What is the best way to value tilt a portfolio?

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springwater
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What is the best way to value tilt a portfolio?

Post by springwater » Mon Jun 04, 2007 11:39 pm

Is it better to get a value tilt starting from the total market fund and then only adding small value?

I've seen many people here add value by also including large value and matching it up with Total Market or the S&P 500 and then including the Small Cap Index Fund and Small Value, using four funds instead of two.

What is the better approach?

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watchnerd
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Post by watchnerd » Tue Jun 05, 2007 1:59 am

I use four funds because:

1. I want to tilt towards small and value, not just value. I think it's easier to fine tune how much small you want if you have a separate sub-allocation for it.

2. I want to avoid overlap. Whenever I tried combining TSM funds with value funds (using M*'s Portfolio X-Ray), I ended up with duplicates of my REIT holdings and way too heavy in financial services. I recall one combo being 38% financial services.

If you didn't want to also tilt towards small, perhaps two funds would work, but I'd check for overlap and sector over-weightings just to be sure.
Tax Sheltered: 35% US Stock | 35% ex-US Stock | 30% TTM || Taxable: 35% US Stock | 35% ex-US Stock | 15% TTM | 15% Munis

Valuethinker
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Post by Valuethinker » Tue Jun 05, 2007 2:21 am

watchnerd wrote:I use four funds because:

1. I want to tilt towards small and value, not just value. I think it's easier to fine tune how much small you want if you have a separate sub-allocation for it.

2. I want to avoid overlap. Whenever I tried combining TSM funds with value funds (using M*'s Portfolio X-Ray), I ended up with duplicates of my REIT holdings and way too heavy in financial services. I recall one combo being 38% financial services.

If you didn't want to also tilt towards small, perhaps two funds would work, but I'd check for overlap and sector over-weightings just to be sure.
You raise a very good point.

We are likely at the end of an enormous liquidity cycle (which really began with the Asia crisis of 1997, but is more normally dated from 9-11-01). *that* has been very good for financial companies and financial stocks.

They look *cheap* so this is not a classic dotcom style bubble. *but* the earnings are essentially derived from ever increasing liquidity. Cut off the liquidity, and those earnings won't be there.

As that liquidity stops, many of these financial companies will be much smaller than they are now (it's already happened in sub prime lending).

The US housing downturn is probably the first tangible sign that the liquidity boom is ending. Looking at the personal debt loads of US and UK consumers, one thinks a period of consolidation and low or no growth in debt is likely.

The problem for index investors is the scale of the financial services industry in most indices. Exactly the problem we got into at the end of the dot com bubble.

I lost a lot of money at the end of the dot com bubble. I was buying the indices, but the indices were 30% TMT stocks. I made far more money in the cases where I bought actively managed 'value' funds that avoided the worst excesses. So much for low cost indexes :)

(UK doesn't have passively managed 'value' index funds, at least not that I could access. There are now ETFs that do that, but not very well).

Now this time my index funds are heavily weighted in financial stocks. :?

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You know...

Post by Trev H » Tue Jun 05, 2007 5:38 am

No one knows for sure which will be the better choice going forward... but you can take a look at how the combinations worked in the past.

You did not mention International Exposure so I will start with the Basic 20% Allocation to International Market (EAFE/EM).

1970-2006 with yearly rebalancing... 10K Growth & Other Stats...

80% US Cap Weighted Market
20% Intl Market
542,276.20
11.40 = CAGR
16.71 = STDEV

If you change to a commonly used S&D approach equally weighting LB LV SB SV on the US Equity Side...

20% Each
500 Index
Large Value
Small Blend
Small Value
Intl Market
946,491.56
13.09 = CAGR
16.62 = STDEV

Nice increase in returns and a reduction in volatility.

If you switch to US Market + SV

40% US Market
40% Small Value
20% Intl Market
926,933.99
13.02 = CAGR
16.31 = STDEV

You have to go near equal weight on US Market and SV to match the performance of the LB LV SB SV combo. If you use the CRSP & F/F Data back to 1927 the results are very similar.

One Other Combo...

40% US Market
20% Large Value
20% Small Value
20% Intl Market
840,679.06
12.72 = CAGR
16.10 = STDEV


REITS, Small Value, Small Blend and Large Value all have a lower correlation with International Market than the US Market Does. So the Higher your Intl Market Exposure (say if you were up around 30-40%) the better the shift to REIT, SV, SB, LV works out.

Again... this is the past and as we all know the future could be quite different.

Good Luck with your decision and your Investments !

Trev H

hans37

Post by hans37 » Tue Jun 05, 2007 6:15 am

Valuethinker wrote:
You raise a very good point.

We are likely at the end of an enormous liquidity cycle (which really began with the Asia crisis of 1997, but is more normally dated from 9-11-01). *that* has been very good for financial companies and financial stocks.

They look *cheap* so this is not a classic dotcom style bubble. *but* the earnings are essentially derived from ever increasing liquidity. Cut off the liquidity, and those earnings won't be there.

As that liquidity stops, many of these financial companies will be much smaller than they are now (it's already happened in sub prime lending).

The US housing downturn is probably the first tangible sign that the liquidity boom is ending. Looking at the personal debt loads of US and UK consumers, one thinks a period of consolidation and low or no growth in debt is likely.

The problem for index investors is the scale of the financial services industry in most indices. Exactly the problem we got into at the end of the dot com bubble.

I lost a lot of money at the end of the dot com bubble. I was buying the indices, but the indices were 30% TMT stocks. I made far more money in the cases where I bought actively managed 'value' funds that avoided the worst excesses. So much for low cost indexes :)

(UK doesn't have passively managed 'value' index funds, at least not that I could access. There are now ETFs that do that, but not very well).

Now this time my index funds are heavily weighted in financial stocks. :?[/quote]


Which in turn I think makes a great case for some sort of fundamental indexing.

Of course taken to an extreme and you are right back at active management.

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Post by tetractys » Tue Jun 05, 2007 12:50 pm

It just seems to make common sense that you'll get better returns, in my view, and when portfolio circumstances allow it, to divide the total us market into sections. For one you reduce the overlap, for another any rebalancing bonus is going to be enhanced.

But there are problems with using say, S&P 500 and small. For one thing your going to miss out on lots of large and mid cap companies (about 250 of them), for another, there's the arbitrage problem with updates to the S&P 500 holdings.

So I think it follows that when convenient it would be best to use Vanguard Large Cap Index Fund (VLACX), rather than S&P 500 Index Fund.

VLACX is the top 750 companies in market cap, this is also the same universe of companies that Value index, VIVAX, draws from. Small cap Index, NAESX, and Small cap Value Index, VISVX draw from the next smaller 1750 companies, so there is a nearly perfect dovetail between large and small.

The numbers here all come from MSCI data.

There is a problem with this approach though, since the 2500 companies or so mentioned above are only about half of those included in the broad market of the TSM fund, which includes thousands stocks smaller than those in NAESX and VISVX. So to get these one would have to invest in a microcap fund. Further, instead of having 5 funds, you might just use a microcap fund instead of the Vanguard small cap (NAESX).

