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This is probably much too simple for all of you, but I will post it.

An interesting concept of investing is the variance drag. If you get 30% one year, and – 10% the next year or vice versa, the arithmetic return is (30 -10)/2 = 10%. But the arithmetic return is not the true return. The true return is the geometric return given by r = sqrt(year 1 * year 2) -1. In this case, it would be sqrt(1.3 * .9) -1 = 8.17%.

What does this mean? It means that the more volatile your returns, the lower your returns. A simple example will show this. You have 1.00. It goes up 50% the first year and down 50% the next year (or vice versa). What do you end up with. 75 cents.
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That's a pretty simple idea, which is why CAGR is used.
You can't average annual returns and get meaningful results.

The more subtle thing is to realize that the ordering of returns usually matters in the real world.
CAGR considers all possible orderings of a given set of returns as equivalent.
But, for example, consider a typical portfolio which is getting continuous small additions (a saver) or withdrawals (a retiree).
An unusually poor result near start of period is far more important to one group than to the other.
There is some academic research showing that one optimal approach for retirees is to have a very
equities-heavy portfolio, but purchase equity put options to protect it for just the first few years after retirement.
That is when sequence of returns is most critical to risk of portfolio failure.

Also, some investment strategies are relatively steady long term but relatively volatile short term.
It can be argued that the slope of a [real log] trend line through this portfolio value history gives a better
idea of expected rate of return than a CAGR calculated from endpoints which might be unusually displaced from the trend.
Shorter version: if you're looking at the CAGR of a time series that ended with a really stupendous month,
depending on your intended use of the figures you're perhaps looking at an overoptimistic figure.
It's arithmetically correct, but perhaps not what you want or need.
e.g., if you're trying to assess the predictive return implied by a backtest.

And one which many people seem to forget.
The only metric which matters for a "save till retirement" portfolio is the real value of the portfolio on retirement day.
It does not matter how volatile the portfolio was, or how much time was in cash, or how diversified it was.
Those may (or may not) matter somewhat to selecting the best strategy to achieve the maximum balance goal, but it's only the final balance that matters.
It's very much better to have a rich retirement after a wild ride than an impoverished retirement after a smooth ride.
A corollary is that bonds with low returns are not risk free. The risk is the "dog food at age 90" problem.

Jim
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What does this mean? It means that the more volatile your returns, the lower your returns. A simple example will show this. You have 1.00. It goes up 50% the first year and down 50% the next year (or vice versa). What do you end up with. 75 cents.

True, although it applies when compounding. If you have a constant position size then the regular average will work.

DB2
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Sorry, you can only recommend a post to the Best of once.

Excellent commentary as usual.

George
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... protect it for just the first few years after retirement.
That is when sequence of returns is most critical to risk of portfolio failure.


Sounds reasonable, I came to agree with this. For a while. But after thinking about it for a while it doesn't make as much sense.

What's the crucial bit of information about the first few years after retirement? That it's the initial few years, right? But isn't EVERY few years the first years of the rest of your (retirement) life? So what makes the 1st and 2nd years any more special than the 9th and 10th years?

Thinking further, it seems to me that the big deal about sequence of return risk is that you need your portfolio to grow large enough that you don't need to fret about future volatility. Underlying presumption is that it _isn't_ large enough at first; and that you hope that it will be after a few years.

So isn't the SOR risk really just "retiring on a showstring" risk? Retire with $1M and maybe you need to be concerned about negative volatility. Retire on $2M-$3M and you can just shrug.




if you're looking at the CAGR of a time series that ended with a really stupendous month, depending on your intended use of the figures you're perhaps looking at an overoptimistic figure.

Yes. I read a paper a while ago that said you should use Excel's "slope" function or "LOGEST" instead of CAGR, because they look at all the datapoints and not just the endpoints. Here's a discussion: "To calculate the correct growth rate you need to be clear about what you want your growth rate to signify." http://www.exceluser.com/formulas/how-to-calculate-both-type...
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<< But isn't EVERY few years the first years of the rest of your (retirement) life? So what makes the 1st and 2nd years any more special than the 9th and 10th years? >>

I believe the point is that prior to retirement, most of us are putting money into out retirement accounts.

After retirement, we start taking money out. This, in effect, changes the entire dynamic of investment risk.


Alan
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What's the crucial bit of information about the first few years after retirement?
That it's the initial few years, right? But isn't EVERY few years the first years of the rest of
your (retirement) life? So what makes the 1st and 2nd years any more special than the 9th and 10th years?



They are in fact qualitatively different in two ways.

First, consider the retirement as a given segment of time.
We don't know in advance how long it will be, but it's finite, with a start and an end.
The start of that sequence is more important than the end, in terms of sequence-of-returns.
That risk, within that segment, is a diminishing curve, no matter the age interval it covers.
So, a period later in retirement is less sensitive to a period earlier in retirement.
On this view, the issue is not actually years since retirement but years till death do us part.

