# The Money Mustache Community

## Learning, Sharing, and Teaching => Ask a Mustachian => Topic started by: MoneyStacher on December 12, 2013, 04:00:32 PM

Title: Mortgage Payoff Contradiction. Can this be right?
Post by: MoneyStacher on December 12, 2013, 04:00:32 PM
The general rule is that if you can get a better rate in the market than your mortgage rate, invest.

But, there is something about the 4% rule that challenges this. I think. Maybe.

I've got an ARM that is at 2.75%. Interest \$240, Principle \$386. Balance \$104,500.

The stache is \$586,000 (includes principle on the house of 46,000).

So, by 4% rule, I can draw 23,440/yr. Then, subtracting mortgage payments of \$7,512/yr, I am left with \$15,928/yr to live on.

Here is where it gets interesting.

Say I take \$104,500 from the stache and payoff the mortgage.

This would leave the stache at \$481,500. Now, let's do the 4% rule again.

I could draw a smaller 19,260 from that smaller stache and pay \$0 mortgage and be left with the same 19,260 after paying nothing. This 19,260 is larger than the 15,928 I was going to have after the previous draw and paying the mortgage every month.

So, this is a mustachian no-brainer, right?

To me, this defies the laws of finance. I should keep the money invested at 8-11% right instead of paying off a loan that is 2.75%? And yet, it seems that the answer is NO.

Okay mustachian brothers and sisters, do I have this right?

Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: huadpe on December 12, 2013, 04:18:10 PM
The part where you're messing up the math is that you're factoring out the chunk of your payment going to principal as a re-investment.

So what you're actually paying out is only the interest, which is about \$2800/yr.  The rest is going towards your home equity.  So your net draw in the first case is about \$20,000.  But because you've kept the mortgage, you've structurally forced yourself to reinvest a chunk of that into home equity, thus why your take-home is lower.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: Heart of Tin on December 12, 2013, 04:59:44 PM
There's an even easier explanation. You've misapplied the 4% rule. You can't price a mortgage with an end date using this formula. The 4% rule is applied to yearly expenses, because we assume that our expenses never change and go on forever making them a perpetuity. A perpetuity is a series of periodic payments that never ends. If you have a perpetuity with payment amount R and interest rate i, then PV = R/i where PV is the present value or price of the perpetuity. MMM switched this formula around to R = PV*i where R is our yearly expenses in retirement, i is our safe withdrawal rate (4% usually), and PV is the necessary value of our investments.

Instead of using the perpetuity formula to price the mortgage, we need to use the annuity formula. Annuities, in this case, are a series of periodic payments over a defined period. You may be familiar with life annuities, usually just called annuities, where the period is defined as the lifetime of the annuitant after a certain age. In this case your mortgage is an annuity where the period is defined as the original term of the mortgage. The annuity formula is PV = R*(1 - (1 + i)^-n)/i where PV is the current value or price of the annuity, R is the monthly payment, and n is the number of payments left. Since we are comparing this to a 4% perpetuity, we will use a 4% annual effective rate converted to a 0.3274% monthly effective rate for i. If I can treat your mortgage like a fixed rate mortgage for a moment, you would have 211 monthly payments of \$626 left, so the present value of the mortgage is PV = 626*(1 - (1.003274)^-211)/.003274 = \$95,270. Since this is less than you would be paying immediately to settle the debt, you should continue to pay \$626 to the mortgage.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: Nicster on December 12, 2013, 05:48:56 PM
That's an easier explanation? ;)

Just kidding. Thanks for the detail.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: dragoncar on December 12, 2013, 06:15:19 PM
As above, but also remember that you can't apply the 4% rule to your equity (first application of 4% rule)
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: arebelspy on December 12, 2013, 06:58:15 PM
There's an even easier explanation. You've misapplied the 4% rule. You can't price a mortgage with an end date using this formula. The 4% rule is applied to yearly expenses, because we assume that our expenses never change and go on forever making them a perpetuity. A perpetuity is a series of periodic payments that never ends. If you have a perpetuity with payment amount R and interest rate i, then PV = R/i where PV is the present value or price of the perpetuity. MMM switched this formula around to R = PV*i where R is our yearly expenses in retirement, i is our safe withdrawal rate (4% usually), and PV is the necessary value of our investments.

