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.

5 thoughts on “Problems with Constant Compound Interest

  1. It will be interesting to see where you go with this, David. It seems as though the problem is a consequence of the fact that we can?t know the future. We?d like to make a decision using a simple calculation, yet we know that such a calculation will likely give the wrong long-term answer. Monte Carlo modeling is one attempt to address this problem, but that has its own problems, and doesn?t give a ?simple? answer, either.

  2. Here’s another compounding example:

    Our revenue as a country (aka GDP) has been growing around 4.5% per year over the last 40-50 years.

    Government spending has grown about 8% per yer over the same period.

    Supposedly learned people like Paul Krugman think the problem is that taxes are not rising fast enough. What tax rate would allow costs to rise almost twice as fast as revenue?

    And for this sort of “analysis”, the guy won a Nobel Prize? (well, economics isn’t actually in Nobel’s will, but whatever)

    People hear what they want to hear. Keynesian economics says the government should run surpluses in good times, and deficits in bad times — but in practice, Keynesian supporters run deficits all the time.

    GDP oscillates, sometimes gaining and sometimes falling, but averaging 4.5%. Government spending rises by a very consistent 5% every year, no matter what the economy is doing.

    So even though the “average” spending increase and “average” GDP increase are very similar — the geometric compound return of government spending grows much faster than GDP.

    A portfolio that loses 10% and then gains 11% does not keep up with a portfolio that gains 1% both years.

    California often leads the nation on many things… the out of control government spending is not isolated to just California. The next 10 years are going to be about the country living with less (within our means, and perhaps slightly below our means to pay off some debt). This will have profound implications on all the unfunded promises that politicians have made over the years

    Never mind life insurance or stock portfolios… the mother of all portfolios — the US economy — is about to learn a hard lesson in compounding

  3. Adapting all of the constant rate models to use, for example, binomial or path dependent (Monte Carlo) models is that they (like the simplified models) rely on the accuracy (prescience) of the inputs. I haven’t seen any empiracle evidence to suggest that complex models are more accurate ex post than simple models. You’d need a crystal ball for that to happen, I think.

    (Someone with statistical prowess should pick this up, as I suspect that studies in this area were largely passed over due to the computational intensity required that is only now becoming available).

    I’m very interested to see where this is going.

  4. Perhaps more accurately, people don’t get the exponential function.

    Retired professor Albert Bartlett has had interesting lectures regarding this topic for decades.

  5. Yep, my baby boy was born in 2007 and a baby girl in 2009. We are doubling our family size every two years. At this rate, there will be more people in our family in several decades than there are Chinese people today.

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