Is There an Optimal Factor Allocation?

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One More Thing
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Is There an Optimal Factor Allocation?

Post by One More Thing »

I have a set of questions centered around this topic. I apologize if this is well-trodden ground.

1. Should there be a hierarchy of priority within a factor-tilted portfolio?

2. Can you invest in so many factors that your portfolio becomes indistinguishable from a TSM?

3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?

Thank you all for any discussion. From my lurking this seems to be a bastion of TSM investors but I know there are factor investors here too.
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Ocean77
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Re: Is There an Optimal Factor Allocation?

Post by Ocean77 »

Different factors will shine at different times. You will know the optimum one for a certain time period only in hindsight.
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alex_686
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Re: Is There an Optimal Factor Allocation?

Post by alex_686 »

I am a modest proponent of factor investing.

There is no hierarchy. One factor is not better than the other. If you invest in to many factors you may well drift to a portfolio that acts like the total stock market.

The total stock market is a very efficient portfolio and the default portfolio. But this does not mean it is the best portfolio for you.

Rather, you should chose assets that fit your goals, risk tolerances, and market expectations best. Different factors tend to have certain characteristics. Maybe a certain factor based portfolio is a better fit than the total stock market. If so, invest.

For example, I am interested in taking some risk off of the table. As such I have a modest tilt towards the "Low Volatility" factor. Even thought it did not provided downside protection during the COVID crisis I am sticking with it because I have a high conviction.
Former brokerage operations & mutual fund accountant. I hate risk, which is why I study and embrace it.
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Re: Is There an Optimal Factor Allocation?

Post by dbr »

What property of a portfolio would you like to optimize? Note optimize usually means to find either a minimum or a maximum of something.

When there are multiple properties in conflict one sometimes makes up figures of merit. An example Sharpe ratio which is the portfolios excess return over a risk free rate divided by the standard deviation of that return, also known as "standardizing" a statistic. The meaning of maximizing the Sharpe ratio would be that it is the maximum return for the risk paid to get that return, if you think the two things can be compared linearly.

Here is an example of utility functions from a paper by Reichenstein about optimizing asset allocation:

The study examines two utility functions: U = ER
– SD/RT and U = ER – SD2/RT. U denotes utility; also,
it is the portfolio’s certainty-equivalent return, meaning
it is the risk-free return that would provide the same
utility as the portfolio. ER is the portfolio’s after-tax
expected returns. SD is after-tax standard deviation. RT
denotes the investor’s risk tolerance.

So, the question is what does one want to optimize.

As far as factor investing if one wants maximum expected return and one believes the Fama French model still works, then one wants to find a portfolio with the largest possible size and value factor loadings. A 100% small cap value fund would certainly be closer to optimum than a total stock market fund. Of course between 2005 and now comparing VBR to VTI that did not actually work out due to any variety of departures from F-F, including for starters that predicting expected return does not predict actual return.
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Re: Is There an Optimal Factor Allocation?

Post by dru808 »

alex_686 wrote: Tue Sep 21, 2021 3:16 pm I am a modest proponent of factor investing.

There is no hierarchy. One factor is not better than the other. If you invest in to many factors you may well drift to a portfolio that acts like the total stock market.

The total stock market is a very efficient portfolio and the default portfolio. But this does not mean it is the best portfolio for you.

Rather, you should chose assets that fit your goals, risk tolerances, and market expectations best. Different factors tend to have certain characteristics. Maybe a certain factor based portfolio is a better fit than the total stock market. If so, invest.

For example, I am interested in taking some risk off of the table. As such I have a modest tilt towards the "Low Volatility" factor. Even thought it did not provided downside protection during the COVID crisis I am sticking with it because I have a high conviction.

What fund or funds are you utilizing?
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alex_686
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Re: Is There an Optimal Factor Allocation?

Post by alex_686 »

dru808 wrote: Tue Sep 21, 2021 4:29 pm What fund or funds are you utilizing?
I am currently using iShares MSCI USA Min Vol Factor ETF (USMV) and iShares MSCI Global Min Vol Factor ETF (ACWV).

Take this with a grain of salt. While I am confident in the minimum volatility factor I am still researching funds.
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secondopinion
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Re: Is There an Optimal Factor Allocation?

Post by secondopinion »

Factor investing is not as simple as looking at expected returns and variance. Factor investing allow for some kind of risk to exist while attempting to reduce the other risks by usual means of diversification. In statistics, factors are often determined as independent sources of variance (in investing, the sources of risk). In the context of factor investing, the willingness to take that factor's risk is more than the other sources of risk; that is, risk tolerance is multi-variate. Same argument can be made for sector investing.

Factors often come in self-negating pairs, which I nickname the other as an anti-factor. Those who buy both a factor and its anti-factor are effectively hedging out that risk (given proper weighting). This results in a decrease in general risk usually, given the other risk factors have not been increased.

However, not all factors are paired. Size, for example, is not a paired factor; it is almost always more risky to have small caps versus large caps.

As long as the factors are independent, then one can have multiple factors in the same portfolio; but the portfolio would then be much smaller in number of holdings, and it will deviate quite a bit from the total stock market for better or worse. If the factors are negating each other, then the portfolio would have more stocks and it will act more like the total stock market.

As far as utility, one has to factor in risk skew. Some people are positive skew-seeking and some are negative skew seeking. For example, "U = ER - SD/RT" should include "SK*SS" where SK is a measure of skew and SS is the positive-skew-seeking coefficient; it results in "U = ER - SD/RT + SK*SS". Linear is probably not right here, but it is the thought that counts.

If the skew is positive and the positive-skew-seeking coefficient is positive, then the investor, for the same utility, will be willing to take more volatility and/or less expected return. If the skew is negative, they will demand more expected return and/or less volatility.

Individual stocks have an inherent positive skew (few major out-performers, many minor under-performers); for positive skew-seeking individuals, they are more willing to hold a small basket of individual stocks (as to cut the volatility considerably while maintaining quite a bit of the positive skew) versus holding the total stock market (despite the lower volatility because the risk skew is almost gone).

High quality individual corporate bonds have an inherent negative skew (many minor out-performers, few major under-performers); for negative skew-seeking individuals, they are more willing to hold a small basket of such bonds (as to cut the volatility considerably while maintaining quite a bit of the negative skew) versus holding all such bonds (despite the lower volatility because the risk skew is almost gone).


In short, I throw out the notion of one single risk tolerance and include the notion of risk skew; both of these affect factor investing.
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Re: Is There an Optimal Factor Allocation?

Post by nisiprius »

In 2015, in 'A Review of Equity Factor Premia,' Jared Kizer wrote:Some factor premia have negative correlation with each other, namely value and momentum. Practically, it is impossible, therefore, to own a stock portfolio that is both deeply tilted toward value and deeply tilted toward momentum. At best, stock portfolios can be moderately tilted toward both. More generally, it is not feasible to build portfolios that capture significant amounts of multiple factor premia.
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Re: Is There an Optimal Factor Allocation?

Post by David Jay »

Gene Fama (of Fama/French) has said that factor investing should be done for a lifetime. If one is not willing to commit for decades he recommends total market rather than a factor tilt.
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Re: Is There an Optimal Factor Allocation?

