Do you think about volatility drag on your portfolio?
Re: Do you think about volatility drag on your portfolio?
There is some discussion here: viewtopic.php?t=273
Re: Do you think about volatility drag on your portfolio?
Random Walker wrote:Volatility does affect CAGR. It lowers CAGR. Prove it to yourself. Create two series of returns where both series has the same average annual return. Assign different standard deviations to the two series. Calculate the CAGR for the two series. You'll see that increased volatility, decreases CAGR. The greater the volatility, the bigger the difference between the weighted average annual portfolio return and the CAGR. Don't even consider average annual return as anything other than a forward looking expected weighted mean of portfolio components. Try different assigned SDs and you'll see the effect on terminal value.
In constructing a portfolio ex ante, we look at expected mean average annual returns for portfolio components, their individual SDs, and correlations. In evaluating the portfolio ex post, we look at the actual compounded CAGR and the portfolio SD. By minimizing the expected portfolio SD for a given expected return , we increase the chances of maximizing CAGR ex post relative to the returns of the portfolio components.
Dave
Dave
Dave, I admit that I am not much of a mathematician but reading your post above I get the sense that you are right. It makes sense that a steadier, lower volatility approach should result in higher returns over time. Even I get that sense and seek to boost returns a bit and reduce volatility.
My opinion is that we should do our best to come up with a solution even knowing that the solution is imperfect, imprecise, and won't work all the time. At least I have given it the old college try.
Where people get frustrated with me is that I am looking at this from a behavioral aspect and that I am trying to be "real world" in my approach. When you invest in stuff and watch how it performs under different market conditions you learn some things. Something about owning investments and having money on the line that motivates learning. I know it all sounds anecdotal but there is something to real life experience which too often just gets dismissed.
The quants can beautifully describe what happened but they seem a bit weak on the "why." The quants see volatility drag as a problem but only have an imperfect and imprecise answer on how to solve it. The best the we can do is invest in volatile, noncorrelating asset classes in order to boost returns a bit and reduce volatility. We get the "correct" asset allocations by using history as a guide and making reasonable projections into the future. Not perfect but far better than nothing.
Just saying that we can avoid volatility drag by diversifying is an incomplete answer. Dave, you have given a pretty good answer about the type of diversification needed and I applaud you for that. Others just say that the rest of us don't understand.
A fool and his money are good for business.
Re: Do you think about volatility drag on your portfolio?
I'll repost it again
This alone already does most of what you can do, with little effort (if you have access to a few low cost funds covering most of the market).
*3!4!/5! wrote:Reposting:
viewtopic.php?p=3278479#p3278479*3!4!/5! wrote:^^ I should add that when it comes to volatility drag, diversification is doing something about it.
This alone already does most of what you can do, with little effort (if you have access to a few low cost funds covering most of the market).

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Re: Do you think about volatility drag on your portfolio?
Nedsaid,
I'm no quant either! I agree strongly with your behavioral perspective. In fact that is one of the biggest reasons behind my focus on diversification across factors. If a person is truly diversified, some component of the portfolio is always underperforming and some component outperforming. By investing in everything and focusing on the portfolio as a whole, I'm way less likely to abandon the plan.
Dave
I'm no quant either! I agree strongly with your behavioral perspective. In fact that is one of the biggest reasons behind my focus on diversification across factors. If a person is truly diversified, some component of the portfolio is always underperforming and some component outperforming. By investing in everything and focusing on the portfolio as a whole, I'm way less likely to abandon the plan.
Dave
Re: Do you think about volatility drag on your portfolio?
Random Walker wrote:Nedsaid,
I'm no quant either! I agree strongly with your behavioral perspective. In fact that is one of the biggest reasons behind my focus on diversification across factors. If a person is truly diversified, some component of the portfolio is always underperforming and some component outperforming. By investing in everything and focusing on the portfolio as a whole, I'm way less likely to abandon the plan.
Dave
I agree. I am attempting to diversify across factors best I can. The reason that I take stock in academic research and Larry Swedroe is that their assertions make sense from a behavioral standpoint and are consistent with what I have observed with my own investments. It is also consistent with what I have heard market professionals talk about for years.
The thing is that I have examined all of this with a skeptical eye and have listened to those who don't believe in factors or the academic research. I can see the strong and weak arguments that both sides make. In other words, I can see both sides of the argument.
To be successful in investing, one doesn't have to do everything right but the most important things right and doing those things consistently. If people don't think I understand concepts like volatility drag and that I don't know what I am talking about, I only have to look at my returns and account balances. So far, I have done well enough.
A fool and his money are good for business.
Re: Do you think about volatility drag on your portfolio?
Random Walker wrote:I'm curious what others think.
Dave
I had to return to the OP to see what the original question was on the table....
My perspective  I understand the difference is between arithmetic and geometric means and I feel like I understand MPT and efficiency frontiers but realistically, I never use any of it. I pretty much am a 3fund investor (OK, I tilt a bit with SCV) and figure I will get what I get. The theory is fun to look at but I never use it to design anything.
So, yes, volatility drag is real but I have no practical use for applying it. I just don't try to guess what my returns will be and never bother to calculate what they have been in the past. I cannot change the past and I have faith that my plan for the future will work out OK. I do pay attention to risk though, and lowandbehold, risk is related to volatility so we end up the same place, just by another path!
Kolea (pron. kolayuh). Golden plover.

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Re: Do you think about volatility drag on your portfolio?
Thought I'd resurrect this thread with a quote from Ang's book Asset Management. Page 146.
"Jensen's terms arise because the difference between geometric returns, which take into account compounding over the long run, and arithmetic returns, which do not compound. In a oneperiod setting, geometric and arithmetic returns are economically identical; they are simply different ways of reporting increases or decreases in wealth. Thus, there is no rebalancing premium for a shortrun investor. Over multiple periods, the difference between geometric and arithmetic returns is a function of asset,volatility, specifically approximately 1/2 sigma ^2, where sigma is the volatility of arithmetic returns. The greater the volatility, the greater the rebalancing premium. As this manifests over time, only longterm investors can collect a rebalancing premium.
For US stocks, the rebalancing premium a long run investor can earn is approximately 1/2(0.2)^2 = 1
Dave
"Jensen's terms arise because the difference between geometric returns, which take into account compounding over the long run, and arithmetic returns, which do not compound. In a oneperiod setting, geometric and arithmetic returns are economically identical; they are simply different ways of reporting increases or decreases in wealth. Thus, there is no rebalancing premium for a shortrun investor. Over multiple periods, the difference between geometric and arithmetic returns is a function of asset,volatility, specifically approximately 1/2 sigma ^2, where sigma is the volatility of arithmetic returns. The greater the volatility, the greater the rebalancing premium. As this manifests over time, only longterm investors can collect a rebalancing premium.
For US stocks, the rebalancing premium a long run investor can earn is approximately 1/2(0.2)^2 = 1
Dave

