How to diversify a Three Fund Portfolio in 8 steps

Discuss all general (i.e. non-personal) investing questions and issues, investing news, and theory.
User avatar
305pelusa
Posts: 1011
Joined: Fri Nov 16, 2018 10:20 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by 305pelusa » Fri Nov 01, 2019 7:29 am

Uncorrelated wrote:
Fri Nov 01, 2019 5:56 am
I did some quick calculations and came to the conclusion that diversification ratio is thoroughly broken. For example take the following portfolio: VTI (50%) + walmart (50%)

Walmart has a correlation of .26 with VTI. This portfolio has a higher sharpe ratio than just VTI and a diversification ratio of 1.25.

Of course, the idea that a portfolio of 50% Walmart is better diversified than VTI is completely nonsensical. I hope that this example is sufficient to explain the dangers of backtesting.



To add to asif408: this is 100% performance chasing. You just defined performance as low correlation instead of high return.
It's not a broken tool. It's just that no one here is using it properly.

Uncorrelated
Posts: 150
Joined: Sun Oct 13, 2019 3:16 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by Uncorrelated » Fri Nov 01, 2019 8:42 am

Hydromod wrote:
Fri Nov 01, 2019 7:08 am
Just out of curiosity, what part of the exercise contained backtesting? I missed it somehow.
The diversification ratio calculation requires the overall portfolio volatility and correlations, in this example these are determined by backtesting the individual assets and portfolio.

User avatar
Topic Author
hdas
Posts: 1270
Joined: Thu Jun 11, 2015 8:24 am

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by hdas » Fri Nov 01, 2019 9:40 am

305pelusa wrote:
Fri Nov 01, 2019 7:29 am
It's not a broken tool. It's just that no one here is using it properly.
Leaving aside the fact that for some funds/strategies there’s only 5-6 years of data, the main flaw of the application of DR is the issue of “comparability” of different number of holding. Could you be more explicit as to what else is needed for a “proper use” of the tool. Cheers :greedy
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

Hydromod
Posts: 256
Joined: Tue Mar 26, 2019 10:21 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by Hydromod » Fri Nov 01, 2019 9:52 am

Uncorrelated wrote:
Fri Nov 01, 2019 8:42 am
Hydromod wrote:
Fri Nov 01, 2019 7:08 am
Just out of curiosity, what part of the exercise contained backtesting? I missed it somehow.
The diversification ratio calculation requires the overall portfolio volatility and correlations, in this example these are determined by backtesting the individual assets and portfolio.
My impression is that backtesting refers to testing investment strategies to estimate portfolio performance using a sequence of historical observations.

In this case, the historical data is only used to estimate parameters.

Maybe I'm missing something.

User avatar
305pelusa
Posts: 1011
Joined: Fri Nov 16, 2018 10:20 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by 305pelusa » Fri Nov 01, 2019 10:04 am

hdas wrote:
Fri Nov 01, 2019 9:40 am
305pelusa wrote:
Fri Nov 01, 2019 7:29 am
It's not a broken tool. It's just that no one here is using it properly.
Leaving aside the fact that for some funds/strategies there’s only 5-6 years of data, the main flaw of the application of DR is the issue of “comparability” of different number of holding. Could you be more explicit as to what else is needed for a “proper use” of the tool. Cheers :greedy
It's a little more complex than just number of holdings. You could've started portfolio 1 as "3-Fund with a 0.1% allocation to every one of the funds from portfolio B". And as you SHIFT the weights to look like your final portfolio, you'd see DR go up. Even though the number of holdings and the holdings themselves are the same.

I'm by no means an expert of DR but here's some things you should keep in mind:
1) The risk of the asset must be properly captured by the St Dev. A poster added Walmart and came out with a higher DR. The reality is that Walmart's risk is actually much bigger than its St Dev suggests (due to the tremendous uncompensated ideosyncratic risk). You don't see it due to survivorship bias. The St Dev is not capturing the tremendous "fat tail" risk of a single security.

