## Three-fund portfolio returns and variance drain

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FrugalInvestor
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### Re: Three-fund portfolio returns and variance drain

sweeneyastray wrote:
Thu Apr 03, 2014 9:12 am
(First post! I have been reading the forum for a while, but I teach percentage math for the GMAT, GRE, SAT, etc., so this is finally an area in which I feel I can contribute!)
And an excellent contribution it was! Thank you sweeneyastray.
IGNORE the noise! | Our life is frittered away by detail... simplify, simplify. - Henry David Thoreau

Rick Ferri
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### Re: Three-fund portfolio returns and variance drain

I read all of this and a few of things come to mind:

1) Fees matter. There's no ambiguity in that equation. A penny saved is a penny earned.
2) The expected return of a total stock market index fund is the market less a negligible fee. There's no ambiguity there either.
3) Any fund or strategy that doesn't always hold the total market will have tracking error with the market. That's where things get messy and it's were all the speculation begins.

Conclusion: a portfolio of total market index funds is low-cost, simple, and the returns are predictable (you get the markets, which ain't so bad).

Rick Ferri
The Education of an Index Investor: born in darkness, finds indexing enlightenment, overcomplicates everything, embraces simplicity.

MIretired
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### Re: Three-fund portfolio returns and variance drain

Random Walker wrote:
Sat May 19, 2018 11:28 pm
I believe this is a very important topic. When we create a portfolio, we look at the expected returns, volatilities, and correlations of potential portfolio additions. The expected return of an investment is an estimate of an arithmetic mean return. The expected return of a portfolio is a weighted average of the expected returns of the individual portfolio components. The expected SD of a portfolio will be less than the weighted average of the component SDs because of less than perfect correlations. So, looking forward we use arithmetic averages.
But the returns we eat are geometric (compounded) averages. ...

Dave
+1. This. Good explanation. Easy to see.

Topic Author
longinvest
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### Re: Three-fund portfolio returns and variance drain

Rick,
Rick Ferri wrote:
Sun May 20, 2018 12:50 pm
I read all of this and a few of things come to mind:

1) Fees matter. There's no ambiguity in that equation. A penny saved is a penny earned.
2) The expected return of a total stock market index fund is the market less a negligible fee. There's no ambiguity there either.
3) Any fund or strategy that doesn't always hold the total market will have tracking error with the market. That's where things get messy and it's were all the speculation begins.

Conclusion: a portfolio of total market index funds is low-cost, simple, and the returns are predictable (you get the markets, which ain't so bad).

Rick Ferri
Thank you for this awesome explanation.
Bogleheads investment philosophy | Lifelong Portfolio: 25% each of (domestic / international) stocks / (nominal / inflation-indexed) bonds | VCN/VXC/VLB/ZRR

Random Walker
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### Re: Three-fund portfolio returns and variance drain

Tyler9000 wrote:
Sun May 20, 2018 11:08 am

Yeah, with the proliferation of articles covering valuations and expected returns I've noticed a trend of authors switching back to arithmetic averages even for their historical analyses. For example, In his book "Your complete guide to factor-based investing" Larry Swedroe exclusively uses arithmetic averages to argue for the historical performance of various investing factors. That's my one complaint in an otherwise excellent book, but it's an important one since ignoring the effects of volatility on real-world compound returns has a significant distorting effect on the resulting numbers.
I think Larry choosing to use simple averages makes good sense for looking at the individual factors. The simple averages give a feel for the size of the premia. In Chapter 9 he shows how diversifying across the premia yields huge advantage, and I think that data must reflect the improved efficiency of decreased variance drag in compounded returns.

Dave

Rick Ferri
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### Re: Three-fund portfolio returns and variance drain

We diversify asset classes to reduce the risk of a large loss. We don't diversify to because there's an expected portfolio benefit from rebalancing. If that happens, great, but it shouldn't be counted on.

To be clear, an expected portfolio benefit from rebalancing asset classes should not be included in a portfolio's expected return. Larry Swedroe and I have disagreed on this for 15 years.

Rick Ferri
The Education of an Index Investor: born in darkness, finds indexing enlightenment, overcomplicates everything, embraces simplicity.

Topic Author
longinvest
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### Re: Three-fund portfolio returns and variance drain

Dear Random Walker,
Random Walker wrote:
Sun May 20, 2018 1:01 pm
Tyler9000 wrote:
Sun May 20, 2018 11:08 am

Yeah, with the proliferation of articles covering valuations and expected returns I've noticed a trend of authors switching back to arithmetic averages even for their historical analyses. For example, In his book "Your complete guide to factor-based investing" Larry Swedroe exclusively uses arithmetic averages to argue for the historical performance of various investing factors. That's my one complaint in an otherwise excellent book, but it's an important one since ignoring the effects of volatility on real-world compound returns has a significant distorting effect on the resulting numbers.
I think Larry choosing to use simple averages makes good sense for looking at the individual factors. The simple averages give a feel for the size of the premia. In Chapter 9 he shows how diversifying across the premia yields huge advantage, and I think that data must reflect the improved efficiency of decreased variance drag in compounded returns.

Dave
In his writings, author Larry Swedroe appeals to the greed and fears of his readers to steer them away from investing into low-cost total market index stock and bond funds and push them into speculating using high-cost active funds and esoteric asset classes.

Bogleheads would be best to ignore such feelings and be satisfied with simply harvesting market returns at low cost.
Bogleheads investment philosophy | Lifelong Portfolio: 25% each of (domestic / international) stocks / (nominal / inflation-indexed) bonds | VCN/VXC/VLB/ZRR

rbaldini
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### Re: Three-fund portfolio returns and variance drain

Random Walker wrote:
Sat May 19, 2018 11:28 pm
I believe this is a very important topic. When we create a portfolio, we look at the expected returns, volatilities, and correlations of potential portfolio additions. The expected return of an investment is an estimate of an arithmetic mean return.
Hmm... Seems to me that to equate "expected return" with "arithmetic mean" is a really bad idea. But I'm not sure if that's what you're saying here... probably not...

Seems to me that the better statement would be
"The historical geometric mean return is an estimate of the future return to the investor (before taxes and fees, depending on the details)",
since the geom mean is (as you later say) the return that matters to an investor. This helps sidestep the whole problem with the word "expectation", which to statisticians means something different from the usual lay meaning.

If you have the historical data, simply calculate the geometric mean directly. Then you don't have worry about any of this stuff directly: the volatility drag will have already been accounted for.