And, kind of separately, it's important because the whole process can be viewed as:
Accumulate...accumulate...accumulate...accumulate...retire...spend...spend...[spend...]...croak.
No matter what age retirement is, and no matter how many "spend" repetitions there are, the first "spend" interval is the most important in terms of sequence risk.

Yes, one could simply observe two individuals who retire at ages 60 and 65.
The risk for their respective intervals 65-70 at first seems the same.
So, on the surface, it seems that the "first few years" of the first guy is equal in risk to the "second few years" of the second guy.
Suggesting that there is nothing special about the 60-65 period for the first guy.
But, in reality, each of them is going to retire at a given date and die at a given date when all is said and done.
They probably have different size pots of money on retirement day, different expenditure rates,
different rates of return during retirement, and different sequences of return.
Critically, no matter what all those numbers turn out to be, year 1 of retirement *for each of
them* is higher risk than year 10 of retirement for that same person, for sequence-of-returns risk.

And, viewed yet another way, a guy who retires at age 87 doesn't have a lot of sequence-of-returns risk.
In reality the whole conversation applies only to those whose retirement depends, in part, on earnings made during retirement.
For a person retiring at age 87, statistically that isn't a factor.
He (or, less likely, she) will be dead before the investment income is more than a rounding error, whether it's good or bad.
From this it follows that sequence of return risk in period N is not the same as the risk in period N+1.
At period N+1 you're older.

Jim
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So isn't the SOR risk really just "retiring on a showstring" risk?

I prefer to think of it this way:
For any given size of retirement pot, the person with that pot wants to have the lowest possible risk of outliving the savings.
The lowest risk of outliving the chosen income from withdrawals, which is pretty much always assumed to be proportional to the size of the retirement pot.
A millionaire and a multi-millionaire might both think a "4% rule" will work.
They will have very different absolute levels of income, but neither of them wants to withdraw too much...to have the withdrawal program fail.

Sure, the rich guy could withdraw 1% instead of 4%. He's rich. But I'm sure he or she doesn't want to.
Nobody wants to withdraw lots less than what they could get a way with.
So, everybody wants to cut off the extreme downside tails of the probability distribution.
Those are concentrated in the scenarios with poor returns in the first few years of retirement.
Truncate those tails, and you can expect to get much closer to the textbook withdrawal rate working [at any given assumed portfolio return rate].

My current thinking is that yes, you're right, you can't really count on the income during your retirement at all.
If you are, you're in the shoestring category.
Not that the observation helps much...if you are, you are. Not much you can do about it.
But the real reason you can't rely on income during retirement these days is that real rates of return on offer are simply too low.
You might beat the market, but nobody should PLAN on that.
The sad corollary of that is when yields are low, if you want to avoid longevity risk, you either have to buy
insurance against that risk or pick a withdrawal rate that assumes you'll live forever even at low portfolio returns.
OK, at the extreme, a 1% withdrawal rate is probably OK.
Even if you're in 100% cash, few people manage 100 years of retirement.

Jim
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The sad corollary of that is when yields are low, if you want to avoid longevity risk, you either have to buy insurance against that risk or pick a withdrawal rate that assumes you'll live forever even at low portfolio returns.
OK, at the extreme, a 1% withdrawal rate is probably OK.
Even if you're in 100% cash, few people manage 100 years of retirement.


As I am prone to remark: It is expensive to be poor.

Whatever you do for this insurance--buy options, large cash allocation, large bond allocation--is a dragging anchor.
If you are rich enough, then you don't need to buy portfolio insurance. Only if you are poor(ish) do you need to buy it---and have an anchor to drag.

I read once -- and playing with Firecalc pretty much bears it out -- that a withdrawal rate for 40 year portfolio survival is good for longer periods, too. The 40 year SWR is the same as the 100 year SWR.

It's only for 20-30 year portfolios that the SWR changes.

Baby boomers are getting to the age when all of a sudden they realize that they don't need a 30 year portfolio---because they aren't going to live another 30 years anyway!
When you hit 70, you probably won't live to 100. So now it makes sense to start looking at a 20 year SWR.

For 95% sucess rate, the SWR is 4.00% for 30 years, but 4.85% for 20 years.

And them the non-financial wife (but she can still do basic math in her head) realizes, Hey, we have $1,000,000 and only spend $40,000 a year. So if our investments do NOTHING it will last for 25 years. So why am I buying bread at the day-old store?

========================================
Okay....had to check it out.
95% survival rate for 40 years is 3.70% SWR.
For 60 years, 3.68%.
For 70 (as if!) years, 3.55%

The people who are running around yelling about the need to do 2% SWR are just being silly.
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And them the non-financial wife (but she can still do basic math in her head) realizes, Hey, we have $1,000,000 and only spend $40,000 a year. So if our investments do NOTHING it will last for 25 years. So why am I buying bread at the day-old store?
--------------------------------------------------------

The big unknown in this discussion of SWR, health costs, which could wipe out a major portion of your money.
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Sure, the rich guy could withdraw 1% instead of 4%.