Another option is to divide the broad US market into S&P 500 and Vanguard Extended Market Index (VEXMX), but this still leaves the S&P 500 arbitrage problem (But on the other hand, could this situation exacerbate or neutralize the problem?).

Tet

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Robert T
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Value indexes

Post by Robert T » Tue Jun 05, 2007 8:45 pm

.
Springwater,

If both approaches lead to the same portfolio size and value loadings and have the same expenses then the expected returns will be the same.

In my opinion it mainly comes down to asset class tracking error regret. For those with low tolerance (i.e. don’t like to see asset classes that they don’t hold do well, which in this case would be large value and small cap funds), the TSM, LV, SM & SV approach maybe the better option. For those with higher asset class tracking error tolerance the TSM & SV approach should suffice [FWIW I lean towards the former group].

As indicated in a couple of other posts, I prefer to define large value as having a zero size (or small positive) size loading and a large and significant value loading. Unfortunately most large value indexes have: (i) negative size loadings which subtract from the objective to tilt away from the market to small and value companies (see table below), and (ii) relatively small value loadings compared to mid and small value indexes (0.47 vs. 0.80 averages for each group of indexes included in the table below over the period analyzed). As a result my preference is to use ‘mid-cap’ value funds for my ‘large value’ exposure.

So to try to answer to question of the thread: What is the best way to value tilt a portfolio? In a way that matches an investor’s value (and size) loading targets and asset class tracking error regret at minimum cost.

Here’s a few factor loadings on several value indexes and associated fund expenses which maybe useful. In addition, my expectation is that S&P value funds would be the most tax efficient (lowest expected turnover, REIT composition), followed by the MSCI indexes and then the Russell indexes (I could be wrong). FWIW alpha on all the indexes listed were negative but not statistically significant – apart from the Russell 2000 value and the S&P500 pure value (these had negative and significant alpha).

Code: Select all

Monthly data used from July 1995 to April 2007

                             Factor Loadings                Expense
Index                        Mkt     Size    Value   ETF     Ratio

LARGE VALUE 

MSCI US Prime Market Value   0.97   -0.16    0.46    VTV     0.11
Russell 1000 Value           1.02   -0.14    0.50    IWB     0.25
S&P 500 Value                0.98   -0.13    0.40    IVE     0.25
Russell 3000 Value           1.01   -0.08    0.52    IWW     0.25


MIDCAP VALUE 

MSCI US Mid Cap Value        1.04    0.12    0.76    VOE     0.13
Russell Mid Cap Value        1.02    0.10    0.72    IWS     0.25
S&P 500 Pure Value           1.13    0.18    1.00    RPV     0.35
S&P 400 Value                1.02    0.22    0.61    IJJ     0.25
S&P 400 Pure Value           0.97    0.33    0.89    RFV     0.35


SMALLCAP VALUE 

MSCI US Small Cap Value      0.99    0.41    0.80    VBR     0.12
Russell 2000 Value           0.97    0.64    0.79    IWN     0.25
S&P 600 Value                1.01    0.67    0.63    IJS     0.25
S&P 600 Pure Value           1.04    0.72    0.99    RZV     0.35

LARGE VALUE AVERAGE          0.99   -0.13    0.47            0.22
MIDCAP VALUE AVERAGE         1.04    0.19    0.80            0.27  
SMALLCAP VALUE AVERAGE       1.00    0.61    0.80            0.24  


Factor loadings estimated using data from S&P, MSCI, Russell, and Ken French websites.
Hope this is helpful.

Robert
.

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Re: What is the best way to value tilt a portfolio?

Post by groovy9 » Tue Jun 05, 2007 10:49 pm

springwater wrote:Is it better to get a value tilt starting from the total market fund and then only adding small value?

I've seen many people here add value by also including large value and matching it up with Total Market or the S&P 500 and then including the Small Cap Index Fund and Small Value, using four funds instead of two.

What is the better approach?
It seems to me that you'd want to use the broadest index funds available to achieve your desired style boxes. Yes, you'll have overlap, but tilting toward anything means overlap. So you want to spread out the overlap as much as possible.

I wanted roughly equal amounts of money in each of large, mid, and small cap. And I wanted a slight tilt toward value.

So I went with 50% total market index, 25% extended market index, and 25% small value index. I get a slight large value tilt in my international holdings to go along with the small/mid value tilt here.

That seems to get me where I want to be without holding 15 funds. And it also avoids the S&P500 indexing issues mentioned above.

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Post by Kevinm1986 » Wed Jun 06, 2007 12:32 am

I use TSM + SV for my domestic equity holdings. TSM gives me what the S&P 500 gives me while also giving me the entire US market; SV lets me tilt to small and value simultaneously. My main reason for using fewer funds is to get to Admiral status sooner (although, alas, there are no Admiral shares for Small Value, just an ETF class).

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Post by TheEternalVortex » Wed Jun 06, 2007 2:05 am

TSM + SV also works better if you hold part of it in taxable.

sterjs
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Re: Value indexes

Post by sterjs » Wed Jun 06, 2007 2:39 am

Robert T wrote: Hope this is helpful.

Robert
Very helpful as always.

P.S. Do you know the factor loading of some of the international funds out there like EFV, DLS, GWX and how they compare to DFA?

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Robert T...

Post by Trev H » Wed Jun 06, 2007 6:35 am

Hey Robert... as usual a great job.

One thing that bothers me a bit is your suggestion to skip LV.

Below is a chart from my backtesting data set back to 1970.
LV in the set is mostly R1000V and Vanguard VIVAX Data.
The Larger of the Large Value that you suggest that should be excluded when value tilting because they don't also fit the "size" difference you consider to be useful when tilting the portfolio.

I find the returns of LV especially attractive considering the Volatility when ranked with other Asset Classes.

LV was the second highest performer.... but was #1 on the least volatile scale.

Microcaps MIC and SCB both place high on the list from a return point of view but fail bigtime on the volatility scale.

Large and Small Growth fail from both a return and volatility measure.

Anyway... just pointing out that LV on the size scale of R1000 or MSCI 750 Value may not have the "size" factors that you consider to be OK... but it sure has had Return and Volatility qualities that I find especially attractive.

Trev H

Code: Select all

1970-2006  Asset Class Returns

Ranked by CAGR

AC.....CAGR....StDev
====================
SCV....14.56...19.59
LCV....13.37...16.77
MIC....12.78...26.57
SCB....12.36...21.73
LCB....11.19...16.80
MKT....11.05...17.10
LCG....09.92...19.95
SCG....09.86...23.73
====================

Ranked by Volatility

AC.....CAGR....StDev
====================
LCV....13.37...16.77
LCB....11.19...16.80
MKT....11.05...17.10
SCV....14.56...19.59
LCG....09.92...19.95
SCB....12.36...21.73
SCG....09.86...23.73
MIC....12.78...26.57
====================

sterjs
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Re: Robert T...

Post by sterjs » Wed Jun 06, 2007 7:12 am

Trev H wrote:Anyway... just pointing out that LV on the size scale of R1000 or MSCI 750 Value may not have the "size" factors that you consider to be OK... but it sure has had Return and Volatility qualities that I find especially attractive.
Does that matter on a portfolio level, though?

i.e. Two portfolios with .2 size loading, .4 value loading. Was the portfolio with LV/LB/SV a superior performer to to LB/SV?