Instead of using the perpetuity formula to price the mortgage, we need to use the annuity formula. Annuities, in this case, are a series of periodic payments over a defined period. You may be familiar with life annuities, usually just called annuities, where the period is defined as the lifetime of the annuitant after a certain age. In this case your mortgage is an annuity where the period is defined as the original term of the mortgage. The annuity formula is PV = R*(1 - (1 + i)^-n)/i where PV is the current value or price of the annuity, R is the monthly payment, and n is the number of payments left. Since we are comparing this to a 4% perpetuity, we will use a 4% annual effective rate converted to a 0.3274% monthly effective rate for i. If I can treat your mortgage like a fixed rate mortgage for a moment, you would have 211 monthly payments of \$626 left, so the present value of the mortgage is PV = 626*(1 - (1.003274)^-211)/.003274 = \$95,270. Since this is less than you would be paying immediately to settle the debt, you should continue to pay \$626 to the mortgage.

Is it weird that this post makes me want to cheer, like I'm a spectator at a sporting event?

Well done Heart of Tin.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: MoneyStacher on December 12, 2013, 07:36:25 PM
There's an even easier explanation. You've misapplied the 4% rule. You can't price a ... annual effective rate converted to a 0.3274% monthly effective rate for i. If I can treat your mortgage like a fixed rate mortgage for a moment, you would have 211 monthly payments of \$626 left, so the present value of the mortgage is PV = 626*(1 - (1.003274)^-211)/.003274 = \$95,270. Since this is less than you would be paying immediately to settle the debt, you should continue to pay \$626 to the mortgage.

So, this is going to have to wait until tomorrow when I've got a full cup of joe and a clear head! A few really like this response so there is much for me to learn here. Thanks for taking the time.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: MoneyStacher on December 13, 2013, 05:15:34 AM
Okay, there was a mistake where I applied the 4% rule to a stache that included home equity. I'll take that out and rerun the numbers. I'll also highlight the error pointed out by another mustachian. I almost tricked myself here into thinking that paying off a 2.75% mortgage was better than keeping the dollars invested.

Option 1 is retire now without paying off the mortgage.
Option 2 is retire now but first pay off the mortgage from current stache.
The stache is 540,000 invested dollars and 46,000 home equity. Total 586K.
Mortgage payment is \$626 monthly on a 2.75% ARM (240 interest, 386 principle right now)
Mortgage balance \$104,500
Mortgage Payoff will require liquidation of long-term assets of ~123,000 so invested dollars is reduced by that amount in Option 2

 Option 1 Option 2 Home Equity 46,000 150,500 <-- irrelevant to the calculations, but noted here Invested Dollars 540,000 417,000 <-- liquidated 123k, paid 15% tax, paid mortgage off 4% Draw from Invested 21,600 16,680 Divided by 12 months 1,800 1,390 Minus Mortgage Pmts 626 0 Remaining Monthly Cash 1,174 1,390 <-- Looks like a \$216/mo. raise to me and it is, but read on

Although the draw in Option 2 is less than in Option 1, I have no mortgage payments to make so it seems I've effectively given myself a \$216 monthly raise by paying off the mortgage from my invested stache just before retiring.

But the error here, as pointed out by Heart of Tin, is that my monthly mortgage payment of 626 will only last for the first 18 or so years of my retirement. Then, it goes to 0. So, although Option 2 will ease my financial situation for the first 18 years of retirement, I'm hurting myself in the long run. At my current age of 46, I'll have a monthly benefit of \$216 until age 64. But, if I live until 90 then the remaining 26 years are lived off \$410 per month less that Option 1.

I have this correct now?
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: fodder69 on December 13, 2013, 05:28:23 AM
I just wanted to say this is a really informative post and wanted to thank the OP for posting it and everyone else for chiming in.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: dragoncar on December 13, 2013, 05:56:09 AM
New numbers look good and  glad you posted the question.

Another consideration in general is mortgage interest deductibility.  This really shouldn't factor for mustachian withdrawal levels, but at higher incomes it makes a difference.

On the flip side, at mustachian levels, you pay more in taxes in order to withdraw more.  Again in your case not so big a deal.  But if we are talking paying off a 500k mortgage vs bumping annual withdrawal from 27k to 54k, that will impact your taxes.