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Re: Do you think about volatility drag on your portfolio?
Random, I have newer thoughts on this re. geo ret. vs arith. I just knew that the geo return over multiple periods (time) was the geo equivalent of a straight line ( the same ret yr after yr.), and that the end result of varying returns (volatility) resulted in a mean (geo) return.
But the mean arith ret. does not factor in (or account for) the compounding; hence not the actual realized return.
But rehashing this, if as dbr mentioned in March, consider forward looking where we don't fully know the possible returns ( as nedsaid has seemed to say.); and I myself see returns as very nonrandom, but caused by a riskon/riskoff factor and general economic conditions, and this gist.
But, it is believed that higher returns are associated with higher volatility. And if we got lower returns from such, that would not be consistent historicallybut, there it is again: backward looking. I really am not sure the usefulness of standard (normal or gaussian? ) arithmetic statistics for markets' behavior This doesn't help me much.
But I look to the innate properties of the equities themselves for expected returns. And again , the more risky/ the more the return gets bidup. If I got an asset that had very low volatility with higher return, I'd have a very very good bond fund. .
So, I just face it as an expected mean return with some volatility.
So, I concede that a 50% decline requires an 100% gain to even, but it's not what I'd expect over time. But I also concede that the sort of 'risk reset', economically, always lurks and happens time to time.
But the mean arith ret. does not factor in (or account for) the compounding; hence not the actual realized return.
But rehashing this, if as dbr mentioned in March, consider forward looking where we don't fully know the possible returns ( as nedsaid has seemed to say.); and I myself see returns as very nonrandom, but caused by a riskon/riskoff factor and general economic conditions, and this gist.
But, it is believed that higher returns are associated with higher volatility. And if we got lower returns from such, that would not be consistent historicallybut, there it is again: backward looking. I really am not sure the usefulness of standard (normal or gaussian? ) arithmetic statistics for markets' behavior This doesn't help me much.
But I look to the innate properties of the equities themselves for expected returns. And again , the more risky/ the more the return gets bidup. If I got an asset that had very low volatility with higher return, I'd have a very very good bond fund. .
So, I just face it as an expected mean return with some volatility.
So, I concede that a 50% decline requires an 100% gain to even, but it's not what I'd expect over time. But I also concede that the sort of 'risk reset', economically, always lurks and happens time to time.

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Re: Do you think about volatility drag on your portfolio?
MIpreretirey,
I agree, for individual assets more risk yields more expected return. And the expected return of a portfolio would be the weighted Mean average expected return of portfolio components. But combining components of equal expected return with less than perfect correlations into a portfolio will keep Mean expected return constant and likely bring the geometric return of the portfolio closer to that simple average.
Dave
I agree, for individual assets more risk yields more expected return. And the expected return of a portfolio would be the weighted Mean average expected return of portfolio components. But combining components of equal expected return with less than perfect correlations into a portfolio will keep Mean expected return constant and likely bring the geometric return of the portfolio closer to that simple average.
Dave

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Re: Do you think about volatility drag on your portfolio?
I was just going to add about the 2 assets mixed, and noncorrelation. True, but I can just say I'm on the fence and leaning toward correlations are unpredictable. And seems this could add another derivative of nonpredictability which is larger and which could [u]add to total volatility. Maybe.[/u]
Edit for ? for anyone:
Is the fact that correlation cannot be greater than 1 disprove an added volatility? for adding asset classes? Hmm, hmm, hmm.
But it could just lower return, regardless.
Edit for ? for anyone:
Is the fact that correlation cannot be greater than 1 disprove an added volatility? for adding asset classes? Hmm, hmm, hmm.
But it could just lower return, regardless.

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Re: Do you think about volatility drag on your portfolio?
Edit:
I probably shouldn't sidetrack this with additional ?s . Just say I don't know enough to know I don't know.
I probably shouldn't sidetrack this with additional ?s . Just say I don't know enough to know I don't know.
Re: Do you think about volatility drag on your portfolio?
I don't think or worry about volatility drag because in general, it does not exist. The example is always given that if the market drops by 30% and then goes up by 30% you end up in a different spot. That is true but it has no applicability to the actual market. Buried in that example is the assumption that there is some type of "conservation of market % moves" at play. Why don't we use the example of the market goes down by 100 points and then goes up by 100 points and end up at the same point to show volatility at work?
Volatility can effect your return if you take some action. The return from the compounding of dividends will depend on the price path of the market. And if you rebalance volatility can change your returnyou may even have a volatility bonus!
But as far as the up and down motion of price the thing that matters is how much money you end up with not the formula you use to calculate return.
TJSI
Volatility can effect your return if you take some action. The return from the compounding of dividends will depend on the price path of the market. And if you rebalance volatility can change your returnyou may even have a volatility bonus!
But as far as the up and down motion of price the thing that matters is how much money you end up with not the formula you use to calculate return.
TJSI

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Re: Do you think about volatility drag on your portfolio?
TJSI,
How much money you end up with is a function of the portfolio's geometric return. By dampening portfolio volatility, the geometric return is a bigger chunk of the average return of portfolio components.
Dave
How much money you end up with is a function of the portfolio's geometric return. By dampening portfolio volatility, the geometric return is a bigger chunk of the average return of portfolio components.
Dave

