio that consists only of the risk free asset and the market portfolio. Because of the nature of the market portfolio and the risk free asset the average exposure to the "tilt" portfolio must be zero. Zero tilt portfolio for everybody is a consistent solution.
Thanks for continuing the debate.

1. I assumed everyone has different aversion to various risks.
2. You said that this assumption is not needed by the theory. Does it mean that you assume that everybody has the same risk aversion? Then everybody will hold the same market portfolio (zero tilt portfolio).

I think #1 is a weaker assumption.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by michaelsieg »

"adding SV and more bonds to market/bonds portfolio will increase the expected return at the same risk. Can you prove the above statement using your risk definition in Q1? "Note 1: The above statement says "will increase" not "has increased.
Not sure if this was said before, but the question by itself is illogical and can't really be answered, if you think of it.
You can only prove facts that you put in some logical sequence/system. But the future has not yet materialized as facts, ergo you can't prove anything that has not happened yet.
The only thing possible is using facts from the past/present and trying to make analogies/probabilities about the future, but that is far from proving something.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

michaelsieg wrote:
"adding SV and more bonds to market/bonds portfolio will increase the expected return at the same risk. Can you prove the above statement using your risk definition in Q1? "Note 1: The above statement says "will increase" not "has increased.
Not sure if this was said before, but the question by itself is illogical and can't really be answered, if you think of it.
You can only prove facts that you put in some logical sequence/system. But the future has not yet materialized as facts, ergo you can't prove anything that has not happened yet.
The only thing possible is using facts from the past/present and trying to make analogies/probabilities about the future, but that is far from proving something.
Thanks for your criticism. Here's my response using an analogy.

How about this statement? Diversification "will lower" the stdev while keeping the same expected return.

Is this illogical and can't really be answered because it has not happened yet? To prove this, do we need facts from the past? No, one can prove this statement using some statistics. Am I wrong?
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Tamales »

acegolfer wrote: How about this statement? Diversification "will lower" the stdev while keeping the same expected return.
Just wanted to add a general point about standard deviation. Low standard deviation isn't always good. A stock or fund can have a low standard deviation (implying that most of the time, the returns are not wildly varying), but it can also have wild outliers with huge upside or downside that may be too much for some to stomach. Standard deviation misses that, and this is where things like kurtosis come in to play. Also, if a large standard deviation includes some large upside swings, that might not be a bad thing either (since standard deviation doesn't distinguish between upside and downside). So I'm just reinforcing the point that standard deviation has its issues.

Since you're looking at risk and reward, would Sharp or Sortino or other risk/reward ratios be more appropriate?
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Rodc »

acegolfer wrote:
Rodc wrote:
That is all fine and fairly well understood by many. It has been discussed here any number of times.

But that is hardly "proof" of anything in the real world which you seemed to desire. Yes, mathematically things can exist in the sense of being potentially true. Given such and such hypotheses such and such follows. But are these hypotheses true, or rather close enough to true to matter, in the real world?

Jury is out.
1. I have not seen the theoretical justification using multi-factor efficient frontier was discussed here any number of times. Perhaps, I missed it.
2. My post was not trying to prove anything in the real world and I never desired so. It's only a mathematical justification for why it's possible for one to increase the E(r) and lower stdev by tilting from the market. I started my post stating this.

I hope that clarifies my real intent.

In addition, I never intended to prove why one should tilt to SV. And I can't prove adding SV will always increase E(r) and decrease risk.
Search the site on "Portfolio advice for a multifactor world, by John Cochrane" for a start. That of course will not find all such mentions of these ideas.

http://www.nber.org/papers/w7170

In fact these ideas were brought up by Epsilon Data in one of your own threads as recently as July 3rd.

http://www.bogleheads.org/forum/viewtop ... 4#p2110684
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Rodc wrote: Search the site on "Portfolio advice for a multifactor world, by John Cochrane" for a start. That of course will not find all such mentions of these ideas.

http://www.nber.org/papers/w7170

In fact these ideas were brought up by Epsilon Data in one of your own threads as recently as July 3rd.

http://www.bogleheads.org/forum/viewtop ... 4#p2110684
Rodc, as usual, your comments are always appreciated.

1. It's great to see someone who read Cochrane (1999). I searched for that paper in BH and found 5+ hits. However, none of these posts (including Epsilon's recent post) showed that it's possible to increase E(R) and lower stdev from the market portfolio. If you read my post carefully, it's not just about what the efficient frontier looks like in a multi-factor model (Epsilon explained that last month). It's more about why the market portfolio (even though it's tangent) is not mean-variance efficient and hence one can increase E(R) and decrease stdev.

2. Cochrane (1999) paper has a flaw in Figure 2
Image

The beta in the graph is a measure of an additional risk (for those who didn't read it, beta in this figure is not the CAPM beta). If you look at the indifference surface (black) in A, it's shaped in the wrong direction. Investors should prefer less beta just like less stdev. But the shape of the surface in A implies investors prefer more beta just like they prefer for more E(R). Using the correct shape surface, the 2 tangency portfolios (market and another multi-factor efficient portfolio) should be on the other side of the cone closer the stdev axis. In other words, given the same E(R) and same stdev, investors prefer small beta to high beta.

If you want to continue the discussion where the MKT and the 2nd portfolio are, let me know.
Last edited by acegolfer on Fri Aug 01, 2014 10:45 am, edited 2 times in total.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by larryswedroe »

cowboys
Repeating the error of isolation thinking. The higher risk-adjusted returns have come not from adding SV but from adding SV and lowering beta at the same time.
Second issue is you are assuming that the advisor adds no value beyond access if only adding cost
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Rodc »

However, none of these posts (including Epsilon's recent post) showed that it's possible to increase E(R) and lower stdev from the market portfolio.
There is value in making the observation explicit, but it strikes me as the obvious conclusion once one understands the generalization of the 2D frontier plots to higher dimensions. You get to trade one type of risk against another from 100%/0% to 0%/100% say, and in between clearly you have less than 100% of either.