The point being, I haven't run the numbers but for bigger mortgages or withdrawal rates there are other considerations.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: PeteD01 on December 13, 2013, 09:13:41 AM
If you can live off \$1147, the lowest risk (still too high for my taste) strategy would be:

pay off the mortgage + decrease draw by .65% to 3.35% + after 18 years increase draw to 4%

Keeping the mortgage equals a leveraged investment in the market and the equivalent of a margin call for you would be either realized loss of principal because of forced sell in a down market or loss of your house under likely unfavorable market conditions.

The problem with all the discussions about paying off the mortgage early or not is that risk management is not mentioned enough.
In the end, leveraged investments in the market are always speculative because they are in essence a bet either on inflation, interest rates, market returns or a combination of these. In the absence of sufficient other discretionary income, to be used to prevent deep losses in unfavorable conditions, they are way too risky.  I personally prefer to use other discretionary income in unfavorable market conditions to buy investments and not to prevent losses.

Peter

Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: arebelspy on December 13, 2013, 09:26:36 AM
I personally prefer to use other discretionary income in unfavorable market conditions to buy investments and not to prevent losses.

Where does that "other discretionary income" come from?
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: PeteD01 on December 13, 2013, 09:36:56 AM
I personally prefer to use other discretionary income in unfavorable market conditions to buy investments and not to prevent losses.

Where does that "other discretionary income" come from?

That's exactly the problem with the scenarios presented - there is no mention of it and that is why keeping the mortgage is so risky.
Things would look quite different if an income from work could support the loan or if the mortgage was supported by rental income especially at a current rate of 2.75%. In that context, it becomes an investment strategy somewhat leveraged for diversification and use value.  Not bad at all and actually common practice.
Without another source of income, it is a leveraged investment strategy which does double duty as a retirement plan - risky, risky, risky.

Peter
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: mpbaker22 on December 13, 2013, 09:54:28 AM
There's an even easier explanation. You've misapplied the 4% rule. You can't price a mortgage with an end date using this formula. The 4% rule is applied to yearly expenses, because we assume that our expenses never change and go on forever making them a perpetuity. A perpetuity is a series of periodic payments that never ends. If you have a perpetuity with payment amount R and interest rate i, then PV = R/i where PV is the present value or price of the perpetuity. MMM switched this formula around to R = PV*i where R is our yearly expenses in retirement, i is our safe withdrawal rate (4% usually), and PV is the necessary value of our investments.

Instead of using the perpetuity formula to price the mortgage, we need to use the annuity formula. Annuities, in this case, are a series of periodic payments over a defined period. You may be familiar with life annuities, usually just called annuities, where the period is defined as the lifetime of the annuitant after a certain age. In this case your mortgage is an annuity where the period is defined as the original term of the mortgage. The annuity formula is PV = R*(1 - (1 + i)^-n)/i where PV is the current value or price of the annuity, R is the monthly payment, and n is the number of payments left. Since we are comparing this to a 4% perpetuity, we will use a 4% annual effective rate converted to a 0.3274% monthly effective rate for i. If I can treat your mortgage like a fixed rate mortgage for a moment, you would have 211 monthly payments of \$626 left, so the present value of the mortgage is PV = 626*(1 - (1.003274)^-211)/.003274 = \$95,270. Since this is less than you would be paying immediately to settle the debt, you should continue to pay \$626 to the mortgage.

Technically, the 4% rule was developed for a 30 year time frame, not perpetuity.  So, if the OP had a 30 year mortgage starting today, it would actually work perfectly.

In my mind, the more important thing to consider is that the 4% rule results in a positive balance in 30 years in 95% (or something like that) of cases, so you run out in 5%.  There are an additional few percent of cases where you basically fall between \$0 and the original balance.   In the vast majority of cases you will actually have far more than the original balance in 30 years.

What you will find is a dichotomy between risk and return.  If you run the calculations (correctly) you'll find that paying off the mortgage lowers the risk to some extent, but you'll likely have a much higher balance in 30 years if you pay it off over 30 years.  That last part might be important if you're 30 and have 60 more years to live.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: Spork on December 13, 2013, 10:04:43 AM
Looks like a \$216/mo. raise to me and it is, but read on

There is another possible error here... I say possible, as I don't know your exact situation.   If your mortgage payment includes payment into an escrow account for insurance/taxes...  You need to make sure you factor that out.  You'll still be paying those.

