Using TSM for Essential Liabilities- TSM's worst rolling averages

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jmk
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Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by jmk » Sun Jan 06, 2019 10:59 pm

In their 2004 book Asset Dedication: How to Grow Wealthy with the Next Generation of Asset Allocation, Stephen Huxley and Brent Burns introduce an intriguing idea of the "equity yield curve". For the purpose of funding essential liabilities, the authors suggest that rather than comparing means between stocks and bonds, the worst case over the historical record should be used as the basis of comparison. They refer to this metaphorically as an "equity yield curve" since it shares with the bond curve a tapering rise over time.

Image

(This chart is from a 2016 article by the same authors, Huxley, Stephen J., J. Brent Burns, and Jeremy Fletcher. 2016. “Equity Yield Curves, Time Segmentation, and Portfolio Optimization Strategies.” Journal of Financial Planning 29 (11): 54–61.)

I thought it would be instructive to re-run the data using Simba's database as its basis and: (a) using TSM rather than sp500, (b) using TBM instead of simulated 10y treasury fund, (4) starting at 1871 rather than starting in 1926, (5) using real inflation-adjusted returns. The results are consistent with Huxley and Burns, though the updated reults push out the "break even" points between stocks and bonds.

Here's the CAGR data for TSM using 1871-2018 over various holding periods (median in orange, 5th percentile worst in dark blue, worst in light blue, and current treasury/tip/CD yields in yellow), all inflation adjusted:
Image

As shown in the chart, the minimum CAGR for TSM (light blue) only "breaks even" with current YTM on individual Bonds/CDs (yellow line/dots) around a 21-23 year hold period. Even using a more generous 95th percentile, the CAGR for TSM only breaks even with current yields on individual bonds/CDs around 18 years.

In other words, if one wants to be super conservative, as one might in, say, planning for essential liabilities, one would only want to utilize TSM for expenses 23 years or so out. Any essential expenses sooner than that would require CD, treasury or TIP with a guaranteed yield if held to maturity..

How about using TBM instead of individual bonds? Surprisingly, using TBM to fund essential liabilities rather than Individual bonds/CDs is dangerous for essential liabilities, as shown by the following chart. The light blue represents minimal TSM and the dark blue represents the "worst case' TBM CAGR for different holding periods 1871-2018 through Simba database:

Image

Except at the very shortest of terms, the "worst case" for TBM is worse than TSM across holding periods. And more importantly much worse than the individual Bond yield curve. This is somewhat counterintuitive, as the median TBM returns for various holding periods are quite similar to the basket of individual bonds; but of course in a rising interest period or when demand is low, TBM can return less than individual bonds held to maturity. The chart speaks for itself: the minimum CAGR is much more dangerous than treasuries and CDS in the current environment. In short: One does not protect liabilities by using TBM.

Interestingly, using 50/50 TSM-TBM doesn't help matters in covering liabilities:

Image

It's only marginally better at its worst through a 16 year holding period, and lower than TSM in every period after that. And far below individual bonds/CDs held to maturity. (Further analyses with other mixtures of TSM and TBM--not posted--have essentially the same result: worse than using individual bonds then switching to 100% TSM.)

In the end, when you really want to know the money will be there there's no substitute over the short and medium term for individual bonds and CDs held to maturity.
Last edited by jmk on Sun Jan 13, 2019 3:34 pm, edited 10 times in total.

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Re: Using TSM for Essential Liabilities

Post by jmk » Tue Jan 08, 2019 5:27 pm

Some cautions about the above analysis and Huxley and Burns' maximin idea in general :
  • there is no law of nature that says the worst case over the historical time period 1871-2018 can't get even worse in the future (cf Taleb)
  • even extending back to 1871, there are relatively few independent 40 and 50 year cycles
  • there is a lot of autocorrelation and overlap between the elements that go into the rolling averages for any time period
In other words, even considering the worst case, would you really trust TSM for your essential liability requirements?

