## Problems with Constant Compound Interest (6)

Doctored Photo Credit: Marvin Isidore Macatol || And I say this is heresy!

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My last post produced the following question:

What if your time horizon was 60 years? Would a 5% real return be achievable?

I am answering this as part of an irregular “think deeper” series on the problems of modeling investment over the very long term… the last entry was roughly six years ago.  It’s a good series of five articles, and this is number six.

On to the question.  The model forecasts over a ten-year period, and after that returns return to the long run average — about 9.5%/year nominal.  The naive answer would then be something like this: the model says over a 60-year period you should earn about 8.85%/year, considering that the first ten years, you should earn around 5.63%/year.  (Nominally, your initial investment will grow to be 161x+ as large.)   If you think this, you can earn a 5% real return if inflation over the 60 years averages 3.85%/year or less.  (Multiplying your capital in real terms by 18x+.)

Simple, right?

Now for the problems with this.  Let’s start with the limits of math.  No, I’m not going to teach you precalculus, though I have done that for a number of my kids.  What I am saying is that math reveals, but it also conceals.  In this case the math assumes that there is only one variable that affects returns for ten years — the proportion of investor asset held in stocks.  The result basically says that over a ten-year period, mean reversion will happen.  The proportion of investor asset held in stocks will return to an average level, and returns similar to the historical average will come thereafter.

Implicitly, this assumes that the return series underlying the regression is the perfectly normal return series, and the future will be just like it, only more so.  Let me tell you about some special things involved in the history of the last 71 years:

• We have not lost a war on our home soil.
• We have not had socialism to the destructive levels experienced by China under Mao, the USSR. North Korea, Cuba, etc.  (Ordinary socialism isn’t so damaging, though there are ethical reasons for not going that way.  People deserve freedom, not guarantees.  Note that stock returns in moderate socialist countries have been roughly as high as those in the US.  See the book Triumph of the Optimists.)
• We have continued to have enough children, and they have become moderately productive workers.  Also, we have welcomed a lot of hard working and creative people to the US.
• Technology has continued to improve, and along with it, labor productivity.
• Adequate energy to multiply force and distribute knowledge is inexpensively available.
• We have not experienced hyperinflation.

There are probably a few things that I have missed.  This is what I mean when I say the math conceals.  Every mathematical calculation abstracts quantity away from every other attribute, and considers it to be the only one worth analyzing.  Qualitative analysis is tougher and more necessary than quantitative analysis — we need it to give meaning to mathematical analyses.  (What are the limits?  What is it good for?  How can I use it?  How can I use it ethically?)

If you’ve read me long enough, you know that I view economies and financial markets as ecosystems.  Ecosystems are stable within limits.  Ecosystems also can only develop so quickly; there may be no limits to growth, but there are limits to the speed of growth in mature economies and financial systems.

Thus the question: will these excellent conditions continue?  My belief is that mankind never truly changes, and that history teaches us that all governments and most cultures eventually die.  When they do, most or all economic arrangements tend to break, especially complex ones like financial markets.

But here are three more limits, and they are more local:

• Can you really hold for 60 years, reinvesting and never taking a material amount out?
• Will the number investing in the equity markets remain small?
• Will stock be offered and retired at ordinary prices?

Most people can’t lock money away for that long without touching it to some degree.  Some of the assets may get liquidated because of panic, personal emergency needs, etc.  Besides, why be a miser?  Warren Buffett, one of the greatest compounders of all time, might have ended up happier if he had spent less time compounding, and more time on his family.  It would have been better to take a small part of it, and use it to make others happy then, and not wait to be the one of the most famous philanthropists of the 21st century before touching it.

Second, returns may be smaller in the future because more pursue them.  One reason the rewards for being a capitalist are large on average is that there are relatively few of them.  Also, I have sometimes wondered if stock returns will fall when the whole world is employed, and there is no more cheap labor to be had.  Should that bold scenario ever come to pass, labor would have more bargaining power in aggregate, and profits would likely fall.

Finally, you have to recognize that the equity return statistics are somewhat overstated.  I’m not sure how much, but I think it is enough to reduce returns by 1%+.  Equity tends to be offered for initial purchase expensively, and tends to get retired inexpensively.  Businessmen are rational and tend to go public when stock valuations are high, pay employees in stock when valuations are high, and do stock deals when valuations are high.  They tend to go private when stock valuations are low, pay employees cash in ordinary times, and do cash deals when valuations are low.

As a result, though someone that buys and holds the stock index does best, less money is in the index when stocks are low, and a lot more when stocks are high.

Inflation Over 60 Years?

I mentioned the risk of hyperinflation above, but who can tell what inflation will do over 60 years?  If the market survives, I feel confident that stocks would outperform inflation — but how much is the open question.  We haven’t paid the price for loose monetary policy yet.  A 1% rise in inflation tends to cut stock returns by 2% for a year in real terms, but then businesses adjust and pass through higher prices.  Vice-versa when inflation falls.

Right now the 30-year forecast for inflation is around 2.1%/year, but that has bounced around considerably even within a calm environment.  My estimate of inflation over a 60-year period would be the weakest element of this analysis; you can’t tell what the politicians and central bankers will do, and they aren’t sure themselves.

Summary

Yes, you could earn 5% real returns on your money over a 60-year period… potentially.  It would take hard work, discipline, cleverness, frugality, and a cast iron stomach for risk.  You would need to be one of the few doing it.  It would also require the continued prosperity of the US and global economies.  We don’t prosper in a vacuum.

Thus in closing I will tell you that yes, you could do it, but there is a large probability of failure.  Don’t count on buying that grand villa on the Adriatic Sea in your eighties, should you have the strength to enjoy it.

## Problems with Constant Compound Interest (5)

This is a continuation of an irregular series which you can find here.  Maybe if I were more scientific, I would have called it “All Exponential Growth Processes Run Into Constraints and Threats,” or if I were more poetic, “Nothing Lasts Forever — Nothing Grows to the Sky.”

Regardless, simple modeling is the bane of long-duration financial calculations.  I remember talking with some friends who served on a charitable board with me, about some investment grade long bonds (11-30 years) that I had purchased for a life insurance client that yielded 7-9% in late 1999.  They said to me that it was foolish to lock up money for so long in bonds, when you could earn so much more in stocks.  My three comments to them were:

• Prohibitive for life insurers to hold equities
• At current levels of the market, the yield of these bonds more than compensates for the possibility of capital growth in equities (valuations are stretched)
• The risk in the bonds is a lot lower.

