Analysis of relative diversification effects

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Robert T
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Analysis of relative diversification effects

Post by Robert T » Sun Apr 22, 2007 2:51 pm

.
I had the data out to look at another question but thought it useful to look at the following question at the same time [apologies for the long post].

Question

What have been the relative portfolio effects of adding international equities, a value and small cap tilt, REITS, commodities, and fixed income of varying duration and quality?

To try to answer this question I back-tested the following portfolios (1972-2006):

P1 - Baseline
75% US Total Stock Market
25% 5 yr Treasury Notes

P2 – Non-US Market Effect
37.5% US Total Stock Market
37.5% Non-US Developed Market
25.0% 5 yr Treasury Notes

P3 – Emerging Market Effect
37.5% US Total Stock Market
28.0% Non-US Developed Market
09.5% Emerging Market
25.0% 5 yr Treasury Notes

P4 – Small Cap and Value Effect
[same market allocation but with an overall size loading of 0.2 and value loading of 0.4]
37.5% US Total Stock Market
28.0% Non-US Developed Market
09.5% Emerging Market
25.0% 5 yr Treasury Notes

P5 – REIT Effect
[REITs added to P4 – value and size tilted equity allocation – taken from US allocation]
32.5% US Total Stock Market
05.0% US REITs
28.0% Non-US Developed Market
09.5% Emerging Market
25.0% 5 yr Treasury Notes

P6 – Collateralized Commodities Futures Effect
[Commodities added to P4 – value and size tilted equity allocation - taken equally from US:Non-US equity]
35.0% US Total Stock Market
26.5% Non-US Developed Market
08.5% Emerging Market
05.0% Collateralized commodities futures
25.0% 5 yr Treasury Notes

P7 – Term Effect [Shorten Fixed Income duration to 2 yrs]
[P4 equity allocation - overall size loading of 0.2 and value loading of 0.4]
37.5% US Total Stock Market
28.0% Non-US Developed Market
09.5% Emerging Market
25.0% 2 yr Treasury Notes

P8 – Term Effect [Extend Fixed Income duration >10 yrs]
[P4 equity allocation - overall size loading of 0.2 and value loading of 0.4]
37.5% US Total Stock Market
28.0% Non-US Developed Market
09.5% Emerging Market
25.0% Long-term Treasury Bonds

P8 – Default Effect [Add Junk Bonds]
[P4 equity allocation - overall size loading of 0.2 and value loading of 0.4]
37.5% US Total Stock Market
28.0% Non-US Developed Market
09.5% Emerging Market
12.5% 5 yr Treasury Notes
12.5% Junk Bonds


Results

Code: Select all

1972-2006
                                    AR       SD    Sharpe    Growth of $1 [since 1972]	

EQUITY EFFECTS

P1- Baseline                       10.95   13.64    0.421               38
P2- Non-US Developed Mkt Effect    11.24   13.38    0.448               42
P3- Emerging Market Effect         12.00   13.61    0.479               53
P4- Value and Small Cap Effect     14.29   13.68    0.662              107


ALTERNATIVES EFFECTS

P5- REIT Effect                    14.21   13.38    0.668              105
P6- Commodities Effect             14.25   12.42    0.713              106


FIXED INCOME EFFECTS

P7- Term Effect [Shorten to 2 yr]  14.20   13.49    0.663              104 
P8- Term Effect [Extend to Long]   14.42   14.20    0.650              111 
P9- Default [Junk]                 14.33   14.18    0.646              108	

AR = Annualized Returns
SD = Standard Deviation
Sharpe = Sharpe Ratio
Observations

1. Value and Small Cap exposure had the greatest impact on enhancing the level of portfolio return and return/SD characteristics. By 2006, the (P4) portfolio value would have been twice as large as a portfolio with the same exposure across US, Non-US Developed, and emerging markets but with no value or small cap tilt ($107 vs $53).

2. Emerging market exposure had greatest international diversification impact. EAFE had a smaller impact (not unexpected with similar long-term risks [beyond short-term exchange rate volatility]). The same conclusion can be derived from 1988 when more accurate EM index returns are available [The corresponding portfolio annualized return/SD/Sharpe ratios were with EAFE - 9.31/12.01/0.499; and when EM was added - 10.14/12.50/0.542].

