Optimal allocation with a DFA portfolio

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boglety
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Optimal allocation with a DFA portfolio

Post by boglety »

What would be the optimal asset allocation with a DFA portfolio to reflect factors such as profitability, small cap and value? Would it be better to just divide the asset allocation into

DFA Domestic Large growth and large value
DFA Domestic Small growth and small value

DFA International large growth and large value
DFA International small growth and small value

DFA Emerging Value and Small cap

or just use Domestic Vector/International Vector/Emerging Core? Wonder if someone can run a model to figure out the best way to tilt towards small value?

Thanks
MN Finance
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Re: Optimal allocation with a DFA portfolio

Post by MN Finance »

There isn't any special formula of DFA funds vs, say VG funds. If you're going to S&D and tilt the portfolio, set an allocation, then choose the funds, not the other way around. You could analyze a VG portfolio and a DFA portfolio and look at the load factors and then attempt to adjust the allocations to make them equal (which I'm sure someone will provide since this is discussed all the time), but IMO that's all rounding error. The easiest portfolio would be just to use the core funds which tilt for you.
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Re: Optimal allocation with a DFA portfolio

Post by YDNAL »

boglety wrote:What would be the optimal asset allocation...
You will know this ONLY in the future - but it is too late then, right?

My suggestion, then, is to avoid over-thinking the process.
Landy | Be yourself, everyone else is already taken -- Oscar Wilde
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Re: Optimal allocation with a DFA portfolio

Post by larryswedroe »

The Only Guide You'll Ever Need for the Right Financial Plan provides questions to ask to help you determine how much to allocate to each asset class.
With that said I would add this, the more you tilt to small and value (especially small value) the less beta risk you need to achieve the same expected returns.
So an all SV portfolio (say US SV, ISV and EMV, which is the Larry Portfolio) would require a lower equity allocation than any other combination to achieve the same expected return. Or you can use the risk premiums to achieve a higher expected return with the same equity allocation
Best wishes
Larry
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matjen
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Re: Optimal allocation with a DFA portfolio

Post by matjen »

If I were designing a DFA portfolio from scratch then I would utilize the core-type funds. There are a few threads where some the DFA approved advisers discuss the benefits and/or marketing purposes behind their creation. In my mind, it makes sense for me to just let DFA handle all the factor loadings, etc. rather than me have to try and balance all that over several funds. So I would go Core 2 or Vector or perhaps a 50/50 mix (vector has more tilt) in US. In international and Emerging I would utilize Core unless you wanted more tilt (or Mel's midcaps theory) or had a already a fair amount of large cap (i.e. VXUS or VEU) exposure. Then I would opt for World ex US Targeted Value Portfolio DWUSX. Although pricey, the nice thing about it is that it will balance your factors/tilt and allocation across International and emerging markets. So it would replace DFIEX and DFCEX.

50% US Core Equity 2 Portfolio (DFQTX) or US Vector Equity Portfolio (DFVEX) or 50/50 mix
30% International Core Equity Portfolio (DFIEX)
10% Emerging Markets Core Portfolio (DFCEX)
10% Global Real Estate Securities Portfolio (DFGEX)
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Robert T
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Re: Optimal allocation with a DFA portfolio

Post by Robert T »

.
Optimal in what sense? There seem to be several possible answers:

1. Mean-variance

2. Limiting short-term tail risk (reducing the left hand tail of the return distribution of possible annual returns) - aka 'shallow risk'

3. Limiting long-term tail risk (reducing the left hand tail of the real return distribution of possible investment lifetime real annualized return distributions) - aka 'deep risk'

4. Maximizing the likelihood of sticking to your chosen investment allocation over the long- term ( no capitulating at exactly the wrong time, includes some of the above, but also tracking error tolerance).

Perhaps a combination of the above.

Robert
.
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boglety
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Re: Optimal allocation with a DFA portfolio

Post by boglety »

Great feedback from everyone, to rephrase the original question. Theoretically, would incorporating the DFA growth/profitability portfolio to small and value reduce tracking error risk to the SP500 compared to the Vector portfolio?

Mean variance is probably not the best route to go in my opinion. As what has been the optimal portfolio in the past may not do well in the future. My goal is to make a decision and just stick with it.

The Swedroe portfolio as Robert detailed in another post has significant tracking error risk. Personally I stuck with my asset allocation during 2008 and early 2009, not sure if I could stick with it during 1982-2000 when the SP500 was shooting the daylights out of everything else (I was not an investor back then). At least I know I can handle 2008 and early 2009.

Robert's post about adding momentum to small value to reduce tracking error interested me as I have been selling my US small cap portfolio to rebalance into emerging market this year. Probably a bit early but no regrets.
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Robert T
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Re: Optimal allocation with a DFA portfolio

Post by Robert T »

.
Here’s a random stream of consciousness … touching on some of the four points I raised earlier with some thoughts on ‘good’ rather than optimal portfolios. It turned out to be a longer post than expected.