And, I said we ought to shift shift our charity’s asset allocation to more bonds, as we were invested past the maximum of our guidelines in equities.  They looked in the rearview mirror and said that we were doing fabulous.  Why change success?

I was outvoted; I was a one-man minority.  There are a lot of people who would have loved to make that change in hindsight, but done is done.  I ended up leaving the board a year later over a related issue.

Now, don’t think that I am advising the same in 2011.  We may be headed for significant inflation or deflation; it is difficult to tell which.  Bonds offer little competition to equities here.  Commodities and cash may be better, but I am reluctant to be too dogmatic.  If the economy turns down again, long Treasuries would be best.

Here’s the difficulty: most people have been trained to think at least one of a few things that are wrong:

• That we can use simple models to forecast future outcomes.
• That average people are capable of avoiding fear and greed when it comes to investing.
• That financial markets are random in the sense that last period’s return has no effect on the returns of future periods.
• Over long periods of time, average investors can beat long Treasuries by more than 2%/year.  (Corollary to the idea that the equity premium is 4-6% versus 0-2%/year over high quality bonds.)
• That financial markets are expressions of what is going on in the real economy.
• That the real economy tends toward stability
• That government actions make the real economy more stable

I’m prompted to write this because of two articles that I ran across in the last day: Retiring Boomers Find 401(k) Plans Fall Short, and Stay Out of the ROOM (registration required).

I’ve written about this before in many places, including Ancient and Modern: The Retirement Tripod.  And yet, when I wrote about these issues 20 years ago, one of the things that I tried to point out was that as the demographic bulge retired, it would be difficult for homes and asset markets to throw off the returns necessary, because there would not be enough buyers for the assets/homes.  If a large portion of the population wants to convert assets into a stream of income — guess what?  They are forced sellers, and yields that they will get will be compressed as a result.

In a situation like that, those that are better off, and can delay turning all of their assets into an earnings stream should be disproportionately better off.  As with corporations, so with individuals/families: those with slack assets and flexibility are able to deal with volatility better than those for whom the environment must be stable/favorable for the plan to succeed.

Now, the Wall Street Journal article points at the problems of 401(k) plans.  What they say is true, but the same is true of other types of defined contribution and defined benefit plans.  When assets underperform, and/or investors make bad choices, guess what?  The pain has to be compensated for somehow:

• 401(k): They will work longer, maybe all of the rest of their lives, and cut back on expenses and dreams.
• Non-contributory DC: maybe the employer will ask them to kick in voluntarily, or he might give more.  Also same as 401(k)…
• Private sector DB plans: employers may contribute more, or they may terminate them.
• Public sector DB plans: Taxes may rise, spending cuts enacted, forced contributions to retiree plans negotiated, plans terminated for a 457 plan, partial plan termination, job cuts, funny accounting practices (worse than the private sphere), brinksmanship over debts, etc.

Note that one of the answers is not “take more risk.”  First, risk and return are virtually uncorrelated in practice.  Only when enough people realize that might risk and return become positively correlated.  Second, there are times to increase and decrease risk exposure.  Typical people won’t want to do that, because of euphoria (the example of my friends above) and panic.  The time to add to high risk assets is when no one wants to touch a high yield bond.  More broadly, always look for asset classes that throw off the best cash flow yields, conservatively estimated, over the next ten-plus years.  Be sure and factor in the likelihood for economic regime changes and capital loss, inflation, deflation, etc.

Good asset allocation marries the time horizon of an investor to the forecasts for future returns, conservatively stated, and considers what could go wrong.  At present, investment opportunities are average-ish.  I would be wary of stretching for yield here, or raising my risk exposure in equities.  Stick with high quality.

And, for those that are retired, I would be wary of taking too much into income.  I have a simple formula for how much one could take from an endowment at maximum:

• 10 Year Treasury Yield
• Plus a credit spread — 2% if spreads are sky-high, 1% if they are good, 0.5% if they are tight.
• less losses and fees of 0.5% — higher if investment expenses are over 0.25%.

Not very scientific, but I think it is realistic.  At a 3.5% 10-yr T-note yield, that puts me at a 4% maximum withdrawal rate, given a 1% credit spread.  This attempts to marry withdrawals to alternative uses for capital in the market.  You may withdraw more when opportunities are high, and less when they are low.  (But who can be flexible enough to have a maximum spending policy that varies over time?)

Now some of the advanced models that calculate odds of retiring successfully are a step in the right direction, but they also need to reflect demographics, time-correlation of returns, regime-shifting returns/economics, etc.  Things don’t move randomly in markets; that doesn’t mean I know which way things are going, but it does mean I should be cautious unless the market is offering me a fat pitch to hit.

These statements apply to governments as well, and their financial security programs.  In aggregate, investments can’t outgrow growth in GDP by much, unless labor takes a progressively lower share of national income.  (And who knows, but that the pressure on union DB plans to earn high returns might lead to takeovers/layoffs in private firms…)  The real economy and the financial economy are one over the long haul, but can drift apart considerably in the intermediate-term.

In summary, any long promise/analysis/plan made must reflect the realities that I mention here.  We’ve spent years on the illusions generated by assuming high returns off of financial assets.  Now with the first Baby Boomers trying to retire, the reality has arrived — sorry, not everyone in a large birth cohort can retire comfortably.  Wish it could be otherwise, but the economy as a whole can’t generate enough to make that proposition work.

I don’t intend that this series have more parts, but if one strikes me, I will write again.

## Problems with Constant Compound Interest (4) (and more)

At the meeting of the eight bloggers and the US Treasury, one of the differences was whether the recovery was real or not.  The Treasury officials pointed to the financial markets, and the bloggers pointed at the real economy (unemployment and capacity utilization).

With T-bills near/below zero, I feel it is reasonable to trot out an old piece of mine about the last recession.  But I will quote most of it here:

I posted this on RealMoney on 5/6/2005, when everyone was screaming for the FOMC to stop raising rates because the “auto companies were dying.”

/*-/*-/*-/*-/*-/*-/*-/*-/*-/*-/*-/*-

On Oct. 2, 2002, one week before the market was going to turn, the gloom was so thick you could cut it with a knife. What would blow up next?