Also in more general terms,
  • it is unclear why the "worst case" returns what matters rather than a more probability based monte carlo analysis
  • it is unclear what role the "worst case" returns play beyond covering the essentials
Last edited by jmk on Sun Jan 13, 2019 3:38 pm, edited 2 times in total.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by antiqueman » Tue Jan 08, 2019 7:19 pm

JMK, thank you for your post.

Does Huxley and Burns research suggest that one should have around 20 years of "safe "assets for essential expenses and not utilize the probability based theory of AA , rebalancing etc?

If so, then this comports with Dr. Bernstein's suggestion of a LMP where he suggest one have 20 to 25 years in safe assets for essential expenses.

Sometimes I have trouble understanding all the graphs and theory posted on the forum. Perhaps I have misunderstood your analysis on all of this. But it appears to me Huxley and Burns research supports Dr. Bernstein's advice.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by jmk » Wed Jan 09, 2019 2:17 pm

antiqueman wrote:
Tue Jan 08, 2019 7:19 pm
Does Huxley and Burns research suggest that one should have around 20 years of "safe "assets for essential expenses and not utilize the probability based theory of AA , rebalancing etc?
No Antiqueman, Huxley and Burns don't use a 20x or probability based AA. They advocate for a more precise liability matching method where you project out your essential expenses year-by-year, and then build a CD/bond ladder that delivers that amount guaranteed. They worry the 20x rule of thumb won't guarantee essentials get covered in the years you need them. Essential liabilities above 17 years out (21 years in my update) will be matched by 100% equity based on the logic of the "stock yield curve" I outlined above. The "rest" of your assets above that amount would be devoted to 100% equity since it is only discretionary. So for them AA is a byproduct of the liability matching, not the key component as for most others. And as your bond ladder gets used up you continually update the bond ladder further and further out as able from the growth (equity) portfolio.

By the way, I'm not arguing for Huxley and Burns' method, just found it interesting that the 'worst case' for TSM was 23 years out compared to old fashioned bonds. There are some nice youtube videos where they explain their whole system. I personally am not convinced it's worth the effort to match things as precisely as they do rather than use a simpler probabilistic approach like Bernstein's. I have adopted their idea of basing my equity AA on "what's left after essentials" rather than a fixed number. And I have adopted the idea of a precise "funded ratio" that represents the npv of all guaranteed streams of income and current assets / npv of the stream of liabilities: that to me is a more useful number than "20x". I also am not sure how Huxley and Burn's use of Bonds/CDs works in terms of tax efficiency.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by dbr » Thu Jan 10, 2019 9:58 am

Remember that plotting annual average (CAGR) over longer and longer time periods is misleading. The actual outcome at the end of a long period of time results from compounding the annual average over that time. While CAGR variation shrinks with extending time by roughly the square root of time, the variation in compounded end-point wealth increases roughly with the square root of time. This confusion of CAGR and end-point with time is called the fallacy of time diversification.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by willthrill81 » Thu Jan 10, 2019 10:07 am

Jeremy Siegel also demonstrated that nominal bonds were riskier than stocks over ~20 year periods and longer.
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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by siamond » Thu Jan 10, 2019 12:53 pm

jmk wrote:
Sun Jan 06, 2019 10:59 pm
In their 2004 book Asset Dedication: How to Grow Wealthy with the Next Generation of Asset Allocation, Stephen Huxley and Brent Burns introduce an intriguing idea of the "equity yield curve". For the purpose of funding essential liabilities, the authors suggest that rather than comparing means between stocks and bonds, the worst case over the historical record should be used as the basis of comparison. They refer to this metaphorically as an "equity yield curve" since it shares with the bond curve a tapering rise over time.
[...]
I thought it would be instructive to re-run the data using Simba's database as its basis and: (a) using TSM rather than sp500, (b) using TBM instead of simulated 10y treasury fund, (4) starting at 1871 rather than starting in 1926, (5) using real inflation-adjusted returns. The results are consistent with Huxley and Burns, though the updated reults push out the "break even" points between stocks and bonds.
That is a creative idea. Thank you for doing that.