For example, take historical S&P 500 returns since 1928 from here: http://pages.stern.nyu.edu/~adamodar/Ne ... retSP.html
Obviously you don't want to think of the arithmetic mean of 11.53% as the estimated return. You could estimate the volatility drag or "variance drain" as 1/2*variance (1.92% in this case), to get an estimated 9.61% geometric mean. Or you could just calculate the geometric mean directly, which is 9.65%, and call it a day.

One case where the variances do come in handy is when you're combining investments, which you also talk about. Although another approach would be to combine the historical data and again calculate CAGR from that directly.

Random Walker
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### Re: Three-fund portfolio returns and variance drain

Hi Rick,
Thanks for chiming in on this topic. I think it is your book that first got me interested in it. Isn’t avoiding the large losses a big part of the variance drain issue? A bigger portfolio compounding at a more consistent yet modest rate can accomplish lots, with or without a rebalancing bonus? Thanks,

Dave

MIretired
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### Re: Three-fund portfolio returns and variance drain

Random Walker wrote:
Sun May 20, 2018 10:34 am
IlliniDave,
I’m no math whiz, but I disagree. The issue is not just looking at past returns as you wrote above. The issue is building efficient portfolios for the future. Looking forward, each potential portfolio addition has an expected return, a simple mean with a potential dispersion of outcomes. And the portfolio will have an expected return based on the components. We know, before the fact, that there will be volatility drag on the portfolio. The portfolio compounded return will be less than the weighted simple average return of the portfolio components. By choosing portfolio components with correlations and volatilities that mix well together, we can minimize that drag. Looking forward, if two portfolios have the same arithmetic mean return but different standard deviations, the compounded return of the less volatile portfolio will be greater.
This effect is a function of the square of the standard deviation! So the drag rises rapidly with increased equity allocations in a portfolio. Anything that can be done to keep expected return constant and minimize portfolio volatility will be beneficial. What a potential portfolio component adds to a portfolio depends on expected return, volatility, correlations, when correlations tend to change, and of course cost.

Dave
I would kind of like to know what the point of this(bolded) is, and if it's really true.

Rick Ferri
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### Re: Three-fund portfolio returns and variance drain

My view is asset class diversification's primary goal is risk diversification. It reduces the risk of a large loss. Any other benefit that might occur is ancillary to this function.

Rick Ferri
The Education of an Index Investor: born in darkness, finds indexing enlightenment, overcomplicates everything, embraces simplicity.

Random Walker
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### Re: Three-fund portfolio returns and variance drain

Rbaldini,
Yes, what matters is the portfolio as a whole. What matters is the geometric return of the portfolio. Sounds like you know statistics better than I do, but my focus is entirely at the portfolio level: how individual assets with different expected returns, correlations, volatilities, mix at the portfolio level in a risky and uncertain world.

Dave

Random Walker
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### Re: Three-fund portfolio returns and variance drain

MIretired,
Yes it’s true. You can prove it yourself on Excel. Create two random series of returns using the Normal distribution and Random functions. Use the same arithmetic mean return for both series, but vary the standard deviations. Then calculate the actual arithmetic and geometric mean returns for the two series. Run the samples as often as you want and vary the standard deviations.
The point is that some portfolios are going to be more efficient than others. Of course though, Rick makes a HUGE point. Costs matter a lot!

Dave

rbaldini
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### Re: Three-fund portfolio returns and variance drain

MIretired wrote:
Sun May 20, 2018 1:23 pm
Random Walker wrote:
Sun May 20, 2018 10:34 am
Looking forward, if two portfolios have the same arithmetic mean return but different standard deviations, the compounded return of the less volatile portfolio will be greater.
I would kind of like to know what the point of this(bolded) is, and if it's really true.
It is true. The point is simply that if you can find a way to reduce volatility, while keeping arithmetic mean return the same, then you will end up with more money.

While that sounds like it might be hard to do, there's actually a very reliable way to do it: diversify! By spreading your money around many similar-ish investments, you can reduce your standard deviation in returns (basically because risk is spread out across many investments, so the good ones counterbalance the bad) without necessarily reducing your expected arithmetic return. Lower volatility -> more money for you. That is basically *the reason* for diversification (though reduced volatility is also inherently a nice thing: you have fewer really bad years.)

Topic Author
longinvest
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### Re: Three-fund portfolio returns and variance drain

MIretired,
MIretired wrote:
Sun May 20, 2018 1:23 pm
Random Walker wrote:
Sun May 20, 2018 10:34 am
Looking forward, if two portfolios have the same arithmetic mean return but different standard deviations, the compounded return of the less volatile portfolio will be greater.
I would kind of like to know what the point of this(bolded) is, and if it's really true.
It is true, but it is pointless because using arithmetic returns is misleading. This been explained in full details previously in this topic by forum member Sweeneyastray: viewtopic.php?p=2016412#p2016412
rbaldini wrote:
Sun May 20, 2018 1:34 pm
It is true. The point is simply that if you can find a way to reduce volatility, while keeping arithmetic mean return the same, then you will end up with more money.

While that sounds like it might be hard to do, there's actually a very reliable way to do it: diversify! By spreading your money around many similar-ish investments, you can reduce your standard deviation in returns (basically because risk is spread out across many investments, so the good ones counterbalance the bad) without necessarily reducing your expected arithmetic return. Lower volatility -> more money for you. That is basically *the reason* for diversification (though reduced volatility is also inherently a nice thing: you have fewer really bad years.)
Targeting similar arithmetic returns with lower volatility is not the main reason many Bogleheads, like me, diversify our portfolios across stocks and bonds. Author Rick Ferri gave the reason why we do it:
Rick Ferri wrote:
Sun May 20, 2018 1:25 pm
My view is asset class diversification's primary goal is risk diversification. It reduces the risk of a large loss. Any other benefit that might occur is ancillary to this function.
Last edited by longinvest on Sun May 20, 2018 2:49 pm, edited 1 time in total.
Bogleheads investment philosophy | Lifelong Portfolio: 25% each of (domestic / international) stocks / (nominal / inflation-indexed) bonds | VCN/VXC/VLB/ZRR

TJSI
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### Re: Three-fund portfolio returns and variance drain

Mlretired,

You don't need to bother with excel to see why there is no such as thing as volatility drag. A thought experiment will suffice.

Assume you have two simple portfolios each consisting of a single stock--stock A is highly volatile while stock B is a dullard-- not much volatility.
You buy them at the same time and same price (Price P1) and hold them for ten years and by a strange coincidence they end up at the same price P2.
There are no dividends to reinvest.