A lot of heavily indebted companies are feeling weak, and the prices for their debt reflected it. I thought we were getting near a turning point; at least, I hoped so. But I knew what I was doing for lunch; I was going to the Baltimore Security Analysts’ Society meeting to listen to the head of the Richmond Fed, Al Broaddus, speak.

It was a very optimistic presentation, one that gave the picture that the Fed was in control, and don’t worry, we’ll pull the economy out of the ditch. When the Q&A time came up, I got to ask the second-to-last question. (For those with a Bloomberg terminal, you can hear Broaddus’s full response, but not my question, because I was in the back of the room.) My question (going from memory) went something like this:

I recognize that current Fed policy is stimulating the economy, but it seems to have impact in only the healthy areas of the economy, where credit spreads are tight, and stimulus really isn’t needed. It seems the Fed policy has almost no impact in areas where credit spreads are wide, and these are the places that need the stimulus. Is it possible for the Fed to provide stimulus to the areas of the economy that need it, and not to those that don’t?

It was a dumb question, one that I knew the answer to, but I was trying to make a point. All the liquidity in the world doesn’t matter if the areas that you want to stimulate have impaired balance sheets. He gave a good response, the only surviving portion of it I pulled off of Bloomberg: “There are very definite limits to what the Federal Reserve can do to affect the detailed spectrum of interest rates,” Broaddus said. People shouldn’t “expect too much from monetary policy” to steer the economy, he said.

When I got back to the office, I had a surprise. Treasury bonds had rallied fairly strongly, though corporates were weak as ever and stocks had fallen further. Then I checked the bond news to see what was up. Bloomberg had flashed a one-line alert that read something like, “Broaddus says don’t expect too much from monetary policy.” Taken out of context, Broaddus’s answer to my question had led to a small flight-to-safety move. Wonderful, not. Around the office, the team joked, “Next time you talk to a Fed Governor, let us know, so we can make some money off it?”

PS —  Before Broaddus answered, he said something to the effect of: “I’m glad the media is not here, because they always misunderstand the ability of the Fed to change things.”  A surprise to the Bloomberg, Baltimore Sun, and at least one other journalist who were there.

/*-/*-/*-/*-/*-/*-/*-/*-/*-/*-/*-/*-

And now to the present application:

Why are commodities rising amid surplus conditions in storage?  Why is it reasonable to take over corporations when it is not reasonable to expand organically?  We are in a position where yields on short  Treasuries are nonexistent, investment grade and junk yields are low for corporates, and equities are rallying, but there is little growth, or some shrinkage in productive capacity.  Why?

The liquidity offered by the Fed is being used by speculators for financial positions, levering up relatively safe positions, rather than speculating on areas that are underwater, like housing and commercial real estate.  This is consistent with prior experience.  When the Fed does not allow a significant recession to occur, one proportionate to the amount of bad loans made, but comes to the rescue to reflate, what gets reflated is the healthy parts of the economy that absorb additional leverage, not the part that is impaired because they can’t benefit from low rates.  They have too much debt already relative to the true value of their assets.

That is why a booming stock market does not portend a good economy.  Banks aren’t lending to fund new growth.  They are lending to collapse capacity through takeovers.  ROE is rising from shrinking the equity base, not by increasing sales and profits.

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There is another current application:

Why do we buy commodities as investments?  Is it that we fear inflation in the short or long run?  Is it that it is a proxy for future prices for consumption in retirement, so we are hedging the future price level in a dirty way?

Think about it.  How do you transfer present resources to the future?  Most consumable goods can’t be stored, or require significant cost for storage.  Services can’t be stored; elderly people can’t store up health care.

Storage occurs through building up productive capacity that will be wanted by other at a later date, such that they will want to trade current goods and services for your productive capacity.  Storage also occurs by purchasing goods that do keep their value, and then trading them for goods and services you need when the time come to consume.

That is how one preserves value over time, and it is not easy.  It will be even harder if there are such disruptions to the economy that markets that are virtual do not survive.  (I.e. paper promises are exchanged, but their is significant failure to deliver at maturity.)

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In an environment where the government is playing such a large role in the economy, it is difficult to see how one can invest for the long term — when we are twisted between deflation and inflation, rational calculations are circumscribed, and simple judgments, such as buying out a competitor and shrinking the overall balance sheet are made.  In one sense, that is the rational thing.  Less capacity is needed.  But unemployment will rise.

That’s sad, but wage rates may be too high for some to be employed, given the lack of demand.  I view this as true in aggregate, but people that are aggressive in seeking employment are able to do much better.  I have seen it.  Even in a bad market, those that strive intelligently get hired.

## Problems with Constant Compound Interest (3)

This post should end the series, at least for now.  Tonight I want to talk about the limits to compounding growth.  Drawing from an old article of mine freely available at TSCM, I quote  the following regarding talking to management teams:

What single constraint on the profitable growth of your enterprise would you eliminate if you could?

Companies tend to grow very rapidly until they run into something that constrains their growth. Common constraints are:

• insufficient demand at current prices
• insufficient talent for some critical labor resource at current prices
• insufficient supply from some critical resource supplier at current prices (the “commodity” in question could be iron ore, unionized labor contracts, etc.)
• insufficient fixed capital (e.g., “We would refine more oil if we could, but our refineries are already running at 102% of rated capacity. We would build another refinery if we could, but we’re just not sure we could get the permits. Even if we could get the permits, we wonder if long-term pricing would make it profitable.”)
• insufficient financial capital (e.g., “We’re opening new stores as fast as we can, but we don’t feel that it is prudent to borrow more at present, and raising equity would dilute current shareholders.”)

There are more, but you get the idea.

Again, the intelligent analyst has a reasonable idea of the answer before he asks the question. Part of the exercise is testing how businesslike management is, with the opportunity to learn something new in terms of the difficulties that a management team faces in raising profits.

As with biological processes, when there are unlimited resources, and no predators, growth of populations is exponential.  But there are limits to business and investment profits because of competition for customers or suppliers, and good untried ideas are scarce.  Once a company has saturated its markets, it needs a new highly successful product to keep the growth up. Perhaps international expansion will work, or maybe not?  Are there new marketing channels, alternative uses, etc?

