With positive profits and a zero discount rate, the price of equities is theoretically infinite. No-one has produced quantitative models that show why this theoretical value never will be attained, e.g., the risk aversion of investors in an environment where profits might drop, and the prospect of a change in the investment opportunity set (exogenous shock, endogenous change in technologies that bring new competitors into the market). The broad indices are still a third lower than their peak values, and the question is how long they need to go before investors give up the 1.25% TIPS yield to buy equities that should offer somewhat better protection than nominal coupon Treasuries against inflation.
The enormous volatility we have seen around 10,000 for the Dow suggests that the market is worth perhaps 8,000 in a double-dip recession and 12,000 in a V-shaped recovery. In a prolonged Japanese-style stagnation, which has always seemed to me the most likely scenario, it probably is worth about where it trades at the moment.
Why shouldn’t stock prices simply regain past levels in the case of higher growth? As I wrote on March 8, stronger growth would imply a significant increase in interest rates, that is, on the discount rate on equities. I concluded:
The recovery of the S&P 500 since its March 2009 lows reflects an anemic level of earnings as well as a very low discount rate. A rise in the short-term interest rate (in reality, in the whole yield curve) could take a very big bite out of equity prices. I don’t quite believe that a 2% risk free rate implies a drop in the S&P by half — this is a numerical example rather than a realistic model — but it does highlight the sensitivity to watch out for.
Another way to measure the sensitivity is to compare the level of the S&P 500 under different expected growth scenarios at different risk-free rates. This we do in the chart below: