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Compounding Interest: Why Washington and the Fed Must Heed This 'Most Powerful' Force


Policies chosen under rising rates could either lead to lower compounding and people resigning themselves to lowered wealth, or higher compounding and faster rebuilding of assets.

In these divisive political times, basing policies on Einstein's recognition of the "most powerful force in the universe" -- compounding interest -- rather than philosophizing about nebulous terms such as risk aversion, risk preference, animal spirits, or irrational exuberances would be a wise approach.

When central bankers use the term risk aversion, it does not refer to a dislike of losing money, but to a mathematical condition of economists' utility function, implying that people give greater weight to dollar losses than to equal dollar gains. The use of other terms' rationalizing policies implies that people's behavior is incomprehensible and utterly unpredictable. But apparently, politicians and central bankers consider themselves exempt from such random fluctuations in moods and can thus compensate for the "hoi polloi's" unpredictable follies.

However, the term risk aversion appears to imply predictability -- namely, an asymmetric reaction when facing prospects of losing or gaining equal dollar amounts. Say you have $100,000 of wealth. You now face the option of losing or gaining $10,000 of this portfolio over the next year with a 50% chance of each possibility. What would you do?

The risk aversion model says this: If your utility function is concave, you will not take on this risk, and you will insure against it. If it is convex -- that is, if you are not risk averse -- you bet. Since nobody knows anything about anyone's utility function, but we do know that it is neither of the above (since people have been gambling and insuring always, everywhere, and at the same time), this description does not offer any insight into people's behavior or grounds for rationalizing policies.

Now look at this bet through the compounding interest angle.

By losing 10% of your wealth, you are left with $90,000. To recoup this wealth within a year, you will have to find either a new asset class to give an 11% return during the year, or invest a greater fraction of this wealth than before in an asset class that offered such a return. You avoided doing so until now, as the higher rate reflected, say, greater risk of default. If you hold on to the traditional portfolio after the loss, you can never recoup it.

The good luck of a $10,000 windfall involves no such search and reconsideration of reallocating the portfolio. If you get the windfall -- say, a company comes up with an innovation, or a mine stumbles on bigger treasures than expected -- the allocation of your portfolio does not have to change. Your wealth increased by 10%, and no reallocation was required. People's asymmetric reaction to losses and gains have to do with this simple implication of compounding, and has nothing to do with tastes, pessimism, optimism, or other "spirits."

The greater the fraction of wealth you lose, the harder the choices and chances of recouping. Losing 20% requires finding assets with a 25% return for the year; losing 40% (as happened roughly in the recent crisis for a good fraction of people) requires finding assets with a 67% gain for the year. Even if one cannot expect to recoup the losses during one year but over a few years, one must still reallocate their portfolio toward assets promising higher returns. That's the "force's" asymmetry.

The Fed

This brings us to the situation we have faced these last few years. In a speech this year, Ben Bernanke had this to say: "[A]lthough a long period of low rates could encourage excessive risk-taking... to this point we do not see the potential costs of the increased risk-taking in some financial market as outweighing the benefits of promoting a stronger economic recovery and more rapid job creation."

Having lost 40% of their nominal wealth (the combined effect of dropping home prices and stock markets) and with interest rates plunging to low levels (and not because of deflation), the gain required to recoup the loss comes to about 67%, net, after taxes. Buying Treasuries over the last few years could have hardly restored the losses... although if people bought while interest rates continued dropping and sold before the recent jumps in the 10-years Treasury rates, they would have done well.

It is also true that if one's timing was perfect, and one had bought the Dow (INDEXDJX:.DJI) or Nasdaq (INDEXNASDAQ:.IXIC) at the lows of 2008-2009, a trader could have realized 100% return (before taxes) -- although in August 2008 to August 2013, the Dow increased by 33% only. However, encouraging shellshocked baby boomers in 2008, in their 50s and 60s, who might have lost 40% of their wealth, to take more risks seems peculiar, even without considering that this loss was correlated with lowered expectations of getting smaller pensions, Social Security, health insurance, or wage increases and finding jobs with pre-2008 ease.

Yes, Greek, Italian, and Spanish government bonds offered high interest and would have qualified for taking on increased risk in the case of a default, but I doubt that Bernanke had these investment vehicles in mind. After all, what if these and other investments paying higher rates defaulted? The chances of the baby boomers -- and they constitute the savers -- recouping even greater losses of wealth are minimal. If they continued to lose capital and were down, say, 60% rather than 40%, they then needed to find assets with a 150% gain per year to recoup their wealth -- or roughly 8% per year for at least ten years -- net of taxes.

Briefly: One does not need assumptions about risk aversion or animal spirits to understand people's asymmetric reactions to losses and gains of wealth, and their increased prudence, caution and pessimism after losing much. To restore confidence is to change policies so as to induce expectations that the after-tax returns on at least some asset classes would become higher now than what they were before the crisis. This would include creating or changing policies that would help people find jobs with less delay and see their after-tax compensations increasing faster.

This wasn't done. Whereas liquidity injections were needed in 2008, the continued fragility of the recovery is reflected both by the extremely low interest rates and by the reaction to rumors about the Federal Reserve buying fewer bonds. Whereas increasing interest rates in normal circumstances reflects greater demand for private borrowing, thus speeding up investments and leading to expectations of less unemployment and increased compensations, the prospect of the Fed stopping to pursue the present Treasury-buying policy, resulting in increased rates, has not have these effects.

The present Fed policy allows the federal government to carry the $17 trillion debt and, by Bernanke's acknowledgement, it is the same policy that allowed the federal government to carry the World War II debts during 1940-1951. It was not called QE then, and nobody pretended that the policy had any goal other than paying for the war and the accumulated debt. The Treasury-dictated policies kept interest rates low, allowing the government to spend money without raising taxes and also redistributed wealth from savers to the younger generation, without explicitly raising taxes -- same as now.

If interest rates were to rise, policies have to change drastically to carry the debt; in contrast to the 1950s, the population is older, and there are significant entitlements that did not exist then. The policies chosen under pressure of rising rates could either lead to lower compounding and people resigning themselves to lowered wealth, or offer the prospects of higher compounding and faster rebuilding of assets.

Simplistic as it might seem, that is how people's asymmetric spirits and recent reactions to policies are seen through the non-political lens of compounding interest.

Reuven Brenner holds the Repap Chair at McGill University's Desautels Faculty of Management, and serves on the Board and Investment Committee of McGill Pension Fund. The article draws on his World of Chance (2008, with G.A. Brenner and A. Brown) and his Force of Finance (2002).
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