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Post by Robert T » Wed Jun 06, 2007 5:13 pm

.
Trev H,

The framework underlying the above analysis is the Fama-French three factor model. Its far from perfect but seems to stand up fairly well after much academic and practitioner critique and use. It has helped me tremendously.

Based on this framework, what matters for expected return (and volatility) is risk factor exposure not asset classes. Allocations to asset classes are just a way to gain factor exposure. The list of asset class returns and volatilities you listed are now viewed as just the result of different combinations of three risk factors (exposure to market, value and size risk).

If we compare two portfolio combinations of these factors – the first with factor loadings of 1.00:-0.15:+0.50 for market:size:value (not unlike many ‘large value’ fund loadings) and the second with factor loadings of 1.00:+0.15:+0.50 respectively. The only difference is the first has a small but negative size loading while the second has a small but positive size loading. The market and value loadings of the portfolios are the same. The portfolios are derived from the Fama-French annual benchmark factor data for 1927-2006 and 1970-2006. In both time periods, the second portfolio (i.e. the one with positive size loading) was more mean-variance efficient (following the return volatility approach you used).

Code: Select all

Time Period     Factor loadings       Annualized    Standard     Sharpe
               (market:size:value)    Return (%)    Deviation    Ratio

1927-2006        1.00:-0.15:+0.50      11.8          21.3        0.480
                 1:00:+0.15:+0.50      12.6          23.0        0.494

1970-2006        1.00:-0.15:+0.50      14.0          15.8        0.577
                 1:00:+0.15:+0.50      14.7          16.8        0.590
But as sterjis indicates its important to look at the portfolio as a whole. If an investor has a portfolio size and value loading target of 0.2 and 0.4 respectively then adding a fund with a negative size loading takes the investor further away from, not closer to, the size loading target and at higher cost. Hence my view is that if there are alternative choices (as in above post) then adding a large value fund with negative size loadings is not the most cost efficient way to reach a positive size (and value) loading target.

Just my take.

Robert

PS. stejis – I will post the factor loadings of two of the intl. indexes (at least my estimates) when I have a bit more time (would like to recheck the size loadings before posting).
.
Last edited by Robert T on Wed Jun 06, 2007 7:06 pm, edited 1 time in total.

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Not sure...

Post by Trev H » Wed Jun 06, 2007 5:22 pm

How to calculate the size and value loading factors...
I have not looked into that.

But I did run a few crunches to see how it worked in the 1970-2006 timeframe "in a Portfolio" type situation, tweaking LV & SV.

1970-2006

US = Cap Weighted US Market
LV = US Large Value
SV = US Small Value
IN = International Market (EAFE/EM)

At the Portfolio Level

Fixed allocation to International Market of 30%
Fixed allocation to US Market of 30%
Tweaking LV & SV allocation with the remaining 40%

Yearly Rebalancing

Code: Select all

US/LV/SV/IN....10K Growth...CAGR....StDev..Sharpe
=================================================
70/00/00/30....567,014.82...11.53...16.80...0.41
30/40/00/30....781,675.38...12.50...16.34...0.47
30/30/10/30....830,782.31...12.69...16.22...0.49
30/20/20/30....878,785.14...12.86...16.18...0.50
30/10/30/30....925,181.69...13.02...16.23...0.51
30/00/40/30....969,459.80...13.16...16.37...0.51
================================================
Holding some LV did reduce volatility over SV alone... but you can't really add anything to SV and increase returns. The Sharpe maxed out when adjusted to all SV or near all SV for the Value Tweak.

Looking at Roberts Portfolio... US Equity Slices...

US Large Cap Market 5%
US Large Cap Value 10%
US Micro Cap Market 5%
US Small Cap Value 20%

I think he said the US Large Value 10% Slice was IJJ actually a MV ETF which has a AMC of 3,403.

Vanguards LV has a AMC of 54,377
The R1000V has a AMC of 48,147
Vanguards SV has a AMC of 1,562

I recall Robert saying his SV allocation included some RZV Micro Cap Value so his 10% LV allocation is quite small... and his SV allocation is even smaller. Probably equates to all of his Value allocation falling into the range of my SV returns which are R2000V and Vanguard SV.

Something like...

10% 500 Index
10% MicroCap Blend
50% Small Value
30% International Market

Would probably work (somewhat close) for loading up his US Equity Mix with the 30% Allocation to International Market (comparison above)...

LB = 500 index, MI = MicroCap Blend

Code: Select all

LB/MI/SV/IN....10K Growth...CAGR....StDev..Sharpe
=================================================
10/10/50/30..1,186,954.48...13.78...17.25...0.53
=================================================
Interesting...


Trev H

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Benchmark performance

Post by Robert T » Wed Jun 06, 2007 6:44 pm

.
Trev H,

I try to monitor annual performance against two benchmarks: (i) a weighted aggregate of the index asset classes used; and (ii) a Fama-French factor benchmark which reflects my portfolio factor loadings. As for my portfolio:

75:25 equity:fixed income
50:50 US:Non-US equity
0.2:0.4 size:value loading (for equities)
0.0:0.5 defualt:term loading (for fixed income)

The factor benchmark performance from 1970-2006 was (best estimate):

Annualized return = 14.14
Standard deviation = 13.44
Share ratio = 0.66

The challenge now is to stick to the benchmark. Have been fairly close over last three years to end 2006: actual annualized returns = 16.3%; factor benchmark annualized returns = 16.8% with the difference close to my expenses. Will this reasonably close tracking continue? I expected a larger difference – time will tell. Portfolio expected return is 7.6%, much lower than past performance.

Robert
.

Trev H
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Hey Robert...

Post by Trev H » Thu Jun 07, 2007 5:43 am

.
I saved a copy of your Portfolio Details from the old board...

Question or two on your Equity Allocations... in trying to understand the Value and Size Factor Loadings issue...

Below is a cut from your posting on the old board.

====

Target Factor Loadings
Beta=1.0; Value=0.4; Size=0.2

Target Asset Allocation to achieve above factor loadings

US Large Cap Market 5%
US Large Cap Value 10%
US Micro Cap Market 5%
US Small Cap Value 20%
===================
Intl Large Cap Market 5%
Intl Large Cap Value 20%
Intl Small Cap Market 5%
Emerging Market Large Cap 10%


If I look at your US Equity slices... and M* X-Ray...

05% Total Stock Market Index

25-27-21
06-07-06
03-03-03

AMC 28,112

Then you offset that with a equal slice of BRSIX
Which changes the combined Size/Valuation to...

12-14-10
04-04-03
15-17-21

AMC 2,933

Then adding in the 10% Slice of IJJ

06-07-06
20-17-09
12-12-11

AMC 3,226

Then best I remember (from another post) your 20% SV allocation is split between two SV Funds/ETF's with part of it being RZV.

If I add 10% Each VISVX and RZV to the size/valuation X-Ray...