I like the fact that you didn't solely focus on the worst case, but also showed the 5% percentile (I would have gone further and used a higher low percentile, actually). The worst case is one data point, one singularity in the past, it really doesn't mean much.

The outcome for bonds (TBM) doesn't surprise me, this is due to the MAJOR bond crisis of the late 40s to the 80s, where bond returns were spectacularly destroyed by inflation, for decades. Whether this can happen again or not is an interesting debate, but this is the main explanation of the dire numbers you've illustrated.

Question 1: did you parameterize your chart, so that it can compare an arbitrary personal portfolio to an arbitrary benchmark portfolio (e.g. like is done in the Simba's Analyze_Portfolio tab)? I'd be curious to check how my AA compared to more classic portfolios based on such 'yield curve'... :wink:

Question 2: it might be interesting to see the same kind of representation for SWR and PWR metrics. Did you play with that, by any chance?

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by siamond » Thu Jan 10, 2019 5:16 pm

^^^^^^^^^^^^^^
I answered my own questions... :wink:

I assembled a Simba derivative spreadsheet, with a data table running this kind of math. You need to customize the portfolios in the left panel of Compare_Portfolios, the first two are the ones displayed on the charts in Data_Table tab. Don't forget to make Excel 'recalculate all', as I disabled the automatic data table recalculations (too performance consuming otherwise). Here is the spreadsheet:
https://drive.google.com/open?id=1YfpGM ... 0rHof9Vneh

Based on the results of such data table, one can end with graphs like this one, similar to what the OP posted. Note that I used a 10% percentile cut-off, and solely focused on the 10yrs to 40yrs rolling cycles. Such parameters are easy to change.

Image

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by ogd » Thu Jan 10, 2019 5:34 pm

jmk wrote:
Sun Jan 06, 2019 10:59 pm
In the end, when you really want to know the money will be there there's no substitute over the short and medium term for individual bonds and CDs held to maturity.
I don't think this conclusion is warranted. Individual bonds do not reduce risk by virtue of holding to maturity and "not taking losses", they do so by having the proper duration at all times vs a known liability date. You could in fact sell at a loss every month as long as you buy a bond with the same maturity date and liquidity is not a significant issue -- the higher coupons will precisely make you good for the capital loss.

The scenario when TBM really loses is when a yield-increase event or period happens just before the liability date, and I think if you dive deep into the data the min-TBM cases look like this. But if you think about it, at that time you were holding 6 year bonds for, say, a 6 month horizon. Someone who wants to support a strict liability date could switch into progressively shorter funds as that date approaches. This may look like work, but if we're talking munis or even corporate bonds (the former are sometimes a requirement for good after-tax returns, the latter not so much), it is only a fraction of the work needed to be your own bond manager.

This is, of course, if the liability date is known at all, which I'd argue is not a clear-cut proposition. Sometimes it's unexpected vs job or medical situation, sometimes it's flexible (I might postpone or cancel some expenses to take advantage of a market dip) and the interaction with rebalancing makes everything fuzzy -- in said market dip, I need to sell many more bonds than I expected, to rebalance. I'm actually curious how your simulated individual bond portfolio handles rebalancing, since I expect that quite often bonds will need to be sold before maturity (i.e. duration mismatching like in the TBM case) and bought at odd terms.

