Do you think about volatility drag on your portfolio?

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Re: Do you think about volatility drag on your portfolio?
MPT requires the input of correlations of assets. So stocks bonds and gold together haven't a lower risk adjusted return. This correlation matrix is usually a fixed input minus some changes that Cochrane made to the model. Ok it is not exact but there is at least some intuition behind it and the concept that diversification can help makes sense. Now add in Fama French factors which seem to have an increased return over most long time periods and in multiple markets. I go back and forth on whether I believe they will hold up against market failures in arbitrage or other issues  but ok
These factors though have a correlation that is extraordinary dependence on time frame and market. Mixing MPT with unstable correlated constructs and then calling it lower volatility seems a step too far. Call it higher return ok maybe. But in my mind they are not good inputs to MPT, a historical analysis or a Monte Carlo model using historical data. There are too many levels of unknowns for a stable model.
These factors though have a correlation that is extraordinary dependence on time frame and market. Mixing MPT with unstable correlated constructs and then calling it lower volatility seems a step too far. Call it higher return ok maybe. But in my mind they are not good inputs to MPT, a historical analysis or a Monte Carlo model using historical data. There are too many levels of unknowns for a stable model.
G.E. Box "All models are wrong, but some are useful."

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Re: Do you think about volatility drag on your portfolio?
Gray fox,
I agree with your bell curve above. But a typical investor can keep the mean expected return the same and decrease the variance by diversifying across sources of return. Isn't it likely worthwhile to give up the right tail hope to avoid the left tail risk. Making the bell curve skinnier by decreasing SD is a worthwhile endpoint. It comes at increased cost in terms of expense ratios, but it is a trade off each investor should consider.
Dave
I agree with your bell curve above. But a typical investor can keep the mean expected return the same and decrease the variance by diversifying across sources of return. Isn't it likely worthwhile to give up the right tail hope to avoid the left tail risk. Making the bell curve skinnier by decreasing SD is a worthwhile endpoint. It comes at increased cost in terms of expense ratios, but it is a trade off each investor should consider.
Dave

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Re: Do you think about volatility drag on your portfolio?
I was just playing around with Excel a bit. Was screwing around with some functions called GeoMean and Norm.Inv.
GeoMean calculates a geometric (compounded) mean and Norm.Inv can generate a random sequence of returns with a given mean and standard deviation. Got a feeling for volatility drag. For a 60/40 portfolio the difference between average return and compounded return can easily be 12% annualized over 20 years. The greater the portfollio SD and the longer the time horizon, the bigger the drag. Seems that anything an individual can do to maintain the portfolio expected return an minimize SD will have a significant positive impact, even with somewhat higher expenses.
Dave
GeoMean calculates a geometric (compounded) mean and Norm.Inv can generate a random sequence of returns with a given mean and standard deviation. Got a feeling for volatility drag. For a 60/40 portfolio the difference between average return and compounded return can easily be 12% annualized over 20 years. The greater the portfollio SD and the longer the time horizon, the bigger the drag. Seems that anything an individual can do to maintain the portfolio expected return an minimize SD will have a significant positive impact, even with somewhat higher expenses.
Dave
Re: Do you think about volatility drag on your portfolio?
Look to me like your formula is wrong.Random Walker wrote:
Geometric return = Mean return  (0.5 X Variance)
This is a typical approximation that I find:
(1 + mean)**2  variance = (1 + CAGR)**2
Looks like volatility drag knocks about 1.5% off the mean SP500 taking it from mean = 10.5% to CAGR = 9%. These are just approximate values.
I tried your formula on some SP500 historical data and I got a geometric return of around 200
But, can you point out where I am doing something wrong?

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Re: Do you think about volatility drag on your portfolio?
Tadamsmar,
Can't point out anything wrong. I think the equation I put up there is only an approximation. I think your 2% drag number is in the same league as the numbers I generated. The greater the SD and the greater the time period, the greater the drag. This is why I'm so focused on diversifying across sources of return. Your S&P 500 example can be an excellent baseline for comparison: it is basically large growth only. We should compare it to a collection of assets with same expected return but likely lower SD. This can be achieved with exposure to international large. Alternatively one could create a portfolio with asset classes that have higher expected returns such as small and value and dampen the expected return to the desired level with bonds. This portfolio should have same expected return and lower SD. Would be interesting to see the difference in GeoMean for the two portfolios with same average.
Dave
Can't point out anything wrong. I think the equation I put up there is only an approximation. I think your 2% drag number is in the same league as the numbers I generated. The greater the SD and the greater the time period, the greater the drag. This is why I'm so focused on diversifying across sources of return. Your S&P 500 example can be an excellent baseline for comparison: it is basically large growth only. We should compare it to a collection of assets with same expected return but likely lower SD. This can be achieved with exposure to international large. Alternatively one could create a portfolio with asset classes that have higher expected returns such as small and value and dampen the expected return to the desired level with bonds. This portfolio should have same expected return and lower SD. Would be interesting to see the difference in GeoMean for the two portfolios with same average.
Dave
Re: Do you think about volatility drag on your portfolio?
I see what I did wrong. I plugged in sd as 18% instead of .18. When I use 0.18 instead of 18, it is a good approximation.
Re: Do you think about volatility drag on your portfolio?
There's absolutely no way a formula like this could be right. It's dimensionally incorrect. It has mixed units. You can look at a formula like this and immediately realize it must be wrong.Random Walker wrote:Geometric return = Mean return  (0.5 X Variance)