3. REITS marginally enhanced risk return characteristics. Lower volatility of returns (SD) came at the expense of lower return, but led to a slightly higher Sharpe ratio.

4. Collateralized Commodities Futures enhanced risk return characteristics by more than REITs. Inclusion of CCFs lowered portfolio volatility at the expense of marginally lower returns to yield a higher Sharpe ratio (0.713) – the highest among all portfolios.

5. Fixed income: Extending bond duration increased returns but led to higher volatility of returns particularly with use of long-term bonds. Adding junk bonds (default risk) did not add favorable risk/return characteristics – marginally higher return with higher volatility leading to a lower Sharpe Ratio.

6. Equity vs. fixed income factors: The variability in the final dollar value of the back-tested portfolios was much smaller for within fixed income allocation ($104 to $111) versus within equity allocations ($38 to $107).


Answer

Getting back to the original question. The results suggests – at least since 1972 – greatest diversification (or greatest improvement in return/SD characteristics) came from:

1. Tilting to value and small cap stocks.
2. Inclusion of international equities - particularly emerging markets.
3. CCFs reduced overall portfolio volatility (more so than REITs).
4. Shorter term fixed income performed better than long-term fixed income.
5. Lower quality bonds didn’t add value.


Data source:

US Total Stock Market: 1972-2006 from Ken French website.

EAFE Market: 1972-1974 from MSCI website (Net Index), 1975-2006 from Ken French website.

Emerging Market: 1972-1987 from IFA website (added back expenses): 1988-1994 from M* principia indices, 1995-2000 spliced EM index from Vanguard website, 2001-2006 from MSCI.

Value and Small Cap: US-SmB, US-HmL and Intl.-HmL from Ken French website.

REIT Index: 1972-1977: NAREIT Index from Roger Gibson's Asset Allocation Book. 1978-2006: Wilshire REIT Index.

GSCI: 1972-1998: http://www.cme.com/files/Exchange_Traded_Derivat.pdf; 1999-2006 : https://www.oppenheimerfunds.com/pdf/sh ... ochure.pdf

2 yr Treasury Notes: 1972-1991 from IFA website (added back expenses). 1992-2006 Lehman 1-5 year Treasury Index (benchmark for Vanguard Short Term Treasury).

5 yr Treasury Notes: 1972-1991 from Ibbotson. 1992-2006 Lehman 5-10 year Treasury Index (benchmark for Vanguard Intermediate Term Treasury Fund).

20 yr Treasury Notes: 1972-1991 from Ibbotson. 1992-2006 Lehman Long Treasury Index (benchmark for Vanguard Long Term Treasury Fund).

Junk bond: 1972-1978: Simulated from default factor derived from Ibbotson (0.5 default loading); 1979-2006 – Vanguard High Yield Bond Fund.
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Last edited by Robert T on Mon Apr 23, 2007 3:20 am, edited 6 times in total.

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Well Done!

Post by JohnYaker » Sun Apr 22, 2007 3:05 pm

.
Well done, Robert T!

Diversification value: Yes.
Yield enhancement: I doubt it.

The small cap and value history are so widely known (I imagine many active managers have jumped on it), I question whether there is any predictive advantage whatsoever. History does not always repeat itself.

We'll see.

John
Last edited by JohnYaker on Sun Apr 22, 2007 3:06 pm, edited 1 time in total.

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Post by Cb » Sun Apr 22, 2007 3:05 pm

Thanks for an excellent post!

Without using DFA funds, how can an investor achieve the sort of small and value loadings you've described?

Thanks,

Cb

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Expectations and loading targets

Post by Robert T » Sun Apr 22, 2007 4:10 pm

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John,

I agree there are signficant limits to extrapolating the past. In addition, the high inflation and interest rates in the 1970-80s (period covered by the back-test) seem to have contributed to the relatively large value premium (see Who Killed Value? http://www.efficientfrontier.com/ef/701/value.htm). However, I think there is a fundamental cost-of-capital story that persists (i.e. not a free lunch but higher risk). So a small and value tilted portfolio should have higher expected return IMO – probably not as high as in the past but still in excess of the market return (re – higher cost of capital).