If the liability period is not known precisely, but a fuzzy 0-6 years in which I might need a good chunk of my portfolio to live on, then I don't think individual bonds can improve things vs even static-duration TBM.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by jmk » Fri Jan 11, 2019 7:55 pm

dbr wrote:
Thu Jan 10, 2019 9:58 am
Remember that plotting annual average (CAGR) over longer and longer time periods is misleading. The actual outcome at the end of a long period of time results from compounding the annual average over that time. While CAGR variation shrinks with extending time by roughly the square root of time, the variation in compounded end-point wealth increases roughly with the square root of time. This confusion of CAGR and end-point with time is called the fallacy of time diversification.
I'm not sure the fallacy of time diversification applies to the equity yield curve. This graph does not give any info about variation of returns. Rather the CAGR over a given holding period has two variables: start total and end total (CAGR=(end total-start total)^1/n). The graph shows the worst case over 150 years for each holding period. It compares the worst end-total-to-start-total over that span for stocks to the end-total-to-start-toal for individual bonds/CDs. For each holding period there is exactly one worst case, with a determinant end amount relative to the start amount. There are other issues one might raise (why does the worst case matter more than overall probability?) but I don't think variation matters since by definition this is looking at the worst case only. My apologies if I'm misunderstanding the fallacy.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by nisiprius » Fri Jan 11, 2019 8:05 pm

I wish I had the quotation, but Nassim Nicholas Taleb has pointed out that the worst case that has ever occurred is always, by definition worse than what had been thought to be the "worst case" up to then.

In the fourth edition of Stocks for the Long Run, Jeremy Siegel wrote:
never in any of the past 175 years would a buyer of newly-issued 30-year bonds have outperformed an investor in a diversified portfolio of common stocks held over the same period.
In the fifth edition he wrote this:
In the first four editions of Stocks for the Long Run, I noted that the last 30-year period when the return on long-term bonds beat stocks ended in 1861, at the onset of the Civil War. That is no longer true. Because of the large drop in government bond yields over the past decade, the 11.03 percent annual returns on long-term government bonds surpassed the 10.98 percent on stocks for the 30-year period from January 1, 1982, through the end of 2011.
Annual income twenty pounds, annual expenditure nineteen nineteen and six, result happiness; Annual income twenty pounds, annual expenditure twenty pounds ought and six, result misery.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by Tyler9000 » Fri Jan 11, 2019 11:28 pm

jmk wrote:
Sun Jan 06, 2019 10:59 pm
In their 2004 book Asset Dedication: How to Grow Wealthy with the Next Generation of Asset Allocation, Stephen Huxley and Brent Burns introduce an intriguing idea of the "equity yield curve". For the purpose of funding essential liabilities, the authors suggest that rather than comparing means between stocks and bonds, the worst case over the historical record should be used as the basis of comparison. They refer to this metaphorically as an "equity yield curve" since it shares with the bond curve a tapering rise over time.
Very interesting! "Equity yield curve" is an especially nice way to frame it, so thanks for sharing that reference.

Following Siamond's idea to study more portfolio ideas, I have a tool that generates a similar chart for any asset allocation you like (although it doesn't extend as far as your data). Of course at that point it's more of a portfolio yield curve, but I've often used that minimum line for a lot of the same thought processes of matching expectations to timeframes.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by jmk » Sat Jan 12, 2019 12:06 pm

nisiprius wrote:
Fri Jan 11, 2019 8:05 pm
I wish I had the quotation, but Nassim Nicholas Taleb has pointed out that the worst case that has ever occurred is always, by definition worse than what had been thought to be the "worst case" up to then.
Well, yes. And I too shared this concern in the second post in the thread above. ("there is no law of nature that says the worst case over the historical time period 1871-2018 can't get even worse in the future; even extending back to 1871, there are relatively few independent 40 and 50 year cycles; there is a lot of autocorrelation between the elements that go into the rolling averages for any time period.")