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Re: Do you think about volatility drag on your portfolio?
RW,
I disagree. If volatility is reduced then the arithmetic mean is brought down towards the geo. mean.
Volatility should be measured as the deviation from the ongoing geo. mean (or the expected mean.)
btw, if you can't show this is wrong, then that mean's I'm right. Try.
I disagree. If volatility is reduced then the arithmetic mean is brought down towards the geo. mean.
Volatility should be measured as the deviation from the ongoing geo. mean (or the expected mean.)
btw, if you can't show this is wrong, then that mean's I'm right. Try.
Re: Do you think about volatility drag on your portfolio?
Dave,
Sorry to disagree. The return of a portfolio only depends on the starting point and ending point. It does not depend on the number of cycles (volatility) it took to get there.
If you compound or rebalance along the way, then the geometric return is correct. Up and downs only effect return if some action occurs during the path of the portfolio.
If you add bonds to your portfolio of stocks to dampen volatility, the return is still the Markowitz returnthe weighted sum of the stock return and bond return. The portfolio will have a lower volatility but the return is calculated without regard to the volatility.
TJSI
Sorry to disagree. The return of a portfolio only depends on the starting point and ending point. It does not depend on the number of cycles (volatility) it took to get there.
If you compound or rebalance along the way, then the geometric return is correct. Up and downs only effect return if some action occurs during the path of the portfolio.
If you add bonds to your portfolio of stocks to dampen volatility, the return is still the Markowitz returnthe weighted sum of the stock return and bond return. The portfolio will have a lower volatility but the return is calculated without regard to the volatility.
TJSI

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Re: Do you think about volatility drag on your portfolio?
MIPreretirey,
Set up a few random return series in Excel. I think the functions are rnd, norm dist. Create different series of annual returns over 2030 years with the same Mean return but different standard deviations. The greater the SD, the bigger the difference between the simple Mean and the geo mean.
If you want I can go back and see exactly what functions I used. If I remember, keeping Mean return about 5%, decreasing SD from like 18 to 14 decreased the volatility drag by about 0.50.7%.
Dave
Set up a few random return series in Excel. I think the functions are rnd, norm dist. Create different series of annual returns over 2030 years with the same Mean return but different standard deviations. The greater the SD, the bigger the difference between the simple Mean and the geo mean.
If you want I can go back and see exactly what functions I used. If I remember, keeping Mean return about 5%, decreasing SD from like 18 to 14 decreased the volatility drag by about 0.50.7%.
Dave

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Re: Do you think about volatility drag on your portfolio?
TJSI,
Sounds like you may know more than me, but I think I am right here. First of all, I am assuming rebalancing. Secondly, could we be confusing sequence of returns with volatility. I think I agree that for fixed AA, two series with same annual returns but in different sequence, terminal amount will be same. But if two series have same simple average return but different volatilities (different annual returns that average the same) and rebalanced, they will have different geo returns.
Are you familiar with this approximation, GeoMean = SimpleMean  1/2(SD)^2.
If I'm wrong, I'm happy to be corrected; eager to learn.
Dave
Sounds like you may know more than me, but I think I am right here. First of all, I am assuming rebalancing. Secondly, could we be confusing sequence of returns with volatility. I think I agree that for fixed AA, two series with same annual returns but in different sequence, terminal amount will be same. But if two series have same simple average return but different volatilities (different annual returns that average the same) and rebalanced, they will have different geo returns.
Are you familiar with this approximation, GeoMean = SimpleMean  1/2(SD)^2.
If I'm wrong, I'm happy to be corrected; eager to learn.
Dave

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Re: Do you think about volatility drag on your portfolio?
Random Walker wrote:MIPreretirey,
Set up a few random return series in Excel. I think the functions are rnd, norm dist. Create different series of annual returns over 2030 years with the same Mean return but different standard deviations. The greater the SD, the bigger the difference between the simple Mean and the geo mean.
If you want I can go back and see exactly what functions I used. If I remember, keeping Mean return about 5%, decreasing SD from like 18 to 14 decreased the volatility drag by about 0.50.7%.
Dave
All right.
But do need to rebalance (means need 2 or more assets, but could be, eg:, a balanced fund.)
(and depends on how optimal is the rebalancing.)
Without rebalancing:
A returns 1.03, 1.05 ... total 1.0815
B returns 1.05, 1.03 ... total 1.0815; result 1.0815
Optimal rebal:
A + B returns 1.04, rebal.; A + B returns 1.04 ... total 1.0816
A lessoptimal rebalance would fall in between.

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Re: Do you think about volatility drag on your portfolio?
I will add my 2 cents as I think I replied a lot to this thread when it started but we all kept talking past each other at that time. Perhaps I can be clearer in my explanation (how I think), this time.
In my view there is NO volatility drag for practical, optimized portfolios. It is just plain nonsense.
Case1: No rebalancing involved. In this case, the N assets in a portfolio are simply independent. All one needs to know is the starting value of each asset, ending value of each asset. The path followed by each asset is irrelevant. After the fact, one can compute a number (geometric mean) which describes the average compounding rate given t0 and t1. Volatility is irrelevant in this case. The argument between arithmetic mean and geometric mean is irrelevant because all you need to know is the initial asset value and final asset value (for each independent asset).
Case2: Rebalancing. There is NO generally accepted history or theory which shows significant rebalancing bonus. If you have N assets and rebalance when some "balance bounds" are exceeded, this may or may not outperform the simple static case where you just bought the assets, ignored volatility and did no rebalancing...
The more accepted idea is of rebalancing as some method to control risk. OK, but that is completely different..you accept that you are willing to decrease returns to decrease risk and to reduce volatility.
My philosophy is to buy multiple assets (in my case US and International stocks at full market weight) and simply let them do what they will. I don't care about them moving up or down in synch or opposite of each other. By leaving them alone, they by definition follow the world stock. Because I don't believe there is a rebalancing bonus, I don't rebalance and hence never worry about this notion of "volatility drag".
So, folks arguing for "volatility drag" have this conundrum: either you don't rebalance, in which case there is no volatility drag or you do rebalance, in which case you should do it for risk..which will likely lead to lower returns anyway..so where is this drag due to volatility? The best approach would have been to just ignore volatility and not rebalance, in which case the drag goes away
In my view there is NO volatility drag for practical, optimized portfolios. It is just plain nonsense.
Case1: No rebalancing involved. In this case, the N assets in a portfolio are simply independent. All one needs to know is the starting value of each asset, ending value of each asset. The path followed by each asset is irrelevant. After the fact, one can compute a number (geometric mean) which describes the average compounding rate given t0 and t1. Volatility is irrelevant in this case. The argument between arithmetic mean and geometric mean is irrelevant because all you need to know is the initial asset value and final asset value (for each independent asset).
Case2: Rebalancing. There is NO generally accepted history or theory which shows significant rebalancing bonus. If you have N assets and rebalance when some "balance bounds" are exceeded, this may or may not outperform the simple static case where you just bought the assets, ignored volatility and did no rebalancing...
The more accepted idea is of rebalancing as some method to control risk. OK, but that is completely different..you accept that you are willing to decrease returns to decrease risk and to reduce volatility.
My philosophy is to buy multiple assets (in my case US and International stocks at full market weight) and simply let them do what they will. I don't care about them moving up or down in synch or opposite of each other. By leaving them alone, they by definition follow the world stock. Because I don't believe there is a rebalancing bonus, I don't rebalance and hence never worry about this notion of "volatility drag".
So, folks arguing for "volatility drag" have this conundrum: either you don't rebalance, in which case there is no volatility drag or you do rebalance, in which case you should do it for risk..which will likely lead to lower returns anyway..so where is this drag due to volatility? The best approach would have been to just ignore volatility and not rebalance, in which case the drag goes away
Re: Do you think about volatility drag on your portfolio?
What do you mean by this?nedsaid wrote:No, it isn't crazy. You argued very passionately about portfolio drag. I asked a very simple question. If this is such a big problem, why haven't you chosen to do anything about it?*3!4!/5! wrote:These threads just get crazy!

