We are on the home stretch to early retirement and in about 18 months or so – if everything goes well – we will sell our expensive condo, pay off the mortgage and move to a less expensive location. We might rent a house there or pay for a modest home with cash. One way or another, we should be completely **mortgage-free**!

Or will we *still* have a mortgage? How about the “mortgage payments” in the form of our future living expenses in retirement? They increase by the rate of inflation every year! That’s the mother of all mortgage payments! Mortgage mayhem! How do we treat a “mortgage” like that on our balance sheet?

Let’s look at how this works for an actual mortgage. The beauty of elementary financial math is that whether you put your current mortgage balance or the discounted flow of all future mortgage payments (principal plus interest, not the tax or insurance!) on your balance sheet, it wouldn’t matter. If you discount your mortgage payments at the mortgage interest rate the two are identical, thanks to the way the mortgage payment is calculated through the amortization formula (subject to some rounding errors and other small potato issues like linear accruals intra-month). This raises the following questions:

**Should we account for our future expected expenses on our balance sheet? **

**And if so, how?**

The answer to the first question is: of course! Not taking into account the future liabilities would be equivalent to a company booking its pension fund portfolio as an asset but not including the future obligations. It’s less about *if* we book future payments, but more about *how* we treat them in our finances.

### Plan for today

Also before we get into the weeds, let’s take a look at what we try to do in today’s post, conceptually. To bridge the disconnect between our net worth (a level variable, measured in dollars) and annual expenses in retirement (a flow variable, measured in dollars *per year*) we normally translate our net worth into a flow, multiplying by our preferred safe withdrawal rate, see diagram below, to see if the projected withdrawals can cover our spending needs.

But we can also go the **other route**: translate the projected flows during retirement back into a level variable and compare that with our current net worth. If the two match, we can retire.

As a side note, in no way would we want to *replace* the good old safe withdrawal rate exercise. We simply like to *supplement* it and gain some additional insights into the whole retirement financial mechanics.

### Numerical results

Let’s start with the parameter assumptions:

- Current portfolio value of $1,000,000
- Annual expenses of $35,000, increasing by an inflation rate of 2% p.a. (our personal situation involves a higher current net worth and higher annual expenses, but to make the numbers nice and round we compute everything per $1 million of initial portfolio value)
- Discount rates between 2% and 7% p.a.
- A retirement horizon of 30-60 years in 10-year increments
- We assume no other cash flows, neither from extra work nor Social Security. The little bit of Social Security income we are expecting will probably go to higher health care expenses at age 70+. And that’s
*if*we get our projected benefits. They might be cut and/or means-tested by then.

Let’s look at the discounted value of our expenses for different discount rates and different retirement horizons:

### Results:

- For discount rates low enough, the discounted value of expenses far exceeds the million dollars initial portfolio value. Ouch! We’re bankrupt, broke, dead-broke whatever you want to call it! For example, if we were to discount our future expenses at the current 30-year Treasury Bond yield (currently around 2.5%), the discounted value of our implicit liability would be about $1,820,344 for a 60-year horizon. That means we’re underwater by over $820,000!
- In the chart, we can also read off what would have to be the average return to make the money last 30, 40, 50, or 60 years, by looking at where the implicit liability line exactly intersects the $1,000,000: 2.34%, 3.85%, 4.58% and 4.98% for 30, 40, 50, and 60 years, respectively.
- The calculations are all for a 3.5% initial withdrawal rate. Since this all scales linearly, we can easily read off the values for folks who prefer the 4% safe withdrawal rate by just scaling up the implicit liability by about 14.29% (4/3.5-1). You would now exceed the $1,000,000 portfolio value even at a 30-year horizon. Ouch!

### So, are we really broke?

The good news is, we’re not really broke. True, our future expenses may have all the features of a string of bond payments. Discounting the future flows at a bond-like interest rate might drive our liabilities above our asset value, but our assets have a much higher expected return than the liabilities. The best analogy for our financial situation would be a company that has an underwater balance sheet (liabilities > assets) but it was smart (or lucky?) enough to have refinanced its liabilities into a low-interest rate bond with payments spread out over the next 60 years. Since this company is profitable with an expected return on its asset much higher than the low bond interest rate, it can** grow out of its balance sheet impasse over time**. This company also has patient debtors who are not going to push it into forced bankruptcy. In our case, we are the debtors (specifically, our future selfs!), so no issues there!