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Re: Do you think about volatility drag on your portfolio?
What are the mixed units? My understanding is that it's a good approximation. Got it from Ang's book.
Dave
Dave
Re: Do you think about volatility drag on your portfolio?
*3!4!/5! wrote:There's absolutely no way a formula like this could be right. It's dimensionally incorrect. It has mixed units. You can look at a formula like this and immediately realize it must be wrong.Random Walker wrote:Geometric return = Mean return  (0.5 X Variance)
It's dimensionally incorrect. It has mixed units. This not only means it cannot possibly be correct, it also means it cannot possibly be an approximation. It's just plain wrong. If you got this formula from a book then throw the book into the rubbish bin.Random Walker wrote:What are the mixed units? My understanding is that it's a good approximation. Got it from Ang's book.
Re: Do you think about volatility drag on your portfolio?
All the investment theories and research that's out there are exactly why I stick with a simple twofund portfolio below and call it a day. For myself, there's no reason to complicate things. I am quite content with my average, market level returns.
Vanguard 500 & Vanguard Total Bond Fund
Vanguard 500 & Vanguard Total Bond Fund

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Re: Do you think about volatility drag on your portfolio?
3!4!/5!
That's a pretty extreme response! Andrew Ang's Asset Management: A Systematic Approach to Factor Investing is an outstanding current book on modern investing. It's almost 800 pages of very solid information. I haven't read it cover to cover, have used it more as a reference, but I have no doubt it's an outstanding book. I have taken from a footnote at the bottom of page 146. I'm sure any error is an interpretation mistake by me. The author goes into much greater detail ( perhaps a bit out of my league) in the appendix.
Dave
That's a pretty extreme response! Andrew Ang's Asset Management: A Systematic Approach to Factor Investing is an outstanding current book on modern investing. It's almost 800 pages of very solid information. I haven't read it cover to cover, have used it more as a reference, but I have no doubt it's an outstanding book. I have taken from a footnote at the bottom of page 146. I'm sure any error is an interpretation mistake by me. The author goes into much greater detail ( perhaps a bit out of my league) in the appendix.
Dave
Last edited by Random Walker on Sat Oct 01, 2016 7:50 pm, edited 1 time in total.
Re: Do you think about volatility drag on your portfolio?
Quote the footnote exactly.
Re: Do you think about volatility drag on your portfolio?
Agree with both posters. Although it dimensionally makes no sense, that doesn't make it useless as an approximation. See the (? unitless) Rule of 72 for interest rates and investment doubling time (https://en.wikipedia.org/wiki/Rule_of_72). Maybe don't throw the whole book away
 triceratop
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Re: Do you think about volatility drag on your portfolio?
This may be the footnote referred to (from Google Books).
"To play the stock market is to play musical chairs under the chord progression of a bidask spread."
Re: Do you think about volatility drag on your portfolio?
Ah I see. That's a bit like saying E=m instead of E=mc^2, by making the declaration that c=1. This trick is used to suppress some terms in a formula and make it look simpler.
 triceratop
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Re: Do you think about volatility drag on your portfolio?
I'll observe that the key difference between that footnote and the above discussion is the notion of an "expected arithmetic/geometric return". That makes a substantial difference.
"To play the stock market is to play musical chairs under the chord progression of a bidask spread."
Re: Do you think about volatility drag on your portfolio?
If return is measured in $, then variance is measured in $^2. That's the incompatible units. Variance should be divided by mean.
geometric mean is approx arithmetic mean  (0.5 X Variance)/mean
(under some assumptions)
But it's true you can get away with suppressing the "/mean" if you scale things so that mean is (approx) a dimensionless 1.
geometric mean is approx arithmetic mean  (0.5 X Variance)/mean
(under some assumptions)
But it's true you can get away with suppressing the "/mean" if you scale things so that mean is (approx) a dimensionless 1.

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Re: Do you think about volatility drag on your portfolio?
Sorry, I've been using equations without full understanding. The point I'm trying to make though is that to one extent or another it may be worthwhile to take on a portfolio with somewhat higher weighted average expense ratio for the sake of getting compounded return closer to average annual return
Dave
Dave
Re: Do you think about volatility drag on your portfolio?
I probably made too much of a fuss about the formula. Instead of saying it's wrong, it would be better to say that is applicable if certain assumptions hold, but not necessarily otherwise. I'm sure the book author is an expert who knows exactly when the formulas apply. To have wider applicability though, the formula should have the "/mean" in it.*
Anyway, I agree with the general point of the OP. The geometric returns are what matters. They differ from the arithmetic returns, by an amount mostly related to variance (volatility).

*Here's an example why you need the "/mean". Suppose you have an investment that will either double or triple (equally likely), so the "return" (as a ratio) is 2 or 3.
arithmetic return = (2+3)/2=2.5="mean"
geometric return = sqrt(2*3)=2.449489743
std dev = 0.5
variance = (0.5)^2 = 0.25
So the approximation is
geometric return = arithmetic return  0.5*variance/mean= 2.5  0.5*0.25/2.5 = 2.45
which is very close to 2.449489743
If you leave out the "/2.5" you get the wrong answer.
Anyway, I agree with the general point of the OP. The geometric returns are what matters. They differ from the arithmetic returns, by an amount mostly related to variance (volatility).