So my personal first axiom is "only use assets whose risks are fully captured by the risk measurement you use". So stick to asset classes that have, to the best extent possible, diversified ideosyncratic risk.

In other even VTI has fat tail risk not properly captured by St Dev but it's about as good as it gets.

2) Assets can't share common holdings. DR is not associative. The theory prevents this by demanding each asset is its own "risk factor".

So you can't add in balanced funds for instance. If you look at your portfolio and see that multiple funds might hold the same security, you've violated this.

You will inevitably violate this somehow. Just keep it to a minimum (Ex: don't use a small cap AND and a small cap value fund).

3) Compare DR between two portfolios if they are similarly "broken down" in hierarchy.
Ex: don't compare VTI vs 50/50 LC/SC. Compare 85% LC/SC (equivalent to VTI) vs 50/50 LC/SC.

Meaning, to avoid unfair inflation of DR by breaking funds down into smaller internal units, always compare apples to apples.

In your case, you can't compare 3 Fund vs Portfolio 8. But if you broke down the 3Fund portfolio into LC/SC/ Low Vol/High Vol/etc, in a mix that equals the 3Fund, THEN you can make the comparison. And make sure the funds themselves are fully diversified and as independent of each other to satisfy the above rules.

You'll get meaningful results following the 3 above

long_gamma
Posts: 352
Joined: Mon Sep 14, 2015 4:13 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by long_gamma » Fri Nov 01, 2019 10:06 am

Uncorrelated wrote:
Fri Nov 01, 2019 5:56 am
I did some quick calculations and came to the conclusion that diversification ratio is thoroughly broken. For example take the following portfolio: VTI (50%) + walmart (50%)

Walmart has a correlation of .26 with VTI. This portfolio has a higher sharpe ratio than just VTI and a diversification ratio of 1.25.

Of course, the idea that a portfolio of 50% Walmart is better diversified than VTI is completely nonsensical. I hope that this example is sufficient to explain the dangers of backtesting.



To add to asif408: this is 100% performance chasing. You just defined performance as low correlation instead of high return.
Where can i subscribe to your newsletter?

You constructed a portfolio of a broadbased index and single stock with in the same index and declared this is sufficient to declare DR is useless. Who is backtesting? All DR is doing is quantifying some reduction in volatility because of correlation.

Here is a better article.
https://blog.thinknewfound.com/2018/12/ ... ification/
"Assuming that your beliefs about correlations, volatilities, and returns align with those needed for the maximum diversification portfolio, three uses of this technique are:

Combine it with leverage and other portfolio construction techniques (for mitigating estimation risk) to target a specific volatility.
Use it to construct a conservative portfolio that requires careful management of sequence risk.
Use it as a benchmark for assessing diversification within an existing portfolio and considering tactical tilts to improve the diversification ratio.
"
"Everyone has a plan 'till they get punched in the mouth." --Mike Tyson

User avatar
Topic Author
hdas
Posts: 1270
Joined: Thu Jun 11, 2015 8:24 am

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by hdas » Fri Nov 01, 2019 10:37 am

305pelusa wrote:
Fri Nov 01, 2019 10:04 am

1) The risk of the asset must be properly captured by the St Dev.
Given the funds I used for my exercise, Check :dollar
305pelusa wrote:
Fri Nov 01, 2019 10:04 am

2) Assets can't share common holdings. DR is not associative. The theory prevents this by demanding each asset is its own "risk factor".
Here are the common overlap of the holdings I used:

MTUM - USMV > 27% - 61 holdings
MTUM - XSLV > 0%
MTUM - VIOV > 0%
VIOV - XSLV > 27% - 90 holdings
VIOV - USMV > 0%
USMV - XSLV > 0%

It's harder to count this for VMNVX, but let's use ACWV as a proxy. The issue its even more complicated by the hedging of VMNVX:

ACWV - MTUM > 16% - 52 holdings
ACWV - USMV > 47% - 141 holdings
ACWV - VIOV > 0%
ACWV - XSLV > 0%

I can fix this here by not using USMV, and replacing MTUM with VUG. I haven't done it yet, but I don't think this will materially change the analysis.
305pelusa wrote:
Fri Nov 01, 2019 10:04 am

3) Compare DR between two portfolios if they are similarly "broken down" in hierarchy.
Ex: don't compare VTI vs 50/50 LC/SC. Compare 85% LC/SC (equivalent to VTI) vs 50/50 LC/SC.
This is practically impossible. You know that. Specially for factor exposure.