### Implications for our asset allocation

Nevertheless, we still have to try our best to grow ourselves out of the bad balance sheet mess. So, the **implications for our asset allocation** are:

- Be
**as aggressive as possible**to drive the expected portfolio return to at least 5% nominal, possibly much more than that to sustain a potentially 60-year retirement horizon. The 4.98% asset return (where the liability = assets) would be the absolute**minimum**return in the absence of any market volatility. Of course, we need an additional cushion to account for the dreaded “sequence of return risk“, so shooting for a cushion of about 1.5% p.a. would imply a 6.5% minimum expected return. - It’s hard to see how a 60% Stock/40% Bond portfolio would get anywhere close to that return target! Even a 20% bond allocation is already pushing it. So, how about the
**bond allocation**? Given that we have a roughly 1.8 million dollar short bond position on our balance sheet, it would be a really, really bad idea to shift into an asset that only yields as much as the outsized liability. Currently, each dollar of our equity portfolio has to work to overcome $1.80 in a short Treasury position. That’s already a tough task. But shifting, say, 20% of our portfolio into bonds means the now $800,000 of equity portfolio have to compensate for a $1,600,000 short bond position. Now, each dollar of the equity portfolio has to overcome $2.00 in a short-bond-position, see diagram below. The more we shift into bonds the more unlikely it becomes that we can grow out of the balance sheet shortfall! For 60% stocks, 40% bonds it gets even worse: You have to overcome $2.33 of short bonds with each $1.00 of equity allocation. You reduce short-term volatility but increase the risk of running out of money long-term! In other words, think about what the company with the underwater balance sheet should do with its assets? It would be crazy to buy any of its own bonds back. It would need to put its assets to work at a much higher expected returns to grow out of the mess.

- If it were
**the other way around**, say, the implicit bond liability were only $750,000 then we could, of course, hold $750,000 in bonds to exactly hedge out that liability (=fully fund all of our future liabilities). One could accomplish that through a bond ladder of nominal bonds (to exactly match the nominal spending targets) or TIPS (to match the real spending targets). Then we could hold the other $250,000 as a bonus or give them away to charity or a gift to our daughter. Or simply increase our spending by 33%! But that’s not in the cards because the implicit liability is so much larger than our assets at the current interest rates. - The only sensible way we would want to hold bonds is in a
**leveraged position**without taking away any weight from high yielding, high return assets (equity, real estate, and option writing). We have written about how to do this in our post “Lower risk through leverage” and back then we argued for buying bonds on leverage from a pure portfolio diversification aspect. But a large leveraged bond position would also be a hedge for the large implicit short-bond-position on our balance sheet, so here’s another rationale for buying bonds on leverage!

### Lining up cash flow priorities with discount rates

One objection we can already foresee:

*“Objection, objection, ERN. Our cash flow in retirement is nothing like the strict non-negotiable contractual arrangement of a 30-year bond. We got wiggle room; flexibility to temporarily adjust our spending. We should not discount our expenses at 2.5%!”*

Glad you asked! Not only can we factor in this flexibility, but our analysis is almost *exactly made* for this type question!

Imagine that out of the $35,000 of annual consumption, $25,000 are the non-negotiable minimum we like to guarantee for essentials like shelter, food, and health. Call it the 4-M (=Mr. Money Mustache Minimum), and the remaining $10,000 p.a. have significant wiggle room because those are non-essentials (travel, entertainment, gifts, apparel, etc.) where we would be willing and able to cut expenses in line with how the stock market performs. For example, cut our expenses by 56% in 2008/9! To price this consumption stream we should discount $25k at the safe government bond rate and $10k p.a. at a higher, equity-like rate of return. Our current personal expected return target for equities is 7% nominal. That’s already a bit aggressive given the high Shiller CAPE ratio but I’m in a good mood today.

Now our implicit liabilities are “only” $1.3m in 30-year Treasury Bonds and just under $200k in equities. In the context of the underwater company mentioned above, this would be equivalent to the debtors owning about $520k less in bonds but holding a 20% equity stake in the company instead. So, what did the spending flexibility buy us? We are now net long $802k in equities (=$1m equity asset minus $197.5k equity liability) and have a 1.3m bond liability on our balance sheet. Every dollar of our equity holdings still has to “fight” $1.62 in short bonds, which is better than the $1.80 above. But we are still in a half million dollar hole! That’s still a lot, so flexibility in retirement is not a panacea!

### Some additional thoughts

- The entire discussion about safe withdrawal rates and risk of running out of money in retirement would be 100% moot if it weren’t for a) the low current bond yields and b) the extremely long retirement horizon we face.
- We have never been big fans of the Trinity Study because we find that their assumptions (asset returns going back to 1926) are not representative in today’s world of low equity expected returns and the low bond yield environment. But in light of our analysis here we get the feeling that even back in 1998 when the original study was written it was already moot. Not completely, but at least in the following sense: with bond interest rates very high back then you could have easily hedged 30 years of retirement expenses (their longest horizon!) with the appropriate bond ladder. In the late 1990s, yields were at 3.5% real (!!!) for the 10 and 30 year TIPS. Since we assumed a 2% inflation rate that means we should discount the future cash flow at 5.5% nominal. The discounted value of 30 years of cash flows ($40,000 initially and then inflation adjusted, see summary table above) would have been only about $755,769 if discounted at 5.5%. So you could have
*fully hedged*a 4% safe withdrawal rate plus inflation adjustment and have almost $250K left over for your heirs (in today’s dollars!). Or scale up your withdrawals to about 5.3% without any risk of running out of money. - Even in today’s environment, all you need is a 3.29% projected nominal bond return to make your portfolio last 30 years. With corporate investment grade bonds, the typical 65-year-old can fund a 30-year retirement at 4% withdrawal rate and 2% annual cost of living increases even with today’s low yields (caution, though, corporate bonds have some credit risk). But of course: For the aggressive savers and early retirees who face a 50-60 year retirement horizon this kind of asset-to-liability matching becomes very hard.