Now stock A was highly volatile--it gave you a lot of anxity over the 10 years but you held on. It had a high variance every year--up 50% then down 40%--what a ride! Stock B dull--up 6% then down 3%. No action with stock B.

But after 10 years, the price of the stocks was the same--P2. The returns are exactly the same! There was no drag. There is no mysterious force(thank you dbr) lowering the return.

Volatility can cause you problems if you make the wrong investment decision. But it can also help you--see the joys of volatility harvesting.

TJSI

Topic Author
longinvest
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### Re: Three-fund portfolio returns and variance drain

As the original poster of this topic, let me try to summarize what I've learned, so far:
• One should never think in terms of average arithmetic returns. One should think in terms of compound returns (CAGR) instead when looking at past returns.
• Future returns are unknown.
• The total bond market is less volatile than the total stock market because it contains a significant amount of short-term bonds (giving it an overall intermediate duration) and, therefore, can't fluctuate as much in value as stocks, thanks to mathematics.
• International stocks are riskier than domestic ones (higher political risk, harder to enforce legal rights, currency conversion costs and spreads, etc).
• The Three-Fund Portfolio promoted by author and Bogleheads forum co-founder Taylor Larimore is an excellent approach to diversify one's exposure to various investment risks and dampen stock volatility with bonds at rock bottom cost.
• Seeking higher returns by trying to bet on future asset correlations, as promoted by author Larry Swedroe (who has an awful track record), is a form of speculation, mostly driven by greed (e.g. the hope to beat the returns of a simple three-fund portfolio using a portfolio of high-cost actively managed funds of similar volatility). (See viewtopic.php?p=3936798#p3936832 for supporting facts).
Last edited by longinvest on Sun May 20, 2018 4:22 pm, edited 1 time in total.
Bogleheads investment philosophy | Lifelong Portfolio: 25% each of (domestic / international) stocks / (nominal / inflation-indexed) bonds | VCN/VXC/VLB/ZRR

anil686
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### Re: Three-fund portfolio returns and variance drain

longinvest wrote:
Sun May 20, 2018 2:04 pm
As the original poster of this topic, let me try to summarize what I've learned, so far:
• One should never think in terms of average arithmetic returns. One should think in terms of compound returns (CAGR) instead when looking at past returns.
• Future returns are unknown.
• The total bond market is less volatile than the total stock market because it contains a significant amount of short-term bonds (giving it an overall intermediate duration) and, therefore, can't fluctuate as much in value as stocks, thanks to mathematics.
• International stocks are riskier than domestic ones (higher political risk, harder to enforce legal rights, currency conversion costs and spreads, etc).
• The Three-Fund Portfolio promoted by author and Bogleheads forum co-founder Taylor Larimore is an excellent approach to diversify one's exposure to various investment risks and dampen stock volatility with bonds at rock bottom cost.
• Seeking higher returns by trying to bet on future asset correlations, as promoted by author Larry Swedroe (who has an awful track record), is a form of speculation, mostly driven by greed (e.g. the hope to beat the returns of a simple three-fund portfolio using a portfolio of high-cost actively managed funds of similar volatility).
I agree with all of the above minus the last statement. I have never seen Larry recommend funds out of “greed” per se to beat the market. He has always put forth investing in “factors” or strategies that have been shown to pay a risk premium in efforts to reduce market exposure and add more bonds to lower the volatility of the portfolio- or at least that is what I remember from reading a few of his books. While I follow the three fund - I don’t think Larry has advocated that one tries to beat the market - but rather match the market’s return with possibly less volatility. And even with that he never guarantees that will happen, also lets it be known that risk premiums can disappear for long (sometimes very long) periods of time and is not for everybody. I, for one, miss his contributions to this site even though I do not factor invest - JMO though...

Topic Author
longinvest
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### Re: Three-fund portfolio returns and variance drain

Dear Anil686,
anil686 wrote:
Sun May 20, 2018 2:19 pm
longinvest wrote:
Sun May 20, 2018 2:04 pm
As the original poster of this topic, let me try to summarize what I've learned, so far:
• One should never think in terms of average arithmetic returns. One should think in terms of compound returns (CAGR) instead when looking at past returns.
• Future returns are unknown.
• The total bond market is less volatile than the total stock market because it contains a significant amount of short-term bonds (giving it an overall intermediate duration) and, therefore, can't fluctuate as much in value as stocks, thanks to mathematics.
• International stocks are riskier than domestic ones (higher political risk, harder to enforce legal rights, currency conversion costs and spreads, etc).
• The Three-Fund Portfolio promoted by author and Bogleheads forum co-founder Taylor Larimore is an excellent approach to diversify one's exposure to various investment risks and dampen stock volatility with bonds at rock bottom cost.
• Seeking higher returns by trying to bet on future asset correlations, as promoted by author Larry Swedroe (who has an awful track record), is a form of speculation, mostly driven by greed (e.g. the hope to beat the returns of a simple three-fund portfolio using a portfolio of high-cost actively managed funds of similar volatility).
I agree with all of the above minus the last statement. I have never seen Larry recommend funds out of “greed” per se to beat the market. He has always put forth investing in “factors” or strategies that have been shown to pay a risk premium in efforts to reduce market exposure and add more bonds to lower the volatility of the portfolio- or at least that is what I remember from reading a few of his books. While I follow the three fund - I don’t think Larry has advocated that one tries to beat the market - but rather match the market’s return with possibly less volatility. And even with that he never guarantees that will happen, also lets it be known that risk premiums can disappear for long (sometimes very long) periods of time and is not for everybody. I, for one, miss his contributions to this site even though I do not factor invest - JMO though...
I do stand by my last point and I invite readers to check the facts. Here are two related posts with some facts:

First post:
longinvest wrote:
Wed Dec 27, 2017 10:12 am
On December 23, 2011, Ron Lieber made the Larry Portfolio known to the wide public with his "Taking a Chance on the Larry Portfolio" article in The New York Times.

Here's an illustration that the article gave of one version of this portfolio along with a benchmark:
For illustration purposes, [Larry Swedroe] points people to the S.& P. 500 index, which returned about 10 percent annually between 1970 and 2010. If you wanted to gin up a portfolio to match closely (at 9.8 percent) that performance with much less risk, all you would have needed to do was put 32 percent of your money in a fund mimicking the United States stock index of small and value companies that Mr. Fama and Mr. French developed. Then you’d put the other 68 percent of your money in one-year Treasury bills.
For the fun of it, I just ran a new comparison of this 32% small-cap value / 68% short-term treasuries versus its S&P 500 benchmark in Portfolio Visualizer, but for the period starting in January 2012 (just a few days after the article was published) and ending in November 2017 (the end of last month, as I'm writing this on December 27, 2017).

