Do you think about volatility drag on your portfolio?

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Random Walker
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Do you think about volatility drag on your portfolio?

Post by Random Walker » Wed Sep 07, 2016 6:47 pm

When it came to me diving into the world of tilting / diversifying across risk factors, a big reason for me was volatility drag. The geometric mean (annualized) return of a portfolio is always less than the average annual return. This gap is caused by volatility, and the greater the volatility the greater the gap. An extreme example is gaining 100% one year and losing 50% the next year. The average return is 25%, but the annualized return (what really counts) is 0%.

Geometric return = Mean return - (0.5 X Variance)

Seems to me a strong reason to diversify across sources of return that are weakly correlated is to minimize the volatility drag. Of course this diversification comes at a cost. Is the cost worth it? I ultimately decided yes based more on faith than knowledge. Interested in what others think.

One of my favorite short reads on power of multi asset class investing is by Gibson:

http://www.amcham-shanghai.org/amchampo ... esting.pdf
(Specifically exhibits 5&6)

And here is a site that shows good examples of volatility drag. I disagree with its conclusions at the end about how to invest, but the explanation of volatility drag is clear.

http://www.investinganswers.com/educati ... umber-1996

I'm curious what others think.

Dave

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patrick013
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Re: Do you think about volatility drag on your portfolio?

Post by patrick013 » Wed Sep 07, 2016 6:57 pm

Random Walker wrote:
I'm curious what others think.



I didn't dissolve the whole thing but my usual comment is
"unconvincing" and secondarily "distracting".
age in bonds, buy-and-hold, 10 year business cycle

Random Walker
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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Wed Sep 07, 2016 7:11 pm

Patrick13,
Strongly recommend you read Gibson's short paper. Also Larry's short 3 page essay: Effective Diversification in a 3 Factor World.
These short reads are some of the very most productive investment reading I have done. Here's the link to Larry's article.

http://thebamalliance.com/pdfs/Effectiv ... wedroe.pdf

When we talk about more efficient portfolios, portfolios with higher Sharpe ratios, I believe we are talking about minimizing volatility drag.

Dave

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patrick013
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Re: Do you think about volatility drag on your portfolio?

Post by patrick013 » Wed Sep 07, 2016 7:16 pm

Random Walker wrote:Patrick13,
Strongly recommend you read Gibson's short paper. Also Larry's short 3 page essay: Effective Diversification in a 3 Factor World.
These short reads are some of the very most productive investment reading I have done. Here's the link to Larry's article.

http://thebamalliance.com/pdfs/Effectiv ... wedroe.pdf

When we talk about more efficient portfolios, portfolios with higher Sharpe ratios, I believe we are talking about minimizing volatility drag.

Dave


I think they're nuts. I flock to trends not particularly
obsolete and minimally correlated data. Learned not to.
age in bonds, buy-and-hold, 10 year business cycle

larryswedroe
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Re: Do you think about volatility drag on your portfolio?

Post by larryswedroe » Wed Sep 07, 2016 7:32 pm

Dave
The research is very clear that diversifying across factors with low correlations and premiums has delivered superior risk-adjusted performance. And reducing tail risk.
The paper by Antti Illmanen and Jared Kizer which appeared in the Journal of Portfolio Management, The Death of Diversification Has Been Greatly Exaggerated, presented the evidence. It won the Journal's best paper of the year.
Larry

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Re: Do you think about volatility drag on your portfolio?

Post by kolea » Wed Sep 07, 2016 8:41 pm

Random Walker wrote:When it came to me diving into the world of tilting / diversifying across risk factors, a big reason for me was volatility drag. The geometric mean (annualized) return of a portfolio is always less than the average annual return. This gap is caused by volatility, and the greater the volatility the greater the gap. An extreme example is gaining 100% one year and losing 50% the next year. The average return is 25%, but the annualized return (what really counts) is 0%.


The problem is using annual averages to estimate an average over an extended period - the two are not the same when there is a variance to the mean. If you want to know the 10-year performance for an asset, use the 10-year mean, not the 1-year mean. The formula you cited is only correct for normally distributed data (which is not the case for equities), so subtracting one half the variance is not going to give the right answer anyway. But you are right that diversification is the way to lessen volatility, which will bring the 1-year mean closer to the mean over multiple years.

As to the title question - I do not think about volatility drag, perhaps because I don't pay attention to annual return data very much. The annual returns are out of my control, I cannot do anything about them. But I do think about diversification and try to make sure I am well diversified. But I always thought that any portfolio that is not TSM, such as a portfolio that is "diversified across factors", is a narrow, not diverse portfolio. I always thought TSM was the maximally diverse equities portfolio.
Kolea (pron. ko-lay-uh). Golden plover.

Random Walker
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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Wed Sep 07, 2016 8:59 pm

Kolea,
As I expect you've read, TSM is really only exposed to one risk factor, beta. Do you still believe it's maximally diverse? What matters is the behavior of the portfolio as a whole, and the potential additional benefit of an asset class to a portfolio depends on its expected returns, volatility, correlations to other portfolio components, and of course COSTS.

Dave

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Re: Do you think about volatility drag on your portfolio?

Post by lack_ey » Wed Sep 07, 2016 9:04 pm

kolea wrote:As to the title question - I do not think about volatility drag, perhaps because I don't pay attention to annual return data very much. The annual returns are out of my control, I cannot do anything about them. But I do think about diversification and try to make sure I am well diversified. But I always thought that any portfolio that is not TSM, such as a portfolio that is "diversified across factors", is a narrow, not diverse portfolio. I always thought TSM was the maximally diverse equities portfolio.

TSM is maximally diverse in terms of not overweighting anything, but it doesn't particularly seem special empirically. It's not actually minimum risk or best risk/return or anythiing like that.

Also, if your asset allocation consists of more than just stocks, you have to consider how pieces fit together. An optimal all-stock allocation may not be the best possible portfolio to use as the stock component of a multi-asset allocation, for all levels of potential risk or return being targeted.

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Tyler9000
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Re: Do you think about volatility drag on your portfolio?

Post by Tyler9000 » Wed Sep 07, 2016 9:20 pm

Random Walker wrote:I'm curious what others think.


Good topic!

Too many people dismiss volatility simply as an emotional issue to be ignored, but you're absolutely correct to also note that it has a measurable effect on your bottom line. I wrote this about a year ago right after the market took a quick dive, but the overall message about the difference between average return and CAGR is as important today as it was then.