Post by Taylor Larimore »

One More Thing wrote: Tue Sep 21, 2021 3:01 pm I have a set of questions centered around this topic. I apologize if this is well-trodden ground.

1. Should there be a hierarchy of priority within a factor-tilted portfolio?

2. Can you invest in so many factors that your portfolio becomes indistinguishable from a TSM?

3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?

Thank you all for any discussion. From my lurking this seems to be a bastion of TSM investors but I know there are factor investors here too.
One More Thing:

Factor investing is betting on which part of the market will outperform usually based on past performance. Speculators may be successful, but they may also be wrong which can devastate a comfortable retirement. Read what experts say:

viewtopic.php?f=10&t=156579

Best wishes.
Taylor
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Re: Is There an Optimal Factor Allocation?

Post by hg064754 »

secondopinion wrote: Tue Sep 21, 2021 6:06 pm Factor investing is not as simple as looking at expected returns and variance. Factor investing allow for some kind of risk to exist while attempting to reduce the other risks by usual means of diversification. In statistics, factors are often determined as independent sources of variance (in investing, the sources of risk). In the context of factor investing, the willingness to take that factor's risk is more than the other sources of risk; that is, risk tolerance is multi-variate. Same argument can be made for sector investing.

Factors often come in self-negating pairs, which I nickname the other as an anti-factor. Those who buy both a factor and its anti-factor are effectively hedging out that risk (given proper weighting). This results in a decrease in general risk usually, given the other risk factors have not been increased.

However, not all factors are paired. Size, for example, is not a paired factor; it is almost always more risky to have small caps versus large caps.

As long as the factors are independent, then one can have multiple factors in the same portfolio; but the portfolio would then be much smaller in number of holdings, and it will deviate quite a bit from the total stock market for better or worse. If the factors are negating each other, then the portfolio would have more stocks and it will act more like the total stock market.

As far as utility, one has to factor in risk skew. Some people are positive skew-seeking and some are negative skew seeking. For example, "U = ER - SD/RT" should include "SK*SS" where SK is a measure of skew and SS is the positive-skew-seeking coefficient; it results in "U = ER - SD/RT + SK*SS". Linear is probably not right here, but it is the thought that counts.

If the skew is positive and the positive-skew-seeking coefficient is positive, then the investor, for the same utility, will be willing to take more volatility and/or less expected return. If the skew is negative, they will demand more expected return and/or less volatility.

Individual stocks have an inherent positive skew (few major out-performers, many minor under-performers); for positive skew-seeking individuals, they are more willing to hold a small basket of individual stocks (as to cut the volatility considerably while maintaining quite a bit of the positive skew) versus holding the total stock market (despite the lower volatility because the risk skew is almost gone).

High quality individual corporate bonds have an inherent negative skew (many minor out-performers, few major under-performers); for negative skew-seeking individuals, they are more willing to hold a small basket of such bonds (as to cut the volatility considerably while maintaining quite a bit of the negative skew) versus holding all such bonds (despite the lower volatility because the risk skew is almost gone).


In short, I throw out the notion of one single risk tolerance and include the notion of risk skew; both of these affect factor investing.
If you measure risk as portfolio beta, you can take that risk out by forming beta neutral portfolios (as opposed to dollar neutral) in the long-short portfolio. This is done by going long in small stocks and short in big stocks, but weigh the components of the long and short leg in such a way that both the long and short leg will have the same beta.
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Re: Is There an Optimal Factor Allocation?

Post by One More Thing »

David Jay wrote: Tue Sep 21, 2021 7:06 pm Gene Fama (of Fama/French) has said that factor investing should be done for a lifetime. If one is not willing to commit for decades he recommends total market rather than a factor tilt.
I realize that one cannot capture a full factor premium without investing in it 100%. Simple logic. Can you not expect to capture an amount proportional to your tilt though?
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Re: Is There an Optimal Factor Allocation?

Post by BJJ_GUY »

hg064754 wrote: Tue Sep 21, 2021 7:25 pm
If you measure risk as portfolio beta, you can take that risk out by forming beta neutral portfolios (as opposed to dollar neutral) in the long-short portfolio. This is done by going long in small stocks and short in big stocks, but weigh the components of the long and short leg in such a way that both the long and short leg will have the same beta.
If you haven't read about the 'quant quake' of August 2007, it would be good for context related to your suggestion above. Many quant (stat arb and market neutral) hedge funds had portfolios they thought were beta neutral with a framework similar to what you've outlined. For reasons more systemic in nature, they had a rude awakening, and found out the hard way that they were not actually beta neutral, and market forces made it difficult to maintain their desired exposures in during the brief crisis.

Now, to be fair, they were leveraged and had to trade far more than an individual would, so liquidity is more of a challenge for large funds. Either way, it's good to recall mistakes made when ex post betas are relied upon for ex ante inputs without sound logic underpinning the strategy.
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Re: Is There an Optimal Factor Allocation?

Post by hg064754 »

One More Thing wrote: Tue Sep 21, 2021 7:30 pm
David Jay wrote: Tue Sep 21, 2021 7:06 pm Gene Fama (of Fama/French) has said that factor investing should be done for a lifetime. If one is not willing to commit for decades he recommends total market rather than a factor tilt.
I realize that one cannot capture a full factor premium without investing in it 100%. Simple logic. Can you not expect to capture an amount proportional to your tilt though?
1- when you are investing in a factor, often you are going long in a group of stocks and short another group of stocks. e.g. HML is the value factor long in value stocks and short growth stocks.

2- if you invest in one factor only, your statement is correct. You can capture the full effect. But if you invest in more than one factor, then some stocks will be both in the long and short leg of your portfolio so you will not capture all the factors.
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Re: Is There an Optimal Factor Allocation?

Post by 000 »

I mean isn't the market the optimal factor allocation as determined by market participants?

So the optimal allocation for you would depend on how you differ from the market (or what you understand better than the market).

Frankly I don't think many people differ from the market in terms of published factors. Someone with large exposure to a sector in their career or privately held businesses is a stronger case for adjusting the default market portfolio than investment enthusiasts who think "I have more tolerance for risk! My SCV portfolio is like me selling insurance!".
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Re: Is There an Optimal Factor Allocation?

Post by hg064754 »

BJJ_GUY wrote: Tue Sep 21, 2021 7:43 pm
hg064754 wrote: Tue Sep 21, 2021 7:25 pm
If you measure risk as portfolio beta, you can take that risk out by forming beta neutral portfolios (as opposed to dollar neutral) in the long-short portfolio. This is done by going long in small stocks and short in big stocks, but weigh the components of the long and short leg in such a way that both the long and short leg will have the same beta.
If you haven't read about the 'quant quake' of August 2007, it would be good for context related to your suggestion above. Many quant (stat arb and market neutral) hedge funds had portfolios they thought were beta neutral with a framework similar to what you've outlined. For reasons more systemic in nature, they had a rude awakening, and found out the hard way that they were not actually beta neutral, and market forces made it difficult to maintain their desired exposures in during the brief crisis.