It is an especially important point given that this analysis is intended to show when it's reasonable for TSM to substitute for individual bonds for essential liabilities. I personally would not depend on TSM even 23 years out just because that's where the worst case has crossed the line in the past. However, IMO it's still an important data point.
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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by jmk » Sat Jan 12, 2019 12:39 pm

siamond wrote:
Thu Jan 10, 2019 12:53 pm
I like the fact that you didn't solely focus on the worst case, but also showed the 5% percentile (I would have gone further and used a higher low percentile, actually). The worst case is one data point, one singularity in the past, it really doesn't mean much.
The "worst case" is the whole point of this particular analysis: on the assumption of "safety first" we know that at least once in history you wouldn't have had your butt covered. (Do remember that that "singularity" covers many decades, though, and gets compared to many other decades!) I personally found 5th percentile fruitful because it was still close to worst case but evened out the extremities. Clearly different parameters matter for different questions (which is more of an art than a science, the median being one of the most useful). But using the 10th percentile as one's basis for liability matching starts to get away from "safety first". Remember, we're comparing to current bond yields, which are among the lowest in history as are expected returns. And as Nisprisius points out, even "the worst case so far" doesn't give you full confidence in "how much worse it might get" so diluting it out even more to the "worst 10th percentile" moves us even further astray for this particular purpose.
The outcome for bonds (TBM) doesn't surprise me, this is due to the MAJOR bond crisis of the late 40s to the 80s, where bond returns were spectacularly destroyed by inflation, for decades. Whether this can happen again or not is an interesting debate, but this is the main explanation of the dire numbers you've illustrated.
Again, that is the point. If I'm covering essentials (housing, medical) I surely do not want to rely on an assumption we not within the worst 40 years for TBM. In fact, it is precisely this possibility that requires we use individual bonds for essential liabilities and not TBM, which works fine for many other purposes.
it might be interesting to see the same kind of representation for SWR and PWR metrics. Did you play with that, by any chance?
Thank you for this, which I hadn't considered at all but gets my mind thinking.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by siamond » Sat Jan 12, 2019 1:30 pm

jmk wrote:
Sat Jan 12, 2019 12:39 pm
The "worst case" is the whole point of this particular analysis: on the assumption of "safety first" we know that at least once in history you wouldn't have had your butt covered. (Do remember that that "singularity" covers many decades, though, and gets compared to many other decades!) [...]
I understand where you're coming from and I agree this is the whole point of such a chart. Still, I would really advise to put things in perspective. Again, the worst US case is just a single data point in history. And if you start looking at historical returns in other developed countries (which I do every now and then), this really puts in perspective the significance of such 'worst case' information. Case in point, the '4% rule' is pretty much a joke. Some countries suffered from significant worse returns (and sequence of returns) issues. So which worst case should we consider? And I am not even speaking of adding to the fray countries like Russia and China which abruptly closed their stock markets for decades...

Anyhoo, I suspect the best approach is the one you used in the OP, showing the worst case as well as a couple of percentile cases, providing various ways to look at the data. As a side note, there is a fairly similar representation on PortfolioCharts.com, the Long-Term Returns calculator. Thank you in any case for a creative OP.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by staythecourse » Sat Jan 12, 2019 2:34 pm

Thank you for the interesting paper AND your original work based on that work. Much to ponder and hope this thread gets A LOT of input as there seems to be a lot of meat to chew on so to speak.

Haven't gotten to your work yet, but did read the original paper that you quoted. Sure you are aware, but for others the paper originally used 1928 as the starting point (start of the Great Depression). That was noted in the paper that nearly ALL the min. return returns used in the graphs consisted of data including those years. The interesting thing is WHY start at the Great Depression? The 5 or so years prior were excellent years and think the graph may have looked much different if started then. If you START (vs. include) the worst drop (-89%) it will undoubtedly pull down all the returns substantial for all the time periods, i.e. sequence of return risk. Starting with such a large handicap changes the data vs. INCLUDING the worst time period.

Another issue I have is his y axis. It should be adjusted to show more % especially between 1-10% which comes in much more use when you are talking about the delta difference when you get out to 10+ years.

Another, of course, is not including international data. I get why (the criticism of the data set not being accurate), but believe other papers I have read quoted the Great Depression trough would have been reduced to -60% or something or so if added in international equity returns (60/40 or something like that). That would have changed the number min. returns for each time horizon COMPLETELY if they started of -60% vs. -89%.