Cb,

This unfortunately requires a bit of work (but worth it IMO). There are essentially just two steps:

1. Estimate the size and value loadings of the funds available to you (following the guidance provided here - http://www.efficientfrontier.com/ef/101/roll101.htm)
2. Combine then in a way that meets your overall factor loading targets.

Typically a non-DFA fund portfolio will need a higher allocation to value funds (due to their lower loadings) to get a similar effect. The loadings used above are similar to an indicative DFA balanced strategy (see – Exhibit 5 in this article - http://www.dfaus.com/library/articles/i ... ced_funds/). FWIW the 0.2 and 0.4 size and value loadings used above are my portfolio targets (based on need to take risk). To get close to these using steps 1 and 2 above I came out needing the asset allocation presented in #57771 #42 (M* Vanguard Diehards) when using non-DFA funds. But suggest you follow steps 1 and 2 to do the size and value loadings match you want.

Robert
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Post by alvinsch » Sun Apr 22, 2007 5:46 pm

Thanks for the analysis. However, it occurs to me that the order in which you added things can make a huge difference in your conclusions. For example, if you swapped the ordering of P4 and P5 by adding REITs to P3 and then added small/value to the portfolio that already had REITs, it's possible that one might conclude that REITs added a lot of diversification and small/value added much less. Anyway if it was easy to do I'd be curious to see how much the ordering affects your conclusions.

Thanks
- Al

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Changing the order

Post by Robert T » Sun Apr 22, 2007 6:57 pm

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Note: Made small correction to the table above - but story doesn't change.

Al,

I agree re-ordering may change the results – but not by much. If we add

P10 – REIT Effect [no value or size tilt]
32.5% US Total Stock Market
05.0% US REITs
28.0% Non-US Developed Market
09.5% Emerging Market
25.0% 5 yr Treasury Notes

Code: Select all

1972-2006

                                       AR          SD         Sharpe     Growth of $1 [since 1972]	

P3                                   12.00       13.61        0.497            53
P10- REIT Effect [no s&v tilt]       12.16       13.20        0.521            56
P5                                   14.21       13.38        0.668           105	
P4                                   14.29       13.68        0.662           107

AR=Annualized Return
SD=Standard Deviation
Sharpe=Sharpe Ratio


Adding REITs to a globally diversified market portfolio increased its return and lowered its standard deviation, which led to a higher Sharpe Ratio (P10 vs P3). The resulting 2006 portfolio value was slightly higher than the market portfolio without REITs (56 vs. 53.). So adding REITS to a non small cap and value tilted portfolio enhanced portfolio return/SD characteristics but had smaller impacts when the portfolio was tilted (P5 - small cap and value tilted with REITS; P4 - small cap and value tilted without REITs).

Robert
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Last edited by Robert T on Mon Apr 23, 2007 3:27 am, edited 2 times in total.

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Post by sterjs » Sun Apr 22, 2007 7:34 pm

3. REITS did not enhance risk return characteristics. Lower volatility of returns (SD) came at the expense of lower return and a lower Sharpe ratio.
Wierd. That doesn't make sense to me unless Trev H's table is wrong:

Code: Select all

1972-2006

Correlations, CAGR, Volatility

Correlation to:.US Market...500 Index...EAFE/EM....CAGR...StDev
===============================================================
US Market.........1.0000......0.9908.....0.5944...11.24...17.46
500 Idx...........0.9908......1.0000.....0.5899...11.32...17.22
LCV...............0.9163......0.9054.....0.5535...13.46...17.24
LCG...............0.9571......0.9680.....0.5309...10.00...20.22
MCB...............0.9019......0.8618.....0.4946...13.72...18.44
SCB...............0.8194......0.7460.....0.4595...13.23...21.66
SCV...............0.7101......0.6410.....0.3585...15.00...19.96
SCG...............0.8328......0.7663.....0.4751...10.43...23.75
MicroCap..........0.6894......0.6043.....0.3756...13.64...26.70
REIT..............0.5284......0.4638.....0.3041...13.88...16.67
EAFE/EM...........0.5944......0.5899.....1.0000...12.07...22.08
LT Treas..........0.2584......0.2806.....0.0935....8.47...11.37
IT Treas..........0.1878......0.2124....-0.0373....8.13....6.90
ST Treas..........0.1628......0.1845....-0.0920....7.12....4.06
T-Bills...........0.0323......0.0497....-0.1239....5.98....3.00
IT Bonds..........0.2724......0.2930....-0.0190....8.06....5.61
S-TIPS............0.1283......0.0942.....0.3974....7.64....6.82
Commodities......-0.2466.....-0.2437....-0.1447....8.00...24.53
===============================================================
From 1972-2006, REIT had the best of all worlds--lowest correlation outside bonds/commodities, 2nd highest return after SCV and the lowest standard deviation outside bonds.