Now, to be fair, they were leveraged and had to trade far more than an individual would, so liquidity is more of a challenge for large funds. Either way, it's good to recall mistakes made when ex post betas are relied upon for ex ante inputs without sound logic underpinning the strategy.
Raised important point. My comment ASSUMES little to no parameter (beta) uncertainty.
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Re: Is There an Optimal Factor Allocation?

Post by 000 »

alex_686 wrote: Tue Sep 21, 2021 3:16 pm For example, I am interested in taking some risk off of the table. As such I have a modest tilt towards the "Low Volatility" factor. Even thought it did not provided downside protection during the COVID crisis I am sticking with it because I have a high conviction.
Why do you have a high conviction in this "Low Volatility" factor?
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Re: Is There an Optimal Factor Allocation?

Post by BJJ_GUY »

hg064754 wrote: Tue Sep 21, 2021 7:54 pm
BJJ_GUY wrote: Tue Sep 21, 2021 7:43 pm
hg064754 wrote: Tue Sep 21, 2021 7:25 pm
If you measure risk as portfolio beta, you can take that risk out by forming beta neutral portfolios (as opposed to dollar neutral) in the long-short portfolio. This is done by going long in small stocks and short in big stocks, but weigh the components of the long and short leg in such a way that both the long and short leg will have the same beta.
If you haven't read about the 'quant quake' of August 2007, it would be good for context related to your suggestion above. Many quant (stat arb and market neutral) hedge funds had portfolios they thought were beta neutral with a framework similar to what you've outlined. For reasons more systemic in nature, they had a rude awakening, and found out the hard way that they were not actually beta neutral, and market forces made it difficult to maintain their desired exposures in during the brief crisis.

Now, to be fair, they were leveraged and had to trade far more than an individual would, so liquidity is more of a challenge for large funds. Either way, it's good to recall mistakes made when ex post betas are relied upon for ex ante inputs without sound logic underpinning the strategy.
Raised important point. My comment ASSUMES little to no parameter (beta) uncertainty.
My point was not really to say you are wrong or anything. I was trying to highlight the fact that betas, and factors too, are dynamic. Adhering to certain strategies in theory is different from doing in practice.

Apologies if I didn't make that point very well in the initial reply.
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Re: Is There an Optimal Factor Allocation?

Post by UpperNwGuy »

000 wrote: Tue Sep 21, 2021 7:47 pm I mean isn't the market the optimal factor allocation as determined by market participants?
Yes.
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Re: Is There an Optimal Factor Allocation?

Post by Nathan Drake »

000 wrote: Tue Sep 21, 2021 7:47 pm I mean isn't the market the optimal factor allocation as determined by market participants?

So the optimal allocation for you would depend on how you differ from the market (or what you understand better than the market).

Frankly I don't think many people differ from the market in terms of published factors. Someone with large exposure to a sector in their career or privately held businesses is a stronger case for adjusting the default market portfolio than investment enthusiasts who think "I have more tolerance for risk! My SCV portfolio is like me selling insurance!".
How someone defines a market, or what is optimal may be a personal risk/reward/adherence.

The data on factors is robust and persistent. Whether an investor is able to stick with it is another matter. But someone that can adhere to a tilt or even 100% SCV has had much greater returns over the long term
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Re: Is There an Optimal Factor Allocation?

Post by David Jay »

One More Thing wrote: Tue Sep 21, 2021 7:30 pm
David Jay wrote: Tue Sep 21, 2021 7:06 pm Gene Fama (of Fama/French) has said that factor investing should be done for a lifetime. If one is not willing to commit for decades he recommends total market rather than a factor tilt.
I realize that one cannot capture a full factor premium without investing in it 100%. Simple logic. Can you not expect to capture an amount proportional to your tilt though?
Certainly (in fact a "tilt" implies a Total Stock base with a factor percentage), but the premium may not show up for 15 years. How long are you willing to hold a tilt that is under-performing the market. If you are not willing to commit to decades, you may well give up at some point and sell, locking in the reduced (compared to the market) performance.

I always say: In order to tilt successfully, you have to believe in the factor enough to convince yourself to stay the course through a decade or more of underperformance. If you don't have that level of belief and intestinal fortitude, stay with Total Stock Market. Total Market is the default, low regret selection which reduces behavioral mistakes.
Last edited by David Jay on Tue Sep 21, 2021 8:57 pm, edited 1 time in total.
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Re: Is There an Optimal Factor Allocation?

Post by 000 »

Nathan Drake wrote: Tue Sep 21, 2021 8:49 pm The data on factors is robust and persistent.
Are they really though? SCV post publication is nothing to write home about...
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Re: Is There an Optimal Factor Allocation?

Post by Nathan Drake »

000 wrote: Tue Sep 21, 2021 8:57 pm
Nathan Drake wrote: Tue Sep 21, 2021 8:49 pm The data on factors is robust and persistent.
Are they really though? SCV post publication is nothing to write home about...
I didn’t realize they handed out Nobel prizes for things that aren’t anything to write home about

Backtesting a SCV portfolio from 50 years ago until now shows a pretty huge difference worth writing home about
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Re: Is There an Optimal Factor Allocation?

Post by 000 »

Nathan Drake wrote: Tue Sep 21, 2021 8:59 pm
000 wrote: Tue Sep 21, 2021 8:57 pm
Nathan Drake wrote: Tue Sep 21, 2021 8:49 pm The data on factors is robust and persistent.
Are they really though? SCV post publication is nothing to write home about...
I didn’t realize they handed out Nobel prizes for things that aren’t anything to write home about

Backtesting a SCV portfolio from 50 years ago until now shows a pretty huge difference worth writing home about
Don't play the fool. You know exactly what I mean that the SCV premium has not been the same post publication and fund availability.

Nobel prizes are silly. Really.
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Re: Is There an Optimal Factor Allocation?

Post by Nathan Drake »

000 wrote: Tue Sep 21, 2021 9:05 pm
Nathan Drake wrote: Tue Sep 21, 2021 8:59 pm
000 wrote: Tue Sep 21, 2021 8:57 pm
Nathan Drake wrote: Tue Sep 21, 2021 8:49 pm The data on factors is robust and persistent.
Are they really though? SCV post publication is nothing to write home about...
I didn’t realize they handed out Nobel prizes for things that aren’t anything to write home about

Backtesting a SCV portfolio from 50 years ago until now shows a pretty huge difference worth writing home about
Don't play the fool. You know exactly what I mean that the SCV premium has not been the same post publication and fund availability.

Nobel prizes are silly. Really.
You said it wasn’t worth writing home about, clearly some Nobel prize winners and a whole segment of investment management thought it was. Regardless of whether you agree with investing directly in that space, I don’t see how you could come to the conclusion that it’s not a very significant finding in academic finance

even a 1% premium over a long enough time is significant, as are more reliably consistent positive outcomes.
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Re: Is There an Optimal Factor Allocation?

Post by 000 »

Nathan Drake wrote: Tue Sep 21, 2021 9:12 pm You said it wasn’t worth writing home about, clearly some Nobel prize winners and a whole segment of investment management thought it was. Regardless of whether you agree with investing directly in that space, I don’t see how you could come to the conclusion that it’s not a very significant finding in academic finance

even a 1% premium over a long enough time is significant, as are more reliably consistent positive outcomes.
Did you even read my post? I said

SCV post publication is nothing to write home about...
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Re: Is There an Optimal Factor Allocation?