I'll also point out that the effects of volatility and diversification are very underappreciated in retirement portfolios as well. Mix drawdowns into the equation, and volatility can really do a number on SWRs to the point where a portfolio with lower average returns can counter-intuitively be a much safer retirement choice in the long run.

Hope that helps!

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nedsaid
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Re: Do you think about volatility drag on your portfolio?

Post by nedsaid » Wed Sep 07, 2016 9:34 pm

I have never thought about volatility drag. I have known for a long time that if your investment falls one year by 50%, to break even you by the end of the next year you need a gain from there of 100%. To say that the average annual return is 25% when actually your return over two years is zero is just an incorrect concept, a meaningless phrase. Average annual return means nothing because the base from which each year's return is calculated keeps changing. What you should be concerned about is the actual growth of your portfolio with the baseline being your original investment plus any additional investments you have made. The important number is the Compound Annual Growth Rate.

The stock market goes up and goes down and doesn't care if I am concerned about volatility drag or not. The stock market just is and the stock market does what the stock market does regardless of how I feel about it. I just know that the market can have violent bursts of volatility either on the way up or the way down.

The way I think about it is that the market in the long run will 100% reflect economic reality. If the US economy and corporate earnings grow over time, so should the US stock market. In the short run, the market will do whatever the heck it wants to do regardless of economic reality. Over longer periods of time, the market will revert to valuations that are supported by actual corporate earnings and actual economic performance.

In theory, you should be able to cut "volatility drag" by investing in non-correlating volatile asset classes that have similar positive returns over time. Small vs. Large, Value vs. Growth, US vs International, stocks vs. real estate investment trusts, etc. During the 2000-2002 bear market, this worked pretty good. Small outperformed Large, Value outperformed Growth which was good as the previous bull market was a Large Growth bull. During the 2008-2009 bear market, all these asset classes fell and fell hard. Small was hit hard, Large was hit hard, Value was hit hard, Growth was hit hard, US was hit hard, REITS were hit hard, and International was hit hard. Most bonds also fell but not as hard as stocks, TIPS and Corporates were down 10% or more. Only nominal Treasuries and certain Government Agency bonds had the diversification effects investors wanted.

So pretty much, asset classes don't always act as expected and markets will do what markets will do. Bonds might lessen volatility but over longer periods of time will put a performance drag on an otherwise 100% equities portfolio. If you wanted to just maximize return, you would go 100% equities. Strategies to minimize volatility drag with "non-correlating" volatile asset classes sometimes doesn't work, in bad markets such volatile asset classes will tend to correlate and correlate on the way down. If you reduce volatility with bonds, my suspicion is that the long term performance drag caused by the bonds will outweigh whatever mythical volatility drag that might exist.

It seems like volatility drag is simply a product of incorrect thinking and not a real phenomenon. Probably a better concept is the sequence of returns problem which is a better concept and a real problem, particularly for retirees and near retirees.
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Random Walker
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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Wed Sep 07, 2016 9:40 pm

Tyler,
What you described was the surprising finding for me when I had a Monte Carlo simulation performed. Although a higher equity allocation will yield a higher mean terminal value, a lower equity allocation may have higher likelihood of yielding a result where one does not outlive their money.

Dave

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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Wed Sep 07, 2016 9:51 pm

NedSaid,
Isn't the sequence of returns risk just an example of the volatility drag issue on steroids? I think the improved efficiency of diversification across sources of return is amplified during withdrawal phase.

Dave

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Re: Do you think about volatility drag on your portfolio?

Post by kolea » Wed Sep 07, 2016 9:59 pm

Random Walker wrote:Kolea,
As I expect you've read, TSM is really only exposed to one risk factor, beta. Do you still believe it's maximally diverse? What matters is the behavior of the portfolio as a whole, and the potential additional benefit of an asset class to a portfolio depends on its expected returns, volatility, correlations to other portfolio components, and of course COSTS.

Dave


TSM is exposed to all risk factors since it contains all stocks, yes? Perhaps it is not weighted to gain maximum exposure to certain risk factors but it is not clear to me that constitutes better diversification. Are you saying that a portfolio that is optimized for factors will have a lower variance?

I agree that the total portfolio needs to be considered, but if so, your formula for drag needs to be modified to contain terms for the covariance drag from correlated (or with correlations less than unity) asset classes.
Kolea (pron. ko-lay-uh). Golden plover.

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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Wed Sep 07, 2016 10:12 pm

Kolea,
NO! TSM has all stocks but it has no net exposure to the risk factors of size and price. The exposure to small is exactly offset by the exposure to large and the exposure to value is exactly offset by the exposure to growth. Size and value are weakly or non correlated to market and to each other. So net exposure to those factors in a portfolio increases portfolio efficiency compared to a TSM portfolio that has net exposure to only one factor, the market.
Portfolio exposed to multiple factors may or may not have higher variance, but it will have greater expected return per unit variance: it will be more efficient.

Dave

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Re: Do you think about volatility drag on your portfolio?

Post by Theoretical » Wed Sep 07, 2016 10:14 pm

kolea wrote:
Random Walker wrote:Kolea,
As I expect you've read, TSM is really only exposed to one risk factor, beta. Do you still believe it's maximally diverse? What matters is the behavior of the portfolio as a whole, and the potential additional benefit of an asset class to a portfolio depends on its expected returns, volatility, correlations to other portfolio components, and of course COSTS.

Dave


TSM is exposed to all risk factors since it contains all stocks, yes? Perhaps it is not weighted to gain maximum exposure to certain risk factors but it is not clear to me that constitutes better diversification. Are you saying that a portfolio that is optimized for factors will have a lower variance?

I agree that the total portfolio needs to be considered, but if so, your formula for drag needs to be modified to contain terms for the covariance drag from correlated (or with correlations less than unity) asset classes.


Actually it would not contain the risk factors because the short side of the factors are also active presences in the portfolio. Meaning that the large stocks offset the smalls, the growths the values, etc.. Or more accurately, it contains the factors, but they're inherently offsetting, since whenever a factor is firing, it's "counterbet"/short-side is failing, mostly offsetting the gain. Further, there's an argument to be made that a total cap weighted market leads to an unintentional large growth tilt.

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Re: Do you think about volatility drag on your portfolio?

Post by nedsaid » Wed Sep 07, 2016 10:16 pm

Random Walker wrote:NedSaid,
Isn't the sequence of returns risk just an example of the volatility drag issue on steroids? I think the improved efficiency of diversification across sources of return is amplified during withdrawal phase.