That said: I know the numbers work for today's artificially low interest rates.  But I'm still a fan of paid off houses.  Both sides of this argument have upsides.  I sort of think it's a choice between win and win.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: Heart of Tin on December 13, 2013, 10:41:56 AM
I have this correct now?

Good. It looks like you understood the concept, but you don't have to wait 18 years to benefit from the mortgage payments if we assume that your portfolio grows at a constant 4% per year (which we already assumed by using the 4% rule).

In the math below I'm going to draw monthly from net worth instead of drawing yearly from investment accounts only and dividing the income by 12 months, so my numbers won't quite match what you figured above. To do this I will multiply the present value of all accounts by the monthly effective discount rate. I will use the discount rate instead of the interest rate since the first payment occurs today, not one month from now. The monthly effective discount rate can be calculated from the monthly effective interest rate, i = 0.3274%, from my post above with the formula d = i/(1+i) = .003274/(1.003274) = 0.3263%.

Option 2 (pay the mortgage off immediately): This will transfer \$104,500 from our investment account to the mortgage leaving us with a present value of \$586,000. Multiplying the monthly effective discount rate by our present value gives us a monthly payment of \$586,000*.003263 = \$1,912.15 for life.

Option 1 (pay the mortgage off in \$626 monthly installments with a smaller last payment): To smooth out our living expenses, we need to figure out the present value of our mortgage payments and subtract that amount from the value of the house plus the amount in the investment accounts. I already showed the math to calculate the present value of the mortgage payments above, but this time I'm going to assume that our first payment is today (whereas the above calculation assumed that the first payment was one month from now) to get a present value of \$95,276.13. Subtracting that from the value of the house plus the value of the investments, we get PV = \$540,000+\$150,500-\$95,276.13 = \$595,223.87. Multiplying the monthly effective discount rate by our present value gives us a monthly payment of \$595,223.87*.003263 = \$1,942.24 for life. Note that this is just the extra amount you get every month on top of the mortgage payments. When the mortgage payments stop, you still get \$1,942.24 every month. That's about \$30 extra in spending money every month for life.

Remember, this is just the value of each option weighted by our assumed 4% interest rate. I cannot account for individual risk/debt tolerance and I have not accounted for the tax implications of each option, since I am unfamiliar with your tax situation, with this math.

I've attached a spreadsheet that illustrates this concept. The whole thing is driven off of the grey cells at the top left of the spreadsheet, so changing the grey cells will allow you model different situations. Here's a link to the Google Docs version for those without Excel or those who don't like to download things from anonymous internet people: https://docs.google.com/spreadsheet/ccc?key=0AoGy5FAuORHndF9xVW5RWFF4X3dCM0VZV2IyXzBFZ2c&usp=sharing
Note that this spreadsheet is for illustrative, comparative purposes only and should not be utilized for actual financial planning without understanding all underlying assumptions of the model.

Tl;dr continuing to pay the mortgage on schedule can result in \$30 extra every month for life under the assumptions of the original post.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: PeteD01 on December 13, 2013, 10:50:48 AM
There's an even easier explanation. You've misapplied the 4% rule. You can't price a mortgage with an end date using this formula. The 4% rule is applied to yearly expenses, because we assume that our expenses never change and go on forever making them a perpetuity. A perpetuity is a series of periodic payments that never ends. If you have a perpetuity with payment amount R and interest rate i, then PV = R/i where PV is the present value or price of the perpetuity. MMM switched this formula around to R = PV*i where R is our yearly expenses in retirement, i is our safe withdrawal rate (4% usually), and PV is the necessary value of our investments.