Post by Nathan Drake »

000 wrote: Tue Sep 21, 2021 9:14 pm
Nathan Drake wrote: Tue Sep 21, 2021 9:12 pm You said it wasn’t worth writing home about, clearly some Nobel prize winners and a whole segment of investment management thought it was. Regardless of whether you agree with investing directly in that space, I don’t see how you could come to the conclusion that it’s not a very significant finding in academic finance

even a 1% premium over a long enough time is significant, as are more reliably consistent positive outcomes.
Did you even read my post? I said

SCV post publication is nothing to write home about...
Still looks like it to me. Less exposed to dead decades, better performance
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Re: Is There an Optimal Factor Allocation?

Post by 000 »

Nathan Drake wrote: Tue Sep 21, 2021 9:24 pm
000 wrote: Tue Sep 21, 2021 9:14 pm
Nathan Drake wrote: Tue Sep 21, 2021 9:12 pm You said it wasn’t worth writing home about, clearly some Nobel prize winners and a whole segment of investment management thought it was. Regardless of whether you agree with investing directly in that space, I don’t see how you could come to the conclusion that it’s not a very significant finding in academic finance

even a 1% premium over a long enough time is significant, as are more reliably consistent positive outcomes.
Did you even read my post? I said

SCV post publication is nothing to write home about...
Still looks like it to me. Less exposed to dead decades, better performance
From the inception of the premier SCV fund DFSVX in March 1993, Vanguard total stock market had a higher sharpe ratio, CAGR difference of less than the typical AUM fee to access DFSVX, and most importantly of all the absolute returns of the two funds were tied as recently as March 2020. All that excess performance was given back.
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Re: Is There an Optimal Factor Allocation?

Post by muffins14 »

000 wrote: Tue Sep 21, 2021 9:32 pm
Nathan Drake wrote: Tue Sep 21, 2021 9:24 pm
000 wrote: Tue Sep 21, 2021 9:14 pm
Nathan Drake wrote: Tue Sep 21, 2021 9:12 pm You said it wasn’t worth writing home about, clearly some Nobel prize winners and a whole segment of investment management thought it was. Regardless of whether you agree with investing directly in that space, I don’t see how you could come to the conclusion that it’s not a very significant finding in academic finance

even a 1% premium over a long enough time is significant, as are more reliably consistent positive outcomes.
Did you even read my post? I said

SCV post publication is nothing to write home about...
Still looks like it to me. Less exposed to dead decades, better performance
From the inception of the premier SCV fund DFSVX in March 1993, Vanguard total stock market had a higher sharpe ratio, CAGR difference of less than the typical AUM fee to access DFSVX, and most importantly of all the absolute returns of the two funds were tied as recently as March 2020. All that excess performance was given back.
This is like the 100th time someone has cited one fund’s performance with one set of endpoints as though it were representative of all global factor investing principles. You and the forum should have higher standards
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Re: Is There an Optimal Factor Allocation?

Post by Nathan Drake »

000 wrote: Tue Sep 21, 2021 9:32 pm
Nathan Drake wrote: Tue Sep 21, 2021 9:24 pm
000 wrote: Tue Sep 21, 2021 9:14 pm
Nathan Drake wrote: Tue Sep 21, 2021 9:12 pm You said it wasn’t worth writing home about, clearly some Nobel prize winners and a whole segment of investment management thought it was. Regardless of whether you agree with investing directly in that space, I don’t see how you could come to the conclusion that it’s not a very significant finding in academic finance

even a 1% premium over a long enough time is significant, as are more reliably consistent positive outcomes.
Did you even read my post? I said

SCV post publication is nothing to write home about...
Still looks like it to me. Less exposed to dead decades, better performance
From the inception of the premier SCV fund DFSVX in March 1993, Vanguard total stock market had a higher sharpe ratio, CAGR difference of less than the typical AUM fee to access DFSVX, and most importantly of all the absolute returns of the two funds were tied as recently as March 2020. All that excess performance was given back.
Not sure where you are getting your data. VTSMX vs. DFSVX Since 1994 (as long as PV goes back). This period is 27 years.

Almost a 1% premium. It's also important to look at the graph in the link below. SCV has outperformed for the vast majority of the period. Out of 27 years, VTSMX has only led in 3 years. So, an end-date coinciding with some of the worst underperformance of SCV on record still ended up ahead. This is an extremely favorable backtest for US TSM, yet still SCV seemed to have a better outcome. It didn't come as a free lunch, it came with extra risk, and you can see that US TSM still had a higher sharpe ratio.

https://www.portfoliovisualizer.com/bac ... ion2_2=100

But that is only looking at the US market. Let's look at Developed markets: A humongous premium of 5%

https://www.portfoliovisualizer.com/bac ... ion2_2=100


And now emerging markets: A 2% premium, and this was only able to capture value loading (not size).

https://www.portfoliovisualizer.com/bac ... ion2_2=100

Seems fairly convincing to me. Now, whether you choose to invest this way is up to your personal risk tolerance because as I mentioned it comes with additional risk. If you cannot stay the course and don't believe in the data then you should stick with what you are comfortable with.
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Re: Is There an Optimal Factor Allocation?

Post by Forester »

One More Thing wrote: Tue Sep 21, 2021 3:01 pm 3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?
If an equity portfolio is 50% TSM and 50% small cap; is it 100% indexed? Some would say yes, others no.

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iShares IJS small cap value, turnover = 52%
iShares IJT small cap growth, turnover = 52%
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Re: Is There an Optimal Factor Allocation?

Post by hg064754 »

BJJ_GUY wrote: Tue Sep 21, 2021 8:03 pm
hg064754 wrote: Tue Sep 21, 2021 7:54 pm
BJJ_GUY wrote: Tue Sep 21, 2021 7:43 pm
hg064754 wrote: Tue Sep 21, 2021 7:25 pm
If you measure risk as portfolio beta, you can take that risk out by forming beta neutral portfolios (as opposed to dollar neutral) in the long-short portfolio. This is done by going long in small stocks and short in big stocks, but weigh the components of the long and short leg in such a way that both the long and short leg will have the same beta.
If you haven't read about the 'quant quake' of August 2007, it would be good for context related to your suggestion above. Many quant (stat arb and market neutral) hedge funds had portfolios they thought were beta neutral with a framework similar to what you've outlined. For reasons more systemic in nature, they had a rude awakening, and found out the hard way that they were not actually beta neutral, and market forces made it difficult to maintain their desired exposures in during the brief crisis.

Now, to be fair, they were leveraged and had to trade far more than an individual would, so liquidity is more of a challenge for large funds. Either way, it's good to recall mistakes made when ex post betas are relied upon for ex ante inputs without sound logic underpinning the strategy.
Raised important point. My comment ASSUMES little to no parameter (beta) uncertainty.
My point was not really to say you are wrong or anything. I was trying to highlight the fact that betas, and factors too, are dynamic. Adhering to certain strategies in theory is different from doing in practice.

Apologies if I didn't make that point very well in the initial reply.
Fully agree with your point. Textbook/theoretical construct is very different from reality.
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Re: Is There an Optimal Factor Allocation?