Here's the comparative growth of \$10,000:

Source: Portfolio Visualizer
Larry Portfolio (red): Vanguard Small Cap Value Index (VISVX) - 32% / Vanguard Short-Term Treasury (VFISX) - 68%
Benchmark (blue): Vanguard 500 Index Investor (VFINX) - 100%

Some readers were possibly thinking that the Larry Portfolio would provide as much returns as the S&P 500 but with less volatility, as it did on paper in the past (in backtests). It didn't in real life after being published in The New York Times.

This reminds me of Rekenthaler’s Rule that William Bernstein is found of telling us about in his writings: "If the bozos know about it, it doesn’t work anymore."
longinvest wrote:
Thu Dec 28, 2017 1:33 pm
Dear QuietProsperity,
QuietProsperity wrote:
Thu Dec 28, 2017 12:36 pm
I still think that 100% US Stocks is an awful benchmark to compare the Larry Portfolio against, even if he (maybe) suggested it in the NYT article.
I just found that Larry Swedroe actually expressed his opinion about the New York Times article on our forums!

First, here's the initiating post of a thread started by forum member EvelynTroy on the morning of December 24, 2011:
On Sat Dec 24, 2011 6:51 am, EvelynTroy wrote: Today's New York Times Your Money section - article by Ron Leiber - The Larry Portfolio.

Named for Larry Swedroe, the director of research and a principal at BAM, a wealth management firm in Clayton, Mo., the portfolio tracks indexes that achieved nearly the same 10 percent annual return between 1970 and 2010 as a portfolio invested entirely in the Standard & Poor’s 500-stock index. And here’s the Larry Portfolio’s trick: It did so with less than a third of its money in stocks, with the rest in one-year Treasury bills.

http://www.nytimes.com/2011/12/24/your- ... your-money

Ev
It's immediately followed with a reply by Larry Swedroe himself:
On Sat Dec 24, 2011 8:48 am, larryswedroe wrote: Thanks Evelyn
Ron IMO is one of the good guys in the media. We spent hours discussing the subject and the issues like tracking error regret. He wanted to be sure he understood all the issues. Even spent quite a bit of time fact checking what he wrote, wanting to be sure it was accurate. And then even after it first went on line and I pointed out two minor errors, he corrected them immediately. Ron is one of the few financial journalists I read.

Best wishes
Larry
He did fact check the article and agreed with its final revision. There's no doubt, anymore, that he agreed to a comparison between a 100% stocks portfolio and a 32% stocks / 68% bonds portfolio.

Best regards,

longinvest
I call this an appeal to greed.
Bogleheads investment philosophy | Lifelong Portfolio: 25% each of (domestic / international) stocks / (nominal / inflation-indexed) bonds | VCN/VXC/VLB/ZRR

Random Walker
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### Re: Three-fund portfolio returns and variance drain

Longinvest,
I agree with you lots regarding diversification. But finance has evolved. We have diversification opportunities available that have not been available in the past. Modern portfolio theory clearly shows the benefit of diversifying across independent sources of return. We now have at our disposal independent sources of return through factors, styles, alternatives have not been so readily available in the past.

Dave

Tyler9000
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### Re: Three-fund portfolio returns and variance drain

longinvest wrote:
Sun May 20, 2018 2:04 pm
As the original poster of this topic, let me try to summarize what I've learned, so far:
...
Seeking higher returns by trying to bet on future asset correlations, as promoted by author Larry Swedroe (who has an awful track record), is a form of speculation, mostly driven by greed (e.g. the hope to beat the returns of a simple three-fund portfolio using a portfolio of high-cost actively managed funds of similar volatility).
Since I brought up Swedroe earlier I feel obliged to point out that I disagree with your summary of his ideas, track record, and motivations. I've learned some very useful things from his books and my earlier minor critique in no way means that I do not value his insights.

Random Walker
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### Re: Three-fund portfolio returns and variance drain

TJSI wrote:
Sun May 20, 2018 2:01 pm
Mlretired,

You don't need to bother with excel to see why there is no such as thing as volatility drag. A thought experiment will suffice.

Assume you have two simple portfolios each consisting of a single stock--stock A is highly volatile while stock B is a dullard-- not much volatility.
You buy them at the same time and same price (Price P1) and hold them for ten years and by a strange coincidence they end up at the same price P2.
There are no dividends to reinvest.

Now stock A was highly volatile--it gave you a lot of anxity over the 10 years but you held on. It had a high variance every year--up 50% then down 40%--what a ride! Stock B dull--up 6% then down 3%. No action with stock B.

But after 10 years, the price of the stocks was the same--P2. The returns are exactly the same! There was no drag. There is no mysterious force(thank you dbr) lowering the return.

Volatility can cause you problems if you make the wrong investment decision. But it can also help you--see the joys of volatility harvesting.

TJSI
TJSI,
I believe there is an error or two in your logic. Firstly, need to account for rebalancing. Secondly, each of your example investments individually had the same CAGR at the end of the period. But the more volatile one required a higher simple average annual return to get there. Now looking forward from the start of your mind experiment, would you rather depend on a higher or lower required simple average return to achieve the CAGR goal at the end of the time series?

Dave

Random Walker
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### Re: Three-fund portfolio returns and variance drain

Tyler9000 wrote:
Sun May 20, 2018 2:36 pm
longinvest wrote:
Sun May 20, 2018 2:04 pm
As the original poster of this topic, let me try to summarize what I've learned, so far:
...
Seeking higher returns by trying to bet on future asset correlations, as promoted by author Larry Swedroe (who has an awful track record), is a form of speculation, mostly driven by greed (e.g. the hope to beat the returns of a simple three-fund portfolio using a portfolio of high-cost actively managed funds of similar volatility).
Since I brought up Swedroe earlier I feel obliged to point out that I disagree with your summary of his ideas, track record, and motivations. I've learned some very useful things from his books and my earlier minor critique in no way means that I do not value his insights.
+10000

Dave

Random Walker
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### Re: Three-fund portfolio returns and variance drain

For those interested, take a look at an excellent book: Successful Investing Is A Process by Jacques Lussier Chapter 4, pages 54-58.

Dave

MIretired
Posts: 757
Joined: Fri Sep 06, 2013 12:35 pm

### Re: Three-fund portfolio returns and variance drain

Hey. If it wasn't for greed, I'd have no greed/desire at all! Well, maybe.
I agree with all the posts re. after mine. But I kind of skimmed over and didn't get at a point to the statement of RandomWalker's, about increasing geomean by reducing variance, all else equal. My point would be that the statemnet seems out of place--not false, but out of context.