Instead of using the perpetuity formula to price the mortgage, we need to use the annuity formula. Annuities, in this case, are a series of periodic payments over a defined period. You may be familiar with life annuities, usually just called annuities, where the period is defined as the lifetime of the annuitant after a certain age. In this case your mortgage is an annuity where the period is defined as the original term of the mortgage. The annuity formula is PV = R*(1 - (1 + i)^-n)/i where PV is the current value or price of the annuity, R is the monthly payment, and n is the number of payments left. Since we are comparing this to a 4% perpetuity, we will use a 4% annual effective rate converted to a 0.3274% monthly effective rate for i. If I can treat your mortgage like a fixed rate mortgage for a moment, you would have 211 monthly payments of \$626 left, so the present value of the mortgage is PV = 626*(1 - (1.003274)^-211)/.003274 = \$95,270. Since this is less than you would be paying immediately to settle the debt, you should continue to pay \$626 to the mortgage.

Technically, the 4% rule was developed for a 30 year time frame, not perpetuity.  So, if the OP had a 30 year mortgage starting today, it would actually work perfectly.

In my mind, the more important thing to consider is that the 4% rule results in a positive balance in 30 years in 95% (or something like that) of cases, so you run out in 5%.  There are an additional few percent of cases where you basically fall between \$0 and the original balance.   In the vast majority of cases you will actually have far more than the original balance in 30 years.

What you will find is a dichotomy between risk and return.  If you run the calculations (correctly) you'll find that paying off the mortgage lowers the risk to some extent, but you'll likely have a much higher balance in 30 years if you pay it off over 30 years.  That last part might be important if you're 30 and have 60 more years to live.

There is the risk that one does run out of money when following the 4% rule and that is about 5%.
The risk the OP is facing in addition is the risk that 4% draws in unfavorable conditions are insufficient to support basic necessities.
So one has to consider both the risk inherent in the 4% rule and the risk of the OP having to violate the 4% rule by withdrawing more than that. Only the OP could tell us if he would be able to survive on sixty percent of currently projected income.

In option 1, only about \$450 a month remain during a 40% down market after paying the mortgage. This is almost 61% less than the projected amount of \$1147 after paying the mortgage.

In option 2, there will be \$688 per month at 3.35% withdrawal rate which could temporarily be bumped to 4% resulting in an income of about \$830 which is only about 28% below the projected draw of \$1147 per month. All without violating the 4% rule.

Only the OP can tell us if he could survive with \$450 without increasing the draw rate and thereby exiting the 4% rule strategy.

By paying off the mortgage and reducing draw initially to 3.35%, volatility of income is much reduced, quite possibly enough to stay at 4% or less draw rates.

So there are two risks to be managed:

The risk inherent to the 4% rule which is commonly given as about 5%.

The risk of being unable to follow the 4% rule due to downside volatility exceeding the minimum income requirements.

The first risk can be discussed in a general way.

The second risk depends on the absolute minimum income requirement. It follows that the higher the net worth is the more volatility and upside potential can be accepted. In this case, the projected income and volatilities seem to disfavor keeping the mortgage.

All this doesn't even include the risks due to inflation, interest rates etc which can also influence the second type of risk.
The four percent rule does include an estimate of those risks based on historical back testing.

Peter
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: Heart of Tin on December 13, 2013, 11:05:07 AM
Technically, the 4% rule was developed for a 30 year time frame, not perpetuity.  So, if the OP had a 30 year mortgage starting today, it would actually work perfectly.

I was just using the general assumption of this forum/blog that you can safely assume a 4% return. You're right that this is, technically, a misapplication since, in the formulas that I've been using, the interest rate usually represents a risk-free interest rate. However, in real life there is no risk-free rate. Everything has some sort of risk. We are simply using these formulas as a model of how the world probably works, since we would otherwise be pretty powerless to calculate anything. All formulas should be understood in relation to their underlying assumptions. Unfortunately, that makes everything we say on this board couched in our own personal assumptions of how the world might work which leads to a tremendous amount of variation and subtlety between threads. I was simply attempting (and perhaps failing) to use OP's assumptions.

However, you have made a slight error in that the risk of OP defaulting on his or her mortgage has been judged by their mortgage lender to be worth 2.75% APR whereas OP's investments likely have a different risk which will give rise to a different interest rate. The present value of different cash flow structures will therefore be different unless we adjust for risk in exactly the same way as the mortgage lender and market forces that will affect the investment. These calculations are very difficult, and I don't have a sufficient background in time series analysis to attempt them.