Post by nisiprius »

Nathan Drake wrote: Tue Sep 21, 2021 8:59 pm
000 wrote: Tue Sep 21, 2021 8:57 pm
Nathan Drake wrote: Tue Sep 21, 2021 8:49 pm The data on factors is robust and persistent.
Are they really though? SCV post publication is nothing to write home about...
I didn’t realize they handed out Nobel prizes for things that aren’t anything to write home about
They don't. Please don't insinuate that Fama's Nobel prize* was awarded for the Fama-French factor papers.

1) Kenneth French is not a Nobel laureate.

2) Eugene Fama is, but his Nobel prize* was not awarded for his work on factors. One capsule description is:
For many of us, the rise and fall of stock prices symbolizes economic development. In the 1960s, Eugene Fama demonstrated that stock price movements are impossible to predict in the short-term and that new information affects prices almost immediately, which means that the market is efficient. The impact of Eugene Fama's, results has extended beyond the field of research. For example, his results influenced the development of index funds.
It has often been observed that the existence of factor premia seems to violate the efficient market hypothesis, and Fama has been at some pains to explain why he thinks they don't. He has stated that he believes the factor premia are reward for risk, plain and simple. In an interview, he said:
Interviewer: Some people cite your research showing that value and small firms have higher average returns over time and they assume that you would recommend most investors have a big helping of small and value stocks in their portfolios. Is that a fair representation of your views?

Fama: Um, no. (Laughs)


*Before someone quibbles: his Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel
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Re: Is There an Optimal Factor Allocation?

Post by Random Walker »

One More Thing wrote: Tue Sep 21, 2021 3:01 pm I have a set of questions centered around this topic. I apologize if this is well-trodden ground.

1. Should there be a hierarchy of priority within a factor-tilted portfolio?

2. Can you invest in so many factors that your portfolio becomes indistinguishable from a TSM?

3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?

Thank you all for any discussion. From my lurking this seems to be a bastion of TSM investors but I know there are factor investors here too.
Here are my responses:
1. I would invest in each factor proportionate to your belief. If your strongest belief is in market factor, give that factor more weight. If you have stronger belief in risk based factors than behavioral ones, give the risk based ones more weight in your portfolio.

2. There are only perhaps 4-6 equity factors to realistically consider: market, size, value, investment, profitability/quality, momentum. I think the purpose of factor investing is to more evenly spread the portfolio risks across unique and independent risks. Most of our portfolios are dominated by the market factor. Diversifying across factors, especially if you increase tilt to SV and decrease overall equity allocation, will move you further away from TSM.

3. Depends how you define risk. Investing in TSM means you are placing all your bets on a single risk factor, market beta. Diversifying across factors, including exposure to term on the fixed income side is a move towards more evenly spreading risk across several unique and independent sources, a move towards risk parity.

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Re: Is There an Optimal Factor Allocation?

Post by dbr »

Random Walker wrote: Wed Sep 22, 2021 8:42 am
One More Thing wrote: Tue Sep 21, 2021 3:01 pm I have a set of questions centered around this topic. I apologize if this is well-trodden ground.

1. Should there be a hierarchy of priority within a factor-tilted portfolio?

2. Can you invest in so many factors that your portfolio becomes indistinguishable from a TSM?

3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?

Thank you all for any discussion. From my lurking this seems to be a bastion of TSM investors but I know there are factor investors here too.
Here are my responses:
1. I would invest in each factor proportionate to your belief. If your strongest belief is in market factor, give that factor more weight. If you have stronger belief in risk based factors than behavioral ones, give the risk based ones more weight in your portfolio.

2. There are only perhaps 4-6 equity factors to realistically consider: market, size, value, investment, profitability/quality, momentum. I think the purpose of factor investing is to more evenly spread the portfolio risks across unique and independent risks. Most of our portfolios are dominated by the market factor. Diversifying across factors, especially if you increase tilt to SV and decrease overall equity allocation, will move you further away from TSM.

3. Depends how you define risk. Investing in TSM means you are placing all your bets on a single risk factor, market beta. Diversifying across factors, including exposure to term on the fixed income side is a move towards more evenly spreading risk across several unique and independent sources, a move towards risk parity.

Dave
What specifically is being optimized here? By definition optimize means to seek a maximum or a minimum of some property of the portfolio. Naively people often mean to maximize expected return but there are any variety of utility functions one could care about. It can be an idea of efficiency, namely having maximum return for a set level of risk (SD of returns) or a minimum risk for a set level of expected return. Are there other ideas that people are pursuing?

The original work by Fama and French was simply an attempt to predict equity returns from other characteristics of the portfolio and never included an attempt to maximize anything. CAPM does include a concept of finding an "ideal portfolio" where the capital market line intersects an efficient frontier. What in general does it mean to find an "optimum" portfolio?
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Re: Is There an Optimal Factor Allocation?

Post by alex_686 »

000 wrote: Tue Sep 21, 2021 7:57 pm
alex_686 wrote: Tue Sep 21, 2021 3:16 pm For example, I am interested in taking some risk off of the table. As such I have a modest tilt towards the "Low Volatility" factor. Even thought it did not provided downside protection during the COVID crisis I am sticking with it because I have a high conviction.
Why do you have a high conviction in this "Low Volatility" factor?
The short answer is that theory and practice are congruent.

Why would a stock have a stable price? Because it has stable and predictable revenue.

Why would a stock have stable revenue? A couple of choices. Well run risk adverse company in a mature sector. Low leverage. It has a decent "moat" around it business making competition hard.

These companies should do better is a down market - expect that crashes all tend to be unique. Who would have guessed that wizzie high-risk tech companies would be the real winner in a last year's crash?
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Re: Is There an Optimal Factor Allocation?

Post by Random Walker »

000 wrote: Tue Sep 21, 2021 8:57 pm
Nathan Drake wrote: Tue Sep 21, 2021 8:49 pm The data on factors is robust and persistent.
Are they really though? SCV post publication is nothing to write home about...
1992-2021 SCV has beaten TSM by about 1.3% annualized
https://www.portfoliovisualizer.com/bac ... ation2_2=0


Since about 2017, the outperformance of TSM over SCV has been completely (more than completely?) explained by P/E expansion. If we look at 1992-2017, SCV wins by about 2.6% annualized.

https://www.portfoliovisualizer.com/bac ... ation2_2=0

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Re: Is There an Optimal Factor Allocation?

Post by Angst »

alex_686 wrote: Tue Sep 21, 2021 4:38 pm
dru808 wrote: Tue Sep 21, 2021 4:29 pm What fund or funds are you utilizing?
I am currently using iShares MSCI USA Min Vol Factor ETF (USMV) and iShares MSCI Global Min Vol Factor ETF (ACWV).

Take this with a grain of salt. While I am confident in the minimum volatility factor I am still researching funds.
Not to sidetrack this thread, but I'm curious if you have any strong opinions regarding either of Vanguard's MV offerings?
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Re: Is There an Optimal Factor Allocation?

Post by Random Walker »

dbr wrote: Wed Sep 22, 2021 9:04 am
Random Walker wrote: Wed Sep 22, 2021 8:42 am
One More Thing wrote: Tue Sep 21, 2021 3:01 pm I have a set of questions centered around this topic. I apologize if this is well-trodden ground.

1. Should there be a hierarchy of priority within a factor-tilted portfolio?

2. Can you invest in so many factors that your portfolio becomes indistinguishable from a TSM?

3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?

Thank you all for any discussion. From my lurking this seems to be a bastion of TSM investors but I know there are factor investors here too.
Here are my responses:
1. I would invest in each factor proportionate to your belief. If your strongest belief is in market factor, give that factor more weight. If you have stronger belief in risk based factors than behavioral ones, give the risk based ones more weight in your portfolio.

2. There are only perhaps 4-6 equity factors to realistically consider: market, size, value, investment, profitability/quality, momentum. I think the purpose of factor investing is to more evenly spread the portfolio risks across unique and independent risks. Most of our portfolios are dominated by the market factor. Diversifying across factors, especially if you increase tilt to SV and decrease overall equity allocation, will move you further away from TSM.

3. Depends how you define risk. Investing in TSM means you are placing all your bets on a single risk factor, market beta. Diversifying across factors, including exposure to term on the fixed income side is a move towards more evenly spreading risk across several unique and independent sources, a move towards risk parity.

Dave
What specifically is being optimized here? By definition optimize means to seek a maximum or a minimum of some property of the portfolio. Naively people often mean to maximize expected return but there are any variety of utility functions one could care about. It can be an idea of efficiency, namely having maximum return for a set level of risk (SD of returns) or a minimum risk for a set level of expected return. Are there other ideas that people are pursuing?

The original work by Fama and French was simply an attempt to predict equity returns from other characteristics of the portfolio and never included an attempt to maximize anything. CAPM does include a concept of finding an "ideal portfolio" where the capital market line intersects an efficient frontier. What in general does it mean to find an "optimum" portfolio?
Not sure I can directly address your thought/question. But I will say this. FF say that S&V represent expected premiums for risk. What they equally say that gets much less attention around here is that market, size, and value are risks that are different and independent of one another. So qualitatively speaking, a tilted portfolio has its exposures to various independent risks more evenly spread. This is especially true if one targets a specific level of expected return and this increases SV tilt, decreases overall equity exposure, increases exposure to bonds/term. Market is just another factor. A portfolio with risks spread evenly across factors has been less likely to have a negative outcome in the past than any single factor. See the charts in chapter 9 of Larry Swedroe’s factor book.

Dave
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Re: Is There an Optimal Factor Allocation?

Post by alex_686 »

Angst wrote: Wed Sep 22, 2021 9:29 am Not to sidetrack this thread, but I'm curious if you have any strong opinions regarding either of Vanguard's MV offerings?
I don't.

I am still picking my way through the nuances of how the various index methodologies and actual practice.

For example, I find the justification of the S&P 500 index weak. The top 500 stocks? That is a arbitrary number. Why not 483 or 574? And we know that the real answer is that 500 is a nice round number. And while it is a arbitrary number it is such a popular index that the resulting efficiency in trading may well offset the better constructed CRSP index.
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Re: Is There an Optimal Factor Allocation?

Post by mrpotatoheadsays »

One More Thing wrote: Tue Sep 21, 2021 3:01 pm 1. Should there be a hierarchy of priority within a factor-tilted portfolio?
2. Can you invest in so many factors that your portfolio becomes indistinguishable from a TSM?
3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?
1. No... and "priority" in your statement is undefined. To one, 'priority" could be low standard deviation; to another, high 'long-term" annualized return.
2. "Indistinguishable" in your statement is undefined. The long-term annualized return delta between a multi-factor portfolio and a TSM could be ~2%. Is that "indistinguishable"? The TSM falls under the "large cap blend" factor. In theory, you could define a multi-factor portfolio with the same risk as the TSM in an effort to get the same long-term return as the TSM. The benefit of the factor-based portfolio could be less volatility. But understand, 'long-term" is 25 to 30 years. Factors, historically, can go out of favor for decades.
3. Your statement is flawed; the TSM has no "safety". The TSM recently went a decade with a near zero annualized return. Historically, the worst drawdown on the TSM is over 50%. If you want 'safety", you want something with guaranteed return like a CD. I don't understand the term 'factor tilting". If you are referring to how people say tilt some percentage of your portfolio to, e.g. small cap value, the risk taken is dependent upon the factor (Its risk) and the percentage tilted.
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Re: Is There an Optimal Factor Allocation?

Post by dbr »

Random Walker wrote: Wed Sep 22, 2021 9:42 am
dbr wrote: Wed Sep 22, 2021 9:04 am
Random Walker wrote: Wed Sep 22, 2021 8:42 am
One More Thing wrote: Tue Sep 21, 2021 3:01 pm I have a set of questions centered around this topic. I apologize if this is well-trodden ground.

1. Should there be a hierarchy of priority within a factor-tilted portfolio?

2. Can you invest in so many factors that your portfolio becomes indistinguishable from a TSM?

3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?

Thank you all for any discussion. From my lurking this seems to be a bastion of TSM investors but I know there are factor investors here too.
Here are my responses:
1. I would invest in each factor proportionate to your belief. If your strongest belief is in market factor, give that factor more weight. If you have stronger belief in risk based factors than behavioral ones, give the risk based ones more weight in your portfolio.

2. There are only perhaps 4-6 equity factors to realistically consider: market, size, value, investment, profitability/quality, momentum. I think the purpose of factor investing is to more evenly spread the portfolio risks across unique and independent risks. Most of our portfolios are dominated by the market factor. Diversifying across factors, especially if you increase tilt to SV and decrease overall equity allocation, will move you further away from TSM.

3. Depends how you define risk. Investing in TSM means you are placing all your bets on a single risk factor, market beta. Diversifying across factors, including exposure to term on the fixed income side is a move towards more evenly spreading risk across several unique and independent sources, a move towards risk parity.

Dave
What specifically is being optimized here? By definition optimize means to seek a maximum or a minimum of some property of the portfolio. Naively people often mean to maximize expected return but there are any variety of utility functions one could care about. It can be an idea of efficiency, namely having maximum return for a set level of risk (SD of returns) or a minimum risk for a set level of expected return. Are there other ideas that people are pursuing?

The original work by Fama and French was simply an attempt to predict equity returns from other characteristics of the portfolio and never included an attempt to maximize anything. CAPM does include a concept of finding an "ideal portfolio" where the capital market line intersects an efficient frontier. What in general does it mean to find an "optimum" portfolio?
Not sure I can directly address your thought/question. But I will say this. FF say that S&V represent expected premiums for risk. What they equally say that gets much less attention around here is that market, size, and value are risks that are different and independent of one another. So qualitatively speaking, a tilted portfolio has its exposures to various independent risks more evenly spread. This is especially true if one targets a specific level of expected return and this increases SV tilt, decreases overall equity exposure, increases exposure to bonds/term. Market is just another factor. A portfolio with risks spread evenly across factors has been less likely to have a negative outcome in the past than any single factor. See the charts in chapter 9 of Larry Swedroe’s factor book.