*Here's an example why you need the "/mean". Suppose you have an investment that will either double or triple (equally likely), so the "return" (as a ratio) is 2 or 3.
arithmetic return = (2+3)/2=2.5="mean"
geometric return = sqrt(2*3)=2.449489743
std dev = 0.5
variance = (0.5)^2 = 0.25
So the approximation is
geometric return = arithmetic return  0.5*variance/mean= 2.5  0.5*0.25/2.5 = 2.45
which is very close to 2.449489743
If you leave out the "/2.5" you get the wrong answer.
Re: Do you think about volatility drag on your portfolio?
But the formula is a good approximation without "/mean" and a bad one with it if you apply it to the historical SP500 where:*3!4!/5! wrote:If return is measured in $, then variance is measured in $^2. That's the incompatible units. Variance should be divided by mean.
geometric mean is approx arithmetic mean  (0.5 X Variance)/mean
(under some assumptions)
But it's true you can get away with suppressing the "/mean" if you scale things so that mean is (approx) a dimensionless 1.
mean ~ 0.10
sd ~ 0.15
You are right about the units being incompatible, but that does not keep formula from giving approximately the right answer for a range of means and variances that are relevant to stock market investing.
Re: Do you think about volatility drag on your portfolio?
In the context where the author is using it, the "mean" that is missing from the formula is approximately 1, which is why you can get away with not dividing by it. The relevant quantities are the ratios between investment values after a short (perhaps infintessimal, in a continuous time model) time has elapsed.tadamsmar wrote:But the formula is a good approximation without "/mean" and a bad one with it if you apply it to the historical SP500 where:*3!4!/5! wrote:If return is measured in $, then variance is measured in $^2. That's the incompatible units. Variance should be divided by mean.
geometric mean is approx arithmetic mean  (0.5 X Variance)/mean
(under some assumptions)
But it's true you can get away with suppressing the "/mean" if you scale things so that mean is (approx) a dimensionless 1.
mean ~ 0.10
sd ~ 0.15
You are right about the units being incompatible, but that does not keep formula from giving approximately the right answer for a range of means and variances that are relevant to stock market investing.
If it is made clear which convention is being used, gain of 0.1% can be expressed by the number 1.001 or by the number 0.001, but for any formula this needs to be made clear, and in this context, the above mentioned "/mean" is the one that is close to 1.

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Re: Do you think about volatility drag on your portfolio?
I did.
No longer care.
It's not one of those things I don't have a great deal of control.
YMMV
No longer care.
It's not one of those things I don't have a great deal of control.
YMMV
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Re: Do you think about volatility drag on your portfolio?
In my example the mean was a proportion, 0.1 or 1/10th. That would be 10%*3!4!/5! wrote:In the context where the author is using it, the "mean" that is missing from the formula is approximately 1, which is why you can get away with not dividing by it. The relevant quantities are the ratios between investment values after a short (perhaps infintessimal, in a continuous time model) time has elapsed.tadamsmar wrote:But the formula is a good approximation without "/mean" and a bad one with it if you apply it to the historical SP500 where:*3!4!/5! wrote:If return is measured in $, then variance is measured in $^2. That's the incompatible units. Variance should be divided by mean.
geometric mean is approx arithmetic mean  (0.5 X Variance)/mean
(under some assumptions)
But it's true you can get away with suppressing the "/mean" if you scale things so that mean is (approx) a dimensionless 1.
mean ~ 0.10
sd ~ 0.15
You are right about the units being incompatible, but that does not keep formula from giving approximately the right answer for a range of means and variances that are relevant to stock market investing.
If it is made clear which convention is being used, gain of 0.1% can be expressed by the number 1.001 or by the number 0.001, but for any formula this needs to be made clear, and in this context, the above mentioned "/mean" is the one that is close to 1.
Also the formula is here:
viewtopic.php?f=10&t=199092&p=3073031#p3072445
The formula uses r, not 1+r. So it's 0.1 not 1.1
Re: Do you think about volatility drag on your portfolio?
@tadamsmar
I stated a formula with "/mean" in it, that is more widely applicable than the one without. Obviously if you choose to misinterpret the terms and plug the wrong numbers in, you are choosing to make it not work. I've already provided enough explanation for you to figure out where you are going wrong.
I stated a formula with "/mean" in it, that is more widely applicable than the one without. Obviously if you choose to misinterpret the terms and plug the wrong numbers in, you are choosing to make it not work. I've already provided enough explanation for you to figure out where you are going wrong.

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Re: Do you think about volatility drag on your portfolio?
Someone can gain 50% in one year, lose 33.33...% the next year, and still end up at an annualized return of 0%. That's half the volatility, but the outcome is the same. The average return per unit time over some period is what matters for earnings, and volatility matters if some or all of that capital might be used at some point in the future.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%.

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Re: Do you think about volatility drag on your portfolio?
Found an excuse to give this thread a bump. Someone this weekend drew our attention to a new investing website by Jason Zweig. It's humbledollar.com. Was perusing the site. And he has a post on the same issue.
http://www.humbledollar.com/moneyguide ... ereturns/
http://www.humbledollar.com/moneyguide ... ainshelp/
The geometric return of a portfolio is what matters. Volatility causes the weighted average annual return of portfolio components to always be greater than the portfolio's geometric return. A more efficient portfolio minimizes the difference between average return and compounded return by minimizing volatility with weakly/non/negatively correlated components.
Dave
http://www.humbledollar.com/moneyguide ... ereturns/
http://www.humbledollar.com/moneyguide ... ainshelp/
The geometric return of a portfolio is what matters. Volatility causes the weighted average annual return of portfolio components to always be greater than the portfolio's geometric return. A more efficient portfolio minimizes the difference between average return and compounded return by minimizing volatility with weakly/non/negatively correlated components.
Dave
Re: Do you think about volatility drag on your portfolio?
It's just part of the game.
Re: Do you think about volatility drag on your portfolio?
Thanks Dave for reviving this thread. It was one of those threads that looked interesting and the topic was something that frankly I hadn't given a lot of thought to. I just dove in and posted and I have to say that I was very pleased with my contribution here. If there was such a thing as "Nedsaid's Greatest Hits", the posts here would be among my best. In general, this was an excellent discussion.Random Walker wrote:Found an excuse to give this thread a bump. Someone this weekend drew our attention to a new investing website by Jason Zweig. It's humbledollar.com. Was perusing the site. And he has a post on the same issue.
http://www.humbledollar.com/moneyguide ... ereturns/
http://www.humbledollar.com/moneyguide ... ainshelp/
The geometric return of a portfolio is what matters. Volatility causes the weighted average annual return of portfolio components to always be greater than the portfolio's geometric return. A more efficient portfolio minimizes the difference between average return and compounded return by minimizing volatility with weakly/non/negatively correlated components.
Dave
Pretty good as I am really not much of a quant. I almost flunked Calculus in College, my GPA took a hit but the rigor of Calculus really benefitted me in upper level courses.
Again, this thread brings up issues that investors should think about.
A fool and his money are good for business.