Trying to maintain a consistently high return on equity [ROE] over a long period of time is a fools bargain and I’ll use an anecdote from a company I know well, AIG.  I was pricing a new annuity product for AIG, and I noticed the pattern for the ROE of the product was not linear — it fell through the surrender charge period, and then jumped to a high level after the surrender charge period was over.

I scratched my head, and said “How can I make a decision off of that?”  I decided to create a new measure called constant return on equity [CROE], where I adjusted for capital employed, and calculated the internal rate of return of the free cash flows.  I.e., what were we earning on capital, on average over the life of the product.

I took it to my higher-ups, hoping they would be pleased, and one said, “You don’t get it!  You don’t argue with Moses!  The commandment around here is a 15% return on average equity after-tax!  I don’t care about your new measure!  Does it give us a 15% return on average equity or not?!”

This person did not care for nuances, but I tried to explain the ROE pattern, and how this measure averaged it out.  It did not fly.  As many have commented, AIG was not a place that prized actuaries, particularly ones with principles.

As it was AIG found ways to keep its ROE high:

• Exotic markets.
• Be in every country.
• Be in every market in the US.
• Play sharp with reinsurers.
• Increase leverage
• Press the accounting hard, including finite reinsurance and other distortions of accounting.
• Treat credit default swap premiums as “found money.”
• Take on additional credit risk, like subprime lending inside the life companies through securities lending.

In the end, it was a mess, and destroyed what could have been a really good company.  Now, it won’t pay back the government in full, much less provide anything to its shareholders, common and preferred.

Even a company that is clever about acquisitions, like Assurant, where they do little tuck-in acquisitions and grow them organically, will eventually fall prey to the limits of their own growth.  That won’t happen for a while there, but for any company, it is something to watch.  Consistently high growth requires consistently increasing innovation, and that is really hard to do as the assets grow.

If True of Companies, More True of Governments

This is not only true of companies, but even nations.  After a long boom period, state and federal governments stopped treating growth in asset values as a birthright, granting them a seemingly unlimited stream of taxes from capital gains, property, and transfer taxes.  They took it a step further, borrowing in the present because they knew they would have more taxes later.  The states, most of which had to run a balanced budget, cheated in a different way — they didn’t lay aside enough cash for their pension and retiree healthcare promises.  The Federal government did both — borrowing and underfunding, because tomorrow will always be better than today.

Over a long enough period of time, things will be better in the future, absent plague, famine, rampant socialism, or war on your home soil.  But when a government makes long-dated promises, the future has to be better by a certain amount, and if not, there will be trouble. That’s why an economic downturn is so costly now, the dogs are behind the rabbit already, running backwards while the rabbit moves forwards makes it that much harder to catch up.

I’ve often said that observed economic relationships stop working when people start relying on them, or, start borrowing against them.  The system shifts in order to eliminate the “free lunch” that many thought was available.

A Final Note

Hedge funds and other aggressive investment vehicles should take note.  Just as it is impossible for corporations to compound their high profits for many decades, it is impossible to do the same as an investor.  Size catches up with you.  It’s a lot easier to manage a smaller amount — there are only so many opportunities and inefficiencies, and even fewer when you have to do so in size, like Mr. Buffett has to do.

“No tree grows to the sky.”  Wise words worth taking to heart.  Investment, Corporate, and Economic systems have limits in the intermediate-term.  Wise investors respect those limits, and look for growth in medium-sized and smaller institutions, not the growth heroes of the past, which are behemoths now.

As for governments, be skeptical of the ability of governments to “do it all,” being a savior for every problem.  Their resources are more limited than most would think. Also, look at the retreat in housing prices, because the retreat there is a display of what is happening  to tax revenues… the dearth will last as long.

Full disclosure: long AIZ

## Problems with Constant Compound Interest (2)

I had many good comments on part 1 of this series.  One was particularly good that focused on the economy as a whole, and how the promises made by the government were unlikely to be fulfilled with Social Security and Medicare.  Our government attempts to finance programs on the cheap by relying on future growth, which does not always happen.  They move up spending rapidly if growth is large, and small if growth is negative.  In either case, the government grows as a fraction of the economy.

But let me consider asset allocation projections.  It is really difficult to consider average projections of asset returns, whether in real or nominal terms.  Asset returns vary considerably, and the number of years from which average returns are calculated are few relative to the volatility of returns.

We have created an industry of asset allocators, many of which have allocated off of foolish long-term historical assumptions, as if the past were prologue.  Even if they use stochastic models, the central tendency is critical.  What do they assume they can earn over long-dated investment grade debt?  The higher that margin is, the more they lead people astray.  Stocks win in the long run, but maybe by 1-2%, not 4-6%.

Consider defined benefit pension funds — after all, it is the same problem.  What is the right long term rate to assume for asset performance?  Alas there is no good answer, and with private DB plans continuing to terminate because of underfunding, the answer is less than clear.

Scoundrels use the mechanism of discounting to their own ends — they make future obligations seem smaller than they should be, magnifying profits, and minimizing capital needs.  Cash flows are inexorable, though.  There are few ways to avoid the promises from pensions.

Investors, be aware.  Realize that long term investment assumptions are probably liberal.  Also realize that long term assets and liabilities that rely on those assumptions have liberal valuations as well.  After all, who wants to under-report income when the accounting is squishy?

Now, for my readers, what have I missed?

## Problems with Constant Compound Interest

This piece is an experiment.  I’m not exactly sure how this will turn out by the time I am done, so if at the end you think I blew it, please break it to me gently.

People in general don’t get compound interest, or exponential processes generally.  It is not as if they are pessimistic, they are not numerate  enough to apply the rule of 72.  (Rule of 72: For interest rates between 3 and 24%, the time it takes to double the money is approximately 72 divided by the interest rate, expressed as a whole number.)

But there is a greater problem, and it applies to the bright as well as the dull.  People don’t understand the limitations of compound interest.

Let me begin with a story: I started my career at Pacific Standard Life, a little life insurer based in Davis, California.  The universal life policieswere crediting 11-12% interest, and annuities were in the 9-10% region.  It was fueled by junk bonds.  One of my first projects was to set the factors that would give us GAAP reserves for the universal life products.  To do this, I was told to project UL account values ahead at 11-12% interest for the life of the policies.

That rate of interest doubles policy account values every six or so years.  What economic environment would it imply to sustain such a rate of interest?

• High inflation, or
• High opportunities, because there is little competition.