Each person seems to prefer a certain asset allocation for their own particular reasons (Larry, Rick, Bill Bernstein, Taylor, Mel etc). There is no right answer for everyone – and perhaps this is just as well. The commonalities seem to be passive, low cost funds. Rather than trying to give you the rationale for others choices and your own, I can only give you the rationale for my own FWIW. In point form.

75:25 stock:bond mix

- Based on need to take risk (needed long-term 7.5% annualized return [4.5% real return]), and risk tolerance (tolerable annual loss of 30-35%), my choice is 75% stocks:25% bonds for the accumulation phase. In the language of Bill Bernstein, this is just enough bonds to meet ‘shallow risk’ tolerance, but enough stocks to meet needed long-term real return needs and protection against longer-term ‘deep risks’ (using the framework from Bernstein’s Deep Risk book). Obviously no guarantees.

- The two main reasons I don’t currently use a Larry style portfolio (although I understand the rationale) is:
  • (i) There seems to be greater ‘deep risk’ in a higher bond allocation during the accumulation phase for the following reasons: Inflation and taxes are the most likely deep risks going forward (Bernstein), both which can significantly and permanently erode portfolio real value. On both these, bonds are less tax efficient than stocks, and in periods of high unexpected inflation bonds do badly. Over the last 110+ years there was no real permanent capital loss with stocks in 19 developed countries, while bonds and bills had real losses in 6 countries, with greater losses from bills than bonds. If we confine ourselves to US analysis/back-tests we may come to a different conclusion, but considering a broader data set (a broader spectrum of outcomes), and assuming that the 19 country outcomes are reflective of the future long-term distribution of outcomes – then its about a 1 in 3 chance of a negative long-term real return on bonds, and a much smaller chance of a negative real return on stocks (if the rising cost of corporate assets – induced by inflation - was not reflected in stock prices, then there would eventually be a point at which investors could buy companies on the stock market and sell off company assets for a profit. Actions to do this would bid up average stock prices [an auto-correction as demand for stocks increases] leading to the longer-term ‘inflation protection’ of stocks. This is a point made by Swensen – in Pioneering Portfolio Management). This longer-term view suggests greater tail risk from bonds than stock, while the reverse seems true over the short-term. If we also consider two ‘events’ – World War I (1914-18) and World War II and its aftermarth (1939-48), the real world bond index declined 39%, and 49% over these two respective periods (Credit Suisse Global Investment Return Yearbook 2011).

    (ii) Tracking error tolerance – as mentioned earlier, I think implementation considerations are integral to investment plan development. Choose an investment allocation you can stick with/implement over the long-term. Tracking error tolerance is part of this – and 1984-1999 is a good period to see the magnitude by which you would have lagged the market. Personally, just as I don’t think I can tolerate a 100% stock holding, I don’t think I could tolerate the extent of the tracking error of the ‘extreme’ version of the ‘Larry portfolio’. Again, it is success in implementation that determines your result. In this respect I am comfortable with 75:25 stock:bond, rather than higher small cap and value tilt with lower beta, but understand reasoning for those using higher tilts. Will give this more consideration in retirement when bond allocation would likely be higher anyway.
Within bonds

No default/credit risk:
  • - already get exposure through equities
    - default/credit risk provides poor diversification benefits in times of financial crises (when needed most e.g. 2008).
    - there are better ways to diversify fixed income than hold the same companies on the bond and stock side of your portfolio (which is often the case if using a corporate bond fund and value fund in the same portfolio). If I recall, the study showing credit risk was rewarded at the short end was looking at bonds in isolation rather than as part of an overall portfolio (an overall portfolio view is more important, rather than asset classes in isolation).
    - US treasuries provides purer diversification (fight to quality) [a point made by Swensen which has merit IMO], particularly if holding higher EM allocation in equities.
Term exposure (5 yr Treasury)
  • - provides protection in financial crises (economic shocks), as Fed often cuts rates to stimulate economy. This benefits longer term bonds (although now nothing much left to cut)
    - historically, long-term real returns on bills was more negative than bonds in the 6 of 19 developed countries in which bills and bonds had negative real returns over the last 110+ years. This suggests that bills may have slightly greater deep risk than bonds (also see charts in Bernstein’s Deep Risk book).
    - in addition to the slightly higher expected return from term exposure, the combination of value exposure in equities and longer term bonds (5yrs) may add diversification benefits as the risk of value stocks - recessions/deflation/flight to quality - are negatively correlated (when they show up) with longer term bonds, while value stocks do relatively well in periods of unexpected inflation when longer term bonds generally lag (e.g. 1970s inflation in US). (see Larry’s book The Successesful Investor Today).
    - with high equity allocations, adding longer-term treasuries has, at least historically, provided superior mean-variance portfolios (see Swedore and Grogan “The Maturity of Fixed Income Assets and Portfolio Risk – Journal of Investing. I get the same results).
Within stocks