Dave
Thanks, this is about my understanding as well. So far the "Larry Portfolio" idea is one of the few that suggests a clearly understandable optimization of a practical consequence based on a factor construction, other than the extreme of concentrating in whatever factor predicts highest return.

So, would one suggest that maximizing Sortino Ratio would be the mathematical analysis one could propose?

I'll look again at Larry's book. It is on my Kindle.
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Re: Is There an Optimal Factor Allocation?

Post by Random Walker »

dbr wrote: Wed Sep 22, 2021 9:54 am
Random Walker wrote: Wed Sep 22, 2021 9:42 am
dbr wrote: Wed Sep 22, 2021 9:04 am
Random Walker wrote: Wed Sep 22, 2021 8:42 am
One More Thing wrote: Tue Sep 21, 2021 3:01 pm I have a set of questions centered around this topic. I apologize if this is well-trodden ground.

1. Should there be a hierarchy of priority within a factor-tilted portfolio?

2. Can you invest in so many factors that your portfolio becomes indistinguishable from a TSM?

3. Is there an optimal balance between the safety of TSM and the risk taken in factor tilting?

Thank you all for any discussion. From my lurking this seems to be a bastion of TSM investors but I know there are factor investors here too.
Here are my responses:
1. I would invest in each factor proportionate to your belief. If your strongest belief is in market factor, give that factor more weight. If you have stronger belief in risk based factors than behavioral ones, give the risk based ones more weight in your portfolio.

2. There are only perhaps 4-6 equity factors to realistically consider: market, size, value, investment, profitability/quality, momentum. I think the purpose of factor investing is to more evenly spread the portfolio risks across unique and independent risks. Most of our portfolios are dominated by the market factor. Diversifying across factors, especially if you increase tilt to SV and decrease overall equity allocation, will move you further away from TSM.

3. Depends how you define risk. Investing in TSM means you are placing all your bets on a single risk factor, market beta. Diversifying across factors, including exposure to term on the fixed income side is a move towards more evenly spreading risk across several unique and independent sources, a move towards risk parity.

Dave
What specifically is being optimized here? By definition optimize means to seek a maximum or a minimum of some property of the portfolio. Naively people often mean to maximize expected return but there are any variety of utility functions one could care about. It can be an idea of efficiency, namely having maximum return for a set level of risk (SD of returns) or a minimum risk for a set level of expected return. Are there other ideas that people are pursuing?

The original work by Fama and French was simply an attempt to predict equity returns from other characteristics of the portfolio and never included an attempt to maximize anything. CAPM does include a concept of finding an "ideal portfolio" where the capital market line intersects an efficient frontier. What in general does it mean to find an "optimum" portfolio?
Not sure I can directly address your thought/question. But I will say this. FF say that S&V represent expected premiums for risk. What they equally say that gets much less attention around here is that market, size, and value are risks that are different and independent of one another. So qualitatively speaking, a tilted portfolio has its exposures to various independent risks more evenly spread. This is especially true if one targets a specific level of expected return and this increases SV tilt, decreases overall equity exposure, increases exposure to bonds/term. Market is just another factor. A portfolio with risks spread evenly across factors has been less likely to have a negative outcome in the past than any single factor. See the charts in chapter 9 of Larry Swedroe’s factor book.

Dave
Thanks, this is about my understanding as well. So far the "Larry Portfolio" idea is one of the few that suggests a clearly understandable optimization of a practical consequence based on a factor construction, other than the extreme of concentrating in whatever factor predicts highest return.

So, would one suggest that maximizing Sortino Ratio would be the mathematical analysis one could propose?

I'll look again at Larry's book. It is on my Kindle.
Personally, especially since we can’t predict the future, I would think much more qualitatively than quantitatively. Invest in the factors proportionate to your belief in them and assume benefit from less than perfect correlation between the factors. Depending on your goals and stage of the investing life cycle, consider maybe decreasing overall equity exposure and increasing term exposure along with the tilt to equity asset classes with increased expected return.

Dave
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Re: Is There an Optimal Factor Allocation?

Post by dbr »

Random Walker wrote: Wed Sep 22, 2021 11:58 am

Personally, especially since we can’t predict the future, I would think much more qualitatively than quantitatively. Invest in the factors proportionate to your belief in them and assume benefit from less than perfect correlation between the factors. Depending on your goals and stage of the investing life cycle, consider maybe decreasing overall equity exposure and increasing term exposure along with the tilt to equity asset classes with increased expected return.

Dave
I can see that as a kind of a pragmatic hope, but this whole concept is supposed to be grounded in portfolio theory and to make concepts such as "optimum portfolio" meaningful. Without mathematical definition it just becomes shadows on the wall.

See perhaps Plato's Allegory or the lyrics "Shadows on the Wall" (not copied in whole due to copyright), also to be taken as an allegory:

https://www.google.com/search?q=Shadows ... 2&dpr=1.25
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Re: Is There an Optimal Factor Allocation?

Post by imak »

In my portfolio, from a morningstar style box perspective, I prefer mid-cap value as a sweet spot.

The average company in such a portfolio, from a unit economics perspective, is not too large to be unsustainable in growth rate and not too small to have no optionality in capital allocation decisions.

From a FF3 factor perspective, this probably means SMB in the range of 0.2-0.4 and HML about 0.2-0.4 (just a guess).
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Re: Is There an Optimal Factor Allocation?

Post by Random Walker »

dbr wrote: Wed Sep 22, 2021 12:20 pm
Random Walker wrote: Wed Sep 22, 2021 11:58 am

Personally, especially since we can’t predict the future, I would think much more qualitatively than quantitatively. Invest in the factors proportionate to your belief in them and assume benefit from less than perfect correlation between the factors. Depending on your goals and stage of the investing life cycle, consider maybe decreasing overall equity exposure and increasing term exposure along with the tilt to equity asset classes with increased expected return.

Dave
I can see that as a kind of a pragmatic hope, but this whole concept is supposed to be grounded in portfolio theory and to make concepts such as "optimum portfolio" meaningful. Without mathematical definition it just becomes shadows on the wall.

See perhaps Plato's Allegory or the lyrics "Shadows on the Wall" (not copied in whole due to copyright), also to be taken as an allegory:

https://www.google.com/search?q=Shadows ... 2&dpr=1.25
But we can only determine optimum for the past. We only invest looking forward. And looking forward, we are dealing with expected returns as opposed to known returns, volatilities that are perhaps quite similar to the past, and correlations that change over time. Add on to that human behavioral foibles and an unknowable future, and I think we are only fooling ourselves if we get too mathematical.

Dave
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Re: Is There an Optimal Factor Allocation?

Post by dbr »

Random Walker wrote: Wed Sep 22, 2021 2:25 pm
dbr wrote: Wed Sep 22, 2021 12:20 pm
Random Walker wrote: Wed Sep 22, 2021 11:58 am

Personally, especially since we can’t predict the future, I would think much more qualitatively than quantitatively. Invest in the factors proportionate to your belief in them and assume benefit from less than perfect correlation between the factors. Depending on your goals and stage of the investing life cycle, consider maybe decreasing overall equity exposure and increasing term exposure along with the tilt to equity asset classes with increased expected return.