In sum, I think we can both agree to:

a.) DR is a flawed measure to conclusively show that Portfolio 8 is more diversified than portfolio 1
b.) Portfolio 8 is more diversified than Portfolio 1

If you don't agree or are agnostic regarding point b.) I'll be very curious to hear why

Cheers :greedy
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

User avatar
305pelusa
Posts: 1011
Joined: Fri Nov 16, 2018 10:20 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by 305pelusa » Fri Nov 01, 2019 11:00 am

hdas wrote:
Fri Nov 01, 2019 10:37 am
305pelusa wrote:
Fri Nov 01, 2019 10:04 am

1) The risk of the asset must be properly captured by the St Dev.
Given the funds I used for my exercise, Check :dollar
305pelusa wrote:
Fri Nov 01, 2019 10:04 am

2) Assets can't share common holdings. DR is not associative. The theory prevents this by demanding each asset is its own "risk factor".
Here are the common overlap of the holdings I used:

MTUM - USMV > 27% - 61 holdings
MTUM - XSLV > 0%
MTUM - VIOV > 0%
VIOV - XSLV > 27% - 90 holdings
VIOV - USMV > 0%
USMV - XSLV > 0%

It's harder to count this for VMNVX, but let's use ACWV as a proxy. The issue its even more complicated by the hedging of VMNVX:

ACWV - MTUM > 16% - 52 holdings
ACWV - USMV > 47% - 141 holdings
ACWV - VIOV > 0%
ACWV - XSLV > 0%

I can fix this here by not using USMV, and replacing MTUM with VUG. I haven't done it yet, but I don't think this will materially change the analysis.
305pelusa wrote:
Fri Nov 01, 2019 10:04 am

3) Compare DR between two portfolios if they are similarly "broken down" in hierarchy.
Ex: don't compare VTI vs 50/50 LC/SC. Compare 85% LC/SC (equivalent to VTI) vs 50/50 LC/SC.
This is practically impossible. You know that. Specially for factor exposure.

In sum, I think we can both agree to:

a.) DR is a flawed measure to conclusively show that Portfolio 8 is more diversified than portfolio 1
b.) Portfolio 8 is more diversified than Portfolio 1

If you don't agree or are agnostic regarding point b.) I'll be very curious to hear why

Cheers :greedy
1) I agree your holdings have little ideosyncratic risk. But this isn't a "check or no check" process. It's a spectrum. Ex: a poster pointed out XSLV heavily tilts to real estate. To the extent this is diversifiable with more sectors, it represents a fat tail uncompensated risk not shown in its St Dev. I dont know how much so theres no right or wrong. Just beware of it. FWIW, I dont think its a big deal here.

2) Its good to avoid common holdings. Again, its a spectrum. You will not avoid completely. But to the extent you can, DR becomes more useful.

3) If you cannot “factor out” the 3 Fund portfolio into an equivalent mix of funds of your final portfolio, you simply cannot compare it to a mix of funds from the final portfolio. This is what i mean when I say DR is relative, not absolute.

Adding funds is fine (like EM bonds) btw.

I dont know if there are high volatiliry funds, high beta funds, etc. You know that more than me. If there are NOT (which you seem to imply), then i agree with point 1. I have since the beginning of the thread.