Dave


The problem I have with volatility drag is that it is simply an observation that markets are volatile. To just say that you cure it by "not losing money", as Buffett says is just a non-starter. How many investors have 100% avoided volatility occurring at the wrong time? My suspicion is zero, including Mr. Buffett. Volatility drag is just a way of saying, "Gosh darn it, why don't investments go up in a predictable straight line? It would be so much easier to do life planning if my investments were predictable."

My other point is that the fix of diversification often works but not always. Bonds dampen volatility but at the price of return. Again, the drag on return from adding bonds is over time greater than any volatility drag on an otherwise 100% equity portfolio.

What sequence of returns says is that even if we know the future Compounded Annual Growth Rate that we don't know the distribution of those returns. The risk is that the negative returns could happen at the worst possible time for an investor.

The problem with the volatility drag concept is that markets can be volatile on the way up and volatile on the way down. No one complains about volatility drag when volatility is on the way up!
We also know that up to a certain point that risk and volatility increase returns. If volatility drag was such a huge problem, shouldn't we be advocating for 100% bond portfolios? I just believe that volatility drag is an incorrect way of looking at the markets and an incorrect concept in general.
A fool and his money are good for business.

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Re: Do you think about volatility drag on your portfolio?

Post by njboater74 » Wed Sep 07, 2016 10:46 pm

Volatility Drag and Sequence Risk are slightly different. Sequence of Return risk implies that volatility only has a negative impact because withdrawals will have to be made during drawdowns. Volatility Drag implies that the volatility will have a permanent negative impact on CAGR, period.

It's a very good question though. Is volatility a real issue during accumulation, or just during distribution?

Consider the effect of owning Long Term Treasuries between 2006 and 2015.
- A 100% stock (VTSAX) portfolio had a CAGR of 7.51%
- A 100% long term treasuries (VUSUX) portfolio had a CAGR of 6.60%
- An 80/20 portfolio of VTSAX/VUSUX has a CAGR of 8.11%
- An 80/20 portfolio of VTSAX/VBMFX (Total Bond Market) had a CAGR of 7.29%

How could a mixed portfolio have a better return than any of the underlying assets? It has to be volatility. Since both assets were uncorrelated, they rose and fell at different times, minimizing drawdown to the overall portfolio and creating rebalancing opportunities.

The 80/20 mix predictably fell in between the return ranges of the two assets. I attribute this to the corporates inside of TBM. They are too closely correlated to stocks. That's not necessarily a bad thing, unless you have volatility.

I'm not suggesting that you trade in total bond market funds for long term treasuries, but you can see the permanent effect of volatilty in certain circumstances. It just doesn't manifest when using TBM because it is not as uncorrelated as Treasuries.
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nedsaid
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Re: Do you think about volatility drag on your portfolio?

Post by nedsaid » Thu Sep 08, 2016 12:10 am

njboater74 wrote:Volatility Drag and Sequence Risk are slightly different. Sequence of Return risk implies that volatility only has a negative impact because withdrawals will have to be made during drawdowns. Volatility Drag implies that the volatility will have a permanent negative impact on CAGR, period.

Nedsaid: I am saying that volatility drag isn't a drag at all, it is only seen at certain vantage points. No one complains about volatility when that volatility is on the up side. Given long enough time periods, whatever volatility drag that existed should disappear. I don't believe that volatility drag is permanent, you just see it if you peek at certain times.

It's a very good question though. Is volatility a real issue during accumulation, or just during distribution?

Nedsaid: It is an issue during both accumulation and distribution. Your risks upon distribution are higher because your human capital is exhausted and your life expectancy gets shorter and shorter giving you less and less time to recover from a bad market. Time and new monies for investment won't bail you out.

Consider the effect of owning Long Term Treasuries between 2006 and 2015.
- A 100% stock (VTSAX) portfolio had a CAGR of 7.51%
- A 100% long term treasuries (VUSUX) portfolio had a CAGR of 6.60%
- An 80/20 portfolio of VTSAX/VUSUX has a CAGR of 8.11%
- An 80/20 portfolio of VTSAX/VBMFX (Total Bond Market) had a CAGR of 7.29%

How could a mixed portfolio have a better return than any of the underlying assets? It has to be volatility. Since both assets were uncorrelated, they rose and fell at different times, minimizing drawdown to the overall portfolio and creating rebalancing opportunities.

Nedsaid: Yes, that is the theory and it should work most of the time. But what happens when these uncorrelated assets fall at the same time? I suspect the 1970's and stagflation would have been hard both on stocks and long term treasuries particularly as Paul Volker, Fed Chairman at the time, hiked interest rates in the late 1970s. In other words, "non-correlating assets" don't always non-correlate.

The 80/20 mix predictably fell in between the return ranges of the two assets. I attribute this to the corporates inside of TBM. They are too closely correlated to stocks. That's not necessarily a bad thing, unless you have volatility.

I'm not suggesting that you trade in total bond market funds for long term treasuries, but you can see the permanent effect of volatilty in certain circumstances. It just doesn't manifest when using TBM because it is not as uncorrelated as Treasuries.


Nedsaid: I guess what you are showing is a volatility premium and not a drag. Long term treasuries are more volatile than Total Bond Market and gave you more return. Stocks by themselves should be more volatile and give more return than even Long Treasuries. More risk and more volatility up to a point equals more return.

When you combined Stocks with LT Treasuries, you got a higher return than from stocks themselves, and I suppose you could cite that is evidence of what happens when you lessen volatility drag. I would concede that this strategy would work most of the time but counter that this doesn't work all of the time. But you can see here why such folks like Ray Dalio like to combine Stocks with Long Term Treasuries as the great majority of time these asset classes are not correlated.

The key is that you say, "You can see the permanent effect of volatility in certain circumstances." If a permanent effect requires certain circumstances then I would argue that the effect isn't permanent.
A fool and his money are good for business.

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Re: Do you think about volatility drag on your portfolio?

Post by lapuce » Thu Sep 08, 2016 12:15 am

The geometric mean of (non-negative) numbers is less than their arithmetic mean, but I cannot figure out the formula in the OP. Kolea mentions it to be correct for normally distributed data. Is there a reference for that (or a trivial computation that eludes me now)? In any event, I don't know what meaning to attach to the arithmetic mean of the returns in the first place. The total return is what it is and the geometric mean is just a way to express it in whatever unit of time I choose (such as annualized in the example). But what is the arithmetic mean? We cannot reconstruct the total return from it. It depends arbitrarily on the underlying unit of time used to compute it. Even if yearly returns were uniform, choosing returns over a smaller time period, such as quarters, would fabricate "volatility gap".