03-03-03
17-12-05
29-20-07

Overall AMC of 1,765

WOW... that sort of blows me away and goes way past what many consider a "extreme" US Equity Allocation "Coffeehouse Style" splitting 4 ways between LB LV SB SV.

X-Ray for the Std Coffeehouse US Equity (x-reit)
25% Each VFINX, VIVAX, NAESX, VISVX

21-16-06
14-09-05
14-10-05

AMC 9,127


Your US Equity holding seem to be very extreme to me and I wonder about the expected 10 pts TE you projected on the portfolio say in a 1995-1999 type situation.

But then again on the International Side... noticed you hold very little small and tilt to Value only on the Large Value Side.
If/when you find a ISV option that you feel good about, I suppose you might make a change on the US SV side and ISV Side

You have a interesting portfolio setup no doubt and I would like to get to the point of having some of the same qualities in my portfolio...

50/50 US/International is a Goal that I have had for some time but I have not made that move since there are no IS or ISV options available to me now (company plan and at Vanguard).

I also like the idea of being 50/50 Large/Small

And... Value Tilted (especially on the small end).

Don't think I could stand the TE with a Small and Value tilt like yours on the US Equity Side.

Still considering the move to WF and ETF's with my VG Rollover IRA...

No changes yet... still thinking about it though.

Do appreciate you sharing your AA and thoughts on your portfolio, expectations and all the other excellent contributions you make here.

Trev H

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Another look...

Post by Trev H » Thu Jun 07, 2007 6:53 am

.
At Value Tilting Options...


In My Company Plan the only International Option is a Large Blend Market type Fund very similar to Vanguards Total International. It does include EAFE and EM in much the same way but also holds a bit of Canada so it may be more similar to FTSE X-US... but still Cap Weighted Market Type International Exposure only.

My Ideal AA would again be:

50/50 US/International
50/50 Large/Small
Value Tilted, especially in the small area.

On the US Equity Side I have LB LV SB SV and REIT options.
The Small Options are not Micro... but are S&P 600 type Size.

Since my only International Option there is International Cap Weighted Market type... this has had me considering what would be the ideal S&D on the US Equity Side to mix with International Large Market only.

If I compromise my US/International Goal and go with 70/30 instead of 50/50.

Here is how it worked in the past...

1970-2006

First looking at US Market and International Market for benchmarks.

Code: Select all

US/IN.............10K Growth...CAGR....StDev...Sharpe
=====================================================
100/00............483,521.56...11.05...17.10...0.38
70/30.............567,014.82...11.53...16.80...0.41
=====================================================
Then changing to LB LV SB SV combinations for US Equity
Limiting the L/S split to 50/50 then SV Tilting

Code: Select all

LB/LV/SB/SV/IN..10K Growth...CAGR....StDev...Sharpe
=====================================================
35/00/35/00/30....713,303.49...12.22...17.23...0.44
35/00/15/20/30....835,378.61...12.70...16.49...0.48
35/00/00/35/30....934,872.24...13.05...16.02...0.51
=====================================================
Then with the same limit of 50/50 L/S tilting to LV as well...

Code: Select all

LB/LV/SB/SV/IN....10K Growth...CAGR....StDev...Sharpe
=====================================================
17.5 Each../30....927,453.73...13.02...16.61...0.50
15/20/15/20/30....961,448.10...13.13...16.54...0.51
15/20/00/35/30..1,072,575.60...13.47...16.13...0.54
00/35/00/35/30..1,184,158.35...13.77...16.29...0.55
=====================================================
I always notice how similar the LB LV SB SV combo performs compared to LB/SV only, very similar on returns... but the low correlation mix of LB/SV only results in less volatility.

And how using LB/LV/SV only... and eliminating SB completely gives better results on Volatility.


Trev H

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Post by Robert T » Thu Jun 07, 2007 6:01 pm

.
Trev H,

I think you have the M* x-ray about right for my US equity holdings. The overweight of small and value on the US side is due to the more limited non-US options (particularly when I set up the portfolio). As/if more non-US options become available I may consider getting more of a balance in factor loadings between US and non-US equity. Its not a perfect plan (no magic) but IMO good enough to achieve my financial objectives with factor loading targets based on willingness, ability, and need to take risk.

On tracking error – using a corresponding portfolio factor benchmark, the worst ‘total equity market’ tracking error in any one year from 1995-1999 (which was also the worst from 1970-2006) was about 10 percentage pts (9.5), obviously higher if the US allocation alone is considered:

For US equity allocation TE:
1998 - lagged ‘total US equity market’ return by 18.3 percentage pts (5.9% vs. 24.3%)
1999 - lagged ‘total US equity market’ return by 19.0 percentage pts (5.9% vs. 24.9%)

For total equity allocation TE:
1998 - lagged ‘total equity market’ return by -9.5 percentage pts (8.1% vs. 17.6%)
1999 - lagged ‘total equity market return by -9.1 percentage pts (22.6% vs. 31.7%)

For total portfolio allocation TE:
1998 - lagged ‘total market’ return by -7.1 percentage pts (9.0% vs. 16.1%)
1999 - lagged ‘total market return by -6.8 percentage pts (16.0% vs. 22.8%)

The above are derived from the US factor benchmark and Intl. data on Ken French’s website.

Obviously the emotions in actually experiencing this tracking error versus just seeing it in simulated benchmark data are very different – but preparation helps IMO.

Thanks also for your contributions.

Robert
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Post by Elysium » Thu Jun 07, 2007 6:51 pm

Robert, valuable contributions as usual. Trev, great contribution from you too.

Couple of questions.

Robert wrote:
Annualized return = 14.14 Portfolio expected return is 7.6%
Why is the expected return substantially lower than historic. How did you arrive at an approximate figure even then. I have an equity heavy portfolio and while historic returns have been great, I too don't believe it will return anywhere near in future, but my expectation is more of a guesswork, within a range of somewhere around 8%.
The challenge now is to stick to the benchmark. Have been fairly close over last three years to end 2006: actual annualized returns = 16.3%; factor benchmark annualized returns = 16.8% with the difference close to my expenses.
What is your benchmark for this portfolio, how do you get factor benchmark annualized returns.

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Post by Robert T » Thu Jun 07, 2007 9:57 pm

.
Dieharder,

This post turned out to be longer than expected. Hope it answers your questions. This is just my modest approach – certainly not perfect but here it is…

How did you arrive at the approximate (expected return) figure?

The 7.6% expected return is a ‘best (gu)estimate’. This is the needed investment return to achieve my financial goals based on invested assets and annual savings (as established when IPS was developed).

It was calculated as follows:

Code: Select all

US equity allocation x expected return                0.50 x 6.5 = 3.25
Non-US developed equity allocation x expected return  0.27 x 7.0 = 2.61
Emerging market equity allocation x expected return   0.13 x 9.0 = 1.11
Expected return from total equity market exposure     1.00       = 7.00
Plus expected returns from value and small cap tilt
Size loading x expected size premium                   0.2 x 2.0 = 0.40
Value loading x expected value premium                 0.4 x 4.0 = 1.60 
Total equity expected return                                     = 9.00

Fixed income expected return                                     = 5.00

75:25 equity:fixed income (0.75 x 9)+(0.25 x 5)                  = 8.00
Less costs                                                       - 0.40
PORTFOLIO EXPECTED RETURN                                        = 7.60

(The US, foreign developed and emerging market equity expected return are from Bernstein’s Four Pillars pg. 72 – assumes a 3% inflation rate).