I don't know if Portfolio 8 is or is not more diversified. That's why we all clicked on this thread. Isn't it your burden to prove it? :confused

Uncorrelated
Posts: 150
Joined: Sun Oct 13, 2019 3:16 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by Uncorrelated » Fri Nov 01, 2019 11:16 am

long_gamma wrote:
Fri Nov 01, 2019 10:06 am

Where can i subscribe to your newsletter?

You constructed a portfolio of a broadbased index and single stock with in the same index and declared this is sufficient to declare DR is useless. Who is backtesting? All DR is doing is quantifying some reduction in volatility because of correlation.

Here is a better article.
https://blog.thinknewfound.com/2018/12/ ... ification/
The data in the article clearly shows that the portfolio with maximum diversification and simple constant allocation are not different in any statistically significant way. The article provides no evidence that DR is useful.


hdas wrote:
Fri Nov 01, 2019 10:37 am
b.) Portfolio 8 is more diversified than Portfolio 1

If you don't agree or are agnostic regarding point b.) I'll be very curious to hear why

Cheers :greedy
That depends on your measure of diversification. For example, a non-believer in factors would claim that portfolio 8 is less diversified than portfolio 1 because the idiosyncratic risk is higher. As a believer in factors, it is clear to me that portfolio 8 has more risk (measured in expected stddev) than portfolio 1, but it is not clear whether that extra risk is adequately compensated with higher expected return. Whether portfolio 8 is actually more 'diversified' than portfolio 1 is irrelevant in my view.

User avatar
Topic Author
hdas
Posts: 1270
Joined: Thu Jun 11, 2015 8:24 am

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by hdas » Fri Nov 01, 2019 11:42 am

Uncorrelated wrote:
Fri Nov 01, 2019 11:16 am
As a believer in factors, it is clear to me that portfolio 8 has more risk (measured in expected stddev) than portfolio 1, but it is not clear whether that extra risk is adequately compensated with higher expected return.
How did you calculate the "expected stddev" ?
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

long_gamma
Posts: 352
Joined: Mon Sep 14, 2015 4:13 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by long_gamma » Fri Nov 01, 2019 12:00 pm

Uncorrelated wrote:
Fri Nov 01, 2019 11:16 am


The data in the article clearly shows that the portfolio with maximum diversification and simple constant allocation are not different in any statistically significant way. The article provides no evidence that DR is useful.


It is ironic that your nick is "uncorrelated"

I will quote this again.

"Assuming that your beliefs about correlations, volatilities, and returns align with those needed for the maximum diversification portfolio, three uses of this technique are:

Combine it with leverage and other portfolio construction techniques (for mitigating estimation risk) to target a specific volatility.
Use it to construct a conservative portfolio that requires careful management of sequence risk.
Use it as a benchmark for assessing diversification within an existing portfolio and considering tactical tilts to improve the diversification ratio."


Here is the OP criterion in his post.

"Considerations:

1.) Balance Risk On/Off based on personal context. For this example I use my own, (80/20)
2.) Have some international risk (bond and stock) exposure
3.) Maximize Diversification given an objective criterion, enter Diversification Ratio.
The diversification ratio is the ratio of the weighted average of volatility divided by the portfolio volatility
4.) Achieve significant exposure to all equity style factors (Market, Quality, Size, Value, Momentum, BAB) [1] See exposure (loadings) with its T stat.
5.) No leverage
6.) Try to get closer to risk parity [2]

"
Where is return criterion specified?

Main purpose traders mostly calculate DR is to figure out how much leverage that can be applied. Leverage upto DR is no brainer. As it was mentioned in the quote, there are uses of calculating DR, but return maximization is not one of them.

OP doesn't want leverage, but want to achieve diversification as much as possible
"Everyone has a plan 'till they get punched in the mouth." --Mike Tyson

User avatar
Topic Author
hdas
Posts: 1270
Joined: Thu Jun 11, 2015 8:24 am

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by hdas » Fri Nov 01, 2019 12:23 pm

305pelusa wrote:
Fri Nov 01, 2019 11:00 am

I don't know if Portfolio 8 is or is not more diversified. That's why we all clicked on this thread. Isn't it your burden to prove it? :confused
I like the challenge, let me modify the experiment with the aim of meeting the "peer review" requirements better.