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Re: Do you think about volatility drag on your portfolio?
Thought I would resurrect this thread. There is a function in Excel that allows one to create a series of randomly distributed returns given normal distribution, a given mean, and given standard deviation:(NORM.INV(RAND). I created six portfolios with the same expected return and different SDs. The gap between average return and geometric return increased quite rapidly as the portfolio SD increased. I've run the simulation many times and the trend is clear. Thought I would add some representative numbers to the thread. I assumed mean portfolio return 5% and varied standard deviations between 10 and 20.
SD 10 average return  Geo return = 0.48%
SD 12 average return  Geo return = 0.60%
SD 14 average return  Geo return = 0.93%
SD 16 average return  Geo return = 1.3%
SD 18 average return  Geo return = 1.4%
SD 20 average return  Geo return = 1.7%
I think this phenomenon is something investors need to consider, especially TSMers with very high equity allocations. Larry made the excellent point that the negative effect of volatility drag on geometric returns is likely overshadowed by the effects of volatility on investor behavior. Either way, diversifying across sources of return to minimize volatility for a given expected return seems to be a winning (albeit more costly) strategy. It could well be worth some modestly increased expense ratios to improve portfolio efficiency.
Dave
SD 10 average return  Geo return = 0.48%
SD 12 average return  Geo return = 0.60%
SD 14 average return  Geo return = 0.93%
SD 16 average return  Geo return = 1.3%
SD 18 average return  Geo return = 1.4%
SD 20 average return  Geo return = 1.7%
I think this phenomenon is something investors need to consider, especially TSMers with very high equity allocations. Larry made the excellent point that the negative effect of volatility drag on geometric returns is likely overshadowed by the effects of volatility on investor behavior. Either way, diversifying across sources of return to minimize volatility for a given expected return seems to be a winning (albeit more costly) strategy. It could well be worth some modestly increased expense ratios to improve portfolio efficiency.
Dave
Re: Do you think about volatility drag on your portfolio?
I can't think of a single reason for anyone to use average return instead of geometric return. It serves no purpose (other than to mislead  oh wait, maybe I just did think of a reason).
Re: Do you think about volatility drag on your portfolio?
You use average return when you are trying to estimate the parameters of the hypothetical distribution from which the annual returns are sampled. That comes up when people are doing academic models of the efficient frontier and so on.*3!4!/5! wrote:I can't think of a single reason for anyone to use average return instead of geometric return. It serves no purpose (other than to mislead  oh wait, maybe I just did think of a reason).
I think the idea that one should or shouldn't "use" a certain formulation is a red herring related to the "shouldness" of the question. What you do is calculate what is relevant and selfconsistent to what one is doing.
The idea that arithmetic and geometric averages are different is just a mathematical fact which is made to sound like some sort of investing strategy issue that it is not. Don't forget that which average someone calculates does not change the actual behavior of the investments involved. It just changes what we know about those investments.
What the issue actually is comes down to whether or not one can get a better result relative to one's objectives from one kind of portfolio construction rather than another. To find that out you just do the appropriate calculations, establish that the result is a robust prediction of future expectations, and then you pay your money and take your choice. Which calculation is appropriate can be either or both depending on how you proceed to get the relevant answers.

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Re: Do you think about volatility drag on your portfolio?
345,
I agree. What we eat is the compounded return of our portfolios. We can construct our portfolios in such a way that the volatility drag is likely to be minimized. Diversifying across factors and maintaining constant expected return should minimize volatility drag on the portfolio.
Dave
I agree. What we eat is the compounded return of our portfolios. We can construct our portfolios in such a way that the volatility drag is likely to be minimized. Diversifying across factors and maintaining constant expected return should minimize volatility drag on the portfolio.
Dave
Re: Do you think about volatility drag on your portfolio?
Just be aware that portfolio returns are not normally distributed and are not random, i.e., independent. We all know the latter as "momentum".Random Walker wrote:Thought I would resurrect this thread. There is a function in Excel that allows one to create a series of randomly distributed returns given normal distribution, a given mean, and given standard deviation:(NORM.INV(RAND).
Dave
Kolea (pron. kolayuh). Golden plover.