How do you get factor benchmark annualized returns?

This is just how I did it (right or wrong).

First my equity portfolio market:size:value loading targets are 1:0.2:0.4 respectively. Derived as:

Code: Select all

                                          Factor loading targets
	                   		Allocation    Market     Size     Value        
US Equity                      0.50        1.0       0.4       0.6
Non-US Equity                  0.27        1.0       0.0       0.3
Emerging Market                0.13        1.0       0.0       0.0 
PORTFOLIO                      1.00        1.0       0.2       0.4
Note: Interestingly for my intl. allocation the positive size loading on the 5% small cap fund allocation just offset the negative size loading on the 20% large value fund allocation to give close to a zero intl. size loading (following the allocation Trev H posted above).

The US, Non-US developed equity, and T-bill data used are from Ken French’s website (use US factor benchmark series), the Emerging Market equity data are from the MSCI website, and the fixed income term data (long-term government bond minus T-bills) are derived from Ibbotson data.

Here’s how the benchmark return data were calculated over the last three years.

Code: Select all

                               2004      2005     2006             
US EQUITY
Mkt	                         11.9       6.2     15.3
SmL                             6.3      -2.7      1.0       
HmL                            13.2       3.7     11.9
[1] 1*Mkt+0.4*SmL+0.6*HmL      22.3       7.3     22.9 

NON-US DEVELOPED EQUITY
Mkt                            20.7      13.2     26.6
HmL                            14.2       2.4      6.4 
[2] 1*Mkt+0.3*HmL              24.9      14.0     28.5

EMERGING MARKET EQUITY
[3] Mkt                        25.6      34.0     32.2       

FIXED INCOME
T-Bill                          1.2       3.0      4.7
Term                            7.3       4.8     -3.0
[4] T-Bill+0.5*Term             4.9       5.4      3.2 

PORTFOLIO BENCHMARK RETURN     19.0      11.2     20.4

Portfolio benchmark = (0.375*[1]+0.280*[2]+0.095*[3]+0.250*[4]) 

2004-2006 annualized return = 16.8%

For some, this is too complicated and I can understand that. But I find that once set up, the benchmark data is very easy to update annually and I find the approach useful as it reflects the Fama-French five factor model which provides the framework for my investment decisions. Just my approach…

Robert
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Post by sterjs » Fri Jun 08, 2007 4:05 am

Re: Factor Loading Volatility

Any idea how volatile the factor loadings of the various indeces are? VOE and VBR have essentially identical value loading on the chart, but VOE is 1.98 P/B compared to 1.72 P/B for VBR at the moment.
Robert T wrote: First my equity portfolio market:size:value loading targets are 1:0.2:0.4 respectively. Derived as:

Code: Select all

                                          Factor loading targets
	                   		Allocation    Market     Size     Value        
US Equity                      0.50        1.0       0.4       0.6
Non-US Equity                  0.27        1.0       0.0       0.3
Emerging Market                0.13        1.0       0.0       0.0 
PORTFOLIO                      1.00        1.0       0.2       0.4
Have you thought about going heavier on Size/Value Loading on the International side? International size and value premia seem to be unique risk factors:

Sinquefield (Table 3C, Panel B, Page 7) found that the intl value and size premia are low or negative correlation with the U.S. equity, size and value premia.

It makes sense to me to treat value and size loadings for U.S. and International separately...

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Post by Robert T » Fri Jun 08, 2007 5:34 am

sterjis,

Any idea how volatile the factor loadings of the various indices are?

No but they do move around, and this seems to be related to both index construction and overall market valuation. On the former hopefully using most index funds will provide some style purity and narrow the volatility relative to more active funds. On the latter, there seems to be a positive relationship between the P/B of the market and value loadings of value funds i.e. as a P/B of the market itself declines so do the value loadings on value funds.

Have you thought about going heavier on Size/Value Loading on the International side?

Yes, and would probably prefer a more even split in factor loading between US and non-US allocation. But as indicated above, the international choices are more limited. When that changes, I may consider a more even balance but am currently comfortable with what I have.

I agree with you that the US and intl. size and value loadings should be treated separately, but as the paper you linked indicates the expected value premium returns are the same globally, same with size (with the exception of ‘segmented markets’ – which I take to mean emerging markets). As a result I use the same expected return for US and intl. size and value. However, annual correlations do matter and intl. factors provide some diversification benefit.

Here’s a correlation matrix I posted in an earlier thread (1975-2006).

Code: Select all


Correlation Matrix 

             US Mkt     US HmL     Intl. Mkt     Intl HmL 
US Mkt         1.00          
US HmL        -0.32      1.00       
Intl. Mkt      0.49     -0.21         1.00    
Intl. HmL     -0.25      0.45         0.01         1.00

I also think that for a 50:50 US:non-US split the paper can be viewed both ways – e.g. the gains from tilting away from a non-US allocation. My take anyway...

[edit: FWIW - here's an earlier post on US versus Intl. value tilt: Does it make a difference?]

Robert
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Post by Elysium » Fri Jun 08, 2007 4:25 pm

Robert,

Thanks for explaining your method. I don't find it complicated, just hard work to get all that data and then compute. I guess once you set them up it becomes a lot easier. I should learn how to do this stuff sometime.

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Hey Robert & Others...

Post by Trev H » Fri Jun 08, 2007 5:00 pm

.
I saved this cut from a Eric/Enels post on the old board...

====

DFA Equity Balanced Strategy Allocation

20% US Large
20% US Large Value
10% US Small
10% US Small Value
10% US REITS
10% Int'l Large Value
5% Int'l Small
5% Int'l Small Value
3% Emerging Markets
3% Emerging Markets Value
4% Emerging Markets Small

(purposely excludes EAFE)

Now with the development of GWX, you could conceivably use this and DLS to get your Int'l Small allocations. Once Wisdometree develops their dividend weighted EM Index, you can also split your EM exposure between VWO and this new Wisdomtree offering.

====

I see where WisdomTree has launched a Div Weighted Intl REIT ETF...
Eric Mentioned they might be doing the same for EM... any news on that ?

If/when they do... what do you think of Getting EM Value via Div Weighted offering from WisdomTree ?

I'm thinking that instead of omitting EAFE all together... you could start with VEU Vanguards FTSE X-US and tilt to LV, SV and EMV using EFV DLS and the Div Weighted EM Value offering from WisedomTree when ever that is available.

Trev H

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Post by Robert T » Fri Jun 08, 2007 11:49 pm

.
Dieharder,

Pleased you could follow my post – not always easy:-)

Once the spreadsheet is set up the factor benchmark is easy to update – much quicker than updating my asset class benchmark! There is a slight delay in the end of year update on the Ken French website but its not a big issues for me.