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Re: Do you think about volatility drag on your portfolio?
I wont let go of this kind of like a bull dog holding on to his chewey toy
https://www.soa.org/Library/Newsletters ... aulay.aspx
Dave
https://www.soa.org/Library/Newsletters ... aulay.aspx
Dave
Re: Do you think about volatility drag on your portfolio?
Dave,
Yes, I am familiar with the formula showing the appox relationship between arith return and geo return. All it means is that if you use a different algorithm to compute return you get a different number. It does not mean there was a loss of money. If you computed the return using continuous computing you would get yet another number and it would be smaller. It would not mean you had a greater loss.
The wiggles along the trajectory of price do not cause a loss. Rebalancing along the way might reduce your return or if you are smart/lucky you may have a gain and we could call it the volatility reward.
TJSI
Yes, I am familiar with the formula showing the appox relationship between arith return and geo return. All it means is that if you use a different algorithm to compute return you get a different number. It does not mean there was a loss of money. If you computed the return using continuous computing you would get yet another number and it would be smaller. It would not mean you had a greater loss.
The wiggles along the trajectory of price do not cause a loss. Rebalancing along the way might reduce your return or if you are smart/lucky you may have a gain and we could call it the volatility reward.
TJSI

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Re: Do you think about volatility drag on your portfolio?
MIpreRetirey wrote:RW,
I disagree. If volatility is reduced then the arithmetic mean is brought down towards the geo. mean.
Volatility should be measured as the deviation from the ongoing geo. mean (or the expected mean.)
btw, if you can't show this is wrong, then that mean's I'm right. Try.
MIpreRetirey wrote:Random Walker wrote:MIPreretirey,
Set up a few random return series in Excel. I think the functions are rnd, norm dist. Create different series of annual returns over 2030 years with the same Mean return but different standard deviations. The greater the SD, the bigger the difference between the simple Mean and the geo mean.
If you want I can go back and see exactly what functions I used. If I remember, keeping Mean return about 5%, decreasing SD from like 18 to 14 decreased the volatility drag by about 0.50.7%.
Dave
All right.
But do need to rebalance (means need 2 or more assets, but could be, eg:, a balanced fund.)
(and depends on how optimal is the rebalancing.)
Without rebalancing:
A returns 1.03, 1.05 ... total 1.0815
B returns 1.05, 1.03 ... total 1.0815; result 1.0815
Optimal rebal:
A + B returns 1.04, rebal.; A + B returns 1.04 ... total 1.0816
A lessoptimal rebalance would fall in between.
I think I'm right, and here's another go. So far I think I'm right.
Asset A returns 1.03, 1.05 , but expected simple return of 1.05/yr.
Asset B "" 1.05, 1.03 , " ".
After yr 1, A at 1.03, B at 1.05. Both, ongoing indef/w/no reversion, still expect 1.04 ongoing.
A should get the 1.03 and a 1.04, B should get a 1.05 and a 1.04.
No rebal result (at 50/50) is 50/50 avg of (1.03, 1.04) and (1.05, 1.04) ; total vectors (1.0712 and 1.092)
With rebal: 1.04, rebal; 1.04 (both). Total , same 1.04 but with 1 year only of volatility.
Got same total without timevolatility multiplication. Hence, rebalancing is purely chance in time.I know.

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Re: Do you think about volatility drag on your portfolio?
And here's another explanation from Lussier's textbook: Successful Investing Is A Process. His explanation is that volatility hinders reinvestment of cash flows.
https://books.google.com/books?id=lyTjI ... an&f=false
Dave
https://books.google.com/books?id=lyTjI ... an&f=false
Dave

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Re: Do you think about volatility drag on your portfolio?
Dave
If you actually follow the book you just quoted and simply go to the next paragraph/next page, that BOOK basically says what many of us have been saying: "if you don't rebalance and the initial and final asset values are the same, the path followed doesn't matter." That is literally what the book your quoted says. If you think it through, your sources are actually saying exactly opposite of what you think they are saying.
If you actually follow the book you just quoted and simply go to the next paragraph/next page, that BOOK basically says what many of us have been saying: "if you don't rebalance and the initial and final asset values are the same, the path followed doesn't matter." That is literally what the book your quoted says. If you think it through, your sources are actually saying exactly opposite of what you think they are saying.

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Re: Do you think about volatility drag on your portfolio?
I assume we all rebalance for risk control.
Dave
Dave
Re: Do you think about volatility drag on your portfolio?
Random Walker wrote:I assume we all rebalance for risk control.
Rebalancing is for reducing volatility drag.
Re: Do you think about volatility drag on your portfolio?
From Mar 10, 2017
Sorry, I didn't see this until now. There is indeed a wiki article: Variance drain
Added to the article:
 This thread
 Random Walker's link to Expected Geometric Returns
 The OP's link to CAGR vs. Average Annual Return: Why Your Advisor Is Quoting the Wrong Number < a good tutorial, new investors should read this.
Comments / questions / concerns are welcome. Wiki editors are welcome to update the page directly.
===========
I don't understand why Rebalancing is part of this discussion, as I thought rebalancing risk was a totally different effect. The bottom of the wiki article references a few papers on this, including a Larry Swedroe article that says rebalancing is for style drift.
Dirghatamas wrote:...If the Boglehead Wiki has an article on that perhaps it should be worded more carefully
Sorry, I didn't see this until now. There is indeed a wiki article: Variance drain
Added to the article:
 This thread
 Random Walker's link to Expected Geometric Returns
 The OP's link to CAGR vs. Average Annual Return: Why Your Advisor Is Quoting the Wrong Number < a good tutorial, new investors should read this.
Comments / questions / concerns are welcome. Wiki editors are welcome to update the page directly.
===========
I don't understand why Rebalancing is part of this discussion, as I thought rebalancing risk was a totally different effect. The bottom of the wiki article references a few papers on this, including a Larry Swedroe article that says rebalancing is for style drift.