The former was a possibility, the latter not.  As it was, inflation was receding, and 1986 was the nadir for the 80s.

People buying policies would see these tremendous returns illustrated, and would buy, because they saw an easy retirement in sight.  Alas, constant compound growth rarely happens in economics.  Policyholders ended up very disappointed; Pacific Standard went insolvent in 1989, and the rump was sold off to The Hartford.

Where do we often see constant compound growth modeled in finance?

• Asset allocation models, including simple illustrations done by financial planners
• Life insurance sales and accounting
• Defined benefit pension accounting
• Long-dated debt obligations
• Simple stock price models, like the Gordon Model, and all of its dividend discount model cousins.
• Social finance systems, like public pensions and healthcare.

There are likely many more.  Whenever we talk about long-dated financial obligations, whether assets or liabilities, we need something simple to aid us in decision-making, because the more variables that we toss in, the harder it is for us to make reasonable comparisons.  We need to reduce calculations to single variables of yield, present values, or future retirement incomes.  Our frail minds need simple answers to aid us.

I’m not being a pure critic here, because I need simple answers also.  Knowing the yield of a long debt obligation has some value, though if that yield is high, one should ask what the is likelihood of realizing the value of  the debt.  Similarly, it would be useful to know how likely it is that one would receive a certain income in retirement.

I’m going to hit the publish button now, and pick this up in a day or so.  Until then.

## On Negative Interest Rates

Photo Credit: Alcino || What is the sound of negative one hand clapping?

As with many of my articles, this one starts with a personal story from my insurance business career (skip down four paragraphs to the end of the story if you want):

25 years ago, when it was still uncommon, I wanted to go to an executive course at the Wharton School for actuaries that wanted to better understand investment math and markets.  I went to my boss at AIG (a notably tight-fisted firm on expenses) and asked if the company would pay for me to go… it was an exclusive course, and very expensive compared to any other conference that I would ever go to again in my life.  I tried not to get my hopes up.

Lo, and behold!  AIG went for it!

A month later, I was with a bunch of bright actuaries at the Wharton School.  The first thing I noticed was aside from the compound interest math, and maybe some bond knowledge, the actuaries were rather light on investment knowledge, and I would bet that all of them had passed the Society of Actuaries investment course.  The second thing I noticed were some of the odd investments described in the syllabus: it was probably my first taste of derivative instruments.  At the ripe old age of 29, I was learning a lot, and possibly more than the rest of my classmates, because I had spent a lot of time studying investments already, both on an academic and practical basis.

I had already studied the pricing of stock options in school, so I was familiar with Black-Scholes.  (Trivia note: an actuary developed the same formula for valuing optionally terminable reinsurance treaties six years ahead of Black, Scholes and Merton.  That doesn’t even take into account Bachelier, who derived it 73 years earlier, but no one knew about it, because it was written in French.)  At this point, the professor left, and a grad student came in to teach us about the pricing of bond options.  At the end of his lesson, it was time for the class to have a break.  I went down to make a comment, and it went like this:

Me: You said that we have to adjust for the fact that interest rates can’t go negative.

Me: But interest rates could go negative.

GS: That’s ridiculous!  Why would you ever lend money and accept back less than you gave them, and lose the time value of money?!

Me: Almost of the time, you wouldn’t.  But imagine a scenario where the demand for loanable funds leaves interest rates near zero, but the times are insecure and violent, leaving you uncertain that if you stored your cash privately, you would run too large of a risk of having it stolen.  You need your cash in the future for a given project.  In this case, you would pay the bank to store your money.

GS: That’s an absurd scenario!  That could never happen!

Me: It’s unlikely, I admit, but I wouldn’t say that you can never have negative interest rates.

GS: I will say it again: You can NEVER have negative interest rates.

Me: Thanks, I guess.

Well, so much for the distant past.  Here is why I am writing this: yesterday, a friend of mine wrote me the following note:

Good evening.  I trust you had a blessed Lord’s Day in the new building.

Talking bonds today with my Econ class.  Here’s our question. Other than playing a currency angle why would anyone buy European debt with a negative yield?  The Swiss and at least one other county sold 10 year notes with a negative yield.  Can you explain that?  No interest and less principle [sic] at the end.

Now, I didn’t quite get it perfectly right with the grad student at Wharton, but most of it comes down to:

• Low demand for loanable funds, with low measured inflation, and
• Security and illiquidity of the funds invested

The first one everyone gets — inflation is low, and few want to borrow, so interest rates are very low.  But that doesn’t explain how it can go negative.

Things are different for middle class individuals and large financial institutions.  Someone in the middle class facing negative interest rates from a checking or savings account could say: “Forget it.  I’m taking most of my money out of the bank, and storing it at home.”  Leaving aside the inconvenience of currency transaction reports if the amount is over \$10,000, and worries over theft, he could take his money home and store it.  Note that he does have to run a risk of theft, though, so bringing the money home is not costless.

The bank has the same problem, but far larger.  If you don’t invest the money, where would you store it?  Could you even get enough currency delivered to do it?  if you had a vault large enough to store it, could you trust the guards?  Why make yourself a target?  If you don’t have a vault large enough to store it, you’re in the same set of problems that exist for those that warehouse precious metals, but with a far more liquid commodity.

Thus in a weak economic environment like this, with low inflation, banks and other financial institutions that want certainty of payment in the future are willing to pay interest to get their money back later.

Part of the problem here is that the fiat currencies of the world exist only to be units of account, and not stores of value.  Thus in this unusual environment, they behave like any other commodity, where the prices for futures are often higher than the current spot price, which is known as backwardation.  (Corrected from initial posting — i.e. it costs more to receive a given cash flow in the future than today, thus backwardation, not contango.)  The rates can’t get too negative, though, or some institutions will bite the bullet and store as much cash as they can, just as other commodities get stored.

To use another analogy, a while ago, some market observers couldn’t get why anyone would accept a negative yield on Treasury Inflation Protected Securities [TIPS].  They did so because they had few other choices for transferring money to the future while still having inflation protection.  Some people argued that they were locking in a loss.  My comment at the time was, “They’re trying to avoid a larger loss.”

Thus the difficulty of managing cash outside of the bond/loan markets in a depressed economy leads to negative interest rates.  The financial institutions may lose money in the process, but they are losing less money than if they tried to store and protect the money, if that could even be done.