Dave
I can see that as a kind of a pragmatic hope, but this whole concept is supposed to be grounded in portfolio theory and to make concepts such as "optimum portfolio" meaningful. Without mathematical definition it just becomes shadows on the wall.

See perhaps Plato's Allegory or the lyrics "Shadows on the Wall" (not copied in whole due to copyright), also to be taken as an allegory:

https://www.google.com/search?q=Shadows ... 2&dpr=1.25


But we can only determine optimum for the past. We only invest looking forward. And looking forward, we are dealing with expected returns as opposed to known returns, volatilities that are perhaps quite similar to the past, and correlations that change over time. Add on to that human behavioral foibles and an unknowable future, and I think we are only fooling ourselves if we get too mathematical.

Dave
Good enough. Thanks

I'll still be interested to see what others propose is being optimized.
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Re: Is There an Optimal Factor Allocation?

Post by nisiprius »

Random Walker wrote: Wed Sep 22, 2021 9:22 am
000 wrote: Tue Sep 21, 2021 8:57 pm
Nathan Drake wrote: Tue Sep 21, 2021 8:49 pm The data on factors is robust and persistent.
Are they really though? SCV post publication is nothing to write home about...
1992-2021 SCV has beaten TSM by about 1.3% annualized
https://www.portfoliovisualizer.com/bac ... ation2_2=0
...
Yes, but that's ignoring risk. If you display the entire PortfolioVisualizer presentation, the risk-adjusted return of small-cap value has been virtually identical--microscopically lower--than Total Stock.

Image

If the small-cap value premium is nothing more than reward for risk, then the benefits don't disappear completely but they become very subtle. The expectation, for example, is that adding small-cap value to a three-fund portfolio would not boost performance any more than boosting risk simply by increasing stock allocation. We can test this by comparing two ways of boosting the risk of a portfolio of 42% US stocks, 18% international stocks, and 40% bonds.

For the first portfolio, I am not sure how much you would shift to small-cap value, but let's say 14% which I think we can agree is a substantial tilt. And I'll use the DFA Small-cap Value Fund as being old and admired. So, 28% VTSMX, 14% DFSVX, 18% VGTSX, and 40% VBMFX.

That turns out to have a standard deviation of 9.69%, compared to 9.28%. For the second fund, by trial and error, I increased the allocation of the two (non-tilted) stock funds to bring the standard deviation up to 9.69%.

(Jan 1997 - Aug 2021)

Source

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  • Yes, the portfolio with small-cap value did have higher average annual return over this time period.
  • But the difference was only 13 basis points.
  • In many presentations claiming to show increased from a small-cap value tilt, most of the increased return can be attributed simply to adding risk.
  • You can get virtually the same result simply by adding risk without tilting, just by increasing stock allocation a trifle.
  • The dramatic difference in the first chart comes from assuming 100% stocks and not controlling for risk difference. In the context of whole portfolios with equal risk most of the difference goes away.
A valid argument for a small-cap value tilt would be that you have a personal preference for the particular kind of risk behavior shown by small-cap value--specifically, the negative skew it is said to have. Negative skew means a small gain most of the time punctuated by big losses occasionally. Do you, personally, have that preference?
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.
SpreadsheetsAreFun
Posts: 30
Joined: Thu Aug 26, 2021 12:23 pm

Re: Is There an Optimal Factor Allocation?

Post by SpreadsheetsAreFun »

Optimal will really depend on the individual investor goals and boundary conditions such as if the return or the risk-adjusted return should be maximized and whether or to which extent the investor is willing to accept tracking errors to the benchmark during good and bad times.

Below is a summary of the data analyzed to derive the equity part of my asset allocation. It might be interesting to OP to understand the thought process of this one investor with specific boundary conditions and hope this will be helpful and contribute to the conversation. I used mostly MSCI historical data because (1) it is index data based on sets of rules that are publicly accessible rather than active stock selection of asset managers and (2) many of their indices have associated ETFs that many can be invested into which makes the analysis applicable.

It is commonly know that factor performance is highly time-dependent (for example value has underperformed in the US for ~15 years). But it is equally important to realize that factor performance can diverge significantly between different regions or capitalization ranges. Below I have plotted in log scale how different factors (thin lines) have performed relative to their US and ACWI indices. There is significant divergence between these. I have also added 3 multi-factor portfolios: An equal-weight approach with 25% each of Value, Quality, Momentum, and Small Cap (Pink) as well as the MSCI Diversified Multiple-Factor indices for Large Caps (Black) and Small Caps (Blue). The stock selection and weighing process for the latter two is complex and obviously this leads to a very different behavior compared to equally the equal factor weight approach.

One thing that I find very interesting is that the equal factor weight approach shows very limited added noise compared to the benchmark and that there are general upwards trends. The Value factor behavior seems to deviate from the general market more in the US than in exUS, which explains both the strong performance of equal factor weight after the Dot-Com bubble bursted and the weak performance since the GFC. In exUS this is less pronounced and has lead to a very consistent outperformance behavior since 2001 relate to ACWI.

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The diversified Multiple-Factor indices show way less consistent behavior and have periods of severe underperformance. US Examples is the period since ~2017 for both Large Cap and Small Cap Multiple-Factor when Value and Small Caps got hammered. In the exUS this includes Large caps since ~2017 because of Value and for Small Caps during the GFC Small Caps and Momentum were suffering. During other periods, the bad performance of one factor was more or less compensated by good performance of others.

What I decided to do for my asset allocation is to tilt to the two best long-term performing indices (over this period): Large Cap Momentum and Small Cap Multiple-Factors. And added some Emerging Markets Multiple-Factor to cover that region.

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This portfolio has periods of underperformance that I find acceptable, at least for the timeframe that data is available. The benchmark is MSCI WORLD. It showed really strong outperformance after the Dot-Com bubble because Small Caps performed well in exUS while at the same time all factors performed well in the US. Since the GFC there was a less pronounced outperformance with periods of underperformance that did last for multiple years. Those periods were dominated by the bad performance of value in the US.

Looking at these data, I think that this portfolio has a good chance of outperforming the extra expense ratio of 0.30% enough for me to accept the periods of underperformance. Can I guarantee that this is the case? No. Do I think that Value is forever going to perform as badly as over the last years? Probably not. So I have reasonable confidence that this allocation will work well for me over my investment horizon.
Have a great day. | Asset allocation: 70% Stocks, 15% Treasuries, 15% Gold (all ETFs)
000
Posts: 8211
Joined: Thu Jul 23, 2020 12:04 am

Re: Is There an Optimal Factor Allocation?

Post by 000 »

muffins14 wrote: Tue Sep 21, 2021 10:02 pm This is like the 100th time someone has cited one fund’s performance with one set of endpoints as though it were representative of all global factor investing principles. You and the forum should have higher standards
No, I also looked at DCA over the same time period and have tested other time periods before. One can find slight outperformance with the right parameters, but it really is just what I said: nothing to write home about. Almost always we are talking about more volatility and drawdown and often the volatility-adjusted return is even less performative. The fact that from most starting points SCV gave it all back in the March 2020 crash speaks volumes.
Last edited by 000 on Wed Sep 22, 2021 4:33 pm, edited 1 time in total.
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