I made a statement in another thread saying that a single asset's (or fund's) SD is reduced by the SQRT(TIME periods). --(a thread by nisi wanting to own the S&P for two years all in the same year.)
I think that shouldv've been the SD of the mean (error?) is reduced by SQRT(multiple number of samples) (ie: 24 monthly variances vs 12 monthly variances.) A more accurate mean. Not totally sure here.
viewtopic.php?f=10&t=248428&p=3910045#p3910045

Also, to this thread, additionally, the more volatile an asset, the more samples(time) needed to reduce to the actual mean.

Now, since we are talking about a potentially exponentially growing asset (or portfolio), we should be taking the mean of the logs of the returns, and taking the variance and SD from those to arrive at an geomean--not an arithmetic mean of arithmetic returns. Even if we are not compoundingour own (investor) returns.
So, isn't the ideas of reducing the variance just a short term solution to the long, long term true geomean (or arith. mean if the asset has no exponential growth(as in inflation, GDP, etc?)

Not sure how off track I became here.

As for expected return, I'll use DCF model. Nothing historic about that, and I don't have to be "mean."
Last edited by MIretired on Sun May 20, 2018 3:12 pm, edited 1 time in total.

Tyler Aspect
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### Re: Three-fund portfolio returns and variance drain

Let's do this thought experiment:

It is true that when you always use multiplication as an operator, an reduction of 10% is stronger than an increase of 10%. However, if you use division to model a loss then gains can be viewed in the same footing as loss. For example, I invest \$100 in something, and this year's return caused a doubling of its value to \$200. If next year's investment resulted in its value divided by 2, then its final value is again \$100. \$100 * 2.0 / 2.0 = \$100

The true inverse of a doubling is a division by two.
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IlliniDave
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### Re: Three-fund portfolio returns and variance drain

Random Walker wrote:
Sun May 20, 2018 10:34 am
IlliniDave,
I’m no math whiz, but I disagree. The issue is not just looking at past returns as you wrote above. The issue is building efficient portfolios for the future. Looking forward, each potential portfolio addition has an expected return, a simple mean with a potential dispersion of outcomes. And the portfolio will have an expected return based on the components. We know, before the fact, that there will be volatility drag on the portfolio. The portfolio compounded return will be less than the weighted simple average return of the portfolio components. By choosing portfolio components with correlations and volatilities that mix well together, we can minimize that drag. Looking forward, if two portfolios have the same arithmetic mean return but different standard deviations, the compounded return of the less volatile portfolio will be greater.
This effect is a function of the square of the standard deviation! So the drag rises rapidly with increased equity allocations in a portfolio. Anything that can be done to keep expected return constant and minimize portfolio volatility will be beneficial. What a potential portfolio component adds to a portfolio depends on expected return, volatility, correlations, when correlations tend to change, and of course cost.

Dave

That's true only is you are switching assests back and forth between distinct classes. If you do it a lot, you will probably encounter some friction. If you never do it you'll wind up with the dollar-weighted average returns (CAGR) of your asset classes no matter how volatile they are individually.

Think of the sentence I underlined in the extreme. What is the drag on a 100% stock portfolio? It should be the highest of all.

What gets blamed on variance is really an artifact of a particular portfolio management style I believe. It's the price of trying to regulate risk in a semi-active fashion.
Last edited by IlliniDave on Sun May 20, 2018 3:36 pm, edited 1 time in total.
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dbr
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### Re: Three-fund portfolio returns and variance drain

Tyler Aspect wrote:
Sun May 20, 2018 3:06 pm
Let's do this thought experiment:

It is true that when you always use multiplication as an operator, an reduction of 10% is stronger than an increase of 10%. However, if you use division to model a loss then gains can be viewed in the same footing as loss. For example, I invest \$100 in something, and this year's return caused a doubling of its value to \$200. If next year's investment resulted in its value divided by 2, then its final value is again \$100. \$100 * 2.0 / 2.0 = \$100

The true inverse of a doubling is a division by two.
Yes, the compound growth model of investing is one where the end result of one period is multiplied by (1+return) in the next period. The inverse of (1-.5 = .5) is (1+1.0 = 2). The reason this is compound growth is that if we consider the result of two periods with returns r1 and r2 the total growth is (1+r1)*(1+r2) = 1+r1+r2+r1*r2. That last term, return on the previous return is what is meant by compounding of return. As more periods are added more and more of the terms are return on return (on return . . .). (1+r1)*(1+r2)*(1+r3) = 1+r1+r2+r3+r1*r2+r1*r3+r2*r3+r1*r2*r3

MIretired
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### Re: Three-fund portfolio returns and variance drain

MIretired wrote:
Sun May 20, 2018 2:56 pm
Hey. If it wasn't for greed, I'd have no greed/desire at all! Well, maybe.
I agree with all the posts re. after mine. But I kind of skimmed over and didn't get at a point to the statement of RandomWalker's, about increasing geomean by reducing variance, all else equal. My point would be that the statemnet seems out of place--not false, but out of context.

I made a statement in another thread saying that a single asset's (or fund's) SD is reduced by the SQRT(TIME periods). --(a thread by nisi wanting to own the S&P for two years all in the same year.)
I think that shouldv've been the SD of the mean (error?) is reduced by SQRT(multiple number of samples) (ie: 24 monthly variances vs 12 monthly variances.) A more accurate mean. Not totally sure here.
viewtopic.php?f=10&t=248428&p=3910045#p3910045

Also, to this thread, additionally, the more volatile an asset, the more samples(time) needed to reduce to the actual mean.

Now, since we are talking about a potentially exponentially growing asset (or portfolio), we should be taking the mean of the logs of the returns, and taking the variance and SD from those to arrive at an geomean--not an arithmetic mean of arithmetic returns. Even if we are not compoundingour own (investor) returns.
So, isn't the ideas of reducing the variance just a short term solution to the long, long term true geomean (or arith. mean if the asset has no exponential growth(as in inflation, GDP, etc?)

Not sure how off track I became here.

As for expected return, I'll use DCF model. Nothing historic about that, and I don't have to be "mean."
I take this back(bolded). You don't have to take the log of the returns 1st. You just have to understand that you will compound the arith. mean. It all becomes getting rid of the variance. The measurement is per the granularity (time segments), the results are compounded if you let it ride. Hmm. Sounds a lot like what he (RM) said. So, it's an arith. mean that is then compounded. Just need more samples (time segments). --I wouldn't do daily returns, lol.