Value and small cap tilt
  • - I prefer to have a higher target exposure to value stocks than small caps stocks. The value premium has been more persistent than the size premium in US markets, and particularly in international markets. I have a target 0.2 and 0.4 size and value load proportionate to the size of the historical annualized premiums of 2 percent and 4 percent respectively. The historical market return has been about 10 percent. Over the 16 years since 1927 when US inflation was above 5%, a 50:50 split in US large value:US small value provided a higher annualized return than each on its own (a portfolio where the size load was about half the value load).
Global diversification
  • -the geographic allocation comprising the global equity market is a good place to start. Even though short-term market crashes can often be global and painful (e.g. 2008), country specific economic performance dominates over the long term (e.g. Japan), which is more important for wealth creation (or destruction). “Global diversification protects investors against the adverse effects of holding concentrated portfolios in countries with poor long-term economic performance” (see – Asness – International Diversification Works (Eventually)). My equity targets are a 50:37:13 US:Non-US Developed:EM allocation. As my bond holdings (which is 100% US) will likely increase in retirement, my overall portfolio foreign currency holdings will decrease – reducing foreign currency risk to US$ based expenditures.
Momentum and quality tilts
  • - Adding momentum to a value tilted portfolio seems to improve mean-variance efficiency given the negative correlation between the two (Asness et al. Value and Momentum Everywhere), and seems to add inflation protection (with a positive momentum premium in inflationary periods – at least this has been the case historically).
    - For the less than extreme value tilters I think adding a separate allocation to momentum can add value (beyond momentum screens at the individual fund level) – if only to reduce a negative alphas of value dominated portfolios. There are some investment options for this now, although still early days in their implementation (e.g. iShares US Momentum)
    - I am less enthusiastic over adding a positive quality load to an equity allocation, as quality tends to be a less effective diversifier than momentum (takes up space), and provides a less effective hedge against unexpected inflation – (less ‘deep risk’ protection).
So what does this mean for an actual portfolio fund allocation?

The ETF[MSCI/S&P] portfolio I track in M* provides one allocation for a 75:25 stock:bond portfolio with a 50:37:13 US:Non-US Developed:EM split with an estimated 0.21, 0.40 size and value load. Another, with more of a RAFI flavor, which matches these global diversification and factor load targets (0.23, 0.42 estimated size and value load), but with a non-negative alpha and a more even value load across global markets is:
  • 37.5% US Allocation – of which
    • 20% iShares US Momentum
      30% Vanguard MidCap Value
      50% Schwab Fundamental US Small Company
    28% Non-US Developed Allocation – of which
    • 60% Powershares RAFI Developed Market Non-US
      40% Powershares RAFI Developed Market Non-US small cap
    9.5% Emerging Market Allocation – of which
    • 100% Powershares RAFI Emerging Markets
    25% Fixed Income
    • 100% iShares 3-7 yr Treasury
Will be interesting to see how it performs. Using DFA funds, there could be many combinations. The simple vector/core is a ‘good’ allocation – although has more size exposure in equities and credit exposure in fixed income than my preferred ‘optimum’, and not sure how tax efficient this allocation will be going forward.
  • 37.5% DFA US Vector
    28% DFA Intl. Vector
    9.5% DFA EM Core
    25% 5-yr Global Fixed Income
But as to your specific question boglety: Adding DFA growth to SV does seem to provide a more mean-variance efficient portfolio than US Vector. Here are some numbers derived from the DFA matrix book - which you/or anyone can replicate and extend the period of analysis: http://www.ifaarchive.com/pdf/DFA/matri ... s_2013.pdf
  • Annualized returns/SD

    1982-2012
    US Vector = 13.1/19.1
    60% Large Growth:40% Targeted Value = 13.1/17.5

    1984-1999
    US Vector = 15.3
    60% Large Growth:40% Targeted Value = 17.3

    2000-2012
    US Vector = 7.9
    60% Large Growth:40% Targeted Value = 6.1

    US Vector = Dimensional US Adjusted Market Value Index
    Large Growth = Dimensional US Large Cap Growth Index
    Tagreted Value = Dimensional US Targeted Value Index
Large cap momentum seems to be a more efficient diversifier than large cap quality, and reduces tracking error more. For example:
  • 1982-2012
    US Vector = 13.1/19.1
    Targeted Value = 14.6/21.5
    50% MSCI US Momentum:50% Targeted Value = 14.5/18.0

    1984-1999
    Targeted Value = 14.8
    50% MSCI Momentum:50% Targeted Value = 18.5

    2000-2012
    Targeted Value = 11.3
    50% MSCI Momentum:50% Targeted Value = 7.6

    The backtest (simulated, not live data) suggests you didn't give up much in expected long-term return of targeted value when adding momentum (14.5 vs. 14.6), but you gained lower tracking error with the market in 1984-1999: 18.5% vs. 14.8%. If I recall S&P return over this period was around 18% so fairly close. Over the full period the combination had lower SD than US vector and higher annualized returns - but would encourage you to do you own analysis to get a better sense of the robustness of the result.
Obviously no guarantees.