## Problems with Tax Reform

As I sit here, my taxes are done, all except for one K-1 that is very late, to put it mildly.  My taxes are complex, but my rule is that I do my own taxes.  If I can’t figure out the code, then I am probably doing something that I don’t understand the full economics behind it, and I should avoid it as a result.  Besides, it keeps me up with trends in the tax code that I might not truly grasp.  Surprises this year included the form for HSAs, and a credit  for promoting domestic production.  I also learned some of the intricacies in accounting for the sale of S corporation stock.  Not fun, but I learned something, and that is good.

It does motivate me to write a piece on tax reform, though.  I don’t fit neatly on the political spectrum: I’m a libertarian on economics, and a conservative on social policy (though conservative really isn’t the right word). Tax reform means different things to different people; let’s consider what it means to conservatives and liberals.

What does tax reform mean to conservatives?

• Eliminate the estate tax
• Eliminate the double taxation of dividends
• Eliminate the marriage penalty (actually should be a goal of liberals, and not conservatives, but hey…)
• Flatten the tax rate structure
• Preferentially tax income classes that aid in capital formation
• More taxation at the state level, less at the federal level
• Carve out exceptions for political allies that support your broad agenda

What does tax reform mean to liberals?

• Roll back the Bush tax cuts
• Keep the estate tax
• Increase the progressivity of tax rates
• More taxation at the federal level, less at the state level
• Preferentially tax wage income at lower rates
• Carve out exceptions for political allies that support your broad agenda

To me, both of them miss a dimension of the problem.  The main problem is how we define income, not the rate at which we tax income.  Both liberals and conservatives support areas in the tax code that allow for deferral of taxation.  To me, that is a core problem in the tax code.  Taxation should be roughly proportionate to the good that a taxpayer is deriving from society.  As a proxy for that, it should be proportional to his increase in net worth, whether the increase in net worth is liquid or not.

I will use Warren Buffett as my example.  Because he rarely sells stock, his taxes are deferred both personally, and at Berkshire Hathaway.  His net worth keeps going up, and the Treasury doesn’t get a piece of it.  Then he has the nerve to show up on Capitol Hill in favor of the estate tax, a tax of which his estate will pay little, because he has given most of it away.

My view is that people should be taxed like traders, on the increase in their net worth, at the same rate, regardless of where the income comes from.  Taxes would be paid on a mark-to-market basis.  There would be no more tax deferral IRAs or 401(k)s, and even pension earnings would get taxed inside DB plans.  Life insurance and annuities would lose their tax breaks.  Even charitable endowments would be taxed.  Private equity would get taxed off of “phantom income” at a 15% compounded rate, i.e., a private equity fund with \$100 million in equity would have to pay taxes on \$15 million of phantom income, at the fund if 15% distributions are not made to shareholders.  Truing up would occur at the dissolution of the fund.

Another key component here would be that there would be no separate tax accounting basis — the IRS would use GAAP.  What you report, is what you get taxed on, with the exception that firms that are heavily indebted to avoid paying taxes would get taxed on phantom income, the same as private equity.  Also, all like-kind exchanges would be taxed.  Even real estate would follow the property assessor, and income taxation would occur on the increase.

Then eliminate all deductions, conservative and liberal ones, and you have a tax code that can operate at a low rate because the entire increase of wealth in the economy is being taxed, without exceptions.  Oh, and since the income has been taxed all of the way up, the estate tax is no longer needed.  It was needed when wealthy people could shelter their increasing net worth from taxation.

Objections to this Outlandish Proposal

• Would you really allow investment losses to reduce someone’s income to zero, or below?  Yes, though there would have to be some safeguards against people who disguise their hobbies to be businesses.
• This will kill investment; the economy won’t grow without tax deferral!  Nonsense.  Most tax deferral incentives don’t change the amount of investment, but just the forms that the investments go into.
• Without tax deferral, people won’t buy life insurance, annuities, and corporations won’t provide pensions.  To some degree, yes, but after the shock wears off people will invest for maximum advantage again, and with an eye toward what is best, not what is tax-favored.  With my proposal, I don’t care if people have pensions or savings.  It’s all the same.  Life insurance and annuities will be bought for risk reduction reasons, not tax reasons.
• This will kill private equity!  It won’t.  It may shrink it a little, but there are many advantage to private equity aside from deferral of taxation.
• But phantom income will require illiquid investments to retain liquidity for taxes, or require equity holders to fund taxes.  Guilty as  charged.  It changes the business model to that degree.
• This discriminates against the poor in favor of the rich.  No, it discriminates against the clever rich, who shield the increase in their net worth from taxation.  Taxes delayed often become taxes avoided in entire.  Poor people should pay some taxes.  They benefit from society a little, and taxes would give them greater interest in voting.
• If there’s no deduction/credit for JKL, then JKL will disappear.  Good, or, maybe I should say, yes, there will be a decrease, but if it is valuable, it will find its own level.
• This proposal is incomplete!  You haven’t considered a lot of other areas.  No doubt; there would be a lot to do here, should it ever see the light of day.  Let John McCain be a real straight-talking maverick, and adopt a proposal like this.  He could be a real conservative, while offending all of the “conservatives.”

I harbor no illusions here.  We have the tax code that we deserve.  Don’t blame the IRS.  Don’t blame the President or Congress.  Blame those who elected them, and those who failed to vote.  The politicians offer us favors from our own money, and we thank them for it, by re-electing them.  I know that my views of tax reform will never be enacted because it steps on too many feet.  Can you imagine how many accountants, attorneys and actuaries would be unemployed by this?  If they fought hard against TRA ’86, just imagine how they would fight against this.  The politicians like fostering the illusion that they create our prosperity, when in reality, they take a share of it.  A proposal like this, that makes taxation more immediate, and more transparent, would make people more concerned about where their taxes go, because they would feel it more acutely.

And then, after all of this, we should move election day to April 15th.  Let the voters feel acutely what the politicians have decided for raising revenue, and they will render a better verdict.

## The Doubling Rule

Picture Credit: Vincent Brown || Einstein never said this, either…

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If you are famous and dead, many people will attribute clever sayings to you that you never said.  As Yogi Berra said:

I really didn’t say everything I said.