MIretired
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### Re: Three-fund portfolio returns and variance drain

When comparing two assets for diversification potential:
Which one got there by exp. growth? Which one got there by higher avg. returns, or by a 'one-off', possibly?
The more volatile, the more sampling or time needed to tell.
Or just look at the economic/asset picture, and take your best guess. shrug.

rbaldini
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### Re: Three-fund portfolio returns and variance drain

longinvest wrote:
Sun May 20, 2018 1:53 pm
Targeting similar arithmetic returns with lower volatility is not the main reason many Bogleheads, like me, diversify our portfolios across stocks and bonds. Author Rick Ferri gave the reason why we do it:
Rick Ferri wrote:
Sun May 20, 2018 1:25 pm
My view is asset class diversification's primary goal is risk diversification. It reduces the risk of a large loss. Any other benefit that might occur is ancillary to this function.
Right. I was referring to diversification within asset classes, e.g. within stocks or within bond markets. In that case, diversification both reduces risk of short-term loss and increases long-term return. Free lunch.
In contrast, diversifying by putting some of your money in bonds (as opposed to just stocks) only reduces risk of short-term loss at the expense of long-term return. That's useful if your financial needs aren't strictly long-term.

MIretired
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### Re: Three-fund portfolio returns and variance drain

MIretired wrote:
Sun May 20, 2018 2:56 pm
Hey. If it wasn't for greed, I'd have no greed/desire at all! Well, maybe.
I agree with all the posts re. after mine. But I kind of skimmed over and didn't get at a point to the statement of RandomWalker's, about increasing geomean by reducing variance, all else equal. My point would be that the statemnet seems out of place--not false, but out of context.

I made a statement in another thread saying that a single asset's (or fund's) SD is reduced by the SQRT(TIME periods). --(a thread by nisi wanting to own the S&P for two years all in the same year.)
I think that shouldv've been the SD of the mean (error?) is reduced by SQRT(multiple number of samples) (ie: 24 monthly variances vs 12 monthly variances.) A more accurate mean. Not totally sure here.
viewtopic.php?f=10&t=248428&p=3910045#p3910045

Also, to this thread, additionally, the more volatile an asset, the more samples(time) needed to reduce to the actual mean.

Now, since we are talking about a potentially exponentially growing asset (or portfolio), we should be taking the mean of the logs of the returns, and taking the variance and SD from those to arrive at an geomean--not an arithmetic mean of arithmetic returns. Even if we are not compoundingour own (investor) returns.
So, isn't the ideas of reducing the variance just a short term solution to the long, long term true geomean (or arith. mean if the asset has no exponential growth(as in inflation, GDP, etc?)

Not sure how off track I became here.

As for expected return, I'll use DCF model. Nothing historic about that, and I don't have to be "mean."
I think the bolded is a mistake here, too.
Should be over time (multiple # of samples) SD of the mean would be the nth root of the nth multiple of samples. And over a single time sample of multiple assets: the SD would be the SQRT of the mean variances.

dbr
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### Re: Three-fund portfolio returns and variance drain

If people are talking about the growth of SD with time the answer is that it increases as SQRT(N) and the annualized SD decreases as 1/SQRT(N). These results are used to confuse people by claiming that over time risk decreases because the annulized SD shrinks when in fact that shrinking annualized SD is compounded and multiplied by N to get to the endpoint distribution which, as we are stating, grows by N*1/SQRT(N)=SQRT(N). Investment risk grows with time. Unfortunately that wonderful article by John Norstad where this is laid out very clearly is no longer available.

Topic Author
longinvest
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### Re: Three-fund portfolio returns and variance drain

Dbr,
dbr wrote:
Sun May 20, 2018 7:18 pm
If people are talking about the growth of SD with time the answer is that it increases as SQRT(N) and the annualized SD decreases as 1/SQRT(N). These results are used to confuse people by claiming that over time risk decreases because the annulized SD shrinks when in fact that shrinking annualized SD is compounded and multiplied by N to get to the endpoint distribution which, as we are stating, grows by N*1/SQRT(N)=SQRT(N). Investment risk grows with time. Unfortunately that wonderful article by John Norstad where this is laid out very clearly is no longer available.
It's in the Way Back Machine:
Bogleheads investment philosophy | Lifelong Portfolio: 25% each of (domestic / international) stocks / (nominal / inflation-indexed) bonds | VCN/VXC/VLB/ZRR

dbr
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### Re: Three-fund portfolio returns and variance drain

longinvest wrote:
Sun May 20, 2018 7:23 pm
Dbr,
dbr wrote:
Sun May 20, 2018 7:18 pm
If people are talking about the growth of SD with time the answer is that it increases as SQRT(N) and the annualized SD decreases as 1/SQRT(N). These results are used to confuse people by claiming that over time risk decreases because the annulized SD shrinks when in fact that shrinking annualized SD is compounded and multiplied by N to get to the endpoint distribution which, as we are stating, grows by N*1/SQRT(N)=SQRT(N). Investment risk grows with time. Unfortunately that wonderful article by John Norstad where this is laid out very clearly is no longer available.
It's in the Way Back Machine:
Thanks. I think reading Norstad should be right up there with getting started on the Wiki.

matjen
Posts: 2012
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### Re: Three-fund portfolio returns and variance drain

Tyler9000 wrote:
Sun May 20, 2018 2:36 pm
longinvest wrote:
Sun May 20, 2018 2:04 pm
As the original poster of this topic, let me try to summarize what I've learned, so far:
...
Seeking higher returns by trying to bet on future asset correlations, as promoted by author Larry Swedroe (who has an awful track record), is a form of speculation, mostly driven by greed (e.g. the hope to beat the returns of a simple three-fund portfolio using a portfolio of high-cost actively managed funds of similar volatility).
Since I brought up Swedroe earlier I feel obliged to point out that I disagree with your summary of his ideas, track record, and motivations. I've learned some very useful things from his books and my earlier minor critique in no way means that I do not value his insights.
Well stated!

Hey, everyone. We have an incredibly knowledgeable forum member who has been quite handily beating the typical three-fund market portfolio over 15 years. No need for a cherry picked 5 year period when equities have gone almost straight up and value has been weak. Larry and Robert are factor investors. Factor investing works and Larry's principles can be used in any type of equity/bond allocation. I recall him saying on more than one occasion that younger colleagues are 90/10 or whatever. Here Robert T. shows how his 75/25 (heavily tilted) Portfolio has beaten a 100% equity market portfolio over 15 years. Not too shabby.