Once you have chosen your stock:bond mix, geographic allocation, and factor tilts - stick with it over the long-term. Save, invest, and be patient, sit on your hands if you have to and let the power of compounding work for you. The only changes I try to make, if any, is if I can achieve my portfolio factor load targets at lower cost (which includes less negative alphas). This has helped me stay the course (implementation is the main part) ... looks easy on paper and in backtests - but more difficult to do in practice for everyone. 11 years, so far so good, 11% annualized nominal returns, 8.5% annualized real returns - slightly ahead of longer-term targets (the performance metric that matters in the end) - but still a long way to go and a lot can happen - no guarantees.

Best,

Robert
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Last edited by Robert T on Sat Aug 01, 2015 6:53 pm, edited 2 times in total.
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pezblanco
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Re: Optimal allocation with a DFA portfolio

Post by pezblanco »

Wow. Thank you Robert. A tremendous post. One of the best (and there are many many good posts on this board) I've read here. There is lots (for me) to think and study about.
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boglety
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Re: Optimal allocation with a DFA portfolio

Post by boglety »

Great post Robert, if I may ask is there a reason why you would pick a 60% growth/40% value portfolio as opposed to 30 to 40% growth and 60 to 70% value? Would that increase both the return and SD?

Annualized returns/SD

1982-2012
US Vector = 13.1/19.1
60% Large Growth:40% Targeted Value = 13.1/17.5

1984-1999
US Vector = 15.3
60% Large Growth:40% Targeted Value = 17.3

2000-2012
US Vector = 7.9
60% Large Growth:40% Targeted Value = 6.1
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Robert T
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Re: Optimal allocation with a DFA portfolio

Post by Robert T »

boglety wrote:Great post Robert, if I may ask is there a reason why you would pick a 60% growth/40% value portfolio as opposed to 30 to 40% growth and 60 to 70% value? Would that increase both the return and SD?

Annualized returns/SD

1982-2012
US Vector = 13.1/19.1
60% Large Growth:40% Targeted Value = 13.1/17.5

1984-1999
US Vector = 15.3
60% Large Growth:40% Targeted Value = 17.3

2000-2012
US Vector = 7.9
60% Large Growth:40% Targeted Value = 6.1
Just picked 60:40 for illustration - it was an allocation that matched the 13.1% return of US Vector over this time period. Adding a lesser allocation to LG still had a beneficial mean-variance effect in the backtests. For example here are results for a 25% LG: 75% Targeted value - which had only slightly higher Standard deviation than US Vector but a 1% higher annualized return.

Annualized returns/SD

1982-2012
US Vector = 13.1/19.1
25% Large Growth:75% Targeted Value = 14.1/19.3

1984-1999
US Vector = 15.3
25% Large Growth:75% Targeted Value = 15.9

2000-2012
US Vector = 7.9
25% Large Growth:75% Targeted Value = 9.1

But as mentioned above, adding momentum had more beneficial portfolio effects over this time period (simulated, not actual). For example.

25% MSCI US Momentum
25% FF US Large Value (Research)
50% Dimensional US Targeted Value Index

Gave the same return as the 25% LG:75% Targeted Value (14.1%), but lower standard deviation (18.0 vs. 19.3), with lower tracking error in 1984-1999 period (a 17.1% return over this period compared to S&P500 of 18.1%, 15.3% for US Vector, and 15.9% for 25% LG: 75% Targeted Value. In this respect, I think those using DFA/AQR funds in a taxable account you could do a lot worse than the following for a US allocation:

25% AQR Tax-managed Momentum
25% DFA Tax-managed US Marketwide Value
50% DFA Tax-managed US Targeted Value

Or for those braver souls - you could skip the marketwide value and use: 25% AQR Tax-managed Mometum:75% DFA Tax-managed US Targeted Value. Using the MSCI momentum index and Dimensonal Targeted value series, the backtests show over this period (1982-1999) that the combination has marginally higher return than Targeted value on its own (14.7% vs. 14.6%), lower standard deviation (19.2 vs. 21.5). And while its standard deviation over this period was similar to US Vector (19.2 vs. 19.1), its return was 1.6% higher (14.7% vs. 13.1%). There was less tracking error than Targeted value on its own in 1984-1999 (16.7% vs. 14.8% - compared to S&P of 18.1%, and 15.3% for US Vector). But overall the backtests show favorable results. Using the AQR momentum index, provides a similar overall result/message. Obviously no guarantees, and implementation adds costs.