1. Let us break the 3 fund portfolio in the almost identical 5 fund portfolio

42.5% IWB
7.5% IWM
24.0% VEA
6.0% VWO
20.0% BND

2. Let us find the most acceptable version of the "diversified portfolio"

20.0% MTUM
30.0% XSLV
12.0% ISCF
3.0% VWO
15.0 VWOB
20.0% VGLT

3. Let us define some objectives measures for diversification

a. Diversification Ratio
b. Factor exposure of US equity
c. Relative approximation to equal risk contributions

Lets run the analysis:

3 Fund Portfolio:

>> Diversification Ratio = 1.13

>> Factor Exposure

Image

>> Difference vs Risk Parity

Image

Diversified Portfolio:

>> Diversification Ratio = 1.57

>> Factor Exposure

Image

>> Difference vs Risk Parity

Image

-----------------------------------------------------------------------------------------------
Ok, some conclusions:

1. In the defined metrics, we can say the portfolio 2 is more diversified.
2. I try to modified the experiment so the DR can be more applicable.
3. You need to believe in a multifactor world to accept the second criterion.
4. You need to believe in .std() and co-variance to accept first and third criterion.

Let me know if this is closer to passing the burden of proof.

Cheers :greedy


Caveats:

>>> One needs to have more data and some simulations to demonstrate that the diff of the DR is significant.
>>> This is all based on last 5-6 years of data
>>> This is not suitable for people with a Talebian bent.
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

Uncorrelated
Posts: 150
Joined: Sun Oct 13, 2019 3:16 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by Uncorrelated » Fri Nov 01, 2019 12:36 pm

hdas wrote:
Fri Nov 01, 2019 11:42 am
Uncorrelated wrote:
Fri Nov 01, 2019 11:16 am
As a believer in factors, it is clear to me that portfolio 8 has more risk (measured in expected stddev) than portfolio 1, but it is not clear whether that extra risk is adequately compensated with higher expected return.
How did you calculate the "expected stddev" ?
By taking the factor loadings of your entire portfolio and multiplying them with the historical factor premia and stddev. This works because it is possible to estimate the factor premia of a fund with short history with reasonable accuracy, and the expected factor premia and stddev are based on the longest time period that we have available. Also, the market, size, value and term factors are all relatively uncorrelated which makes estimation issues less likely. The situation with momentum and BAB is more complicated because momentum is correlated with value in strange ways and I don't see correlation coefficients in the BAB paper (possibly because they are useless?).

Inferring the correlation between two funds based on historical data doesn't work well because you need hundreds of years before your t-stat approaches something remotely useful. Most of the time, bogleheads can't even agree on the sign of the correlation coefficient between stocks and bonds.

The hard part is that academics give the expected factor stddev for a long-short fund. If you get factor exposure from a long-only fund then the stddev is higher than you would expect due to higher idiosyncratic risk (it would be nice if there was research on this..). Based on intuition and factor loadings I would expect the stddev of portfolio 8 to be around 50% to 150% higher than portfolio 1.

Remember that a fund with factor loadings of 1.0 market and 1.0 value is more risky than a fund with exposure to only the market factor because you take value risk in addition to market risk. But a fund with 0.5 market and 0.5 value exposure exchanges market risk for value risk which might results in less overall risk.

garlandwhizzer
Posts: 2508
Joined: Fri Aug 06, 2010 3:42 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by garlandwhizzer » Fri Nov 01, 2019 12:47 pm

hdas wrote:

Let me know if this is closer to passing the burden of proof.