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Re: Do you think about volatility drag on your portfolio?
Hi Kolea,
Yes I know they are not normally distributed. I've read lognormal. Not quite sure what that is. Looked it up and it seemed normal + a little skew to the left. I'm familiar with Momentum, but think assuming random returns year over year is a good assumption. Overall, think assuming normal distribution and random returns yields a meaningful result with regard to volatility drag.
One question I have is whether rebalancing blunts the damage of volatility drag.
Dave
Yes I know they are not normally distributed. I've read lognormal. Not quite sure what that is. Looked it up and it seemed normal + a little skew to the left. I'm familiar with Momentum, but think assuming random returns year over year is a good assumption. Overall, think assuming normal distribution and random returns yields a meaningful result with regard to volatility drag.
One question I have is whether rebalancing blunts the damage of volatility drag.
Dave
Re: Do you think about volatility drag on your portfolio?
To the extent that rebalancing successfully times the market, I would say it would "blunt" the effect of volatility drag. I personally view rebalancing as a strategy to control risk but there are people who believe it has a positive effect on return. If that is true, it must be blunting the drag effect.Random Walker wrote:Hi Kolea,
One question I have is whether rebalancing blunts the damage of volatility drag.
Dave
Kolea (pron. kolayuh). Golden plover.

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Re: Do you think about volatility drag on your portfolio?
I too see rebalancing primarily as risk control. But hard for me not to believe there is usually some additional return benefit when rebalancing between equity asset classes.
Dave
Dave

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Re: Do you think about volatility drag on your portfolio?
Random Walker
I had not read this thread the first time, just read it right now because I had followed your thread on buying used cars from yesterday
I am going to give you some tough love so don't take it with any bad intent.
This thread just shows seriously confused thinking. Assets that have high expected returns are almost always accompanied by risk and volatility. Cash is not volatile but almost always has negative expected returns. So, the decision whether or not to invest in volatile assets like stocks, bonds, gold, real estate etc. must be done with that understanding. If one can't handle volatility, one shouldn't invest in volatile assets.
Having said that, what exactly does looking at arithmetic series vs. geometric series tell us? Not much. The fact that for a volatile asset class, geometric means are different from arithmetic means is just mathematics. If you hold such an asset over a long period (and reinvest earnings), the total returns are only known after the fact. They don't care about what mathematical model you used to model returns..there are so many moving pieces: growth of companies, revenue growth, earnings vs. revenues, taxes on said earnings, price investors are willing to pay for said earnings at the beginning of your investing and at the end..
The returns on your investing is NOT some precise mathematical series. It is simply the (end value  beginning value)/beginning value. That's all. What intermediate values you got each year or each month are irrelevant (except for price of dividends reinvested). The sequence of returns is also irrelevant (at least in accumulation). Given such movement in the underlying assets, I always find it funny that people try to model these as either an arithmetic or a geometric series. Clearly modeling it as arithmetic is wrong but even geometric doesn't tell us much.
The actionable piece would be if we could use this fact (arithmetic return is different from geometric) to do something. If low volatility was a factor in increased returns, it would be known (like value, momentum, size etc.). As far as I know, it is not. Similarly, if the argument is that by putting different assets say stocks and bonds with low correlation, one ends up with higher returns, there would be data. That is called the re balancing bonus and there is NO peer reviewed paper showing any such bonus. The data is clear that simply holding the higher return asset for long time, leads to higher returns while re balancing is mostly a "risk" thing. Now we are back to square one of the definition of risk..
Then on top you question/wonder if paying an advisor to get access to these low volatility investments would be a good idea. But you have shown no underlying data that low volatility leads to higher returns in the first place, never mind the advisor cost..
Sorry but thinking in terms of arithmetic returns or geometric returns etc. isn't shedding any light on the topic you started.
I had not read this thread the first time, just read it right now because I had followed your thread on buying used cars from yesterday
I am going to give you some tough love so don't take it with any bad intent.
This thread just shows seriously confused thinking. Assets that have high expected returns are almost always accompanied by risk and volatility. Cash is not volatile but almost always has negative expected returns. So, the decision whether or not to invest in volatile assets like stocks, bonds, gold, real estate etc. must be done with that understanding. If one can't handle volatility, one shouldn't invest in volatile assets.
Having said that, what exactly does looking at arithmetic series vs. geometric series tell us? Not much. The fact that for a volatile asset class, geometric means are different from arithmetic means is just mathematics. If you hold such an asset over a long period (and reinvest earnings), the total returns are only known after the fact. They don't care about what mathematical model you used to model returns..there are so many moving pieces: growth of companies, revenue growth, earnings vs. revenues, taxes on said earnings, price investors are willing to pay for said earnings at the beginning of your investing and at the end..
The returns on your investing is NOT some precise mathematical series. It is simply the (end value  beginning value)/beginning value. That's all. What intermediate values you got each year or each month are irrelevant (except for price of dividends reinvested). The sequence of returns is also irrelevant (at least in accumulation). Given such movement in the underlying assets, I always find it funny that people try to model these as either an arithmetic or a geometric series. Clearly modeling it as arithmetic is wrong but even geometric doesn't tell us much.
The actionable piece would be if we could use this fact (arithmetic return is different from geometric) to do something. If low volatility was a factor in increased returns, it would be known (like value, momentum, size etc.). As far as I know, it is not. Similarly, if the argument is that by putting different assets say stocks and bonds with low correlation, one ends up with higher returns, there would be data. That is called the re balancing bonus and there is NO peer reviewed paper showing any such bonus. The data is clear that simply holding the higher return asset for long time, leads to higher returns while re balancing is mostly a "risk" thing. Now we are back to square one of the definition of risk..
Then on top you question/wonder if paying an advisor to get access to these low volatility investments would be a good idea. But you have shown no underlying data that low volatility leads to higher returns in the first place, never mind the advisor cost..
Sorry but thinking in terms of arithmetic returns or geometric returns etc. isn't shedding any light on the topic you started.