### We hope you found this thought-provoking. How broke are you? We’re looking forward to your comments!

Cerebral post ERN. The think about discount rates and return projections is that even small changes can result in massive difference in outcomes. The only consolation I take here is that discount rate is correlated to other factors so the retirement horizon doesn’t materially change.

Oh, thanks a lot. Yes, we were surprised how small changes in the discount rate create several $100k in discounted value!

Cheers,

ERN

Absolutely ERN. Less cerebral than yours but makes similar case (looking from a traditional WR perspective, ‘cos you gotta live with what you can withdraw!) is a simple post of mine here for your perusal: http://tenfactorialrocks.com/how-long-vs-how-much/

No mortgage on the new lower-cost home (in the event y’all buy)? I’m a little surprised. Why not let the leveraging effect mitigate some of the sequence of returns risk by reducing cash outflows in the first couple years? (I’m asking these questions because you guys seem to have a pretty well-planned schematic in place, and I wonder if there’s something I’m missing…)

The additional leveraging of a mortgage also would arguably reduce your opportunity cost of capital and thus the applicable discount rate range in the PV study.

Just some thoughts. This seems like a conversation that would be fun to have over a beer. Mmmm…beer. Gotta run! Good luck with the next 18 months!

That’s a great point! As always, very thoughtful, FL!

The advantage of not having a mortgage is to have peace of mind: If something goes wrong with our investments (2008 repeat), it’s easy to hunker down and cut expenses down to the bare essentials, MMM-style.

Another advantage: Keeping taxable income low enough to qualify for Obamacare health insurance benefits. If the income we have to generate to pay the mortgage puts us just over the edge and out of reach of the subsidy, we might say “hasta la vista mortgage!”

Another issue: we could potentially face a 30% marginal tax rate on ordinary income (Federal): https://earlyretirementnow.com/2016/07/13/that-sneaky-30-federal-income-tax-bracket/

If that’s the case we just slapped a factor of 1/0.7=1.43 onto the mortgage rate. That’s how much we have to generate in pre-tax income.

But then again: peace of mind is expensive! Maybe too expensive. I definitely remember your excellent post on the 15 vs 30Y mortgage (http://www.financialibre.com/a-15-year-mortgage-costs-409112-more-than-you-think/). So, the “zero-year mortgage” i.e., no mortgage at all has some serious opportunity cost attached to it.

I hope I am not heading for broke even with our conservative approach. I don’t have the 60 yr roadmap ahead of me . I’ll be happy with 40+ therefore our sub 2% withdrawal rate topped off with annuitized pension should do the trick and keep the doomsters at bay from telling me cat food will be my last supper.

I’m always impressed when you show the details of your financials! Only 2% withdrawal rate and company pensions. It looks like your financials put you into the region where you could fully hedge your future cash flow needs, say, with a TIPS ladder and still have money left over to invest in equities to leave a bequest or for charity.

That means you actually could have retired already years ago!

Cheers to that!

ERN

You know we are conservative right……?

That low WR allows for creep from who knows what. E.g healthcare costs, kids having the genius for Ivy League (unlike parents), desire to splurge and travel the globe endlessly, purchase more exotic cat food…..

Yes, it’s always good to have that cushion! But don’t overdo it. That’s like going to the airport 5 hours before the flight leaves. 🙂

Cheers,

ERN

Challenging post… I will have to reread it a few times to see what I think about it.

As mentioned in the comments above, a lot depends on the discount rates you put in.

The way I see it: the cash flow does indeed represents a liability worth today a certain amount (2,1 mio for 60 year at 2 pct) According to me, this also assumes that this amount would not yield over time. Correct? That is where part 2 of your article comes in: what asset allocation do you need for that.

I am with you on having doubts on the trinity study. I see that more as a guideline to define when I can tell :y boss that I quit. What I mean is, I quit to work for the man and go work on my own terms. Then again, what is holding me back to that already now?

Yup, everything depends on the discount rate.

“this also assumes that this amount would not yield over time. Correct? ”

Not sure what you mean, but the calculation would be equivalent to assuming a 2% return on your investments, then withdrawing your projected cash flow (including cost of living adjustments) and exactly running out of money after 60 years. So in that sense, we did assume that there is a 2% yield.

Thanks!

Thx, I got it now.

This gives another view to define FI.

My personal idea is more FF: have enough to be flexible in what I do.

I thought I was really close to FIRE. I am going to have to digest this post in the morning and really look back at my analysis. Thank you for giving me nightmares before I fall asleep 🙂

Haha, oh no, please rest easy and don’t worry! As I mentioned, we can probably grow out of that hole. 😉