Tuesday, October 23, 2007

Risk Aversion -- a pseudocode!

There has been much talk about risk aversion indices rising – indicating that investors are willing to hold to low yielding savings, cash or cash-equivalents instead of high yielding investments. In essence, as the Mafia says, investors have been hitting the mattresses.

Standard global indicator of risk aversion is the EURCHF – with the CHF being the currency of choice when currency investors are unsure of their immediate next move. So, any R.A.I must be correlated to EURCHF. The biggest puzzle however has been that volatility of the difference in returns between stocks and bonds is greater than the volatilities of consumption or t-bill yields. So, what could explain this? One conjecture has been that risk-aversion is a time-varying factor. i.e., Investors at different times in the business cycle demand different risk premia. This has been the thrust of research since at least Lucas (1978). So how to capture this number for risk aversion?

The generic modeling structure has been as follows:

  1. A fictional investor has a utility function with consumption as a variable and risk aversion and discount factor as constants.
  2. This investor has intertemporal budge constraint – where delayed gratification is the theme. i.e., decide to consume today or consume tomorrow by investing in risky asset.
  3. Maximize the expected utility subject to this constraint and arrive at equilibrium conditions for consumption, S&P 500 returns, t-bills returns and risk aversion parameters.
  4. The equilibrium conditions capture a fictitious state where marginal cost from investing today in risky asset is matched by the marginal benefit of consumption tomorrow.
  5. Assume t-bill returns and S&P 500 returns are normally distributed.
  6. Using market data for returns, using root-finding algorithms, solve for the discount factors and risk aversion.

For times of the year, solve for the risk aversion numbers. So, ideally as risk aversion numbers rise, one should observe the EUR-CHF to decrease (i.e., Swiss franc appreciates).

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