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Re: Do you think about volatility drag on your portfolio?
LadyGeek wrote:Dirghatamas wrote:...If the Boglehead Wiki has an article on that perhaps it should be worded more carefully
Sorry, I didn't see this until now. There is indeed a wiki article: Variance drain
===========
I don't understand why Rebalancing is part of this discussion, as I thought rebalancing risk was a totally different effect. The bottom of the wiki article references a few papers on this, including a Larry Swedroe article that says rebalancing is for style drift.
Long post below. Sorry about that but simplifying just seems to lead to folks talking past each other.
LadyGeek I was out on a business trip so just getting to reply on Bogleheads forum posts. Yes, I do think that while the math behind all this is straightforward, how is this ACTIONABLE is mostly around rebalancing (or not). While all this will not affect experienced investors, it MIGHT help new investors think more clearly about some concepts.
First, for the visually inclined, here is an article I felt did a great job of describing the issue:
The myth of volatility drag https://blogs.cfainstitute.org/investor/2015/03/23/themythofvolatilitydragpart1/
Basic math everybody agrees on: For an asset that compounds over time, one can model its performance over time
Final Value = Initial Value* (1+r1)*(1+r2)...(1+rt). Here rn is typically called the return in the nth interval. One can do this daily, monthly, yearly or at whatever intervals. Note that if r1, r2..rt are NOT the same number, then the asset is said to have volatility. Usually, assets with significant returns also have significant volatility..so many of us consider volatility to be a feature rather than a bug.
If one wants to simplify/abstract this modeling, they can create a number called a geometric mean, such that
Final value = Initial Value* (1+rGM)^t. Or, 1+ rGM = ((1+r1)*(1+r2)..(1+rt))^1/t
Creating this model/abstraction leaves less information (volatility) in the model but still models the total returns correctly. Geometric means are the natural way to model a simple 1 asset compounding asset.
One can also create another (more complex) model using arithmetic mean, variance and volatility drag to model the same system. Here we define rAM = (r1+r2+...rt)/t. We also define rAM rGM = Volatility drag. Note that this is just putting a visual/cool sounding name to the well known approximation: AM  GM ~ V/2 where V is the variance of the samples.
Now, let's look at practical application to investments
1) Investor holds a single asset e.g. 100% US stocks or 100% world stocks or 100% bonds or whatever. In this case, there is no rebalancing obviously. The returns one gets are adequately modeled by the time series, r1,r2..rt and if one wants to simplify (leaving volatility out of the model) by the Geometric mean. Proponents of volatility drag as a REAL thing argue that if you could have an asset that had the same arithmetic returns as your present asset, but less volatility, its geometric returns would have been higher. As such, your 100% stock portfolio, has a volatility drag. People like me point out that the only asset that had stock like returns with no volatility was Bernie Madoff's portfolio in other words, this is searching for Unicorns and Rainbows. Volatility is a part of the high return assets and there is no reason to introduce such mythical concepts because there is nothing actionable..if we could all find high return assets with no volatility, of course we would all move out of stocks
2) Multiple assets with no rebalancing: One could have say 60/40 stocks/bonds or 50/50 US/ex US stocks or whatever. If one doesn't rebalance (money isn't moving between assets), then this system is just like 1. The portfolio's initial value and final value are just the weighted sums of individual assets. As such, one can again find returns r1...rn over the time intervals and calculate simplifications/abstractions like geometric mean to model returns. How one decides on the initial allocation is left out as that depends on many factors: risk tolerance, age and many other things. However, strictly from the point of modeling returns, there is no reason to go away from geometric means and no real advantage to thinking in terms of arithmetic means, variance, volatility drag.
3) Multiple assets with rebalancing. Now we are getting somewhere. The argument here is that instead of thinking in terms of returns, we create a portfolio by thinking in terms of "risk adjusted returns". We look (in the past) at the volatility and returns (as well as correlation) of various assets: US stocks, International stocks, US bonds, Gold..whatever. Then we create some kind of efficient frontier. Instead of having say 100% US stocks or 100% world stocks, one goes with say 50% bonds and replaces the US stocks with some factor (say small cap value). By calculating the past returns and variance (volatility) of each asset class, you can (apparently with rebalancing) create an overall asset that will meet the total returns of the simple asset portfolio (say 100% US stocks or World Stock) but do it with much less volatility. This (if true) then delivers the early promise of Unicorns.
My concern is that this is only possible with rebalancing (for returns not just risk control). If this is possible WITHOUT rebalancing, then you simply have a better asset class. You should have simply used it in the first place e.g. if you do believe with full conviction that US small cap value will outperform the US total market, then go there..and thinking in terms of volatility drag was useless. If the property came out due to this rebalancing/time correlations, then one needs to backtest it and if true, one could argue for something called volatility drag.
As should be obvious, I am highly skeptical of finding Unicorns. Higher returns usually come with higher risk and one should think of volatility as a feature, not a bug. Reducing risk is fine and it will likely reduce returns. I am highly skeptical that bringing the concept of volatility drag will help Bogleheads do something actionable.