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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Thu Sep 08, 2016 12:24 am

Nedsaid,
Let's consider two portfolios with the same expected return. The first portfolio is say 80/20 TSM/TBM. The second portfolio is diversified across equity asset classes with same and higher expected return than TSM and the % bonds is increased to keep the expected return same as our TSM/TBM 80/20 portfolio. Perhaps this portfolio is 60% equity / 40% bonds. Every year the two portfolios will have the same expected return. But the dispersion of returns for the more diversified portfolio will be lower and the CAGR will be closer to the weighted mean average of the portfolio components than the 80/20 CAGR will be to its weighted mean of portfolio components. So yes, bonds will decrease expected return, but we can use more risky equity asset classes to make up the difference in expected returns of the portfolio.
Really hope people will read Gibson's essay I referenced above and comment on it.

Dave

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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Thu Sep 08, 2016 12:35 am

Lapuce,
I'm not super strong on math and stats. I think the equation I stated above is an approximation from some much more serious math. I saw it in Andrew Ang's Asset Management: A Systematic Approach to Factor Investing p.145-146. Need to read footnotes at bottom too.

Dave

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Re: Do you think about volatility drag on your portfolio?

Post by nedsaid » Thu Sep 08, 2016 12:37 am

If you want to avoid the effects of a volatility drag, you have to keep in mind two basic concepts that all investors should understand. The two concepts are valuation and quality. What I am saying is that valuations matter and quality matters.

I am not worried about volatility if I have confidence that the depressed prices of my assets will bounce back and at some point will be even higher than the previous high. This is where quality comes in. Quality stocks should bounce back. The hope is that quality stocks will bounce back in a timely fashion. Sort of like the illustration of tennis balls and chicken eggs. Tennis balls will bounce back and chicken eggs will splatter.

We saw this in the bear market that followed the high tech and internet mania of the 1990's. A lot of stocks never recovered and indeed some of them don't even exist today. Low quality companies that were bid up to the stratosphere with investor enthusiasm that became a buying panic or a mania crashed very, very hard. Many were down 70, 80, 90, or even 100%. Many of the high tech and internet companies that survived never recovered to their former highs. This would be a case of permanent volatility drag. You pretty much had splattered eggs. Many of those that didn't splatter didn't bounce back very high.

Valuation is important as you can overpay even for quality companies. In most cases, even when you overpay, quality should rebound to new highs but it might take a very long time. I think of my "Four Horsemen of Underperformance": GE, Microsoft, Pfizer, and AIG. These were highly admired and highly priced darlings from the 1990's that I bought at lower prices during the 2000's but they were still overpriced when I bought them. I estimate my annual return from GE is less than 1% a year, probably 4% for Pfizer (mostly from dividends), and a respectable 8% from Microsoft. The lion's share of my Microsoft returns came during the last three years out of the 10 years I have owned the stock. I lost over 90% on AIG in the 2008-2009 crash so I would hate to think what my CAGR would be for that.

During the 2000-2002 and the 2008-2009 bear markets, quality stocks bounced back each time after 50% plus losses. If you look at the time period from 2000-2012, you might say that it took twelve years to bounce back to new highs.

Even markets as a whole can be overpriced, from 2000 through 2012, the US Stock Market was flat and any returns came from dividends. It took the averages twelve years or more for the averages to hit new highs. A 60% stocks/40% bonds balanced portfolio would have done better than 100% stocks but I see that as a result of a bad decade plus for stocks. No one complained about the returns of stocks in the 1980's and 1990's as being too high, those two decades saw a volatility premium but a volatility drag during the 2000's. Hard for me to argue that a volatility drag would have permanent effects any more than a volatility premium. All depends on when you look.
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Re: Do you think about volatility drag on your portfolio?

Post by nedsaid » Thu Sep 08, 2016 12:46 am

Random Walker wrote:Nedsaid,
Let's consider two portfolios with the same expected return. The first portfolio is say 80/20 TSM/TBM. The second portfolio is diversified across equity asset classes with same and higher expected return than TSM and the % bonds is increased to keep the expected return same as our TSM/TBM 80/20 portfolio. Perhaps this portfolio is 60% equity / 40% bonds. Every year the two portfolios will have the same expected return. But the dispersion of returns for the more diversified portfolio will be lower and the CAGR will be closer to the weighted mean average of the portfolio components than the 80/20 CAGR will be to its weighted mean of portfolio components. So yes, bonds will decrease expected return, but we can use more risky equity asset classes to make up the difference in expected returns of the portfolio.

Really hope people will read Gibson's essay I referenced above and comment on it.

Dave


Dave, what you say makes perfect sense. I am a slicer and dicer and attempt to diversify across factors as Larry Swedroe suggests. Your scenario above makes sense and I don't disagree with you except to say that in times of crisis, asset classes don't act as expected. The diversifiers that worked in the 2000-2002 bear market didn't work during the 2008-2009 bear market. What should work according to portfolio theory and the best thinking of market experts just don't always work in real life. It isn't that people are stupid, it is that markets are so unpredictable. The only asset classes that worked across both bear markets were nominal treasuries (any duration would have worked but longer would have worked better) and certain government agency bonds. That's it.
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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Thu Sep 08, 2016 1:02 am

Nedsaid,
I'm sure you'd agree that we need to expect that in times of crisis correlations go to 1. That's where highest quality and short duration fixed income help most. We expect correlations to vary over time too.

Dave

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Re: Do you think about volatility drag on your portfolio?

Post by daveydoo » Thu Sep 08, 2016 1:32 am

lapuce wrote:The geometric mean of (non-negative) numbers is less than their arithmetic mean, but I cannot figure out the formula in the OP. .


I think this is an enormous factor and one I underappreciated for a long time. Yes, the arithmetic mean of the annual returns is not the same as the compounded return, as many have pointed out. I suppose you could just use the nth root of the ratio of the final value to the initial value, where n = the number of years. I was thinking of doing this for M* data where the ten-year total return (with dividend and CG reinvestment) is always shown from a baseline of $10,000. The "average" annual return is very unhelpful.