Cheers :greedy


Caveats:

>>> One needs to have more data and some simulations to demonstrate that the diff of the DR is significant.
>>> This is all based on last 5-6 years of data
Is 5-6 years of backtesting data actually a reliable basis on which to construct a maximally diversified and effective risk/reward return portfolio going forward? Personally, I think not. I have serious questions about any time frame of backtesting as being predictive to the future, let alone 5-6 years. People fall in love with backtesting models, largely in my opinion because they give unequivocal and exact answers in numbers about what worked over the time period in question given the underlying assumptions of the model. Unlike the real market which is notoriously unpredictable in the short and intermediate term, these models give the illusion of certainty. Will the model portfolio perform the same way over the next decade as it has over the past 5-6 years? I believe the odds that it will are less than a coin flip. Factor models are intellectually interesting, no doubt. Where the doubt comes in is how predicative they are of the future in the real market with real funds. You get the right answer to that question only after the fact.

Garland Whizzer

User avatar
Topic Author
hdas
Posts: 1270
Joined: Thu Jun 11, 2015 8:24 am

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by hdas » Fri Nov 01, 2019 1:20 pm

Uncorrelated wrote:
Fri Nov 01, 2019 12:36 pm
hdas wrote:
Fri Nov 01, 2019 11:42 am
Uncorrelated wrote:
Fri Nov 01, 2019 11:16 am
As a believer in factors, it is clear to me that portfolio 8 has more risk (measured in expected stddev) than portfolio 1, but it is not clear whether that extra risk is adequately compensated with higher expected return.
How did you calculate the "expected stddev" ?
By taking the factor loadings of your entire portfolio and multiplying them with the historical factor premia and stddev.
But this is useless without taking into account the covariance matrix of the factors you used.
Uncorrelated wrote:
Fri Nov 01, 2019 12:36 pm

Inferring the correlation between two funds based on historical data doesn't work well because you need hundreds of years before your t-stat approaches something remotely useful. Most of the time, bogleheads can't even agree on the sign of the correlation coefficient between stocks and bonds.
Here's the thing, regardless of the spirit of this comment, most people are making implicit assumptions of correlation when the assemble a portfolio, whether you acknowledge them as such or not, or look for some quantification. That is the whole purpose of the 3 fund Portfolio..........Would you care to share your Retirement beta portfolio allocation and support why is it diversified?. If you don't care about diversification in your portfolio we can end the interaction here because we are so far away there's no possible way to learn from each other. Cheers :greedy
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

User avatar
Topic Author
hdas
Posts: 1270
Joined: Thu Jun 11, 2015 8:24 am

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by hdas » Fri Nov 01, 2019 1:27 pm

garlandwhizzer wrote:
Fri Nov 01, 2019 12:47 pm

Is 5-6 years of backtesting data actually a reliable basis on which to construct a maximally diversified and effective risk/reward return portfolio going forward? Personally, I think not. I have serious questions about any time frame of backtesting as being predictive to the future, let alone 5-6 years. People fall in love with backtesting models, largely in my opinion because they give unequivocal and exact answers in numbers about what worked over the time period in question given the underlying assumptions of the model. Unlike the real market which is notoriously unpredictable in the short and intermediate term, these models give the illusion of certainty. Will the model portfolio perform the same way over the next decade as it has over the past 5-6 years? I believe the odds that it will are less than a coin flip. Factor models are intellectually interesting, no doubt. Where the doubt comes in is how predicative they are of the future in the real market with real funds. You get the right answer to that question only after the fact.

Garland Whizzer
Garland,
I appreciate your philosophical bent, but let's bring it down to implementation. The whole capture of the equity risk premium and the reason we like index funds is an exercise in back testing..... mixing it with some bonds and cash as we taper off risk when we age is an exercise in looking at the covariance of the different asset classes.When you build your own portfolio, you are making all this assumptions that are supported on the data.

In this post I'm not making any claims of future or past performance, only of diversification and I defined 3 objective criteria for it. Would you share your "objective" criteria for evaluating diversification?