Except that Yogi did say that.  Now, if Einstein didn’t do enough for us, he supposedly made many statements praising compound interest, but the articles I have seen haven’t been able to trace it back to an original source.  Personally, I think compound interest is overrated, because business processes can’t forever compound wealth at a steady rate.

But some also have tried to credit Einstein with the Rule of 72.  You know, the rule that says the time it takes to double your money in years is equal to 72 divded by the annual compound interest rate expressed as as an integer.  E.g., at 8% your money doubles in 9 years.  At 9% you money doubles in 8 years.

Pretty nice, and easy to remember.  It is an approximation though.  If Einstein ever did look at the rule of 72, he would have noticed that the approximation is pretty good between 3% and 13%.  Outside that it gets further away.

One advantage of the rule of 72 is that it is simple.  The second one is that 72 = 3 x 3 x 2 x 2 x 2.  That makes it divide more intuitively by many integral interest rates, e.g., 3, 4, 6, 8, 9, 12 — allowing for some intuitive interpolation to aid it.

There is a more complex version of the doubling rule though:

The doubling constant starts (in the limit) at 100 times the natural logarithm of 2 [69.3147], and increases almost linearly from there.  If you estimate a “best linear fit” line on the observations where the interest rate is between 0 and 30, the R-squared will be over 99.98%.  The equation would be:

K = 69.3856 + 0.3313 * interest rate  [Linear Fit K]

To make it a little more memorable rule, it can be turned into:

K = 70 + (interest rate – 2)/3  [Rule K]

Thus at 2% the doubling constant would be 70 — money doubles in 35 years.  At 5%, 71, money doubles in 14.2 years.  8% is the rule of 72 — nine years to double.  At 11%, 73, 6.6 years to double.  At 14%, 74, 5.3 years to double. 17%, 75, 4.4 years to double. 20%, 76, 3.8 years to double.  I did those in my head.

As you can see from the graph above, the actual doubling constant and its two approximations lie on top of each other.  Not that I hope we see ultrahigh interest rates, but Rule K does quite well over a long span of rates.  Here’s how small the deviations are:

Now, almost no one will use “Rule K” because the two advantages of the Rule of 72 are huge, and if interest rates get really high, someone could create an easy smartphone app to calculate the doubling period. (and constant if they wanted)

This is interesting for me, because I ran across what I call the “Rule of K” earlier in my career, and I was able to reproduce it on my own after reading the WSJ article that I cited above.  Who knows, maybe Einstein took the doubling rule and did a first order Taylor expansion around 2% — that would have produced something very close to the “Rule of K” back when regressions were hard to do.

That’s all, and if you made it this far, thanks for bearing with me.

## One Dozen Thoughts on Dealing with Risk in Investing for Retirement

Photo Credit: Ian Sane || One of many ways to supplement retirement income…

Investing is difficult. That said, it can be harder still. Let people with little to no training to try to do it for themselves. Sadly, many people get caught in the fear/greed cycle, and show up at the wrong time to buy and/or sell. They get there late, and then their emotions trick them into action. A rational investor would say, “Okay, I missed that move. Where are opportunities now, if there are any at all?”

Investing can be made even more difficult.  Investing reaches its most challenging level when one relies on his investing to meet an anticipated and repeated need for cash outflows.

Institutional investors will say that portfolio decisions are almost always easier when there is more cash flowing in than flowing out.  It means that there is one dominant mode of thought: where to invest new money?  Some attention will be given to managing existing assets — pruning away assets with less potential, but the need won’t be as pressing.

What’s tough is trying to meet a cash withdrawal rate that is materially higher than what can safely be achieved over time, and earning enough consistently to do so.  Doing so as an amateur managing a retirement portfolio is a particularly hard version of this problem.  Let me point out some of the areas where it will be hard:

1) The retiree doesn’t know how long he, his spouse, and anyone else relying on him will live.  Averages can be calculated, but particularly with two people, the odds are that at least one will outlive an average life expectancy.  Can they be conservative enough in their withdrawals that they won’t outlive their assets?

It’s tempting to overspend, and the temptation will get greater when bad events happen that break the budget, whether those are healthcare or other needs.  It is incredibly difficult to avoid paying for an immediate pressing need, when the soft cost is harming your future.  There is every incentive to say, “We’ll figure it out later.”  The odds on that being true will be low.

2) One conservative estimate of what the safe withdrawal rate is on a perpetuity is the yield on the 10-year Treasury Note plus around 1%.  That additional 1% can be higher after the market has gone through a bear market, and valuations are cheap, and as low as zero near the end of a bull market.

That said, most people people with discipline want a simple spending rule, and so those that are moderately conservative choose that they can spend 4%/year of their assets.  At present, if interest rates don’t go lower still, that will likely (60-80% likelihood) work.  But if income needs are greater than that, the odds of obtaining those yields over the long haul go down dramatically.

3) How does a retiree deal with bear markets, particularly ones that occur early in retirement?  Can he and will he reduce his expenses to reflect the losses?  On the other side, during bull markets, will he build up a buffer, and not get incautious during seemingly good times?

This is an easy prediction to make, but after the next bear market, look for a scad of “Our retirement is ruined articles.”  Look for there to be hearings in Congress that don’t amount to much — and if they do amount to much, watch them make things worse by creating R Bonds, or some similarly bad idea.

Academic risk models typically used by financial planners typically don’t do path-dependent analyses.  The odds of a ruinous situation is far higher than most models estimate because of the need for withdrawals and the autocorrelated nature of returns – good returns begets good, and bad returns beget bad in the intermediate term.  The odds of at least one large bad streak of returns on risky assets during retirement is high, and few retirees will build up a buffer of slack assets to prepare for that.

4) Retirees should avoid investing in too many income vehicles; the easiest temptation to give into is to stretch for yield — it is the oldest scam in the books.  This applies to dividend paying common stocks, and stock-like investments like REITs, MLPs, BDCs, etc.  They have no guaranteed return of principal.  On the plus side, they may give capital gains if bought at the right time, when they are out of favor, and reducing exposure when everyone is buying them.  Negatively, all junior debt tends to return worse on average than senior debts.  It is the same for equity-like investments used for income investing.

Another easy prediction to make is that junk bonds and non-bond income vehicles will be a large contributor to the shortfall in asset return in the next bear market, because many people are buying them as if they are magic.  The naive buyers think: all they do is provide a higher income, and there is no increased risk of capital loss.