This point about the crippling effect of volatility was driven home in a 2005 (?) book by Easterling that was recommended to me. A family member's advisor mentioned it and I confess I was kinda calling his bluff at first. I don't think the author's a BH so I can say it's not a great book, and I haven't even gotten to the back half where (I believe) he tells you his "system" for beating volatility. But he does point out that ~ 70% of calendar years end with a > 10% increase or > 10% decrease in stock prices so the opportunities for volatility drag are pervasive. I had always shrugged at volatility or had a limited "sequence-of-returns" fear vis-a-vis retirement only, but this really made me want to stabilize things to a greater degree.

As an aside, he also employs a scare tactic where he points out all the 20-year intervals over the past century where no money was made in the stock market; however, he fails to account for dividend reinvestment (arguing for a non-BH audience that fees alone would negate that 2% annual increment). He also fails to account for the remarkable effect of dollar-cost averaging across each of those non-productive 20-year intervals, as most of us do in our earning years; I don't plan to get rich from from asset appreciation during retirement.

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Re: Do you think about volatility drag on your portfolio?

Post by grayfox » Thu Sep 08, 2016 2:49 am

Random Walker wrote:When it came to me diving into the world of tilting / diversifying across risk factors, a big reason for me was volatility drag. The geometric mean (annualized) return of a portfolio is always less than the average annual return. This gap is caused by volatility, and the greater the volatility the greater the gap. An extreme example is gaining 100% one year and losing 50% the next year. The average return is 25%, but the annualized return (what really counts) is 0%.

Geometric return = Mean return - (0.5 X Variance)



I don't no what to make of Volatility Drag. It seems like a numerical curiosity. It's just something that comes out of the calculation of two different statistics, Arithmetic Mean and Geometric Mean. It's kind of like to convert from Celsius to Kelvin, add 273.15. To get from Arithmetic Mean to Geometric Mean, subtract half the variance. (I don't think that is an iron-clad formula, just an approximation under certain conditions.)

One thing that I know is relevant is Total Return over the holding period. If you put $10,000 in VTSMX and after 20 years it is worth $40,000, TR = (P1-P0)/P0 = 3, regardless of the path that got there. Give me the one that gets the highest TR. Does variance matter. Yes, but variance of 20-year TR, not annual volatility.

E.g. A is a CD and goes up exactly 5% every year. No volatility. After 20 years it is $26,533
B is a stock and it price goes up and down. Very volatile. In year 19 it's worth $80,000. The it falls 50% and ends year 20 at $40,000.
B wins.

As kola said, are annual statistics relevant for a 20-year investment? And why annual? Why not average monthly return, average daily return or average 18-month return?

Now as Ned said, if you are making annual withdrawals from a portfolio, then annual TR each year is relevant, but never the average annual return.
Last edited by grayfox on Thu Sep 08, 2016 3:21 am, edited 2 times in total.
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Re: Do you think about volatility drag on your portfolio?

Post by grayfox » Thu Sep 08, 2016 3:02 am

On the other hand, if you feel annual volatility is important (say you are withdrawing 4% of value of the fund at the end of each year), why not minimize annual volatility with Vanguard Global Minimum Volatility Fund Admiral Shares (VMNVX). That tries to find the portfolio on the very tip of the Markowitz bullet.

That would make more sense than trying to reduce volatility by tilting to more volatile funds like small-cap or emerging market.
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Re: Do you think about volatility drag on your portfolio?

Post by JoMoney » Thu Sep 08, 2016 5:04 am

Theoretical wrote:
kolea wrote:
Random Walker wrote:Kolea,
As I expect you've read, TSM is really only exposed to one risk factor, beta. Do you still believe it's maximally diverse? What matters is the behavior of the portfolio as a whole, and the potential additional benefit of an asset class to a portfolio depends on its expected returns, volatility, correlations to other portfolio components, and of course COSTS.

Dave


TSM is exposed to all risk factors since it contains all stocks, yes? Perhaps it is not weighted to gain maximum exposure to certain risk factors but it is not clear to me that constitutes better diversification. Are you saying that a portfolio that is optimized for factors will have a lower variance?

I agree that the total portfolio needs to be considered, but if so, your formula for drag needs to be modified to contain terms for the covariance drag from correlated (or with correlations less than unity) asset classes.


Actually it would not contain the risk factors because the short side of the factors are also active presences in the portfolio. Meaning that the large stocks offset the smalls, the growths the values, etc.. Or more accurately, it contains the factors, but they're inherently offsetting, since whenever a factor is firing, it's "counterbet"/short-side is failing, mostly offsetting the gain. Further, there's an argument to be made that a total cap weighted market leads to an unintentional large growth tilt.

From what I keep hearing about in these theoretical "risk premium" schemes for investing, it sounds like double speak.
The proponents claim that these are "risk factors" representing real unique risks, and some people choose to load up on that risk... then they want to claim that a portfolio that doesn't bear that risk isn't diversified enough because it doesn't bear the risk? The reason for diversifying is to reduce risk, TSM doesn't bear those other "risks" so it doesn't need to diversify into a more risky portfolio. It sounds to me like the factor portfolios aren't measuring the risk of their portfolios properly if they really believe these factors represent risk :confused
Any way around it... I don't think I buy into most of the "risk premium" argument to begin with. Most of it looks to me like performance chasing for people who put too much faith in the EMH.
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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Thu Sep 08, 2016 7:29 am

Two portfolios can have the same expected return. One may be a TSM/TBM type portfolio. The other may be tilted to factors with increased expected returns on the equity side but have bigger dose of safer bonds. The second portfolio would be more diversified according to drivers of return.

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Re: Do you think about volatility drag on your portfolio?

Post by larryswedroe » Thu Sep 08, 2016 8:13 am

fwiw, the big issue is not only volatility "drag" but the fact that volatility leads to investor mistakes, abandoning of even well thought out plans, panicked selling to avoid even worse losses, losses that could not be tolerated. Thus if you can cut tail risk it helps to reduce the behavioral errors, let alone reduce the risk of the black swans that can be very long term in duration (see Japan since 1990). So if can reduce volatility without reducing expected returns all investors should prefer than as have less risk without less returns. At least historically portfolios that have been more of "risk parity", diversifying across factors have produced more efficient portfolios.
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Re: Do you think about volatility drag on your portfolio?