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Re: Changing the order

Post by alvinsch » Sun Apr 22, 2007 7:38 pm

Robert T wrote:I agree re-ordering may change the results – but not by much.
Thanks for adding P10. Like you said it didn't change things by that much but interesting to know for that timeframe small / value swamps REITs for diversification.

- Al

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Post by cherijoh » Sun Apr 22, 2007 7:53 pm

sterjs wrote:
3. REITS did not enhance risk return characteristics. Lower volatility of returns (SD) came at the expense of lower return and a lower Sharpe ratio.
Wierd. That doesn't make sense to me unless Trev H's table is wrong:

Code: Select all

1972-2006

Correlations, CAGR, Volatility

Correlation to:.US Market...500 Index...EAFE/EM....CAGR...StDev
===============================================================
US Market.........1.0000......0.9908.....0.5944...11.24...17.46
500 Idx...........0.9908......1.0000.....0.5899...11.32...17.22
LCV...............0.9163......0.9054.....0.5535...13.46...17.24
LCG...............0.9571......0.9680.....0.5309...10.00...20.22
MCB...............0.9019......0.8618.....0.4946...13.72...18.44
SCB...............0.8194......0.7460.....0.4595...13.23...21.66
SCV...............0.7101......0.6410.....0.3585...15.00...19.96
SCG...............0.8328......0.7663.....0.4751...10.43...23.75
MicroCap..........0.6894......0.6043.....0.3756...13.64...26.70
REIT..............0.5284......0.4638.....0.3041...13.88...16.67
EAFE/EM...........0.5944......0.5899.....1.0000...12.07...22.08
LT Treas..........0.2584......0.2806.....0.0935....8.47...11.37
IT Treas..........0.1878......0.2124....-0.0373....8.13....6.90
ST Treas..........0.1628......0.1845....-0.0920....7.12....4.06
T-Bills...........0.0323......0.0497....-0.1239....5.98....3.00
IT Bonds..........0.2724......0.2930....-0.0190....8.06....5.61
S-TIPS............0.1283......0.0942.....0.3974....7.64....6.82
Commodities......-0.2466.....-0.2437....-0.1447....8.00...24.53
===============================================================
From 1972-2006, REIT had the best of all worlds--lowest correlation outside bonds/commodities, 2nd highest return after SCV and the lowest standard deviation outside bonds.
Sterjs,

Trev H's data only looked at the correlation between 2 asset classes at a time. That doesn't address the issue of 4 - 6 asset classes combined together as in this example. For that you need to use multivariate techniques - which is not something you probably want to know about in any great detail. I took a class in this for my MS in Applied Statistics, so you can take my word on this... :lol:

C

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REITs Effect

Post by Robert T » Sun Apr 22, 2007 8:25 pm

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sterjs,

Thanks for checking on the data. I rechecked the REIT series and the key seems to be what data is used for 1972 to 77 for the backtest. If we use the series from Gibson's book for the period the results do change a little (rather than what I extracted from the NAREIT website - not sure why they were different?).

I have used Gibson's series (as they are published) and adjusted the table and data sources above together with those presented for Al (to ensure the results appear in one place).

The results suggest that adding REITs - reduced returns but this was offset by lower standard deviation to give a marginally higher Sharpe Ratio. The assumption here is that the factor loading of the equity portion remains the same. This assumption may not hold as the problem I had was that including REITs would likely reduce my equity factor loadings and yield a less positive result.

I have amended the above accordingly.