It occurs to me that one could reduce the early-years risk by varying the withdrawal percentage. It doesn't have to be a constant. The first year one could take out 2%, up it to 3% for the next year or two and then go forward with the canonical 4%.

DB2
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It occurs to me that one could reduce the early-years risk by varying the withdrawal percentage. It doesn't have to be a constant. The first year one could take out 2%, up it to 3% for the next year or two and then go forward with the canonical 4%.

It occurs to me that part of the assumption in taking a fixed percentage of your savings (whatever value you choose) out each year is that the price-value of your savings, and especially its increase or decrease, reflects the increase or decrease of your experienced inflation rate.

For example, if your savings increase, you will need to withdraw more. But if that is not the case (perhaps only the cost of buying a house increases, but you will not be buying houses), you need not take more. So leave it in. That way things will last longer.

Of course, even if you select 4% or 3% or whatever, if your experienced inflation rate increases, you may have to take out more, and die sooner (when the money runs out).
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<The big unknown in this discussion of SWR, health costs, which could wipe out a major portion of your money.>

One can budget for most ordinary problems of old age. Think insurances.
Medicare and a good Medicare backup insurance plan should cover most health
problems. If you don't travel far from home much, Medicare Advantage plans are
really cheap considering many cover both eye exams,drugs and most deductibles and co-pays. My in-laws used that. If you are an international traveler, Medicare won't be available, but some policies cover most of the expenses 'out of network', which includes foreign travel. I kept my employer's costly retiree plan since it covers all of the above. Parkinson's, dementia and other chronic
debilitating problems might need institutional care, so add some long term care
insurance. Taken together these might stress your budget, but they allow management of most devastating hits to savings and assets.

rrjjgg
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For example, if your savings increase, you will need to withdraw more.

Well, you don't *have* to take more out. :-)

It's not like the IRS minimum withdrawal amounts, but more of a prudent annual maximum to minimize the risk of running out.

I do like the idea of buying puts as insurance for the first couple of years -- not enough puts to cover you entire portfolio but enough to cover your withdrawals for a year or two.

For example, SPY was around 280 this morning. Let's say you were retiring tomorrow at the end of March. SPY puts are currently available as far out as December 2021, over two and a half years. 20% out of the money would indicate buying some puts at the 225 strike.

The cost for one contract covering 100 shares of SPY was $1,245. If the market dropped 20% in the next year or two to the 225 level each put contract would be worth more than $22,500 and could be sold for cash. If your retirement plans included, say, $50-60K in drawdowns each year then five put contracts should have you covered.

DB2
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You might enjoy the Rich, Broke, or Dead calculator:

https://engaging-data.com/will-money-last-retire-early/

You can vary the inputs as you like, but bottom line is if you are retiring in your 50s with a 4% SWR, you are vastly more likely to wind up either rich or dead, than broke.
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The cost for one contract covering 100 shares of SPY was $1,245. If the market dropped 20% in the next year or two to the 225 level each put contract would be worth more than $22,500 and could be sold for cash.

How do you estimate value of the put into the future? Currently, an at-the-money Sep-30-19 put (6 months remaining) has an of approx value of 12.80 ($1,280)

Thanks,
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https://engaging-data.com/will-money-last-retire-early/

A health warning reminder:

Bear in mind one should never pay attention to probabilities of success/failure that are based on historical results,
UNLESS it a simulator that takes into account starting security valuation levels. Which this one, like most, does not.

Stock and bond valuations are both very much higher now than in the past.
Phrased another way, history ending today includes a general trend of rising valuations.
Therefore predictions based on that history implicitly assume that valuations will keep rising higher and higher forever.

Instead, a bit of mean reversion the other way seems a bit more likely to me.
Historically, average returns starting from high(ish) valuations are always lower than average returns starting at low(ish) valuations.
At the very least I'd want to assume that valuation levels will stop rising.

Separately, the correlation between stock and bond returns was not very high for a very long time. Not recently.
Again, many history-based simulators will tend to assume that the low past correlations will remain the norm in future.
That may not be true.
And of course, the really bad simulators assume historical returns from bonds even though those yields are no longer available.
It's hard to see how a bond ladder can beat its initial yield.

Jim
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The cost for one contract covering 100 shares of SPY was $1,245. If the market dropped 20% in the next year or two to the 225 level each put contract would be worth more than $22,500 and could be sold for cash.
---
How do you estimate value of the put into the future? Currently, an at-the-money Sep-30-19 put (6 months remaining) has an of approx value of 12.80 ($1,280)


Thanks for noticing my error. The value of the puts a year of now with SPY down to 220 and high implied volatility (it was around 29 at the beginning of this year) would give a price of around $2200, not $22,000.

DB2
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