My take away from the original article is the methodology is likely skewed based on the STARTING point of 1928. It did show me an unusual inference that it would take about 20 years of being 100% SP500 STARTING at the worst case scenario in U.S. History to have close to the same minimum returns of the best min. return portfolio. SO would seem the usual thrown out of 20 years if you hold stocks is about right to feel you would have matched any other portfolio in the worst case scenario using min. returns as your benchmark.

I look forward to reading and mulling over your work. Since it starts much further back will be interesting to see what those results will be. Will post again when I get a chance to read your work more in depth.

Again great work.

Good luck.
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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by jmk » Sun Jan 13, 2019 3:15 pm

staythecourse wrote:
Sat Jan 12, 2019 2:34 pm
Another, of course, is not including international data. I get why (the criticism of the data set not being accurate), but believe other papers I have read quoted the Great Depression trough would have been reduced to -60% or something or so if added in international equity returns (60/40 or something like that). That would have changed the number min. returns for each time horizon COMPLETELY if they started of -60% vs. -89%.
Yes, a major defect in the data!
I look forward to reading and mulling over your work. Since it starts much further back will be interesting to see what those results will be. Will post again when I get a chance to read your work more in depth.
Short version: with extension of data and compared to today's individual 10-20 year TIP/treasury bond rates, it extends out the "break even" between TSM to about 23 years. In the paper they had 18 years as break even.

If you like the Huxley and Burn's original article, in addition to the three youtube videos I posted above I highly recommend Wade Pfau's 3 part in-depth evaluation of the liability matching system. He finds it very effective, and includes his own adaptation of the equity yield curve chart comparing stocks to ITT.
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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by jmk » Sun Jan 13, 2019 3:27 pm

Tyler9000 wrote:
Fri Jan 11, 2019 11:28 pm
Following Siamond's idea to study more portfolio ideas, I have a tool that generates a similar chart for any asset allocation you like (although it doesn't extend as far as your data). Of course at that point it's more of a portfolio yield curve, but I've often used that minimum line for a lot of the same thought processes of matching expectations to timeframes.
Cool! I think your reframe (with ranges) is an improvement. Out of curiosity, why did you limit the range of holding periods to 15 years? Given the 'break even' is 23 years and we typically want a 30-50 year retirement this seems unnecessary. Of course your chart doesn't include the use of individual bonds held to maturities at today's yields (which the key cross over point of the analysis); but that can easily be projected onto your graph as needed.

I was surprised in my own charts that all mixtures of TSM with TBM (from 30%-70%) didn't seem to accomplish anything in terms of liability matching: it merely made the break-even point further out than TSM or individual bonds. I think this is because TBM accomplishes nothing in terms of "minimum" return relative to TSM and relative to individual bonds/CDs so adding it in does same. I think I was hoping for some kind of "sum is more than the parts" due to correlations.

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Re: Using TSM for Essential Liabilities- TSM's worst rolling averages

Post by Tyler9000 » Sun Jan 13, 2019 3:43 pm

jmk wrote:
Sun Jan 13, 2019 3:27 pm
Cool! I think your reframe (with ranges) is an improvement. Out of curiosity, why did you limit the range of holding periods to 15 years? Given the 'break even' is 23 years and we typically want a 30-50 year retirement this seems unnecessary.
The mathematical reason is that in a database of ~50 years of data (the most I can find for so many assets), limiting the chart to 15 years 1) provides enough rolling timeframes to make the "baseline" and "stretch" metrics statistically significant, and 2) avoids the situation of too many overlapping periods skewing the results for longer timeframes (a big problem with a 20-year stock bubble square in the middle of the data). If I had more data I'd certainly add more years, but it's a nice place to start.

And the practical reason is that I've found most investors really don't have the patience to watch their portfolio struggle for 15 years without making a change anyway. :wink:

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