Thanks,

Rob
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Post by lswswein » Wed Apr 25, 2007 1:04 am

Hi Robert
Great analysis. A question about the funds you are using in your AA you referenced in 57771. Are you using Vanguard funds for most of the asset classes? Also what are you using for Micro and Intl Small?

thanks
-h

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Post by BrianTH » Wed Apr 25, 2007 6:19 am

Not a surprising result I suppose, but quite helpful nonetheless--thanks!

By the way, my two cents view is that everything seemed to work but long bonds and junk. So, this might be considered validation for all these ideas, even if some work a bit better than others.

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Post by Robert T » Wed Apr 25, 2007 12:13 pm

.
One addition: The Expense Effect

These include:
- Taxes
- Fund expenses (expense ratio)
- Trade costs (commissions, bid-ask spreads etc)
- Account fees (minimum balance, wrap fees etc)
- Advisor fees (if used)

Using the P4 portfolio from the above analysis:

Code: Select all

1972-2006

                          AR     SD     Sharpe    Growth of $1 [since 1972]
P4 [no expenses]        14.29   13.68   0.662            107
P4 [0.4% expense]       13.83   13.62   0.630             93
P4 [1.4% expense]       12.69   13.49   0.552             65	

AR=Annualized return
SD=Standard deviation
Sharpe=Sharpe Ratio
An annual expense of 0.4% of fund assets is used (about my current total expenses), which in the back-test would have reduced the 2006 value by 13% (from 107 to 93). If these expenses were 1.4% then the final value would be reduced by 30% (from 107 to 65). For the latter case the 1.4% annual expenses eroded about three quarters of the value and size effect (Value and size effect: 107-53=+54; Expense effect: 65-107=-42; so expenses eroded 42/54*100=78% of the value and size effect). So minimizing expenses can significantly enhance returns.

What matters over the long-term is factor exposure and expense – William Bernstein [excuse the repetition but I find it useful]

As indicated in an earlier thread on M*, and consistent with the above I find it useful to focus on these two areas (factor exposure and expense), as well as diversification across global markets [US, Non-US developed, Emerging market equity and US treasuries]. For reasons discussed elsewhere I don’t currently include REITs or CCFs.

_______________

H,

For my retirement account, I currently use:

- Vanguard funds for ‘large and small market exposure’ where available (incl. Intl. small).
- Mainly iShares for value exposure (although added RZV to tax advantaged account to try to stick to my portfolio factor loading targets when ishares changed their benchmarks from Barra to Citigroup in Dec 2005. The Citigroup benchmarks have lower value loadings).
- Bridgeway for microcap (despite the criticisms have held it since 2003 and intended to continue to hold it).

FWIW - for college education for our two year old, I do used DFA funds through the WV529 plan (IMO expected excess return (after costs) is higher than alternatives – time will tell).

Robert
.

sterjs
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Re: Changing the order

Post by sterjs » Mon May 07, 2007 12:53 pm

Robert T wrote: Adding REITs to a globally diversified market portfolio increased its return and lowered its standard deviation, which led to a higher Sharpe Ratio (P10 vs P3). The resulting 2006 portfolio value was slightly higher than the market portfolio without REITs (56 vs. 53.). So adding REITS to a non small cap and value tilted portfolio enhanced portfolio return/SD characteristics but had smaller impacts when the portfolio was tilted (P5 - small cap and value tilted with REITS; P4 - small cap and value tilted without REITs).
I read on another website that Small Value and REITs have a high correlation. In that light, this result makes a lot of sense.

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REITS and SV

Post by SmallHi » Mon May 07, 2007 1:20 pm

I wouldn't say they have "high correlation". I would say REITS and SV correlations are higher than REITS and TSM. That in itself is not the reason to avoid them

As Robert illustrated, once you own SV and T-Notes, REITS don't give you a lot more added efficiency.

The future maybe different, but that has been the case in the past.

We are good at predicting past performance, aren't we? 8)

SH

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Post by Elysium » Mon May 07, 2007 2:48 pm

Robert,

Thanks for your analysis. I find it very useful.
1. Value and Small Cap exposure had the greatest impact on enhancing the level of portfolio return and return/SD characteristics. By 2006, the (P4) portfolio value would have been twice as large as a portfolio with the same exposure across US, Non-US Developed, and emerging markets but with no value or small cap tilt ($107 vs $53).
What about only Value effect, or only Small effect? It will be useful to see how much one of them add without the other one also present.