IMO the benefit of the approach is that it provides a much clearer framework for portfolio decisions – following Buffet’s guidance - "To invest successfully over a lifetime does not require a stratospheric IQ, unusual business insights, or inside information. What's needed is a sound intellectual framework for making decisions and the ability to keep emotions from corroding that framework." For me currently the Fama-French five factor model provides the ‘intellectual framework’ for investment decisions – and also helps with the emotions.

Trev H,

I have not looked at the Wisdomtree funds in any great detail so cannot say much on them – only that they are higher cost than my current holdings – and given I don’t need more tilt to small and value at a portfolio level they are unlikely to lower the cost of achieving my current targets. For investors wanting allocations to the ISV and EMV asset classes, then Widomtree seems to be the only non-DFA choice in the near term (at least that I am aware of).

FWIW – my portfolio equity factor loadings are similar to the sample DFA Balanced strategy allocation you highlighted. The back-tested comparisons of a 75:25 equity:fixed income split are:

Code: Select all


1970-2006	                                                                                                                                                                                                                                        
                                               AR      SD        Sharpe
Portfolio benchmark (less fund expenses)      13.8    13.4        0.64
DFA Balanced Strategy sample                  13.3    12.5        0.64

AR = annualized return, SD = standard deviation, Sharpe = Sharpe ratio

Note:  The DFA Balanced Strategy sample is the back-test of the IFA65 portfolio with the IFA 0.9% annual management fee added back to get an apples to apples – benchmark minus mutual fund expenses - comparison. If the 0.9% management fee is subtracted the Balanced Strategy annualized returns were 12.4, standard deviation 12.5, and Sharpe ratio 0.57.

Personally I don't think I’m losing much by excluding a few asset classes (incl REITS).

Have a good weekend.

Robert
.
Last edited by Robert T on Sat Jun 09, 2007 4:52 am, edited 1 time in total.

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Re: Hey Robert & Others...

Post by sterjs » Sat Jun 09, 2007 2:41 am

Trev H wrote:If/when they do... what do you think of Getting EM Value via Div Weighted offering from WisdomTree ?
I'm not a big fan of Wisdomtree's products.

Dividend weighting doesn't produce much value weighting at all. DLS's Price/Book is 1.94 compared to 2.12 for EFA (EAFE).

The Vanguard emerging markets product is pretty awesome--I think it is the best bargain of any etf. It covers the total market cap, doesn't rely on ADRs and has the lowest ER of any retail EM ETF. I doubt WT's product will be competitive.

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Post by Chip » Sat Jun 09, 2007 5:34 am

Is it correct to assume that the Fama-French US benchmark portfolios include ADRs from the US exchanges? I've skimmed French's web site and haven't found anything definitive, though it appears he includes all NYSE, AMEX and NASDAQ stocks. I would think ADRs would be caught in that net.

My portfolio includes quite a few ADRs. I've regressed its returns against the F-F US benchmarks. My concern is that the regression is invalid if ADRs aren't part of the F-F US portfolios.

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Post by Elysium » Sat Jun 09, 2007 8:38 am

RobertT wrote:
Once the spreadsheet is set up the factor benchmark is easy to update – much quicker than updating my asset class benchmark! There is a slight delay in the end of year update on the Ken French website but its not a big issues for me.
I was reading your post again and realized that you are calculating factors loadings at each sub component level, not just at the portfolio level. To get this do you track the monthly returns for your four major sub-components separately. The four being, U.S Equity, Intl Equity, EM Equity, and Fixed.

I do see the need to do this, because the factor returns are not the same for u.s equity, intl equity, and em equity. Fixed of course is a no brainer since they are totally different.

Too much work for me :)

.. but may be if I get used to this model not too hard.

How do you find international factors, is the data for this available from Ken French's web site. I would like to be able to find this for international funds.

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Benefits, limitations, and costs of the FF risk factor appro

Post by Robert T » Sat Jun 09, 2007 9:36 pm

.
Dieharder,

Most of the upfront work in the approach is to estimate the factor loadings on each individual fund/index and then choose an allocation across the selected funds in a way that matches a factor loading target. This does take some time but I have found it to be worth the effort. To do this for domestic funds, I used the monthly research data on US mkt, SmB, and HmL from Ken French’s website. For the intl. funds, I used the Intl mkt and HmL factors from the same website – for Intl. SmB we are on our own (none on Ken French’s website) I calculated two series one from the MSCI website (a short series) and one from the S&P/Global index website. (IMO its important to use US factors to estimate factor loadings on US funds, and intl. factors to calculate factor loadings on intl. funds to provide meaningful results).

As long a time period as possible was used in the analysis (to try to get representative long-term characteristics of a fund/index) and the same period was used for all funds. Where funds have only recently come into existence or where benchmarks indexes of existing funds have changed, the index was used. I monitor subsequent performance against the portfolio factor benchmark annually (not monthly, quarterly etc).

To find the international mkt and HmL factor on Ken French’s website: Go to: http://mba.tuck.dartmouth.edu/pages/fac ... brary.html. Under section on International Research Returns Data (Downloadable Files) open Index Portfolios formed on B/M, E/P, CE/P, and D/P, Open Ind_all, Subtract Low BE/ME from High BE/ME to get High BE/ME minus Low BE/ME or HmL. This is the Intl HmL I used to estimate value loadings on Non-US developed market value funds and use it to construct this part of my portfolio benchmark.

FWIW – here is what I view to be the three main disadvantages and three main advantages of the approach (obviously I think the advantages way exceed the disadvantages).

Disadvantages:
  • Upfront time cost: to determine factor loadings on potential funds and to select funds in a way that achieves portfolio factor loading targets takes some time.

    Just a model: Its far from an exact science and should be viewed as just a model (but a good one IMO). There are some statistical criticisms (multi-collinearity and simultaneity biases) that may affect results dependent on how the model is used. Given there is a small portion of the variability in returns not explained by the model (about 5 percent sometimes more) this may show up in tracking error against a benchmark constructed from the model results.

    Data limitations: The fund and index data series that are available are often fairly short (and not representative of all market conditions) so factor loading estimates may not be truly representative of fund/index characteristics. Factor loadings do sometimes drift over time but hopefully not too significantly if index funds are used.
Advantages:
  • Provides a clear framework for investment decisions: Provides a clear framework for portfolio decisions. Its based on rigorous peer reviewed research and not on hunches or gut feel. The research has been reviewed, critiqued, and used by researchers and practitioners for fifteen years and still stands up fairly well.

    Simplifies: It simplifies an extraordinary complex system into five main risk factors. Once an investor has selected the appropriate exposure to these risks through selection of factor loading targets (based on willingness, ability, and need to take risk), then security (fund) selection is simplified to minimizing cost to achieve factor loading targets. With the multitude of new ETF product coming to market the simple screening questions is – will it lower the cost of achieving an already fixed set of portfolio factor loading targets?

    Helps keep emotions in check: IMO it (i) significantly reduces the likelihood of continual tweaking of a portfolio with new products, changing market conditions etc..; and (ii) significantly increases the likelihood of staying the course in both good and bad markets. A couple of messages from Swensen captures some of the reason failry well “lightly held positions invite casual reversal, exposing vacillating investors to the costly consequences of market whipsaw.” The upfront cost can be an important investment cost to ensure more committed positions. “Without a rigorous process that is informed by thorough analysis and implemented with discipline, investment portfolios respond to human instinct, tending to follow whims and fashion”. IMO the approach provides the thorough analysis that also helps implementation discipline.
Hope this is helpful.