5) Leaving retirement behind for a moment, consider the asset accumulation process.  Compounding is trickier than it may seem.  Assets must be selected that will grow their value including dividend payments over a reasonable time horizon, corresponding to a market cycle or so (4-8 years).  Growth in value should be in excess of that from expanding stock market multiples or falling interest rates, because you want to compound in the future, and low interest rates and high stock market multiples imply that future compounding opportunities are lower.

Thus, in one sense, there is no benefit much from a general rise in values from the stock or bond markets.  The value of a portfolio may have risen, but at the cost of lower future opportunities.  This is more ironclad in the bond market, where the cash flow streams are fixed.  With stocks and other risky investments, there may be some ways to do better.

Retirees should be aware that the actions taken by one member of a large cohort of retirees will be taken by many of them.  This makes risk control more difficult, because many of the assets and services that one would like to buy get bid up because they are scarce.  Often it may be that those that act earliest will do best, and those arriving last will do worst, but that is common to investing in many circumstances.  As Buffett has said, “What a wise man does in the beginning a fool does in the end.”

6) Retirement investors should avoid taking too much or too little risk. It’s psychologically difficult to buy risk assets when things seem horrible, or sell when everyone else is carefree.  If a person can do that successfully, he is rare.

What is achievable by many is to maintain a constant risk posture.  Don’t panic; don’t get greedy — stick to a moderate asset allocation through the cycles of the markets.

7) With asset allocation, retirees should overweight out-of-favor asset classes that offer above average cashflow yields.  Estimates on these can be found at GMO or Research Affiliates.  They should rebalance into new asset classes when they become cheap.

Another way retirees can succeed would be investing in growth at a reasonable price – stocks that offer capital growth opportunities at an inexpensive price and a margin of safety.  These companies or assets need to have large opportunities in front of them that they can reinvest their free cash flow into.  This is harder to do than it looks.  More companies look promising and do not perform well than those that do perform well.

Yet another way to enhance returns is value investing: find undervalued companies with a margin of safety that have potential to recover when conditions normalize, or find companies that can convert their resources to a better use that have the willingness to do that.  After the companies do well, reinvest in new possibilities that have better appreciation potential.

8 ) Many say that the first rule of markets is to avoid losses.  Here are some methods to remember:

• Always seek a margin of safety.  Look for valuable assets well in excess of debts, governed by the rule of law, and purchased at a bargain price.
• For assets that have fallen in price, don’t try to time the bottom — buy the asset when it rises above its 200-day moving average. This can limit risk, potentially buying when the worst is truly past.
• Conservative investors avoid the areas where the hot money is buying and own assets being acquired by patient investors.

9) As assets shrink, what should be liquidated?  Asset allocation is more difficult than it is described in the textbooks, or in the syllabuses for the CFA Institute or for CFPs.  It is a blend of two things — when does the investor need the money, and what asset classes offer decent risk adjusted returns looking forward?  The best strategy is forward-looking, and liquidates what has the lowest risk-adjusted future return.  What is easy is selling assets off from everything proportionally, taking account of tax issues where needed.

Here’s another strategy that’s gotten a little attention lately: stocks are longer assets than bonds, so use bonds to pay for your spending in the early years of your retirement, and initially don’t sell the stocks.  Once the bonds run out, then start selling stocks if the dividend income isn’t enough to live on.

This idea is weak.  If a person followed this in 1997 with a 10-year horizon, their stocks would be worth less in 2008-9, even if they rocket back out to 2014.

Remember again:

You don’t benefit much from a general rise in values from the stock or bond markets.  The value of your portfolio may have risen, but at the cost of lower future opportunities.

That goes double in the distribution phase. The objective is to convert assets into a stream of income.  If interest rates are low, as they are now, safe income will be low.  The same applies to stocks (and things like them) trading at high multiples regardless of what dividends they pay.

Don’t look at current income.  Look instead at the underlying economics of the business, and how it grows value.  It is far better to have a growing income stream than a high income stream with low growth potential.

Deciding what to sell is an exercise in asset-liability management.  Keep the assets that offer the best return over the period that they are there to fund future expenses.

10) Will Social Security take a hit out around 2026?  One interpretation of the law says that once the trust fund gets down to one year’s worth of payments, future payments may get reduced to the level sustainable by expected future contributions, which is 73% of expected levels.  Expect a political firestorm if this becomes a live issue, say for the 2024 Presidential election.  There will be a bloc of voters to oppose leaving benefits unchanged by increasing Social Security taxes.

Even if benefits last at projected levels longer than 2026, the risk remains that there will be some compromise in the future that might reduce benefits because taxes will not be raised.  This is not as secure as a government bond.

11) Be wary of inflation, but don’t overdo it.  The retirement of so many people may be deflationary — after all, look at Japan and Europe so far.  Economies also work better when there is net growth in the number of workers.  It will be tempting for policymakers to shrink what liabilities they can shrink through inflation, but there will also be a bloc of voters to oppose that.

Also consider other risks, and how assets may fare.  Retirees should analyze what exposure they have to:

• Deflation and a credit crisis
• Expropriation
• Regulatory change
• Changes in taxes
• Asset illiquidity
• Reductions in reimbursement from government programs like Medicare, Medicaid, etc.
• And more…

12) Retirees need a defender of two against slick guys who will try to cheat them when they are older.  Those who have assets are a prime target for scams.  Most of these come dressed in suits: brokers and other investment salesmen with plausible ways to make assets stretch further.  But there are other scams as well — retirees should run everything significant past a smart younger person who is skeptical, and knows how to say no when it is necessary.

Conclusion

Some will think this is unduly dour, but this is realistic.  There are not enough resources to give all of the Baby Boomers a lush retirement, without unduly harming younger age cohorts, and this is true over most of the developed world, not just the US.

Even with skilled advisers helping, retirees need to be ready for the hard choices that will come up. They should think through them earlier rather than later, and take some actions that will lower future risks.

The basic idea of retirement investing is how to convert present excess income into a robust income stream in retirement.  Managing a pile of assets for income to live off of is a challenge, and one that most people are not geared up for, because poor planning and emotional decisions lead to subpar results.

Retirees should aim for the best future investment opportunities with a margin of safety, and let the retirement income take care of itself.  After all, they can’t rely on the markets or the policymakers to make income opportunities easy.