 Posts: 2230
 Joined: Fri Feb 23, 2007 8:21 pm
Re: Do you think about volatility drag on your portfolio?
Dirghatamas,
Sorry, but I think your dose of tough love is a bit misguided and a sign that you have a little more reading to do yourself. Yes, at the individual asset level increased risk (volatility) is generally required to obtain increased return. But here we are talking PORTFOLIOS. It is possible to have two portfolios with the same expected return based on the weighted average mean expected return of the portfolio components. But the two portfolios can have different standard deviations. What I'm showing is that if one can create a more efficient portfolio with lower SD for a given expected return, that results in a higher terminal portfolio value at the end. That's because it is the geometric return that we eat, and it's always less than the weighted average return of the portfolio components.
What determines the benefit of a new potential portfolio addition is it's expected return, volatility, correlations to other portfolio components, and of course costs. If one is only invested in the S&P 500 with an SD of about 20, they are highly likely to do worse over the long term than if they are 50/50 S&P 500/EAFE. Ignoring the issue of current valuations, they are basically slightly less than perfectly correlated asset classes: large cap blend in different geographies. Now extrapolate the effect of that improved portfolio efficiency to a portfolio diversified across geographies, asset classes, factors, sources of return, and that can translate into real $ for the amount of risk taken. To be honest, I'm not really sure I get the meaning of the Sharpe ratio in isolation for a given asset class. But what the addition of an asset to a portfolio does to the portfolio's Sharpe ratio can be very clear, significant, and affect real $ accumulated.
Yes costs matter big time! But if it's 19992000, and you've got all your eggs in a single beta basket, isn't it worth it to pay some increased cost to be diversified across sources of return? Unfortunately, the link I have previously provided to Roger Gibson's short paper The Rewards Of Multi Asset Class Investing seems to no longer work. I would be very interested to hear your comments if you can find a copy of it. He also outlines the issue well in his book Asset Allocation. Sorry if I got a bit rantish . I am truly interested to hear your response. We may be more in line than we realize.
Dave
Sorry, but I think your dose of tough love is a bit misguided and a sign that you have a little more reading to do yourself. Yes, at the individual asset level increased risk (volatility) is generally required to obtain increased return. But here we are talking PORTFOLIOS. It is possible to have two portfolios with the same expected return based on the weighted average mean expected return of the portfolio components. But the two portfolios can have different standard deviations. What I'm showing is that if one can create a more efficient portfolio with lower SD for a given expected return, that results in a higher terminal portfolio value at the end. That's because it is the geometric return that we eat, and it's always less than the weighted average return of the portfolio components.
What determines the benefit of a new potential portfolio addition is it's expected return, volatility, correlations to other portfolio components, and of course costs. If one is only invested in the S&P 500 with an SD of about 20, they are highly likely to do worse over the long term than if they are 50/50 S&P 500/EAFE. Ignoring the issue of current valuations, they are basically slightly less than perfectly correlated asset classes: large cap blend in different geographies. Now extrapolate the effect of that improved portfolio efficiency to a portfolio diversified across geographies, asset classes, factors, sources of return, and that can translate into real $ for the amount of risk taken. To be honest, I'm not really sure I get the meaning of the Sharpe ratio in isolation for a given asset class. But what the addition of an asset to a portfolio does to the portfolio's Sharpe ratio can be very clear, significant, and affect real $ accumulated.
Yes costs matter big time! But if it's 19992000, and you've got all your eggs in a single beta basket, isn't it worth it to pay some increased cost to be diversified across sources of return? Unfortunately, the link I have previously provided to Roger Gibson's short paper The Rewards Of Multi Asset Class Investing seems to no longer work. I would be very interested to hear your comments if you can find a copy of it. He also outlines the issue well in his book Asset Allocation. Sorry if I got a bit rantish . I am truly interested to hear your response. We may be more in line than we realize.
Dave
Re: Do you think about volatility drag on your portfolio?
Sometimes people will criticize some mathematical model of a real world situation.Dirghatamas wrote:Random Walker
I had not read this thread the first time, just read it right now because I had followed your thread on buying used cars from yesterday
I am going to give you some tough love so don't take it with any bad intent.
This thread just shows seriously confused thinking. Assets that have high expected returns are almost always accompanied by risk and volatility. Cash is not volatile but almost always has negative expected returns. So, the decision whether or not to invest in volatile assets like stocks, bonds, gold, real estate etc. must be done with that understanding. If one can't handle volatility, one shouldn't invest in volatile assets.
Having said that, what exactly does looking at arithmetic series vs. geometric series tell us? Not much. The fact that for a volatile asset class, geometric means are different from arithmetic means is just mathematics. If you hold such an asset over a long period (and reinvest earnings), the total returns are only known after the fact. They don't care about what mathematical model you used to model returns..there are so many moving pieces: growth of companies, revenue growth, earnings vs. revenues, taxes on said earnings, price investors are willing to pay for said earnings at the beginning of your investing and at the end..
The returns on your investing is NOT some precise mathematical series. It is simply the (end value  beginning value)/beginning value. That's all. What intermediate values you got each year or each month are irrelevant (except for price of dividends reinvested). The sequence of returns is also irrelevant (at least in accumulation). Given such movement in the underlying assets, I always find it funny that people try to model these as either an arithmetic or a geometric series. Clearly modeling it as arithmetic is wrong but even geometric doesn't tell us much.
The actionable piece would be if we could use this fact (arithmetic return is different from geometric) to do something. If low volatility was a factor in increased returns, it would be known (like value, momentum, size etc.). As far as I know, it is not. Similarly, if the argument is that by putting different assets say stocks and bonds with low correlation, one ends up with higher returns, there would be data. That is called the re balancing bonus and there is NO peer reviewed paper showing any such bonus. The data is clear that simply holding the higher return asset for long time, leads to higher returns while re balancing is mostly a "risk" thing. Now we are back to square one of the definition of risk..
Then on top you question/wonder if paying an advisor to get access to these low volatility investments would be a good idea. But you have shown no underlying data that low volatility leads to higher returns in the first place, never mind the advisor cost..
Sorry but thinking in terms of arithmetic returns or geometric returns etc. isn't shedding any light on the topic you started.
Some such critics fully understand the model, but understand its limits of applicability.
But some other critics just plain don't even understand the math to start with.