Robert.
Last edited by Robert T on Fri Jun 21, 2013 10:41 am, edited 2 times in total.

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Post by DaveTH » Sun Jun 10, 2007 6:10 pm

Trev H wrote:DFA Equity Balanced Strategy Allocation

20% US Large
20% US Large Value
10% US Small
10% US Small Value
10% US REITS
10% Int'l Large Value
5% Int'l Small
5% Int'l Small Value
3% Emerging Markets
3% Emerging Markets Value
4% Emerging Markets Small

(purposely excludes EAFE)
I'm curious, do you know why they exclude EAFE/Int'l Large Cap? It doesn't seem consistent given that they include U.S. Large Cap.

Dave

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Re: Beta/Size/Value = 1/.2/.4

Post by zalzel » Tue Oct 23, 2007 3:21 am

Robert T wrote:.


Code: Select all

Monthly data used from July 1995 to April 2007

                             Factor Loadings                Expense
Index                        Mkt     Size    Value   ETF     Ratio

LARGE VALUE 

MSCI US Prime Market Value   0.97   -0.16    0.46    VTV     0.11
Russell 1000 Value           1.02   -0.14    0.50    IWB     0.25
S&P 500 Value                0.98   -0.13    0.40    IVE     0.25
Russell 3000 Value           1.01   -0.08    0.52    IWW     0.25


MIDCAP VALUE 

MSCI US Mid Cap Value        1.04    0.12    0.76    VOE     0.13
Russell Mid Cap Value        1.02    0.10    0.72    IWS     0.25
S&P 500 Pure Value           1.13    0.18    1.00    RPV     0.35
S&P 400 Value                1.02    0.22    0.61    IJJ     0.25
S&P 400 Pure Value           0.97    0.33    0.89    RFV     0.35


SMALLCAP VALUE 

MSCI US Small Cap Value      0.99    0.41    0.80    VBR     0.12
Russell 2000 Value           0.97    0.64    0.79    IWN     0.25
S&P 600 Value                1.01    0.67    0.63    IJS     0.25
S&P 600 Pure Value           1.04    0.72    0.99    RZV     0.35

LARGE VALUE AVERAGE          0.99   -0.13    0.47            0.22
MIDCAP VALUE AVERAGE         1.04    0.19    0.80            0.27  
SMALLCAP VALUE AVERAGE       1.00    0.61    0.80            0.24  


Factor loadings estimated using data from S&P, MSCI, Russell, and Ken French websites.
In the full post above (http://www.diehards.org/forum/viewtopic ... ght=#37271) Robert T explains how, and why, he has used this data to construct a 50% US/50%Int'l equity portfolio, with Beta, small, and value Fama-French factor loadings of Beta=1.0, s=.2, v=.4 respectively.

For those intimidated by the seeming complexity of Robert's portfolio, a portfolio that should have very similar risk/return characteristics can be assembled with:

50% VG Small Val. Index (Beta 0.99, s 0.41, v 0.80), or VBR,

and,

50% EAFE/EM or VG World minus US (Beta 1.?, s 0.0, v 0.0), or equivalent ETFs.

In contrast to Robert T., my interest in such a portfolio is less to capture a higher return than what is expected with a non-tilted internationally diversified portfolio, but rather, (by tilting to a higher volatility/higher expected return equities portfolio) to be able to deploy a smaller percentage of assets to equities without sacrificing expected return.


Zalzel

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Post by kurata » Tue Oct 23, 2007 5:24 am

This has been a very interesting discussion. I'm curious about these and similar results:

Code: Select all

LB/LV/SB/SV/IN..10K Growth...CAGR....StDev...Sharpe
=====================================================
35/00/35/00/30....713,303.49...12.22...17.23...0.44
35/00/15/20/30....835,378.61...12.70...16.49...0.48
35/00/00/35/30....934,872.24...13.05...16.02...0.51
=====================================================
Is the software used for these computations available somewhere? I've been thinking of writing my own, in Perl or C, but if there are tested tools/datasets already out there it would be great to know.

Thanks!

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Post by Michael Weiss » Tue Oct 23, 2007 5:28 am

I agree that value tilting makes sense. It is well documented that value stocks outperform growth stocks over time. However, before anyone decides to create a portfolio based on historical data, they should know that a good deal of the data is biased in favor of value stocks. IMO, any data that uses BtM as a way to select growth stocks will have the effect of reducing the returns of this investment style. Selecting the most expensive stocks in the universe is hardly an investment strategy. Buffett and others have commented that value and growth strategies are related. What manager strives to deliberately select stocks that are overpriced or the most expensive in the universe?

If you run the data, (with survivorship bias included), you will see that growth managers, especially small-cap, have a much easier time beating benchmarks and data groups than value managers. IMO, this is related to how growth indexes or data groups are created.

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Post by Robert T » Tue Oct 23, 2007 11:38 am

.
Zalzel,

I agree there are several possible reasons to value tilt – here are some of them.
  • 1. For higher expected return (and risk): If your need to take risk is higher than market risk (and you are willing and able take higher risk) then value tilting can increase a portfolio expected return. For better or worse, this was my primary reason to value tilt.

    2. For lower dispersion of the same expected returns: The same expected market return with lower expected standard deviation of returns can be achieved by simultaneously value tilting and increasing the fixed income share of a portfolio. This point has been raised and put into practice by Larry. But my sense is even a moderate value tilt (e.g. 0.4 value loading) can capture much of the ‘dispersion’ benefit based on an earlier look at the question.

    3. For diversification of human capital: If an investor works for a ‘growth’ company they may want to diversify their human capital with a value tilt in their portfolio.
Investors who do tilt away from the market to any degree should be sure they can withstand the divergence in portfolio returns with the market which is often significantly negative (tracking error regret) as illustrated this year in the US (and it can get much larger).

Different index combinations to achieve same value tilt: You are right – there are many combinations of index funds that can approximate a particular factor loading target. I just listed the estimated factor loading targets for some of the commonly used indexes. IMO other things to consider when choosing index funds are tax-efficiency and asset class tracking error regret. In addition - one caveat – the factor loadings are estimates for a particular period in time July 1995 to April 2007. These loadings can often vary over time quite substantially and these estimates may not be exactly the same as the eventual long-term average factor loading for the fund. But IMO these are the best estimates we have as of today.


Michael,
If you run the data, (with survivorship bias included), you will see that growth managers, especially small-cap, have a much easier time beating benchmarks and data groups than value managers. IMO, this is related to how growth indexes or data groups are created.
This earlier article by Bill Bernstein may be of interest.

From the article:

…”In other words, active small growth managers succeed to the extent that they are free to invest elsewhere” (i.e. not in the small growth category defined by low BtM)

…”But the big picture is that with small stocks value beats growth by a wide margin. Whether your approach is active or passive, the best advice about small growth investing is to just say no.”