Tyler you should incorporate the Robert T. Portfolio in your work!
2003-2017: Annualized return (%) / Standard Deviation / Max calendar year loss (%) (2008)

9.0 / 18.8 / -42.2 = 100% MSCI All Cap World Stock Index
9.9 / 15.4 / -28.7 = Actual portfolio
9.9 / 15.3 / -29.1 = DFA Balanced portfolio*

*75% DFA Balanced Equity: 25% DFA Balanced Fixed Income. Had same return even though DFA Balanced Equity = 70:30 US:Intl, while my portfolio = 50:50 US:Intl.

Obviously no guarantees.
viewtopic.php?f=10&t=240477&p=3763518&h ... t#p3763426
Last edited by matjen on Sun May 20, 2018 8:26 pm, edited 1 time in total.
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Topic Author
longinvest
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### Re: Three-fund portfolio returns and variance drain

Before considering the opinion of an author, I look at his track record. The track record of Larry Swedroe is awful:
His track record is what it is. Others are free to ignore it. I won't.
Bogleheads investment philosophy | Lifelong Portfolio: 25% each of (domestic / international) stocks / (nominal / inflation-indexed) bonds | VCN/VXC/VLB/ZRR

Random Walker
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### Re: Three-fund portfolio returns and variance drain

Longinvest,
I think your critique of the above Larry recommendations is off base. Alternative histories can play out, and one goal of portfolio construction is to build a portfolio robust to different possible alternative histories playing out. CCF’s are a sort of portfolio insurance; you don’t necessarily write off insurance as a bad decision just because the risk didn’t show up. And with regard to the Larry Portfolio, it’s not an iron clad black and white portfolio. It’s a concept: increase tilt to the highest returning equity asset classes, diversify broadly internationally, and increase bond holdings. By looking at one short 5 year period when equity markets rose greatly, you are giving way to much weight to financial noise.

Dave

MIretired
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### Re: Three-fund portfolio returns and variance drain

The big mistake I keep making in logic (I've been attempting to deduce this) is that I assume stocks will always tend to go up. Well sometimes they go down or sideways for 10+ years, ie. 2000-2009.
So, it's the harmonic mean, not the exp mean, which I've tried to make it. So, like the S&P is still below the 200MA? So, I assume the arith. mean can be lower than the geomean when stocks are falling over time(2000-2009.)
And the Norstad chart and paper always still gives me a double take. It's hard to believe that reversion to the mean would not have a bigger affect on that compounding. It also must depend on the dates used, 'cause that thing must be very generalized. I'll try to absorb it again.

A big thing to me in all of this compounding is that what if you remove the compounding. And you get the actual growth/decaying of the equity market.

MIretired
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### Re: Three-fund portfolio returns and variance drain

I think a possible misconception of the Norstad chart is tat it is looking at probabilities 40 yrs out. It's like looking at the yield to cost 40 yrs out.

ETA: OK. I was reading the Norstad article. And true enough, I'm somewhat messed up with the time relationships. I'm probably more messed up with statistics. I have no/little training. A lot of it is something I read: if this is a word 'anti-intuitive.'

MIretired
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### Re: Three-fund portfolio returns and variance drain

Hey. I finally get this. I get the point. Lower volatility of returns results in higher compounded return. Period.

dbr
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### Re: Three-fund portfolio returns and variance drain

MIretired wrote:
Tue May 22, 2018 9:34 am
Hey. I finally get this. I get the point. Lower volatility of returns results in higher compounded return. Period.
Not forgetting "for the same expected return." A lot of people get confused about that and also there needs to be quantification showing how much can be gained how consistently.

ying_yang
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### Re: Three-fund portfolio returns and variance drain

longinvest wrote:
Sun May 20, 2018 2:04 pm
[*] The total bond market is less volatile than the total stock market because it contains a significant amount of short-term bonds (giving it an overall intermediate duration) and, therefore, can't fluctuate as much in value as stocks, thanks to mathematics.
Even if it didn't contain short term bonds, wouldn't it be less volatile?

Topic Author
longinvest
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### Re: Three-fund portfolio returns and variance drain

ying_yang wrote:
Tue May 22, 2018 9:48 am
longinvest wrote:
Sun May 20, 2018 2:04 pm
[*] The total bond market is less volatile than the total stock market because it contains a significant amount of short-term bonds (giving it an overall intermediate duration) and, therefore, can't fluctuate as much in value as stocks, thanks to mathematics.
Even if it didn't contain short term bonds, wouldn't it be less volatile?
That depends on average duration. From February 2008 to April 2018, Vanguard Extended Duration Treasury ETF (EDV, average duration 24.4 years) had a 22.74% standard deviation, higher than Vanguard Total Stock Market ETF (VTI) which had a 15.39% standard deviation. Source: Portfolio Visualizer.

It's important to consider average duration before investing into a bond fund.
Bogleheads investment philosophy | Lifelong Portfolio: 25% each of (domestic / international) stocks / (nominal / inflation-indexed) bonds | VCN/VXC/VLB/ZRR

Random Walker
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### Re: Three-fund portfolio returns and variance drain

dbr wrote:
Tue May 22, 2018 9:38 am
MIretired wrote:
Tue May 22, 2018 9:34 am
Hey. I finally get this. I get the point. Lower volatility of returns results in higher compounded return. Period.
Not forgetting "for the same expected return." A lot of people get confused about that and also there needs to be quantification showing how much can be gained how consistently.
An approximation of the volatility drag effect is Geo Mean = Ari Mean - 1/2 SD^2. So the difference in Geo Mean Of two portfolios with the same Ari Mean expected return and different volatilities would be Geo1-Geo2 = -1/2(SD1^2-SD2^2).
Keeping expected return (Ari Mean) constant, decreasing the SD of a portfolio from 15 to 11 would add about 0.5% to the expected Geo Mean of the Portfolio.
This can be done by diversifying across sources of return: increase international equity exposure, tilt heavily to size and value, add other factor exposures, increase bond allocation, add alternatives. Doing the above will definitely increase portfolio cost, but highly likely lessen volatility drag, which is a significant cost in its own right. And this is all just math, totally separate from behavioral issues related to big volatility and big drawdowns.

Dave

vineviz
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### Re: Three-fund portfolio returns and variance drain

longinvest wrote:
Tue May 22, 2018 10:03 am
ying_yang wrote:
Tue May 22, 2018 9:48 am
Even if it didn't contain short term bonds, wouldn't it be less volatile?
That depends on average duration. From February 2008 to April 2018, Vanguard Extended Duration Treasury ETF (EDV, average duration 24.4 years) had a 22.74% standard deviation, higher than Vanguard Total Stock Market ETF (VTI) which had a 15.39% standard deviation. Source: Portfolio Visualizer.