I would also note that SD is not really "risk", though is more directly risk than "value". I think all these observations and line of thinking can be generalized to risk dimensions, though without a formula to apply it is hard to draw graphs and surfaces from data. I think this the primary reason SD is so often called risk when really it is just a measure that is related to risk. Going down this road rather quickly leads to what is risk anyway, which is a sticky wicket.

One thing I find interesting here is I think it is widely accepted that bonds have multiple dimensions of risk (default risk, interest rate risk, call risk, inflation risk etc), with associated risk premiums. For example depending on use one might care a lot or not at all about inflation risk, and thus favor TIPS or Nominal bonds. But somehow many people won't accept that stocks also have different dimensions of risk with associated risk premiums (which may or may not be as easy to trade against each other as with bonds; just because something is true does not automatically mean you can do much about it, hence the endless debate about TSM vs Tilt).
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by acegolfer »

Rodc wrote: I would also note that SD is not really "risk", though is more directly risk than "value". I think all these observations and line of thinking can be generalized to risk dimensions, though without a formula to apply it is hard to draw graphs and surfaces from data. I think this the primary reason SD is so often called risk when really it is just a measure that is related to risk. Going down this road rather quickly leads to what is risk anyway, which is a sticky wicket.

One thing I find interesting here is I think it is widely accepted that bonds have multiple dimensions of risk (default risk, interest rate risk, call risk, inflation risk etc), with associated risk premiums. For example depending on use one might care a lot or not at all about inflation risk, and thus favor TIPS or Nominal bonds. But somehow many people won't accept that stocks also have different dimensions of risk with associated risk premiums (which may or may not be as easy to trade against each other as with bonds; just because something is true does not automatically mean you can do much about it, hence the endless debate about TSM vs Tilt).
+1

I would also like to add for other readers that market portfolio not being mean-variance efficient doesn't necessarily imply one should tilt (not saying tilt to SV) to increase E(R) and lower stdev. If one manages to achieve that, he will be exposed to another risk that he may not be aware of. Without understanding this additional risk, IMO, it's better to stay with TSM index funds, which have a lot more pros than cons.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by MrMatt2532 »

I just ran a bunch of numbers using the FF data from 1927-2013. Figured it might be useful for the discussion. Generally, you can see, the data shows one could have owned a mix of small and value, decreased beta, and still achieved the same expected return as the market. I computed the sharpe ratio and a few others to assess the risk adjusted return. Omega and sortino ratio are specifically formulated to handle effects besides just return and standard deviation of returns (i.e. other features of the distribution). As you can see, the skew and kurtosis numbers are favorable for small value tilting as compared with the market. Let me know if there are any questions.

Image

edit: small fix to sortino ratio calc
Last edited by MrMatt2532 on Fri Aug 01, 2014 4:56 pm, edited 1 time in total.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by Rodc »

I would also like to add for other readers that market portfolio not being mean-variance efficient doesn't necessarily imply one should tilt (not saying tilt to SV) to increase E(R) and lower stdev. If one manages to achieve that, he will be exposed to another risk that he may not be aware of. Without understanding this additional risk, IMO, it's better to stay with TSM index funds, which have a lot more pros than cons.
Agreed. It took me a while to get to this point of understanding.

I still do tilt small and value because for example I have an above average ability to handle "risk that shows up at bad times", and because if I factor in pensions, social security and low debt and low need for additional income I could actually rationally increase the risk I do hold even with the tilt. But I could do fine with TSM as well. And I don't think small or value is a free lunch.

It does give me pause that it is hard to really quantify this additional risk, so hard to really make a rational decision. In part I don't make changes unless there is a specific good reason to do so, so I continue to hold SCV, and also I don't hold a huge amount anyway. I would be more concerned if I held a very large amount.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by larryswedroe »

ace
just wanted to correct statement--yes the conclusion of the EMH is that TSM is efficient portfolio and in CAPM world it would be mean variance efficient also. In multi-factor world it's still efficient but just not mean variance efficient. With that said we know that the TSM is not (or hasn't been) the efficient portfolio because of anomalies that exist.
Whether one should tilt or not is a very personal decision and clearly not everyone should do so, especially those subject to behavioral errors, like tracking error regret.
IMO there is strong evidence and logic to lead one to conclude that a high tilt low beta portfolio will produce more efficient results with less tail risk due to diversification benefits and premiums. But that of course should only be an expectation, not a guarantee. However, it clearly should cut left tail risk dramatically due to low beta exposure.

Larry
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Re: Prove adding SV will lower the risk, given the same E(r)

Post by hafius500 »

Rodc wrote:...
One thing I find interesting here is I think it is widely accepted that bonds have multiple dimensions of risk (default risk, interest rate risk, call risk, inflation risk etc), with associated risk premiums. For example depending on use one might care a lot or not at all about inflation risk, and thus favor TIPS or Nominal bonds. But somehow many people won't accept that stocks also have different dimensions of risk with associated risk premiums (which may or may not be as easy to trade against each other as with bonds; just because something is true does not automatically mean you can do much about it, hence the endless debate about TSM vs Tilt).
But the same people who claim that stocks have multiple dimensions of "risk" with associated higher or lower expected returns stress that the multiple dimensions of bond "risk" have not been and will not be related to higher or lower expected returns. I.e., these bond risks will not be rewarded by higher expected returns.

Maybe the history of bond "risk" premiums predicts the future of equity "risk" premiums?
One should add that the existence of such (stock) "risk" premiums is hypothetical.
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