 Posts: 506
 Joined: Fri Jan 01, 2016 6:18 pm
Re: Do you think about volatility drag on your portfolio?
Random Walker
The example you gave was combining US and International stocks. I do this. I am always invested 100% global stocks market weight. So I am obviously not going to argue about diversification. I consider the global cap weighted stocks as market neutral and starting point for stock portfolio. You then tilt from it by doing things like country bias, growth vs. value, small vs. big etc..I don't do any tilts. There is no re balancing in this approach because you are by definition always in balance. This is different from holding say US and International in a fixed % of the portfolio. This simple portfolio works just fine and I have had the exact same portfolio now for ~25 years.
However, I DON'T do this for higher returns or reducing volatility. I do it for tail risk (US going through a Japan like 2550 year period of no growth or facing a serious natural disaster). There isn't any compelling data that shows combining International stocks DECREASES your volatility. Correlations actually go to 1 in times of crisis e.g. the 2008 crisis. So, reducing volatility is simply NOT a factor in my portfolio design.
Leaving International stocks aside, the common re balancing thing people talk about is stocks vs. bonds. Again there isn't any compelling data that mixing these two assets and re balancing between them, adds to returns. If you do this in a taxable account, all math has to be done after taxes. The consistent data is that if you ignore volatility, the portfolio with the higher return (also higher volatile) asset, left alone just does better.
That's all I am trying to get to. If you claim that decreasing volatility leads to better returns, than just leaving the high volatility/high returns assets like stocks alone and let them do their thing..then you need to point to back testing and academic literature.
Thinking in terms of Sharpe's ratio at the asset level or portfolio level is nice but I have always just scratched my head at the concept. If I am not worried about volatility, all the data indicates you should be invested in diversified, high return assets. That is usually stocks (US or International is a separate discussion).The argument then made is one can have a better return if you build a portfolio with better risk adjusted returns and then use LEVERAGE. So you combine stocks and bonds and then lever or use options or futures..
Most of us are not going to use leverage. Already 100% stocks is considered risky enough..so I am going to ignore the much more advanced and much more extreme ideas of using large leverage on portfolios.
So, then again please help us with how does low volatility or thinking in terms of arithmetic or geometric returns (the start of this thread) help us with actionable items in our portfolios, either in terms of better returns or in terms of changing our portfolios?
The example you gave was combining US and International stocks. I do this. I am always invested 100% global stocks market weight. So I am obviously not going to argue about diversification. I consider the global cap weighted stocks as market neutral and starting point for stock portfolio. You then tilt from it by doing things like country bias, growth vs. value, small vs. big etc..I don't do any tilts. There is no re balancing in this approach because you are by definition always in balance. This is different from holding say US and International in a fixed % of the portfolio. This simple portfolio works just fine and I have had the exact same portfolio now for ~25 years.
However, I DON'T do this for higher returns or reducing volatility. I do it for tail risk (US going through a Japan like 2550 year period of no growth or facing a serious natural disaster). There isn't any compelling data that shows combining International stocks DECREASES your volatility. Correlations actually go to 1 in times of crisis e.g. the 2008 crisis. So, reducing volatility is simply NOT a factor in my portfolio design.
Leaving International stocks aside, the common re balancing thing people talk about is stocks vs. bonds. Again there isn't any compelling data that mixing these two assets and re balancing between them, adds to returns. If you do this in a taxable account, all math has to be done after taxes. The consistent data is that if you ignore volatility, the portfolio with the higher return (also higher volatile) asset, left alone just does better.
That's all I am trying to get to. If you claim that decreasing volatility leads to better returns, than just leaving the high volatility/high returns assets like stocks alone and let them do their thing..then you need to point to back testing and academic literature.
Thinking in terms of Sharpe's ratio at the asset level or portfolio level is nice but I have always just scratched my head at the concept. If I am not worried about volatility, all the data indicates you should be invested in diversified, high return assets. That is usually stocks (US or International is a separate discussion).The argument then made is one can have a better return if you build a portfolio with better risk adjusted returns and then use LEVERAGE. So you combine stocks and bonds and then lever or use options or futures..
Most of us are not going to use leverage. Already 100% stocks is considered risky enough..so I am going to ignore the much more advanced and much more extreme ideas of using large leverage on portfolios.
So, then again please help us with how does low volatility or thinking in terms of arithmetic or geometric returns (the start of this thread) help us with actionable items in our portfolios, either in terms of better returns or in terms of changing our portfolios?

 Posts: 640
 Joined: Fri Sep 06, 2013 12:35 pm
Re: Do you think about volatility drag on your portfolio?
This thread has bothered me from the start, and there were other threads. Just the term "volatility drag" makes me cringe. I was waiting for it to be realized that there is no such affect to actual $ returns. I thought, "Who on earth coined this term?" But here it is in the wiki. Note the mentions of average return (arithmetic) and compound return:
https://www.bogleheads.org/wiki/Variance_drain
OP seems to now explain it as "portfolio rebalancing bonus" nullifies " volatility drag." 2 of 'em in one shot.
https://www.bogleheads.org/wiki/Variance_drain
OP seems to now explain it as "portfolio rebalancing bonus" nullifies " volatility drag." 2 of 'em in one shot.
Last edited by MIpreRetirey on Fri Mar 10, 2017 5:35 pm, edited 1 time in total.