Why the beneficial effects of momentum? Over this time period, the simulated data had relatively good returns and low average correlations with other factors. Here are some correlation coefficients using data from Jason Hsu's website. In summary they show that the US momentum premium had, on average, over the full periods analyzed:

- Negative correlation with market premiums across US, Developed Markets-ex US, and EM
- Negative correlation with value premiums across US, Developed Markets-ex US, and EM
- Small but positive correlation with small cap premiums across US, Developed Markets-ex, and EM
- Large positive correlation among momentum premiums across US, Developed Markets-ex US, and EM - larger than the correlations among the respective market premiums (this seems to suggest that if an investor wants exposure to momentum factor, then perhaps no need to try to get exposure to momentum in all markets - US will suffice given its high correlation with momentum in other markets). [Similar to Asness finding in Momentum and Value everywhere]

US-Developed Market correlations 1982-2011
EM correlations with US and Developed Mkt ex-US 1995-2011

Mkt = equity premium
HML = value premium
SmB = size premium
MoM = Momentum premium
  • US Momentum Correlation Coefficients using monthly data.

    Negative correlations
    US Mkt...............................-0.24
    US HmL..............................-0.17
    Developed-ex US Mkt.............-0.19
    Developed-ex US Mkt HML.......-0.04
    Emerging Mkt......................-0.30
    Emerging Mkt HML................-0.20

    Positive correlations
    Developed-ex US Mkt Mom......+0.87
    Emerging Mkt Mom...............+0.40
    US SMB.............................+0.06
    Developed Mkt-ex SU SmB......+0.08
    Emerging Mkt SmB...............+0.11
Just sharing this further due dilligence on momentum. Again, obviously no guarantees moving forward. Anyone interested in momentum - would suggest reading the Asness et al. JoF paper on Momentum and Value Everywhere.

Robert
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pingo
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Re: Optimal allocation with a DFA portfolio

Post by pingo »

I suppose optimal is in the eye of the beholder?

I am not very familiar with DFA funds and you have the attention of those who understand exactly what you are asking to help you meet your needs. With that in mind (and realizing the following may ignore question of profitability, momentum, whathaveyou, I would suggest looking at the DFA Global Allocation 60/40 Fund (DGSIX) ER 0.30%, even if only for reference as you try to build the right portfolio. DGSIX appears to be a fund of funds assembled by DFA itself (letting them do the heavy lifting for). I have seen it in a few employer-sponsored plans on this site, so I don't know if it is available outside of such plans. DGSIX is an all-in-one fund with a classic 60/40 stock-bond asset allocation. 65% of the stock allocation is U.S.; 35% of stocks are International. It has tilts to size and value. For example, nearly 1/2 of all equities are Mid and Small Caps. Here is the Stock Style Diversification per Morningstar.com:

26-16-14
11-11-08
06-06-05

If 40% bonds is not to your taste, an alternative might be to use DFA Global Equity (DGEIX) which is merely the equity part of DGSIX. It's 100% equity, it is still 65/35 US-International, and it has the exact same tilts/stock style. (Like I said, it is the equity portion of DGSIX.) After determining your desired stock-bond ratio, you simply use DGEIX for your equity portion, where all the work is done for you, and then add a bond fund or funds to fill your bond-side of the portfolio. The above posters, may give you some help selecting appropriate bonds, and you could also look through the bonds used by DGSIX for reference (click here.

Of course it all depends on whether you can access those particular funds and whether or not they would serve you're desire to balance tilting with tracking error, etc. etc. I personally like the simplicity those funds offer. They may also serve for some guidance in assembling your own portfolio.

Best of luck!
solonseneca
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Re: Optimal allocation with a DFA portfolio

Post by solonseneca »

Robert T wrote:.
Here’s a random stream of consciousness … touching on some of the four points I raised earlier with some thoughts on ‘good’ rather than optimal portfolios. It turned out to be a longer post than expected.

Each person seems to prefer a certain asset allocation for their own particular reasons (Larry, Rick, Bill Bernstein, Taylor, Mel etc). There is no right answer for everyone – and perhaps this is just as well. The commonalities seem to be passive, low cost funds. Rather than trying to give you the rationale for others choices and your own, I can only give you the rationale for my own FWIW. In point form.

75:25 stock:bond mix

- Based on need to take risk (needed long-term 7.5% annualized return [4.5% real return]), and risk tolerance (tolerable annual loss of 30-35%), my choice is 75% stocks:25% bonds for the accumulation phase. In the language of Bill Bernstein, this is just enough bonds to meet ‘shallow risk’ tolerance, but enough stocks to meet needed long-term real return needs and protection against longer-term ‘deep risks’ (using the framework from Bernstein’s Deep Risk book). Obviously no guarantees.

