Saturday, 10 February 2018

Life expectancy and the cost of capital

It is popular in many financial circles to compare the level of asset prices (which is the inverse of the cost of capital) to 100-year market valuation averages (or sometimes even longer - I heard some hyperbole the other day that asset prices were at '2,000 year highs').

It is argued both that asset prices mean revert over time, and that they mean revert (or ought to mean revert) towards some stable, constant underlying cost of capital/valuation level. GMO, for instance, has made this assumption for many years (although they appear to be slowly beginning to question it). The former assumption about the mean reversionary nature of markets is correct, but the latter assumption about the cost of capital inevitably being constant over time is fundamentally incorrect in my view.

There is not only no law of the universe dictating that the cost of capital ought to remain the same over time, but also very sound reasons why we should expect it not to. One of the most important and overlooked contributors in this regard is that human life expectancies have significantly increased over the past century, and from a first principles perspective, this ought to have lowered the cost of capital to a material degree. This means that while asset prices will continue to be volatile and mean revert towards an underlying trend over time, they ought to be mean reverting towards a gradually lower equilibrium cost of capital over time, not a constant one. Allow me to explain.

A good way to understand first-principled concepts is to consider how they would work when taken to the extreme (provided no scalability distortion or fallacy of composition is present). If what is true in the extreme is also true at a scaled-down level, then this process can yield useful insights.

Hypothetically, let's say that we knew with 100% certainty that we were all going to die exactly one year from now (perhaps due to an asteroid being on a collision course with earth). Please forgive the morbidity and bear with me for a moment for the sake of argument. What would the cost of capital be? Would you agree to lend all your money for slightly less than 12 months for a 10% rate of return? Highly unlikely. You might require a rate of interest of several hundred percent merely for 6 months. After all, money will be worthless to you 12 months from now. And as the doomsday arrival drew ever closer, the rate of interest would continue to skyrocket and trend towards infinity.

Now let's look at the other extreme: imagine that we were all immortal and lived forever. What would the cost of capital now be? If we were immortal and lived forever, then investing even at a 1% real rate of return after taxes (or even 0.01% for that matter), would eventually - through the forces of compound interest - make anyone who cared to save even a trivial amount of initial capital unfathomably rich. Just a single dollar, invested at a compound real rate of just 1.0% pa for 3,000 years, would grow to a staggering US$9.2tr. It would therefore be logical for the cost of capital to be extremely low - indeed it would trend asymptotically towards zero.

Consequently, life expectancy is actually extremely relevant to the cost of capital - perhaps the most relevant variable - and as human life expectancies have lengthened over time, it is logical to expect the cost of capital to have fallen (it is amazing to me that the economics discipline has never considered this reality - the discipline is shockingly closed-minded and ideological). Consequently, very long term averages for the cost of capital/asset prices that fail to adjust for lengthening life expectancies are likely to yield estimates of 'fair' market value/asset prices that are systematically much too low.

When guaranteed state pensions were first introduced for retirees in the early 20th century, the life expectancy was 65 years. It is now slightly above 80 years in most developed countries. This means the productive and saving lifespan of the average individual has increased by approximately 15 years over the past century. This ought to have meaningfully lowered the cost of capital - perhaps by something in the order of 200bp.

A simplified example might suffice to highlight the potential extent of the impact. Consider someone starting out at age 20 with a lump sum they would like to have grow to a real US$500,000 by a retirement age 10 years less than their life expectancy. If life expectancy is 65 years, the funds will need to grow to US$500,000 by age 55. If we posit a real rate of interest of 7.00%, the said 20 year old would need to invest US$46,832 today for it to grow to US$500,000 by his/her 55th birthday.

Now let's consider a 20 year old that plans to invest the same US$46,832 today, but who can expect to live to 80. In this scenario, only a 4.85% pa return would be required to yield the same US$500,000 lump sum payout at a retirement age 10 years less than one's life expectancy (age 70 in this example). In other words, holding all else constant, the cost of capital in this hypothetical has fallen by 215bp from 7.00% to 4.85%, purely on account of rising life expectany.