Can we see the following added to P3 (or one with REIT):

1. large value effect with small blend (no small value)
2. small value effect with large blend (no large value)
3. large value effect (no small)
4. small blend effect (no value)


I think this will complete all scenarios.

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Post by johnb » Mon May 07, 2007 7:29 pm

Hi Robert,

Thanks for sharing that info. When you calculated the Sharpe Ratio, what value did you use for the risk-free rate?

Also, how often did you rebalance the portfolios?

Best regards,
John

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Post by Robert T » Mon May 07, 2007 9:32 pm

.
SmallHi,

Predicting the past – I know we are excellent at it:). The future will almost definitely be different.

However, like many others (including you), I place some value in what historical numbers have to say. As Bernstein puts it (from The Intelligent Asset Allocator) – “If you’re trying to capture lightening in a jar, you a better off in Texas than Alaska. There are certain asset combinations and portfolios which are likely (but not certain) to do reasonably well.” Analysis of long-term historical performance played a roll in “positioning myself in Texas” (small and value tilt). Since developing my IPS at the start of 2003 there been lots of 'lightening' so we are probably due for some prolonged clear spells soon. I am currently not sorry for placing some weight on long-term historial performance. Only time will tell if this will change.

Sticking with Bernstein (54255 #12 from M*)

“It's like everything else in finance. There is no certainty, only probabilities, and you go where they are the highest. (This is also true of the value and small premia. If they were absolutely certain, then they would have been arbitraged away. And, in 2006, maybe they have already. But the rational investor should still place his or her bets there.)”

This is certainly not for everyone - but based on a review of some of the research, a look at the numbers, and willingness, ability and need to take risk, I am currently comfortable 'in Texas' (small and value tilt).

Dieharder,

What about only a value effect or only a small effect?

I will try to get to the numbers again soon – the easiest way to do this is just to compare the impact of (i) adding a 0.4 and 0 value and small loading to the portfolio (i.e. a portfolio that captures 40% of any value premium [as defined by Fama-French] and 0% of the small cap premium) with (ii) adding a 0 and 0.4 value and size loading to the portfolio. Now some would argue that to ensure an apples to apples comparison the common Small cap minus Big cap return variable (SmB) – which measures the small cap premium relative to large caps) needs to be adjusted. I will look at both and post the numbers when I have more time.
  • [Details if interested: The value premium as defined by Fama-French is the return on the 30% of highest book-to-market stocks minus return on the 30% stocks of lowest book to market. However the current size premium as defined by FF is the return on the smallest 50% by market cap minus the largest 50% by market cap. So an apples to apples comparison some argue would be the return on 30% smallest market cap minus 30% largest market cap. I looked at the numbers a while ago and using the 30% approach the value and size premium were fairly close but the size premium still had much higher correlation to the total market than the value premium].
If you are wondering why I bother with factor loadings its because it's a portfolio factor loadings that matters for portfolio performance, more so than simply asset classes used. There are many many small and large, value and blend funds each with differing factor loading so the interpretation of subsequent simulation results is dependant on the index fund used. And in many cases FF French indexes are used for backtests – but these can often give a false impression to investors as these indexes have higher loadings than average investors have access to through non-DFA funds. For example, a 10% FF large value allocation will have a significantly different portfolio impact than a 10% Vanguard value index allocation - as with other large value funds (IMO). Using factor loadings reduces the ambiguity (at least to me).

Johnb,

I used the risk free-rate (RF) from Ken French’s website - average over the period used (look in the data library under Fama/French Factors). The portfolio was rebalanced annually.

Robert
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Post by johnb » Tue May 08, 2007 8:43 am

Robert T wrote:.


Johnb,

I used the risk free-rate (RF) from Ken French’s website - average over the period used (look in the data library under Fama/French Factors). The portfolio was rebalanced annually.

Robert
.
Hi Robert,

I wasn't able to find that. Was it 5%? I ask because I'm doing my own backtesting, and I was wondering what the "standard" risk-free rate is.

Best regards,
John

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