- The two main reasons I don’t currently use a Larry style portfolio (although I understand the rationale) is:
  • (i) There seems to be greater ‘deep risk’ in a higher bond allocation during the accumulation phase for the following reasons: Inflation and taxes are the most likely deep risks going forward (Bernstein), both which can significantly and permanently erode portfolio real value. On both these, bonds are less tax efficient than stocks, and in periods of high unexpected inflation bonds do badly. Over the last 110+ years there was no real permanent capital loss with stocks in 19 developed countries, while bonds and bills had real losses in 6 countries, with greater losses from bills than bonds. If we confine ourselves to US analysis/back-tests we may come to a different conclusion, but considering a broader data set (a broader spectrum of outcomes), and assuming that the 19 country outcomes are reflective of the future long-term distribution of outcomes – then its about a 1 in 3 chance of a negative long-term real return on bonds, and a much smaller chance of a negative real return on stocks (if the rising cost of corporate assets – induced by inflation - was not reflected in stock prices, then there would eventually be a point at which investors could buy companies on the stock market and sell off company assets for a profit. Actions to do this would bid up average stock prices [an auto-correction as demand for stocks increases] leading to the longer-term ‘inflation protection’ of stocks. This is a point made by Swensen – in Pioneering Portfolio Management). This longer-term view suggests greater tail risk from bonds than stock, while the reverse seems true over the short-term. If we also consider two ‘events’ – World War I (1914-18) and World War II and its aftermarth (1939-48), the real world bond index declined 39%, and 49% over these two respective periods (Credit Suisse Global Investment Return Yearbook 2011).

    (ii) Tracking error tolerance – as mentioned earlier, I think implementation considerations are integral to investment plan development. Choose an investment allocation you can stick with/implement over the long-term. Tracking error tolerance is part of this – and 1984-1999 is a good period to see the magnitude by which you would have lagged the market. Personally, just as I don’t think I can tolerate a 100% stock holding, I don’t think I could tolerate the extent of the tracking error of the ‘extreme’ version of the ‘Larry portfolio’. Again, it is success in implementation that determines your result. In this respect I am comfortable with 75:25 stock:bond, rather than higher small cap and value tilt with lower beta, but understand reasoning for those using higher tilts. Will give this more consideration in retirement when bond allocation would likely be higher anyway.
Within bonds

No default/credit risk:
  • - already get exposure through equities
    - default/credit risk provides poor diversification benefits in times of financial crises (when needed most e.g. 2008).
    - there are better ways to diversify fixed income than hold the same companies on the bond and stock side of your portfolio (which is often the case if using a corporate bond fund and value fund in the same portfolio). If I recall, the study showing credit risk was rewarded at the short end was looking at bonds in isolation rather than as part of an overall portfolio (an overall portfolio view is more important, rather than asset classes in isolation).
    - US treasuries provides purer diversification (fight to quality) [a point made by Swensen which has merit IMO], particularly if holding higher EM allocation in equities.
Term exposure (5 yr Treasury)
  • - provides protection in financial crises (economic shocks), as Fed often cuts rates to stimulate economy. This benefits longer term bonds (although now nothing much left to cut)
    - historically, long-term real returns on bills was more negative than bonds in the 6 of 19 developed countries in which bills and bonds had negative real returns over the last 110+ years. This suggests that bills may have slightly greater deep risk than bonds (also see charts in Bernstein’s Deep Risk book).
    - in addition to the slightly higher expected return from term exposure, the combination of value exposure in equities and longer term bonds (5yrs) may add diversification benefits as the risk of value stocks - recessions/deflation/flight to quality - are negatively correlated (when they show up) with longer term bonds, while value stocks do relatively well in periods of unexpected inflation when longer term bonds generally lag (e.g. 1970s inflation in US). (see Larry’s book The Successesful Investor Today).
    - with high equity allocations, adding longer-term treasuries has, at least historically, provided superior mean-variance portfolios (see Swedore and Grogan “The Maturity of Fixed Income Assets and Portfolio Risk – Journal of Investing. I get the same results).
Within stocks

Value and small cap tilt
  • - I prefer to have a higher target exposure to value stocks than small caps stocks. The value premium has been more persistent than the size premium in US markets, and particularly in international markets. I have a target 0.2 and 0.4 size and value load proportionate to the size of the historical annualized premiums of 2 percent and 4 percent respectively. The historical market return has been about 10 percent. Over the 16 years since 1927 when US inflation was above 5%, a 50:50 split in US large value:US small value provided a higher annualized return than each on its own (a portfolio where the size load was about half the value load).
Global diversification
  • -the geographic allocation comprising the global equity market is a good place to start. Even though short-term market crashes can often be global and painful (e.g. 2008), country specific economic performance dominates over the long term (e.g. Japan), which is more important for wealth creation (or destruction). “Global diversification protects investors against the adverse effects of holding concentrated portfolios in countries with poor long-term economic performance” (see – Asness – International Diversification Works (Eventually)). My equity targets are a 50:37:13 US:Non-US Developed:EM allocation. As my bond holdings (which is 100% US) will likely increase in retirement, my overall portfolio foreign currency holdings will decrease – reducing foreign currency risk to US$ based expenditures.
Momentum and quality tilts
  • - Adding momentum to a value tilted portfolio seems to improve mean-variance efficiency given the negative correlation between the two (Asness et al. Value and Momentum Everywhere), and seems to add inflation protection (with a positive momentum premium in inflationary periods – at least this has been the case historically).
    - For the less than extreme value tilters I think adding a separate allocation to momentum can add value (beyond momentum screens at the individual fund level) – if only to reduce a negative alphas of value dominated portfolios. There are some investment options for this now, although still early days in their implementation (e.g. iShares US Momentum)
    - I am less enthusiastic over adding a positive quality load to an equity allocation, as quality tends to be a less effective diversifier than momentum (takes up space), and provides a less effective hedge against unexpected inflation – (less ‘deep risk’ protection).
So what does this mean for an actual portfolio fund allocation?

