Suppose the Bernoulli Fairy comes down from the sky and offers you a choice: she can flip a coin and with heads your lifetime annual income will be $50,000 while with tails your lifetime annual income will be $200,000, or she can eliminate the risk and give you a lifetime annual income of $X. What, then, is the highest annual income at which you would still gamble?
Think for a moment: I will be back.
For most people the tipping point for $X = $100,000 or so: each doubling seeming equally worthwhile, and so a 50% chance of loosing half your lifetime income being worth risking only if it comes with a 50% chance of a double. Some people appear to be more risk-averse: you can find people for whom $X is as low as $68,000--although they are rare.
But if you take a look at financial market returns--stocks, junk bonds, corporate bonds, and Treasuries--over the past century, and you ask what is the value of $X implicit in the risk premia that financial markets have yielded, you get an answer more like $55,000: the market acts as though prices are set by people--as if the market is ruled by "representative agents" of the kind who appear in economists' models and theories--who are indifferent between (a) a $55,000 annual lifetime income with certainty, and (b) a 50-50 gamble between a lifetime annual income of $50,000 and one of $200,000 (see Mehra and Prescott (1`985), "The Equity-Premium: A Puzzle," Journal of Monetary Economics 15, 145-62; Rabin and Thaler (2001), "Anomalies: Risk Aversion" http://www.behaviouralfinance.net/risk/RaTh01.pdf; DeLong and Magin (2008), "The Equity Premium: Past, Present, and Future" http://delong.typepad.com/berkeley_pe_notes/2008/09/2008-9-1-delong.html; and millions of others).
This has five implications:
- If you are willing to take on risk in financial markets to a greater than average degree, you can make huge fortunes. Think of it: you are accepting assets that promise an average return of $125,000, and yet the market is silling to sell them to you for only $55,000. As long as the risk does not turn out to be much bigger than expected and blow you up, life can be very lucrative.
- The average rate of return on capital invested in Wall Street is high--that $125,000-$55,000 again--which means that the financial interest rate for risky investments (like highly-leveraged corporations or junk bonds or subprime mortgages) is very high too. The fact that the interest rate on risky investments is high means that the value of long-duration assets (like mortgages) is low: the cash flows come to you far in the future, and if you had the cash now you could deploy it very profitably.
- Heaven help you if you have borrowed short-term and invested long-term and perceived riskiness or the price of risk rises--because then you are bankrupt because your future cash flows are discounted at a ferocious rate.
- The markets as they are constituted do a very bad job of mobilizing the collective risk-bearing capacity of society. Risky and long-duration assets really ought--in a fundamental sense--to sell for much more than they do, and that they would if financial markets were doing their job to properly diversify risk away across all of the savers and wealth holders of the global economy.
- There is no reason to take past averages or ratios as in any way reflecting the "fundamental" values of financial assets. The "fundamental" configuration of prices and asset values has a somewhat higher risk-free interest rate, a somewhat lower risky bond rate, and much higher equity prices and dividend-price ratios than the world we see.
I am still unsure whether there is a sixth valid implication. If there were, it would be:
It is time for the government to seize control of the price of risk and turn it into an administered price set by centrally-planning technocrats in the interest of social welfare--just as between fifty and a hundred years ago we decided that the short-term price of liquidity, the Bank Rate or the Federal Funds Rate, was too important to be left to the market and was turned into an administered price set by centrally-planning technocrats in the interest of social welfare.