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Re: Do you think about volatility drag on your portfolio?
Dirghatamas,
It is very real and very actionable. Diversify across as many weakly, non, negatively correlated sources of return as possible and rebalance. The arithmetic Mean return of the portfolio will be the weighted average Mean return of the components. The Mean volatility of the portfolio will be less than the weighted Mean of the individual portfolio component volatilities because of less than perfect correlations. The lower the portfolio volatility, the closer it's geometric Mean will be to its arithmetic mean.
I've found an excellent description of the effect: Jacques Lussier's Successful Investing Is A Process p. 5463. I really like this book!!! Strong recommend.
Here's a recommendation of the book from CFA Institute.
https://blogs.cfainstitute.org/investor ... aprocess/
Dave
It is very real and very actionable. Diversify across as many weakly, non, negatively correlated sources of return as possible and rebalance. The arithmetic Mean return of the portfolio will be the weighted average Mean return of the components. The Mean volatility of the portfolio will be less than the weighted Mean of the individual portfolio component volatilities because of less than perfect correlations. The lower the portfolio volatility, the closer it's geometric Mean will be to its arithmetic mean.
I've found an excellent description of the effect: Jacques Lussier's Successful Investing Is A Process p. 5463. I really like this book!!! Strong recommend.
Here's a recommendation of the book from CFA Institute.
https://blogs.cfainstitute.org/investor ... aprocess/
Dave
I've never found arguments for volatility drag convincing. Yes, there are a number of mathematical artifacts out there, but these issues can be simplified away by looking at the correct numbers.
An easy way to simplify is to simply look at the final amount of money in one's portfolio. That is what is in fact used to show volatility drag exists does it not?
The math gets complicated after awhile. The concepts get too abstract.
My personal guiding light in conducting analysis is always arranging my dichotomy as such: How much would I have at the end if I followed course A vs course B?
If you start following things like geometric return, then yes, the numbers can indeed be misleading.
In my personal portfolio, volatility drag is of no consequence. Because my investment philosophy is 100% stocks (meaning I don't rebalance) stay the course, the idea that I should worry about an odd scenario where my stocks drop 50%, then rise 100% then drop 50% again, then rise 100% again, which may produce misleading numbers on my annual percentage gains is something I don't see value in worrying about.
An easy way to simplify is to simply look at the final amount of money in one's portfolio. That is what is in fact used to show volatility drag exists does it not?
The math gets complicated after awhile. The concepts get too abstract.
My personal guiding light in conducting analysis is always arranging my dichotomy as such: How much would I have at the end if I followed course A vs course B?
If you start following things like geometric return, then yes, the numbers can indeed be misleading.
In my personal portfolio, volatility drag is of no consequence. Because my investment philosophy is 100% stocks (meaning I don't rebalance) stay the course, the idea that I should worry about an odd scenario where my stocks drop 50%, then rise 100% then drop 50% again, then rise 100% again, which may produce misleading numbers on my annual percentage gains is something I don't see value in worrying about.
Re: Do you think about volatility drag on your portfolio?
*3!4!/5! wrote:Random Walker wrote:I assume we all rebalance for risk control.
Rebalancing is for reducing volatility drag.
For example consider two asset A and B which are perfectly anticorrelated, and each time period, with equal probability, one gains 25% and the other loses 24%.
More generally make it "one gains X% and the other loses Y%" where XY>0 but (1+X/100)(1Y/100)<1.
Dirghatamas, TomCat96, I strongly suggest you try to understand this example.
Re: Do you think about volatility drag on your portfolio?
*3!4!/5! wrote:*3!4!/5! wrote:Random Walker wrote:I assume we all rebalance for risk control.
Rebalancing is for reducing volatility drag.
For example consider two asset A and B which are perfectly anticorrelated, and each time period, with equal probability, one gains 25% and the other loses 24%.
More generally make it "one gains X% and the other loses Y%" where XY>0 but (1+X/100)(1Y/100)<1.
Dirghatamas, TomCat96, I strongly suggest you try to understand this example.
I don't see what you're trying to show here.
If you're a math guy, which your handle suggests, then this is what I recommend, coming from an engineering background.
Complete the argument in words. There seems to be this inherent assumption among STEM that by merely showing the math, there is only one indisputable argument and conclusion that can be drawn.
From what I can see, what you cited is a frequent example of what volatility drag is. I think you must be assuming that if I were to understand that that 1.25 * .76 < 1, then it should be clear to me that volatility drag is in fact real and something I cannot dismiss.
Did you however understand my counter to that in my original post?
Re: Do you think about volatility drag on your portfolio?
Random Walker,
The example you give is correct but there may be a wrong implication.
As you explain, when you add a volatile asset to a portfolio the expected return is just the weighted sum of the assets' returns. The volatility did not reduce the return. There was no drag on return. The volatility of the resultant mix does change but not the expected return.
Yes, the arithmetic return is greater than the geometric return. But you should not care for what matters is how much money you end up with.
TJSI
The example you give is correct but there may be a wrong implication.
As you explain, when you add a volatile asset to a portfolio the expected return is just the weighted sum of the assets' returns. The volatility did not reduce the return. There was no drag on return. The volatility of the resultant mix does change but not the expected return.
Yes, the arithmetic return is greater than the geometric return. But you should not care for what matters is how much money you end up with.
TJSI
Re: Do you think about volatility drag on your portfolio?
Think about it. Try to understand.

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Re: Do you think about volatility drag on your portfolio?
*3!4!/5! wrote:*3!4!/5! wrote:Random Walker wrote:I assume we all rebalance for risk control.
Rebalancing is for reducing volatility drag.
For example consider two asset A and B which are perfectly anticorrelated, and each time period, with equal probability, one gains 25% and the other loses 24%.
More generally make it "one gains X% and the other loses Y%" where XY>0 but (1+X/100)(1Y/100)<1.
Dirghatamas, TomCat96, I strongly suggest you try to understand this example.
[OT comment removed by admin LadyGeek] Or is it more likely they are arguing at a higher level, that finding asset classes with high returns with GUARANTEED anticorrelation and then rebalancing with perfect timing to get an outsized return..is looking for Unicorns and Rainbows.
Either way, as I stated many times in this thread, all this matters only if you rebalance for higher returns (not lower risks). There is precious little backtesting to show the higher performance of rebalancing (so called rebalancing bonus). Backtesting consistently shows that simply having a higher % in the higher returns asset e.g. 100% stocks usually leads to higher returns. Till you show that rebalancing leads to higher returns than that, a much simpler model is to think in terms of geometric returns, ignore volatility and ignore mythical concepts like volatility drag.
For the record, I have been investing now for 25 years in 100% world stocks and have never found this concept of volatility drag to be worth even 1 penny YMMV.
Re: Do you think about volatility drag on your portfolio?
The problem has nothing to do with mathematical facts and everything to do with statements such as "volatility drag is real." What does "real" mean in that statement? As far as that goes, what do people think they mean by "volatility drag"? The problem might have something to do with when in a discussion we should refer to arithmetic mean and when in a discussion we should refer to geometric mean. It also has to do with which of the two would be used to answer which questions and when we have to consider both and the relationship between the two. In the end it has to do with what things might be done, if any, to design a portfolio that results in expecting to have more money after a period of time than might be obtained by some other portfolio.