It's important to consider average duration before investing into a bond fund.
It's a whole other topic, but I'll just add that bonds aren't the only assets for which a duration can be calculated. It is possible to estimate the duration of an equity portfolio as well. This was a much more common topic of discussion when I first started investing than it is now, but it can help understand how asset class behaviors are related.

https://www.ipe.com/equity-duration-how ... ullarticle

The first-order approximation of equity duration is the price/dividend ratio (i.e. the inverse of the dividend yield). Right now the implied duration of the S&P500 index is about 38 years.
"Far more money has been lost by investors preparing for corrections than has been lost in corrections themselves." ~~ Peter Lynch

Northern Flicker
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### Re: Three-fund portfolio returns and variance drain

The expected return of an investment is an estimate of an arithmetic mean return.
This is overloading the term arithmetic mean, and also has it backwards (sample means are estimates of the expected values of the random variable being sampled). The expected return of an investment over the holding period is the average or mean of all possible future outcomes weighted by their probability. That is, it is the mean of the random variable defined as future return over some prescribed period. There is no reason to believe it is the most likely outcome, or what an investor should expect to happen, as is often misconstrued when the word “expected” is interpreted in a non-technical way by non-mathematicians, as is all too common in writings by investment professionals. “Lottery ticket” stocks like penny stocks are an extreme example of where the likelihood of earning the expected return is very low. Combining the two interpretations of “expected” in one sentence: it would be unexpected to earn the expected return for such a stock.

The purpose of CAGR or geometric/compound mean is to rescale the investment period. If you are looking at an expected or actual 10-year return and want to rescale it to a 1-year Return that you would earn over the 10 years, that is how to do it.

The expected value of the random variable of future returns (expected return) may be estimated statistically by computing an arithmetic average of actual returns from a random sample of historical returns. If you compute the average of 1-year returns then you are estimating future expected 1-year returns even if you use a sample of 50 years of returns. If you are trying to estimate expected 20-year returns then you need a sample where each data point in the sample is a 20-year period in which return is determined.

Suggesting the use of arithmetic mean instead of compound mean to estimate average return is really conflating the two activities (rescaling the time period of return and estimating future expected returns with historical sample statistics).

dbr
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### Re: Three-fund portfolio returns and variance drain

jalbert wrote:
Tue May 22, 2018 1:36 pm
The expected return of an investment is an estimate of an arithmetic mean return.
This is overloading the term arithmetic mean, and also has it backwards (sample means are estimates of the expected values of the random variable being sampled). The expected return of an investment over the holding period is the average or mean of all possible future outcomes weighted by their probability. That is, it is the mean of the random variable defined as future return over some prescribed period. There is no reason to believe it is the most likely outcome, or what an investor should expect to happen, as is often misconstrued when the word “expected” is interpreted in a non-technical way by non-mathematicians, as is all too common in writings by investment professionals. “Lottery ticket” stocks like penny stocks are an extreme example of where the likelihood of earning the expected return is very low. Combining the two interpretations of “expected” in one sentence: it would be unexpected to earn the expected return for such a stock.

The purpose of CAGR or geometric/compound mean is to rescale the investment period. If you are looking at an expected or actual 10-year return and want to rescale it to a 1-year Return that you would earn over the 10 years, that is how to do it.

The expected value of the random variable of future returns (expected return) may be estimated statistically by computing an arithmetic average of actual returns from a random sample of historical returns. If you compute the average of 1-year returns then you are estimating future expected 1-year returns even if you use a sample of 50 years of returns. If you are trying to estimate expected 20-year returns then you need a sample where each data point in the sample is a 20-year period in which return is determined.

Suggesting the use of arithmetic mean instead of compound mean to estimate average return is really conflating the two activities (rescaling the time period of return and estimating future expected returns with historical sample statistics).
Yes, in some cases what may be missing from the picture is the concept of a distribution of possible annual returns from which the return in a given year is a random sample. To characterize that distribution we want to estimate the mean and whatever additional parameters are needed to characterize it. We do that by taking returns in a set of years as a sample of the distribution. The sample average is an estimate of the mean of the return distribution. After all that a completely different problem is estimating the properties of the distribution of outcomes derived from compounding annual returns over some number of periods. Note, by the way, that geometric average and compound annual growth rate are different averages though for investments usually nearly the same in value. For example, see here: https://en.wikipedia.org/wiki/Generalized_mean. I forget the name if goes by but a general concept of mean of a data set is the number R with respect to a function F of the data points (R1, . . . ,Rn) such that F(R, . . . ,R) = F(R1, . . . ,Rn). If F is the sum, the mean is arithmetic mean, if F is the sum of the logs of the data, the mean is the geometric mean, if F is the sum of the inverses of the data, the mean is the harmonic mean, if F is 100*(the geometric mean of the set (1+Ri/100) - 1, where Ri are returns in %, then the mean is the compound average growth rate, and so on.

Northern Flicker
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### Re: Three-fund portfolio returns and variance drain

Yes, it also is a significant problem that non-random samples are used when estimating sample means of historical investment samples.

MIretired
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### Re: Three-fund portfolio returns and variance drain

Random Walker wrote:
Tue May 22, 2018 11:40 am
dbr wrote:
Tue May 22, 2018 9:38 am
MIretired wrote:
Tue May 22, 2018 9:34 am
Hey. I finally get this. I get the point. Lower volatility of returns results in higher compounded return. Period.
Not forgetting "for the same expected return." A lot of people get confused about that and also there needs to be quantification showing how much can be gained how consistently.
An approximation of the volatility drag effect is Geo Mean = Ari Mean - 1/2 SD^2. So the difference in Geo Mean Of two portfolios with the same Ari Mean expected return and different volatilities would be Geo1-Geo2 = -1/2(SD1^2-SD2^2).
Keeping expected return (Ari Mean) constant, decreasing the SD of a portfolio from 15 to 11 would add about 0.5% to the expected Geo Mean of the Portfolio.
This can be done by diversifying across sources of return: increase international equity exposure, tilt heavily to size and value, add other factor exposures, increase bond allocation, add alternatives. Doing the above will definitely increase portfolio cost, but highly likely lessen volatility drag, which is a significant cost in its own right. And this is all just math, totally separate from behavioral issues related to big volatility and big drawdowns.

Dave
I'm going to agree with others about expected return. Arithmetic means of two portfolios happening to be equal is a rare happening in the real world--you'd have to time it just right.