The ETF[MSCI/S&P] portfolio I track in M* provides one allocation for a 75:25 stock:bond portfolio with a 50:37:13 US:Non-US Developed:EM split with an estimated 0.21, 0.40 size and value load. Another, with more of a RAFI flavor, which matches these global diversification and factor load targets (0.23, 0.42 estimated size and value load), but with a non-negative alpha and a more even value load across global markets is:
  • 37.5% US Allocation – of which
    • 25% iShares US Momentum
      25% Vanguard MidCap Value
      50% Powershares RAFI Pure Small Value
    28% Non-US Developed Allocation – of which
    • 67% Powershares RAFI Developed Market Non-US
      33% Powershares RAFI Developed Market Non-US small cap
    9.5% Emerging Market Allocation – of which
    • 100% Powershares RAFI Emerging Markets
    25% Fixed Income
    • 100% iShares 3-7 yr Treasury
Will be interesting to see how it performs. Using DFA funds, there could be many combinations. The simple vector/core is a ‘good’ allocation – although has more size exposure in equities and credit exposure in fixed income than my preferred ‘optimum’, and not sure how tax efficient this allocation will be going forward.
  • 37.5% DFA US Vector
    28% DFA Intl. Vector
    9.5% DFA EM Core
    25% 5-yr Global Fixed Income
But as to your specific question boglety: Adding DFA growth to SV does seem to provide a more mean-variance efficient portfolio than US Vector. Here are some numbers derived from the DFA matrix book - which you/or anyone can replicate and extend the period of analysis: http://www.ifaarchive.com/pdf/DFA/matri ... s_2013.pdf
  • Annualized returns/SD

    1982-2012
    US Vector = 13.1/19.1
    60% Large Growth:40% Targeted Value = 13.1/17.5

    1984-1999
    US Vector = 15.3
    60% Large Growth:40% Targeted Value = 17.3

    2000-2012
    US Vector = 7.9
    60% Large Growth:40% Targeted Value = 6.1

    US Vector = Dimensional US Adjusted Market Value Index
    Large Growth = Dimensional US Large Cap Growth Index
    Tagreted Value = Dimensional US Targeted Value Index
Large cap momentum seems to be a more efficient diversifier than large cap quality, and reduces tracking error more. For example:
  • 1982-2012
    US Vector = 13.1/19.1
    Targeted Value = 14.6/21.5
    50% MSCI US Momentum:50% Targeted Value = 14.5/18.0

    1984-1999
    Targeted Value = 14.8
    50% MSCI Momentum:50% Targeted Value = 18.5

    2000-2012
    Targeted Value = 11.3
    50% MSCI Momentum:50% Targeted Value = 7.6

    The backtest (simulated, not live data) suggests you didn't give up much in expected long-term return of targeted value when adding momentum (14.5 vs. 14.6), but you gained lower tracking error with the market in 1984-1999: 18.5% vs. 14.8%. If I recall S&P return over this period was around 18% so fairly close. Over the full period the combination had lower SD than US vector and higher annualized returns - but would encourage you to do you own analysis to get a better sense of the robustness of the result.
Obviously no guarantees.

Once you have chosen your stock:bond mix, geographic allocation, and factor tilts - stick with it over the long-term. Save, invest, and be patient, sit on your hands if you have to and let the power of compounding work for you. The only changes I try to make, if any, is if I can achieve my portfolio factor load targets at lower cost (which includes less negative alphas). This has helped me stay the course (implementation is the main part) ... looks easy on paper and in backtests - but more difficult to do in practice for everyone. 11 years, so far so good, 11% annualized nominal returns, 8.5% annualized real returns - slightly ahead of longer-term targets (the performance metric that matters in the end) - but still a long way to go and a lot can happen - no guarantees.

Best,

Robert
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Awesome post.

I take it you don't see any benefit in CCFs & Reits. Also, I assume you'd replace treasuries for munis of similar durations if taxes were an issue. Question: In respect to DFA funds, if one could avoid paying for access through an advisor, would you personally use DFA?
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matjen
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Re: Optimal allocation with a DFA portfolio

Post by matjen »

solonseneca wrote: Awesome post.