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Re: Do you think about volatility drag on your portfolio?
TomCat,
100% Equity is not relevant. You can be 100% Equity and diversify across non, negatively, weakly, correlated sources of return (value, size, Momentum, geography) or not diversify and just be 100% TSM. Sharpe ratio increased and volatility drag decreased when diversify. The diversification power is increased the more equal the exposure to the risks and the lower the correlations.
PS in another way, your 100% equity is VERY RELEVANT. The Variance drain is worst for equity heavy portfolios. The drain is proportional to Variance, which means proportional to SD^2! So say you can find a way to decrease the SD of a portfolio from 20 to 18 (Perhaps tilt equity to SV and add 10% bonds or something analogous). That would decrease the drag on returns by (20%^2  18%^2) / 2 = 0.38%. That is not at all insignificant on a website. Where people talk a lot about 0.2% differences in expense ratios!!!
Dave
100% Equity is not relevant. You can be 100% Equity and diversify across non, negatively, weakly, correlated sources of return (value, size, Momentum, geography) or not diversify and just be 100% TSM. Sharpe ratio increased and volatility drag decreased when diversify. The diversification power is increased the more equal the exposure to the risks and the lower the correlations.
PS in another way, your 100% equity is VERY RELEVANT. The Variance drain is worst for equity heavy portfolios. The drain is proportional to Variance, which means proportional to SD^2! So say you can find a way to decrease the SD of a portfolio from 20 to 18 (Perhaps tilt equity to SV and add 10% bonds or something analogous). That would decrease the drag on returns by (20%^2  18%^2) / 2 = 0.38%. That is not at all insignificant on a website. Where people talk a lot about 0.2% differences in expense ratios!!!
Dave
Last edited by Random Walker on Mon Jun 05, 2017 5:41 pm, edited 1 time in total.

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Re: Do you think about volatility drag on your portfolio?
Dbr,
This is my take on the issues. All that matters is final wealth, which is a function of the portfolio's geometric return. Looking forward, when constructing portfolios, we can use estimates of mean expected returns of individual potential portfolio components to make decisions about whether a specific investment should be added to the portfolio.
Dave
This is my take on the issues. All that matters is final wealth, which is a function of the portfolio's geometric return. Looking forward, when constructing portfolios, we can use estimates of mean expected returns of individual potential portfolio components to make decisions about whether a specific investment should be added to the portfolio.
Dave

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Re: Do you think about volatility drag on your portfolio?
TJSI,
How much money you end up with is the geometric return. Take two portfolios with the same yearly average return and different volatilities. The one with less volatility will have a greater geometric return, greater terminal wealth.
And one can also look at it this way. Say one is looking for a given geo mean from a portfolio. He generates two portfolios with the same expected geo mean but different volatilities. Necessarily, the investor is expecting a greater simple weighted mean return of the components of the more volatile portfolio.
By focusing not only on the expected return of portfolio components, but also on how they mix, one can actually increase returns. Once again, strongly recommend Lussier's book p.5363 for the explanation. Gibson's book helpful too, but doesn't show it with numbers.
Dave
How much money you end up with is the geometric return. Take two portfolios with the same yearly average return and different volatilities. The one with less volatility will have a greater geometric return, greater terminal wealth.
And one can also look at it this way. Say one is looking for a given geo mean from a portfolio. He generates two portfolios with the same expected geo mean but different volatilities. Necessarily, the investor is expecting a greater simple weighted mean return of the components of the more volatile portfolio.
By focusing not only on the expected return of portfolio components, but also on how they mix, one can actually increase returns. Once again, strongly recommend Lussier's book p.5363 for the explanation. Gibson's book helpful too, but doesn't show it with numbers.
Dave
Re: Do you think about volatility drag on your portfolio?
I removed an offtopic comment and several replies. As a remind, see: General Etiquette
We expect this forum to be a place where people can feel comfortable asking questions and where debates and discussions are conducted in civil tones.
...
At all times we must conduct ourselves in a respectful manner to other posters. Attacks on individuals, insults, name calling, trolling, baiting or other attempts to sow dissension are not acceptable.

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Re: Do you think about volatility drag on your portfolio?
Simp = expected simple average return of portfolio
Geo = expected geometric (compound) average return of portfolio
We can look at the expected effect of different volatilities on two portfolios with same expected return.
Geo1 = Simp1  1/2 SD1^2
Geo2 = Simp2  1/2 SD2^2
To see effect of changes in portfolio volatility, keep expected Simple Average constant and vary the SD of two different portfolios: Simp1 = Simp2
Geo1  Geo2 = Simp1  Simp2  1/2(SD1^2  SD2^2)
Geo1  Geo2 = 1/2 (SD1^2  SD2^2)
Dave
Geo = expected geometric (compound) average return of portfolio
We can look at the expected effect of different volatilities on two portfolios with same expected return.
Geo1 = Simp1  1/2 SD1^2
Geo2 = Simp2  1/2 SD2^2
To see effect of changes in portfolio volatility, keep expected Simple Average constant and vary the SD of two different portfolios: Simp1 = Simp2
Geo1  Geo2 = Simp1  Simp2  1/2(SD1^2  SD2^2)
Geo1  Geo2 = 1/2 (SD1^2  SD2^2)
Dave

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Re: Do you think about volatility drag on your portfolio?
Random Walker wrote:Simp = expected simple average return of portfolio
Geo = expected geometric (compound) average return of portfolio
We can look at the expected effect of different volatilities on two portfolios with same expected return.
Geo1 = Simp1  1/2 SD1^2
Geo2 = Simp2  1/2 SD2^2
To see effect of changes in portfolio volatility, keep expected Simple Average constant and vary the SD of two different portfolios: Simp1 = Simp2
Geo1  Geo2 = Simp1  Simp2  1/2(SD1^2  SD2^2)
Geo1  Geo2 = 1/2 (SD1^2  SD2^2)
Dave
Well, I lost my post by taking too much time.
Don't want to show my math fail. .
I couldn't find such a thing as a Geo var by experimenting quickly. So,,,, Yep .
I'm kind of getting that now. The arith mean is abstract. The data points are all that's real. The Geo mean is also abstract/derived on the data.
Geo1  Geo2 = 1/2 (SD1^2  SD2^2)
s/b : Geo1  Geo2 = 1/2 (SD2^2  SD1^2), so higher var. = lower geo mean. (missed a minus sign).