Cheers :greedy
"whenever there is a randomized way of doing something, then there is a nonrandomized way that delivers better performance but requires more thought" ET Jaynes

Uncorrelated
Posts: 150
Joined: Sun Oct 13, 2019 3:16 pm

Re: How to diversify a Three Fund Portfolio in 8 steps

Post by Uncorrelated » Fri Nov 01, 2019 2:18 pm

hdas wrote:
Fri Nov 01, 2019 1:20 pm
Uncorrelated wrote:
Fri Nov 01, 2019 12:36 pm
hdas wrote:
Fri Nov 01, 2019 11:42 am
Uncorrelated wrote:
Fri Nov 01, 2019 11:16 am
As a believer in factors, it is clear to me that portfolio 8 has more risk (measured in expected stddev) than portfolio 1, but it is not clear whether that extra risk is adequately compensated with higher expected return.
How did you calculate the "expected stddev" ?
By taking the factor loadings of your entire portfolio and multiplying them with the historical factor premia and stddev.
But this is useless without taking into account the covariance matrix of the factors you used.
Size, value and TERM have correlations near zero (between -.07 and 0). It's probably safe to assume that they are zero. MKT is correlated with each of the factors, you can add that in if you think that is important.

source: Fama & French 1993, Common risk factors in the returns on stocks and bonds.
Uncorrelated wrote:
Fri Nov 01, 2019 12:36 pm

Inferring the correlation between two funds based on historical data doesn't work well because you need hundreds of years before your t-stat approaches something remotely useful. Most of the time, bogleheads can't even agree on the sign of the correlation coefficient between stocks and bonds.
Here's the thing, regardless of the spirit of this comment, most people are making implicit assumptions of correlation when the assemble a portfolio, whether you acknowledge them as such or not, or look for some quantification. That is the whole purpose of the 3 fund Portfolio..........Would you care to share your Retirement beta portfolio allocation and support why is it diversified?. If you don't care about diversification in your portfolio we can end the interaction here because we are so far away there's no possible way to learn from each other. Cheers :greedy
I don't care about diversification and neither should you. I care about meeting my financial goals, to do so I attempt to maximize the return and minimize the risk of my portfolio. A more diversified portfolio might meet these characteristics, but it is pointless to optimize for diversification in itself.

Diversification ratio doesn't even appear to be a robust indicator of diversification.

hdas wrote:
Fri Nov 01, 2019 1:27 pm
garlandwhizzer wrote:
Fri Nov 01, 2019 12:47 pm

Is 5-6 years of backtesting data actually a reliable basis on which to construct a maximally diversified and effective risk/reward return portfolio going forward? Personally, I think not. I have serious questions about any time frame of backtesting as being predictive to the future, let alone 5-6 years. People fall in love with backtesting models, largely in my opinion because they give unequivocal and exact answers in numbers about what worked over the time period in question given the underlying assumptions of the model. Unlike the real market which is notoriously unpredictable in the short and intermediate term, these models give the illusion of certainty. Will the model portfolio perform the same way over the next decade as it has over the past 5-6 years? I believe the odds that it will are less than a coin flip. Factor models are intellectually interesting, no doubt. Where the doubt comes in is how predicative they are of the future in the real market with real funds. You get the right answer to that question only after the fact.

Garland Whizzer
Garland,
I appreciate your philosophical bent, but let's bring it down to implementation. The whole capture of the equity risk premium and the reason we like index funds is an exercise in back testing.....
No, that is a simple application of the efficient market hypothesis. Backtesting states that we should buy Amazon or Berkshire Hathaway instead, depending on the time period tested. Why are you investing internationally anyway? The US has outperformed international. Clearly, the seasoned backtester should invest only domestically.
mixing it with some bonds and cash as we taper off risk when we age is an exercise in looking at the covariance of the different asset classes.
No, that is the result of risk appetite that varies throughout time. See viewtopic.php?f=10&t=293469 for details. Although this research makes some assumptions about future returns, a good amount of the conclusion depends only on the existence of the equity risk premium, not on how large it is.

Post Reply