I agree with your sentiment to use caution when basing decisions on historical FF data. It’s as much about how the data are used as what they historically say. As most value and growth funds (including index funds) use different stock selection criteria, return differences between them will differ from the FF ‘high-BtM minus low BtM’ numbers. However, IMO the FF three factor model which used BtM measures provides a useful framework for making decisions – i.e. to help structure a portfolio to capture a target share of any future (FF defined) value and small cap premium (obviously doesn’t guarantee anything on the future size of these premiums).

Robert
.

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Beta=1.0?

Post by zalzel » Fri Jan 11, 2008 9:50 pm

Code: Select all

Monthly data used from July 1995 to April 2007

                             Factor Loadings                Expense
Index                        Mkt     Size    Value   ETF     Ratio

SMALLCAP VALUE 

MSCI US Small Cap Value      0.99    0.41    0.80    VBR     0.12
Russell 2000 Value           0.97    0.64    0.79    IWN     0.25
S&P 600 Value                1.01    0.67    0.63    IJS     0.25
S&P 600 Pure Value           1.04    0.72    0.99    RZV     0.35

SMALLCAP VALUE AVERAGE       1.00    0.61    0.80            0.24  



Robert, I'm puzzled at the Beta of 1.0 (average) for SCV. That is inconsistent with the observation that SCV has greater Volatility than the Market Portfolio. In a similar vein, in constructing your Portfolio you used Beta of 1.0 for EM. This is inconsistent with EM's greater Volatility compared with International Equity. Your thoughts?

Thanks,

Stay Free,

Zalzel

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Robert T
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Post by Robert T » Sat Jan 12, 2008 9:01 pm

.
Zalzel,

Here's an attempt at your questions.
I'm puzzled at the Beta of 1.0 (average) for SCV. That is inconsistent with the observation that SCV has greater Volatility than the Market Portfolio.
  • My interpretation is that this is the difference between a one-factor model (CAPM), and the FF three factor model.
  • Beta in the one factor model: Over some time periods the one-factor model shows that the ‘betas’ on value stocks are higher that one. For example, the current M* beta estimate for the ishares S&P 600 value index (IJS) is 1.36 for the last three years to end December 2007. This implies that the returns of IJS should have been 36% higher than the positive S&P500 returns over the period.

    Problems with the one factor model: There have been several related problems highlight with the one-factor model. Two important ones IMO are: (i) lack of explanatory power of actual returns (for example ‘beta’ alone only explains about 60% of the variability in monthly returns of IJS, and historically the returns implied by the model differ significantly from actual returns); and (ii) misspecification of the model reflected in non-random error terms in the regression (which suggests omitted explanatory variables). An example of the first is illustrated by the M* alpha estimate for IJS over the last three years of –3.5. This suggested that the fund has underperformed by 3.5% (I presume annually) against its expected return implied by the fund’s estimated beta.

    The three factor model: The three factor model seems to correct for both of the problems highlighted above. The explanatory power increases significantly (to just over 90% of the return variability of IJS), and the error-terms seem to be more random. So the three-factor model implies that its not just variability relative to the market (as measured by beta) that matters for determining excess return but the extent of exposure to value and small cap stocks. More specifically - the ‘beta’ close to or equal to one in the three factor model implies that (almost) all the excess return of a fund above the market is determined by its degree of exposure to value and small cap stocks (at least this has been a more precise estimate than using just beta).
In a similar vein, in constructing your Portfolio you used Beta of 1.0 for EM. This is inconsistent with EM's greater Volatility compared with International Equity. Your thoughts?
  • My comparison of EM is with EM equity not international equity, hence the beta of 1.
Not sure if this is clear.

Robert
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Misspecification

Post by zalzel » Sun Jan 13, 2008 3:59 am

Robert T wrote: (snip)
... misspecification of the model...
(snip)
I will have to learn about misspecification, but if I've got you right, Beta had to be "stretched" in the CAPM to account for Return that is better explained by the addition of HmL and SmB Premiums to an "unstretched" (more specific) Beta Premium in the FF3F Model?

Thanks much,

Zalzel
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Post by Rodc » Sun Jan 13, 2008 10:12 am

I have not read the thread, but my take is that in the long run it matters little how you get your tilt, similar amounts of tilt result in similar outcomes. You might find the graph I posted in this thread of interest.

http://www.diehards.org/forum/viewtopic.php?t=11086

The three more or less different portfolios that have more or less similar amounts of tilt (4x25, 3x33, TSM/SV) have similar results. Tilting only small but not value gets a result between small/value tilt, and no tilt.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

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Post by Robert T » Sun Jan 13, 2008 11:06 am

.
Rod,

I would add one caveat. If I recall, the large value series used in your earlier simulations was the FF large value (B/H) benchmark portfolio. The factor loads of this series (as shown below) are more similar to the indexes tracked by non-DFA midcap value funds rather than to those tracked by large cap value funds [i.e. the FF LV series has on average captured about 80% of the value premium, similar to the mid-cap (and small-cap) value indexes, while the large cap value indexes have only on average captured about 50% of the value premium - all simulated of course but nevertheless instructive]. If the large cap value series used in the earlier analysis had similar factor loads to indexes tracked by non-DFA large cap value index funds I would on average expect a larger difference.

Code: Select all

                              Factor Loadings               
Index                         Mkt     Size    Value   

LARGE VALUE AVERAGE           0.99   -0.13    0.47 
MIDCAP VALUE AVERAGE          1.04    0.19    0.80  

FF LV Benckmark Portfolio     1.09    0.02    0.79

The large and mid cap value averages are from an earlier post in the thread, and the FF LV Benchmark Portfolio factor loads are for the period 7/1926 to 11/2007.
Best,

Robert
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Post by zalzel » Sun Jan 13, 2008 11:35 am

Hi Rod.

I sent you a PM (private message) yesterday regarding this very graphic. I bring this to your attention here as it is still in my Outbox and, while I am a bit confused as to the PM function, I think that means you have not accessed your PM.

Thanks,

Zalzel
"What we can't say we can't say, and we can't whistle it either." | Frank P. Ramsey

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Post by Rodc » Sun Jan 13, 2008 4:29 pm

I would add one caveat. If I recall, the large value series used in your earlier simulations was the FF large value (B/H) benchmark portfolio. The factor loads of this series (as shown below) are more similar to the indexes tracked by non-DFA midcap value funds
A fair caveat. I don't have the amount of data I'd like otherwise, but I expect what matters most in expecting two portfolios to average out about the same is the factor loadings. If one can and wants to compute factor loads that is a good thing to do. For other people they should sleep well at night knowing they can do fine with one of the standard portfolios that get discussed. There will of course be differences between real portfolios built with different funds or ETFs.
zalzel wrote:
Hi Rod.

I sent you a PM (private message) yesterday regarding this very graphic. I bring this to your attention here as it is still in my Outbox and, while I am a bit confused as to the PM function, I think that means you have not accessed your PM.

Thanks,

Zalzel
Hi Zalzel, I expect the notifications go to my computer at work, and so I don't see them over the weekend, and I simply did not see the tiny little flag at the top of the page. Replies have been sent.
We live a world with knowledge of the future markets has less than one significant figure. And people will still and always demand answers to three significant digits.

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