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Re: Do you think about volatility drag on your portfolio?
Wait a minute. Isn't that equation for volatility drag?
Anyway. These equations : Geo mean = Simp mean  1/2 SD^2 ?? = 50 ?
Oh. I see. The data are percentages? .
Anyway. These equations : Geo mean = Simp mean  1/2 SD^2 ?? = 50 ?
Oh. I see. The data are percentages? .

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Re: Do you think about volatility drag on your portfolio?
The arithmetic mean is the arithmetic average of multiplications. .
See wiki on variance drain:
https://www.bogleheads.org/wiki/Variance_drain.
See the 2nd link from the 1st post in this thread:
http://www.investinganswers.com/education/howinvest/cagrvsaverageannualreturnwhyyouradvisorquotingwrongnumber1996.
See wiki on variance drain:
https://www.bogleheads.org/wiki/Variance_drain.
See the 2nd link from the 1st post in this thread:
http://www.investinganswers.com/education/howinvest/cagrvsaverageannualreturnwhyyouradvisorquotingwrongnumber1996.

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Re: Do you think about volatility drag on your portfolio?
To get back on track; aren't we supposed to be saying:
Arith. mean return = (Pf/Pin  1) * (1/n data points) ; data(2400,2500,2600) , A.M.R. = ((2600/2400)  1) * 1/2 = .4.167% avg. ret.
Geo. mean return = nth root(Pf/Pin)  1 ; SQRT(2600/2400) 1 = 4.08329% CAGR
Arith. mean value is totally something else.
Arith. mean return = (Pf/Pin  1) * (1/n data points) ; data(2400,2500,2600) , A.M.R. = ((2600/2400)  1) * 1/2 = .4.167% avg. ret.
Geo. mean return = nth root(Pf/Pin)  1 ; SQRT(2600/2400) 1 = 4.08329% CAGR
Arith. mean value is totally something else.

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Re: Do you think about volatility drag on your portfolio?
MIpreRetirey wrote:To get back on track; aren't we supposed to be saying:
Arith. mean return = (Pf/Pin  1) * (1/n data points) ; data(2400,2500,2600) , A.M.R. = ((2600/2400)  1) * 1/2 = .4.167% avg. ret.
Geo. mean return = nth root(Pf/Pin)  1 ; SQRT(2600/2400) 1 = 4.08329% CAGR
Arith. mean value is totally something else.
Let me correct that:
A.M.R. = ((1+r1) *(1+r2)1)/n = ((25/24 * 26/25)1)/2 = 4.167% A.M.R. , which is the same.

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Re: Do you think about volatility drag on your portfolio?
Oicurvy provided a link to this excellent website. There's a lot of math, but if you breeze to the bottom of the page there is some very interesting stuff. There's a calculator one can use to see the effects of volatility on geo return, a graph showing how for a given average return geo return decreases with increased SD, and some real life examples. Thanks for posting!
http://www.financialwisdomforum.org/gum ... vsGM.htm
Dave
http://www.financialwisdomforum.org/gum ... vsGM.htm
Dave
Re: Do you think about volatility drag on your portfolio?
Random Walker wrote:Oicurvy provided a link to this excellent website. There's a lot of math, but if you breeze to the bottom of the page there is some very interesting stuff. There's a calculator one can use to see the effects of volatility on geo return, a graph showing how for a given average return geo return decreases with increased SD, and some real life examples. Thanks for posting!
http://www.financialwisdomforum.org/gum ... vsGM.htm
Dave
That's from our sister Canadian site's wiki: Gummystuff  finiki, the Canadian financial wiki
Part I is here: Average Gains
Part II is here (Random Walker's link): Average and Annualized Gains: part 2
Re: Do you think about volatility drag on your portfolio?
Someone correct me if I'm mistaken. But I'm still of the opinion that volatility drag is a nonissue.
This is like one of those times someone goes into great elaboration of minor points, but fails to address the threshold question.
Why not simply look at the starting dollar value and the ending dollar value? That's all that matters.
That's the central thrust of my objection. Yes if you look at percentage returns, the numbers can be fudged. But I fail to see how volatility drag is of any consequence beyond giving your financial advisor some creative ways to mislead you.
Every counterargument to my point has been mathematical obscura regarding different expressions of "annualized returns, percentage returns, etcetc. None of that addresses Objection Alook at the starting dollar amount and the ending.
Now let's look at other counterarguments. You have Portfolios X and Y which each start off with 1000 dollars. They both have 10% average returns. One has higher volatility. The one with lower volatility has highers returns. Volatility drag confirmed.
Alright. That counter is fine. I wasn't contending that. But it still doesnt address objection A. Look at the starting and ending dollar amounts.
Now let's look at yet another counter.
Variance drag is a function of standard deviation squared. Alright. No arguments there. But it still doesnt address objection A. Look at the starting and ending dollar amounts.
Now let's look at yet another counter
If a portfolio starts at 100%, loses 25%, and then grows 25%, you have less than 100% of your portfolio. Volatility drag confirmed. Alright.
But it still doesnt address objection A. Look at the starting and ending dollar amounts.
What am I missing?
This is like one of those times someone goes into great elaboration of minor points, but fails to address the threshold question.
Why not simply look at the starting dollar value and the ending dollar value? That's all that matters.
That's the central thrust of my objection. Yes if you look at percentage returns, the numbers can be fudged. But I fail to see how volatility drag is of any consequence beyond giving your financial advisor some creative ways to mislead you.
Every counterargument to my point has been mathematical obscura regarding different expressions of "annualized returns, percentage returns, etcetc. None of that addresses Objection Alook at the starting dollar amount and the ending.
Now let's look at other counterarguments. You have Portfolios X and Y which each start off with 1000 dollars. They both have 10% average returns. One has higher volatility. The one with lower volatility has highers returns. Volatility drag confirmed.
Alright. That counter is fine. I wasn't contending that. But it still doesnt address objection A. Look at the starting and ending dollar amounts.
Now let's look at yet another counter.
Variance drag is a function of standard deviation squared. Alright. No arguments there. But it still doesnt address objection A. Look at the starting and ending dollar amounts.
Now let's look at yet another counter
If a portfolio starts at 100%, loses 25%, and then grows 25%, you have less than 100% of your portfolio. Volatility drag confirmed. Alright.
But it still doesnt address objection A. Look at the starting and ending dollar amounts.
What am I missing?
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