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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.
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