Post by njboater74 » Thu Sep 08, 2016 8:25 am

nedsaid wrote:The key is that you say, "You can see the permanent effect of volatility in certain circumstances." If a permanent effect requires certain circumstances then I would argue that the effect isn't permanent.[/color]

I think we're mostly in agreement on this. Although I should have clarified that the 'certain circumstances' i was referring to was the non-correlated assets being together in a portfolio, not certain market conditions. I do believe that the effect can be permanent if the market remains more volatile permanently. That is, we have more overcorrections and corrections of the overcorrections.

If you’re looking at a single asset, I would agree that volatility is just volatility. If you don’t look at it, eventually it’ll revert to the mean.

You mentioned though, that it is an issue during both accumulation and distribution. If you believe the effect isn’t permanent, how would it be an issue during accumulation? Are you thinking that the volatility provides buying and rebalancing opportunities?
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Re: Do you think about volatility drag on your portfolio?

Post by bengal22 » Thu Sep 08, 2016 8:28 am

"Do you think about volatility drag on your portfolio?"

No.

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Re: Do you think about volatility drag on your portfolio?

Post by Theoretical » Thu Sep 08, 2016 9:41 am

JoMoney wrote:From what I keep hearing about in these theoretical "risk premium" schemes for investing, it sounds like double speak.
The proponents claim that these are "risk factors" representing real unique risks, and some people choose to load up on that risk... then they want to claim that a portfolio that doesn't bear that risk isn't diversified enough because it doesn't bear the risk? The reason for diversifying is to reduce risk, TSM doesn't bear those other "risks" so it doesn't need to diversify into a more risky portfolio. It sounds to me like the factor portfolios aren't measuring the risk of their portfolios properly if they really believe these factors represent risk :confused
Any way around it... I don't think I buy into most of the "risk premium" argument to begin with. Most of it looks to me like performance chasing for people who put too much faith in the EMH.


Actually, the modern portfolio theory of diversification involves putting risky assets together to produce a less risky whole because the pieces smooth things out. That includes even short-term treasuries, which have interest rate sensitivity, or emerging markets, which have anywhere from "a lot" to "a bajillion" risks beyond normal stocks. A total stock fund is diversified because a bunch of individual stocks smooth out idiosyncracies and company-specific risks. Factor investors would say that the factors provide additional diversification beyond simply having more companies or different types of bonds/bond issuers.

All I meant about a total market is that the risk factors other than beta are neutral because the small and value stocks are offset by large and growth stocks. Even if a potential premium is strictly positive (with no negative counterweight), it still means that loading up on the not-premium stocks will reduce or eliminate the benefit. However, since everything involved in a total stock market fund is a stock, whether it's higher or lower risk, the total nets out to positive overall exposure for beta/market exposure.

As I recall, you use the S&P 500, which historically has had a bit of quality due to the earnings requirements, which helped a bunch during the 1990s Tech Bubble, and it is mostly less-risky, more established large cap stocks. Based on the way the academic factors are structured, large caps offset small exposure, growth stocks offset value, etc... The S&P 500 is certainly less risky than a small cap US fund (international small caps are a bit different), and so that's a good reason to value holding it.

If you believe the academic factors can be profitably exploited in actual investments, then there's documented and serious non-correlation with the "market" to exploit that does provide diversification. For example, Japanese value investors have made decent returns since 1989 while Total Japanese market investing (nothing but beta) has been flat for over 20 years. If you believe the factors can't be profitably exploited or desire portfolio simplicity, a TSM or large cap is "good enough" and should be the starting base for any investor.

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Re: Do you think about volatility drag on your portfolio?

Post by Tyler9000 » Thu Sep 08, 2016 10:00 am

njboater74 wrote:
nedsaid wrote:The key is that you say, "You can see the permanent effect of volatility in certain circumstances." If a permanent effect requires certain circumstances then I would argue that the effect isn't permanent.[/color]

I think we're mostly in agreement on this. Although I should have clarified that the 'certain circumstances' i was referring to was the non-correlated assets being together in a portfolio, not certain market conditions.


Well, that's one thing I like about portfolios like the Permanent Portfolio and Dalio's All-Seasons portfolio that are very intentional about selecting assets that perform well in different economic conditions. It's true the correlations change with the ebb and flow of the economy, but if your economic bases are covered then the individual correlations behind the scenes at any point in time matter a lot less.

BTW, I think the distinction between volatility of individual assets and the volatility of the overall regularly rebalanced portfolio is important in this conversation. The important thing to focus on from a volatility drag perspective is the portfolio. Adding additional uncorrelated volatile assets to (counter-intuitively) balance and smooth out your overall portfolio is modern portfolio theory in a nutshell. So volatility isn't all bad in investing, and by using it intelligently in one area you can minimize it in another.

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Re: Do you think about volatility drag on your portfolio?

Post by rbaldini » Thu Sep 08, 2016 10:22 am

Random Walker wrote:Geometric return = Mean return - (0.5 X Variance)

I just want to note that this is only an approximation of the geometric mean. It is accurate only when the variance is quite small. The exact formulas are these:

Arithmetic mean (the usual one): Take N numbers, add them together, and divide by N.

Geometric mean: Take N numbers, *multiply* them together, and *take the Nth root*.
(Usually this method will cause a calculator to flip out. An equivalent formula that is more stable is this: take the natural log of each number, take the arithmetic mean of these logs, and then exponentiate the result. I.e. exp(mean(ln(x))).)

The reason we care about the geometric mean is because it tells us that average rate of compounding growth. Returns are given in proportion to share, so the process is *multiplicative*, not additive. Note that if the series has at least one 0 in it, then the geometric mean is 0; any number multiplied by 0 is 0. So, if you lose all your money, you have nothing to compound!

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Re: Do you think about volatility drag on your portfolio?

Post by rbaldini » Thu Sep 08, 2016 10:36 am

grayfox wrote:I don't no what to make of Volatility Drag. It seems like a numerical curiosity. It's just something that comes out of the calculation of two different statistics, Arithmetic Mean and Geometric Mean. It's kind of like to convert from Celsius to Kelvin, add 273.15. To get from Arithmetic Mean to Geometric Mean, subtract half the variance. (I don't think that is an iron-clad formula, just an approximation under certain conditions.)

It's not quite like that.

If room 1 is hotter than room 2 in Fahrenheit, then it is also hotter in Celsius and Kelvin. This is always true. They are linear transformations.

But it's totally possible to create two sequences where one has a higher arithmetic mean and the other has a higher geometric mean. The geometric mean is really the relevant quantity if you care about long-term growth rate.

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Re: Do you think about volatility drag on your portfolio?