I take it you don't see any benefit in CCFs & Reits. Also, I assume you'd replace treasuries for munis of similar durations if taxes were an issue. Question: In respect to DFA funds, if one could avoid paying for access through an advisor, would you personally use DFA?
Well I am not Robert T. Perhaps not as smart but much better looking. ;-)

Let me answer a couple of the questions you ask since I pay pretty close attention to all these types of threads. The % (can be 1% or can be much, much, much, much less) that goes to an adviser is what generally has kept Robert T. from utilizing DFA BUT he does use it in a 529 plan which avoids adviser fees. On the munis/treasuries question it is important to make sure the munis are top quality to be most equivalent to treasuries. So a fund like BMBIX would be a good example.

I think his links to the portfolio in morningstar reflects his real AA so no CCF or REIT.

Having said that (and I do have some DFA and am increasing my DFA), it seems to me that there are potential alternatives and more and more are coming to the market.

Robert T. if I have misrepresented what you have said in the past I apologize.
A man is rich in proportion to the number of things he can afford to let alone.
solonseneca
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Re: Optimal allocation with a DFA portfolio

Post by solonseneca »

matjen wrote:
solonseneca wrote: Awesome post.

I take it you don't see any benefit in CCFs & Reits. Also, I assume you'd replace treasuries for munis of similar durations if taxes were an issue. Question: In respect to DFA funds, if one could avoid paying for access through an advisor, would you personally use DFA?
Well I am not Robert T. Perhaps not as smart but much better looking. ;-)

Let me answer a couple of the questions you ask since I pay pretty close attention to all these types of threads. The % (can be 1% or can be much, much, much, much less) that goes to an adviser is what generally has kept Robert T. from utilizing DFA BUT he does use it in a 529 plan which avoids adviser fees. On the munis/treasuries question it is important to make sure the munis are top quality to be most equivalent to treasuries. So a fund like BMBIX would be a good example.

I think his links to the portfolio in morningstar reflects his real AA so no CCF or REIT.

Having said that (and I do have some DFA and am increasing my DFA), it seems to me that there are potential alternatives and more and more are coming to the market.

Robert T. if I have misrepresented what you have said in the past I apologize.
Now that I look (and with no disrespect to Robert T), you are indeed quite handsome. Thanks for the response.
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Robert T
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Re: Optimal allocation with a DFA portfolio

Post by Robert T »

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Ahh – yes. Beauty is in the eye of the beholder. :)
solonseneca wrote:I take it you don't see any benefit in CCFs & Reits. Also, I assume you'd replace treasuries for munis of similar durations if taxes were an issue. Question: In respect to DFA funds, if one could avoid paying for access through an advisor, would you personally use DFA?
matjen – not so far off.

In point form.

No separate REIT allocation
  • - There has been no significant REIT alpha beyond factor exposure. Using NAREIT equity REIT monthly data from 1972-2013 factor loads were: beta=0.72, size=0.42, value=0.68, alpha = -0.07. Low R^2 of 0.6 is likely a reflection of it being a sector fund (not dissimilar from other sector funds), rather than unexplained ‘risk factors’ IMO.
    - There is no apparent diversification benefit of adding a separate REIT allocation to a portfolio with similar small cap and value loads (backtests from 1982-2012 adding 10% REITS to the US side of the above listed RAFI flavored portfolio lowered both returns and standard deviation with no effect on the Sharpe ratio – adding it to the MSCI/S&P ETF portfolio had a similar result). Adding REITs to a Total Stock Market fund adds diversification benefits because of its smaller cap and value tilt.
    - There is already REIT exposure in many small value funds (DFA seems to be the exception)
No separate commodity (CCF) allocation
  • - The most significant rationale for adding commodities through CCFs IMO is to hedge ‘event risk’. Events, even though short-term can trigger high levels of longer-term inflation (and are possibly the most likely source of hyperinflation – see Montier piece MV=PQ, if downward shock of Q, with MV unchanged, P must increase by a lot). In this respect, CCFs may only provide a very temporary hedge. If investors pile into CCFs then spot price changes and CCF returns could diverge because of the negative roll return, giving low CCF returns just when you need them to be high and to follow spot prices. Given this magnitude and duration uncertainty on whether the insurance with actually pay out when needed, and the relatively higher certainty (IMO) and tax efficiency of value stocks (and even momentum) doing relatively well during inflationary periods, I am reluctant to make the space for CCFs.
On munis vs. treasuries. Not sure, as I have not looked at it in much detail. Treasuries have exemptions from state and local taxes, so not sure how much of a benefit after factoring in municipal default risk. But it would need to be a fairly convincing case to switch from treasuries to munis IMO.

If I could buy DFA funds though Vanguard/Fidelity I would probably use their Tax-managed funds as they have the ability to manage both dividends and capital gains, the latter only seems to apply to ETFs. As matjen indicated, I use DFA funds in 529 as it’s the best choice available for a globally diversified small cap value tilted portfolio in 529 plans IMO.

Robert
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