 Posts: 1123
 Joined: Tue Aug 19, 2014 10:09 pm
Re: Do you think about volatility drag on your portfolio?
I think you can simulate some of the effects of leverage on the stock side with a small/value/small value tilt (especially deep value) and on going longer with duration with treasuries, at least to a point.

 Posts: 2230
 Joined: Fri Feb 23, 2007 8:21 pm
Re: Do you think about volatility drag on your portfolio?
Dirghatamas,
One can create very different portfolios with the same expected return, but very different portfolio expected volatility based on the volatilities and correlations of the portfolio components. One can even use asset classes with higher expected return to decrease overall equity exposure and maintain constant expected return. This would especially help in the circumstances you rightly describe where correlations go to 1. If two portfolios have the same weighted mean return but different standard deviations, the portfolio with the lower standard deviation will have the higher geometric return in the end. It's the geometric return that matters. Take a look at my numeric examples above. All the portfolios had the same average annual return, but the geometric return decreased as SD increased. Take the simplest example given on the board. Make 100% in year one, lose 50% year two. Average annual return 25%, Geometric return 0%.
I think it's clear that it is worthwhile to attempt to minimize portfolio volatility for a given level of expected return. The first few, most basic, diversifiers are the easiest and cheapest: bonds, international, REITS. Beyond that improvements in portfolio efficiency get more expensive. How much improvement in efficiency is worth what cost is where I think the real argument is.
I'll give you the rebalancing bonus argument. I know it's tenuous and in general (not Japan) one is rebalancing into the asset class with lower expected returns.
Dave
One can create very different portfolios with the same expected return, but very different portfolio expected volatility based on the volatilities and correlations of the portfolio components. One can even use asset classes with higher expected return to decrease overall equity exposure and maintain constant expected return. This would especially help in the circumstances you rightly describe where correlations go to 1. If two portfolios have the same weighted mean return but different standard deviations, the portfolio with the lower standard deviation will have the higher geometric return in the end. It's the geometric return that matters. Take a look at my numeric examples above. All the portfolios had the same average annual return, but the geometric return decreased as SD increased. Take the simplest example given on the board. Make 100% in year one, lose 50% year two. Average annual return 25%, Geometric return 0%.
I think it's clear that it is worthwhile to attempt to minimize portfolio volatility for a given level of expected return. The first few, most basic, diversifiers are the easiest and cheapest: bonds, international, REITS. Beyond that improvements in portfolio efficiency get more expensive. How much improvement in efficiency is worth what cost is where I think the real argument is.
I'll give you the rebalancing bonus argument. I know it's tenuous and in general (not Japan) one is rebalancing into the asset class with lower expected returns.
Dave

 Posts: 2230
 Joined: Fri Feb 23, 2007 8:21 pm
Re: Do you think about volatility drag on your portfolio?
No, I'll happily remove all references to rebalancing bonus from the conversation. And purely focus on volatility. Which investment would you rather have: one that goes up 100% then down 50% giving you an average return of 25% or one that goes up 25% in two consecutive periods, also giving you an average return of 25%. I'll take the real money associated with the compound return of the second scenario.
Dave
Dave
Re: Do you think about volatility drag on your portfolio?
"The Myth of Volatility Drag"
https://blogs.cfainstitute.org/investor ... agpart1/
https://blogs.cfainstitute.org/investor ... agpart1/

 Posts: 2230
 Joined: Fri Feb 23, 2007 8:21 pm
Re: Do you think about volatility drag on your portfolio?
I found this link that explains what I'm talking about:
http://swanglobalinvestments.com/2016/0 ... isadrag/
Dave
http://swanglobalinvestments.com/2016/0 ... isadrag/
Dave

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Re: Do you think about volatility drag on your portfolio?
Tamales,
Do you have a link to Part 2? Looks like that's where this issue is really addressed.
Dave
Do you have a link to Part 2? Looks like that's where this issue is really addressed.
Dave

 Posts: 640
 Joined: Fri Sep 06, 2013 12:35 pm
Re: Do you think about volatility drag on your portfolio?
I'll take the 2nd:Random Walker wrote:No, I'll happily remove all references to rebalancing bonus from the conversation. And purely focus on volatility. Which investment would you rather have: one that goes up 100% then down 50% giving you an average return of 25% or one that goes up 25% in two consecutive periods, also giving you an average return of 25%. I'll take the real money associated with the compound return of the second scenario.
Dave
1st: 100% (2) times 50% (.5) = 1 (started $100, then had $200, ended with $100.
2nd: 25% (1.25) times 25% (1.25) = 1.5625

 Posts: 640
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Re: Do you think about volatility drag on your portfolio?
Random Walker wrote:I found this link that explains what I'm talking about:
http://swanglobalinvestments.com/2016/0 ... isadrag/
Dave
1.1 * .95 ...Again, we start with a simple illustration. If one were asked which of the following three scenarios would yield the best tenyear results, one might be tempted to choose the last of these three options:
Up 10% one year, down 5% the next, repeated for ten years
Up 25% one year, down 20% the next, repeated for ten years
Up 40% one year, down 35% the next, repeated for ten years
In fact, the opposite is true. After a decade:
Scenario A, with its most modest gains and losses, performs best and is the only scenario that is profitable;
Scenario B breaks even and;
Scenario C loses money.
1.25 * .80 ...
1.4 * .65 ...
These are just really downward trending markets over 20 yrs. (lower lows and lower highs.)