Post by rbaldini » Thu Sep 08, 2016 10:48 am

Mind you, when Vanguard (and probably anyone else) reports the annual average performance of a fund (over some specified time period), they are reporting the geometric mean. So the volatility drag is already baked into that.

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Re: Do you think about volatility drag on your portfolio?

Post by njboater74 » Thu Sep 08, 2016 11:20 am

Tyler9000 wrote:Well, that's one thing I like about portfolios like the Permanent Portfolio and Dalio's All-Seasons portfolio that are very intentional about selecting assets that perform well in different economic conditions. It's true the correlations change with the ebb and flow of the economy, but if your economic bases are covered then the individual correlations behind the scenes at any point in time matter a lot less.

BTW, I think the distinction between volatility of individual assets and the volatility of the overall regularly rebalanced portfolio is important in this conversation. The important thing to focus on from a volatility drag perspective is the portfolio. Adding additional uncorrelated volatile assets to (counter-intuitively) balance and smooth out your overall portfolio is modern portfolio theory in a nutshell. So volatility isn't all bad in investing, and by using it intelligently in one area you can minimize it in another.

I agree. And I think we can be a bit too quick to dismiss volatility’s ‘mental’ drag on the portfolio. If you believe that stocks will produce a better long term return, then there’s no reason no to be 100% stocks.

Most people can’t tolerate losing half their portfolio over a few months, so we buy bonds to reduce the volatility.

We’re not buying bonds to reduce a 10% drawdown to 6%, I think most of us could handle that. I'm holding them to reduce a 50% drawdown to 30%, which means I only own bonds for black swan events, not for prosperity or even modest corrections.

The amount of bonds needed to reduce the drawdown to 30% in 2008-2009 for Corporate, TBM, and Int-Term Treasuries, is 51,42, and 36 percent, respectively.

When viewed this way, volatility isn’t a temporary condition, but is one that requires me to permanently alter my asset allocation to account for it.
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Re: Do you think about volatility drag on your portfolio?

Post by Oicuryy » Thu Sep 08, 2016 11:49 am

If you prefer arithmetic means to geometric means use nepers. Measure each year's gain/loss in nepers. Add up the nepers and divide by the number of years. The result is the rate of gain in nepers per year.

Or you could use continuously compounded returns.

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Re: Do you think about volatility drag on your portfolio?

Post by daveydoo » Thu Sep 08, 2016 12:17 pm

rbaldini wrote:Mind you, when Vanguard (and probably anyone else) reports the annual average performance of a fund (over some specified time period), they are reporting the geometric mean. So the volatility drag is already baked into that.


Is this true? Then it wouldn't be an "average." Is there some way to verify this? That would make a lot of this moot.

It's not so much the impact of volatility (since that's not actionable within an asset class), but whether there is a point to which one can reduce average annual returns in pursuit of stability and still come out ahead. I say this because the "smoothing" strategies to reduce volatility seem likely to lower total returns (by adding lower-performing but less-correlated assets like bonds to a stock market index, etc.). An "easy" way to test this would be to Monte Carlo-simulate cumulative returns for large cap and small cap over a very long baseline. The latter "should" win with slightly higher returns at the expense of greater volatility. But maybe they wouldn't. (The fact that they have won, historically, only represents an n of one, for sequence of returns.) The crux there would be how one iteratively "samples" the universe of possible annual returns for each asset class: randomly choosing from within the range; choosing in a normal distribution (if this is relevant to how annual returns are historically distributed); etc. I know some of the on-line "fortune-telling" reports that advisors share with their clients incorporate sliders for changing parameters in a Monte Carlo but I don't think the range of future returns can be constrained.

And I'm fine ignoring the "mental" drag (i.e., inopportune selling) since that's completely controllable by anyone reading this thread.

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Re: Do you think about volatility drag on your portfolio?

Post by njboater74 » Thu Sep 08, 2016 12:25 pm

daveydoo wrote:And I'm fine ignoring the "mental" drag (i.e., inopportune selling) since that's completely controllable by anyone reading this thread.

I'm not sure if you were referring to what I wrote.

What I meant by mental drag wasn't the fact that you might sell during a crisis, but that you factor in volatility when coming up with your AA as part of your long term plan. For instance, we're not in the midst of a crisis now and my AA is 65/35, and it will remain 65/35 during crises.

But if I were certain there would be no crisis (no volatility) in the future, my AA would be 100/0.
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Re: Do you think about volatility drag on your portfolio?

Post by rbaldini » Thu Sep 08, 2016 12:32 pm

daveydoo wrote:
rbaldini wrote:Mind you, when Vanguard (and probably anyone else) reports the annual average performance of a fund (over some specified time period), they are reporting the geometric mean. So the volatility drag is already baked into that.


Is this true? Then it wouldn't be an "average." Is there some way to verify this? That would make a lot of this moot.

Well, it's still an average - it's the geometric average (as opposed to the arithmetic average).

I looked at the reported annual "average" return to VTMSX on Vanguard's site. Then I used the annual returns of the fund on Yahoo to compute both the arithmetic and geometric means. It was a lot closer to the geometric mean.

If it's not the geometric mean, then that would be a very naughty thing on Vanguard's part. The arithmetic mean annual return does not give you the long term growth rate of the fund (assuming future = past); geometric mean does. The arithmetic mean would be an overestimate, i.e. optimistically misleading.

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Re: Do you think about volatility drag on your portfolio?

Post by nedsaid » Thu Sep 08, 2016 1:20 pm

Random Walker wrote:Nedsaid,
I'm sure you'd agree that we need to expect that in times of crisis correlations go to 1. That's where highest quality and short duration fixed income help most. We expect correlations to vary over time too.

Dave


You have it exactly right. I would also say that valuations matter and quality matters. On the valuations side, as long as you don't performance chase you should be okay. As far as quality, the broad indexes have you covered as the top 100 stocks by market cap are about 50% of the Total US Stock Market. The broad indexes are populated by mostly quality companies.

Where you get into trouble is getting carried away in a mania like the late 1990's. Those who piled into the hot high tech and internet stocks got socked with the toxic mix of overvaluation and low quality.

And yes, correlations vary.
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Re: Do you think about volatility drag on your portfolio?

Post by nedsaid » Thu Sep 08, 2016 1:37 pm

njboater74 wrote:
nedsaid wrote:The key is that you say, "You can see the permanent effect of volatility in certain circumstances." If a permanent effect requires certain circumstances then I would argue that the effect isn't permanent.[/color]

I think we're mostly in agreement on this. Although I should have clarified that the 'certain circumstances' i was referring to was the non-correlated assets being together in a portfolio, not certain market conditions.