What you said about risk being inversely proportional to return assumes an efficient market, but there are many economists out there that disagree with that assumption in certain situations. I, personally, don't have an opinion about that particular topic.
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: PeteD01 on December 13, 2013, 11:19:57 AM
Technically, the 4% rule was developed for a 30 year time frame, not perpetuity.  So, if the OP had a 30 year mortgage starting today, it would actually work perfectly.

I was just using the general assumption of this forum/blog that you can safely assume a 4% return. You're right that this is, technically, a misapplication since, in the formulas that I've been using, the interest rate usually represents a risk-free interest rate. However, in real life there is no risk-free rate. Everything has some sort of risk. We are simply using these formulas as a model of how the world probably works, since we would otherwise be pretty powerless to calculate anything. All formulas should be understood in relation to their underlying assumptions. Unfortunately, that makes everything we say on this board couched in our own personal assumptions of how the world might work which leads to a tremendous amount of variation and subtlety between threads. I was simply attempting (and perhaps failing) to use OP's assumptions.

However, you have made a slight error in that the risk of OP defaulting on his or her mortgage has been judged by their mortgage lender to be worth 2.75% APR whereas OP's investments likely have a different risk which will give rise to a different interest rate. The present value of different cash flow structures will therefore be different unless we adjust for risk in exactly the same way as the mortgage lender and market forces that will affect the investment. These calculations are very difficult, and I don't have a sufficient background in time series analysis to attempt them.

What you said about risk being inversely proportional to return assumes an efficient market, but there are many economists out there that disagree with that assumption in certain situations. I, personally, don't have an opinion about that particular topic.

Yes, there are some simplifications but they do not change things in a major way.
The risks in the OP's investments is different than the risk the lender assessed. This is actually what leveraged investments are based upon. The OP must assume risks promising returns in excess of 4%+2.75% for the portion of the investment derived from the mortgage loan in order to come out ahead and being able to draw within the constraints of the 4% rule. That rules out pretty much anything but 100% stock funds for that portion of the investment - hence the volatility. Inflation will help him over time - but that is exactly what makes it a bet.

Peter
Title: Re: Mortgage Payoff Contradiction. Can this be right?
Post by: mpbaker22 on December 13, 2013, 11:26:14 AM
Technically, the 4% rule was developed for a 30 year time frame, not perpetuity.  So, if the OP had a 30 year mortgage starting today, it would actually work perfectly.

I was just using the general assumption of this forum/blog that you can safely assume a 4% return. You're right that this is, technically, a misapplication since, in the formulas that I've been using, the interest rate usually represents a risk-free interest rate. However, in real life there is no risk-free rate. Everything has some sort of risk. We are simply using these formulas as a model of how the world probably works, since we would otherwise be pretty powerless to calculate anything. All formulas should be understood in relation to their underlying assumptions. Unfortunately, that makes everything we say on this board couched in our own personal assumptions of how the world might work which leads to a tremendous amount of variation and subtlety between threads. I was simply attempting (and perhaps failing) to use OP's assumptions.

However, you have made a slight error in that the risk of OP defaulting on his or her mortgage has been judged by their mortgage lender to be worth 2.75% APR whereas OP's investments likely have a different risk which will give rise to a different interest rate. The present value of different cash flow structures will therefore be different unless we adjust for risk in exactly the same way as the mortgage lender and market forces that will affect the investment. These calculations are very difficult, and I don't have a sufficient background in time series analysis to attempt them.

What you said about risk being inversely proportional to return assumes an efficient market, but there are many economists out there that disagree with that assumption in certain situations. I, personally, don't have an opinion about that particular topic.

But that's not a general assumption of this forum.  I think it's pretty well assumed that you can safely assume a return higher than 4 percent.  The SWR and rate of return are two completely different things. The SWR of 4% says you can withdraw 4% and increase by inflation each year, and have a 95% chance of not running out.  I would say a pretty safe assumption of investment returns over 30 years is 5-7%, but expected investment returns isn't a relevant number to someone who is retiring today.  That's where SWR rate comes in, it's normalized so that even if you experience a 4% drop in year 1, you still have pretty good odds of not running out of money.

I mean, I don't think we're really arguing anything, but I'm trying to make clear that SWR and rate of return are not the same thing, but they are somewhat related.