That is far from a trivial difference. From a stock market earnings yield perspective, it would be the difference between the market trading at 14.3x earnings (1/0.07) and 20.6x earnings (1/0.0485). That is a level of valuation difference many market commentators would argue constitutes a bubble and a cause to hold significant levels of cash in anticipation of a coming major market correction.

Now, I'm not trying to argue that the US stock market is not expensive at the moment. It is. Nor am I arguing that the very low rates the world has seen in recent years can be solely (or even predominantly) explained by lengthening life expectancies (they are but one of many contributing factors). However, life expectancies are playing some role, and need to be accounted for when comparing current valuation levels to very long-term historical averages, in my view.



  1. I completely agree. I reached the same conclusion many years ago, but by thinking about stasis (hibernation) technology. The only logical outcome is a zero real interest rate. Seems like an easy topic for a PhD thesis.

    1. Agree. The problem is that the stultifying atmosphere of most economics departments drive a lot of the creative & innovative thinkers away. There is a lot of low hanging PhD fruit out there for creative economics thinkers, but the dogma in the field makes the number of fruit-pickers rather sparse.

  2. Interesting article. However, I am not sure I agree that life expectancy is "perhaps the most relevant variable" in determining the cost of capital.

    I believe the life expectancy of a nation is a bigger determinant.

    If I am building my cost of capital and I use a government treasury yield as my risk free rate, my cost of capital is heavily determined by the full faith and credit of the country behind the the bond.

    So my theory is that the cost of capital is less tied to human life expectancy than it is to the life expectancy of the debt-issuing nation. This may sound preposterous. I live in the States, so I will use my country as an example. Surely the US could never implode like the Weimar Republic. Or could it? It could default on it's debt some day. After all, we abandoned the gold standard. We could abandon our obligations to creditors too. Congress has to raise our debt ceiling each year. Some day they might stop. Suddenly the bedrock of the cost of capital is no longer risk free.

    So back to life expectancy...

    What if the trend of lower costs of capital over time has been the result of the compounding nature of the United States' (perceived or real) economic security? The longer our republic exists, the more people consider the debt to be riskless. Human life expectancy has a compounding effect, but so does a nation's. In the long run, we are all dead. Countries included.

    1. Thanks for your thoughts Bert,

      At a practical level I think you're right. Fluctuations in the level of sovereign risk (including inflation risk) ought to be the largest practical determinate of government bond yields (which I think are erroneously described as the 'risk free rate' - there is always some risk, however small).

      However, I'm talking at a more theoretical/conceptual level. If life expectancy alone can justify a risk free rate anywhere between zero and infinity, then by definition it must be the most important variable :-)

      In addition, it is arguable that because the government bond yield is not a genuinely risk free asset, it is comprised of the purist cost of capital (the pure cost of waiting), plus a sovereign risk premium related to the risk of inflation and/or default. The life expectancy could still impact the former without impacting the latter, and my theoretical quantitative example above was both (1) simplified for the sake of argument; and (2) held all other things constant.

      I also dispute the conventional practice of using the nominal bond yield as the basis for the cost of equity capital as well. Bonds need a risk premium for something peculiar to their own characteristics - there exposure to inflation risk. Some equities are relatively immune from this risk (e.g. franchised companies such as Coke with pricing power). It therefore ought to be theoretically possible in environments with high inflation risk for nominal bond yields to be higher than the cost of equity.


    2. I think the risk that the asset/debt record won't be enforced is well captured by convenience yield spreads for catastrophe assets like physical gold.

      Side note on government longevity: countries come and go but cities survive. Sewer systems in major cities are often designed, and occasionally financed, for 100+ year lifespans.

  3. I would assume even more demographic variables influence saving rates. Having 8 children will lower your saving rate vs having only one. if you have 8 kids, after housing and food expenses will leave you little income for saving. If you have 1 child the ability and also need to save for retirement increases.