Nedsaid: I am a believer in portfolio theory and I am on board with putting non-correlated asset classes in a portfolio as you have described. I have Large and Small, Value and Growth, US and International, and also have owned REITs for many years. Investing across factors and asset classes. Worked beautifully in 2000-2002 but didn't work in 2008-2009. All I am saying is that things sometimes don't work as expected. I was also surprised that TIPS got hit too in the 2008-2009 financial crisis.

I do believe that the effect can be permanent if the market remains more volatile permanently. That is, we have more overcorrections and corrections of the overcorrections.

Nedsaid: The problem I have with this statement is that unexpected volatility can be on the upside. No one is arguing for a permanent volatility bonus on this thread.

If you’re looking at a single asset, I would agree that volatility is just volatility. If you don’t look at it, eventually it’ll revert to the mean.

You mentioned though, that it is an issue during both accumulation and distribution. If you believe the effect isn’t permanent, how would it be an issue during accumulation? Are you thinking that the volatility provides buying and rebalancing opportunities?

Nedsaid: Volatility is an issue during accumulation and I like Larry Swedroe's answer on this thread. He talks about volatility tempting investors into behavioral errors. You raise a good point about buying and rebalancing opportunities, wasn't thinking of that, thank you for bringing it up.

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Re: Do you think about volatility drag on your portfolio?

Post by mptfan » Thu Sep 08, 2016 2:16 pm

daveydoo wrote:
rbaldini wrote:Mind you, when Vanguard (and probably anyone else) reports the annual average performance of a fund (over some specified time period), they are reporting the geometric mean. So the volatility drag is already baked into that.


Is this true? Then it wouldn't be an "average." Is there some way to verify this? That would make a lot of this moot.

Yes, it is true that Vanguard uses the geometric mean and calls it "average annual return." It is still an average...it is the "compound average growth rate". It does create confusion, I agree.
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Re: Do you think about volatility drag on your portfolio?

Post by njboater74 » Thu Sep 08, 2016 2:41 pm

nedsaid wrote:Nedsaid: The problem I have with this statement is that unexpected volatility can be on the upside. No one is arguing for a permanent volatility bonus on this thread.

I think I understand what you're saying. Another way of looking at 2008 might be that we benefited from an overly volatile 2006 in which REITs shot up 35% and gave us rebalancing opportunities for our other asset classes.

Thanks, my head hurts now. :confused
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Re: Do you think about volatility drag on your portfolio?

Post by kolea » Thu Sep 08, 2016 7:18 pm

rbaldini wrote:Mind you, when Vanguard (and probably anyone else) reports the annual average performance of a fund (over some specified time period), they are reporting the geometric mean. So the volatility drag is already baked into that.


So, this piqued my curiosity as to what exactly is being reported by everyone. I looked at several reporting sites. Performance data with 1, 3, 5, 10 year returns, is always expressed as CAGR, i.e., geometric average return (although it will often be called "average return"). I have not seen performance reported as an arithmetic average. It is always the most recent trailing period (1, 3, etc. years). When the asset's statistics (mean, standard deviation, etc.) are shown, the mean is the arithmetic average of 1-year returns and the standard deviation is the variance of the 1-year data.

For the most part I think volatility drag is a red herring - if you want to know 10-year performance, use 10-year data, not 1-year data. This really shows up in a bad way when doing efficiency horizons - those are typically plotted out with 1-year data and are then used to make assumptions about how a portfolio will behave over 10,15,20 year holding periods. The trouble is, there is not a lot of 10-year (or longer) statistics available so 1-year is used even though the results are questionable.

Of course there is still the question of whether it is wise to make projections about future performance anyway.
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Re: Do you think about volatility drag on your portfolio?

Post by Random Walker » Thu Sep 08, 2016 8:54 pm

Kolea,
Volatility drag is not a red herring at all! You're talking about individual fund statistics. I'm talking about how funds act as components of a portfolio. How they mix in the portfolio determines how close the CAGR is to the weighted average return of the components.

Dave

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Re: Do you think about volatility drag on your portfolio?

Post by kolea » Thu Sep 08, 2016 11:55 pm

Random Walker wrote:Kolea,
Volatility drag is not a red herring at all! You're talking about individual fund statistics. I'm talking about how funds act as components of a portfolio. How they mix in the portfolio determines how close the CAGR is to the weighted average return of the components.

Dave


That is fine to determine how they mix in a portfolio. If you want to know how they mix for a 1-year holding period, use 1-year statistics. If you want to know how they mix for a 5-year holding period use 5-year statistics. If you do that you will never have to consider volatility drag. You are using the appropriate statistics for the period that you are trying to model and volatility drag never is part of the analysis.
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Re: Do you think about volatility drag on your portfolio?

Post by grayfox » Fri Sep 09, 2016 3:05 am

kolea wrote:
Random Walker wrote:Kolea,
Volatility drag is not a red herring at all! You're talking about individual fund statistics. I'm talking about how funds act as components of a portfolio. How they mix in the portfolio determines how close the CAGR is to the weighted average return of the components.

Dave


That is fine to determine how they mix in a portfolio. If you want to know how they mix for a 1-year holding period, use 1-year statistics. If you want to know how they mix for a 5-year holding period use 5-year statistics. If you do that you will never have to consider volatility drag. You are using the appropriate statistics for the period that you are trying to model and volatility drag never is part of the analysis.


This is correct, at least according to Modern Portfolio Theory, which is a single period analysis.

If you invest $10,000 for 20 years in some portfolio, there is a distribution of possible outcomes. The distribution has a mean, which is the expected return, there is a median, which is the 50 percentile, there is a variance, which measures the spread. You might also be interested in the 5 percentile, or 1 percentile. The 1%-tile is useful because it tells you that 99% of the outcomes are greater than some value, and there is a 1% chance of doing worse than that.

It probably looks something like this, although this is for monthly returns. (I couldn't find a 20-year graph.) For 20-year returns, I once calculated the mean to be about 7x and the median about 5x. The range of outcomes was from about 1.5x to 18x.

Image

That's really all you need to know. The distribution and statistics of a 1-year investment is not relevant to a 20-year holding period. Of course, the 1-year statistics would be relevant for a 1-year holding period. But who's going to buy stocks and sell 1-year later? Maybe a speculator. Stocks are a long term investment.
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