# How Much do NGDP expectations matter to the Stock Market?

The inspiration for this post was a brief discussion with a friend, when I attempted to explain why I think of the stock market as a prediction market for NGDP. We might pose the following question, if NGDP expectations were to increase from 5% per year to 6% per year for every year from now to forever, how much would that matter to the stock market?

The short answer is, a lot.

To answer this, lets take a slightly round about route of asking, what is the Net Present Value ,$M$, of Corporate America? Its reasonably well known that Corporate Profits as a share of NGDP has been a very stable time series for decades, oscillating in the band of 3-7%.

There is some evidence that we might expect it to be at the higher end of this range going forward due to having more tech with higher profit margins, and more overseas earnings. So lets assume that this is stable at $P = 6%$ going forwards. Let us likewise assume that the ten year interest rate,$i = 3%$, and the equity risk premium $\rho = 4.5\%$ is stable going forward. In that case we have a discount rate of 7.5%. The total net present value of corporate america’s future earnings would be

$\frac{M}{NGDP} = \sum_{t} \frac{P \times g^{t}}{(1+i+\rho)^{t}} \approx \frac{1}{i+\rho - g}$

Where we have $g$ as the growth rate of NGDP.

Given the assumptions above, if we assume that everything grows at a stable growth rate (i.e we are ignoring possible path dependency), then

$\begin{tabular}{|c|c|} \hline g & M /(P N) \\ \hline 4\% & 28.6 \\ \hline 5\% & 40 \\ \hline 6\% & 66.7 \\ \hline \end{tabular}$

So a 1% increase in NGDP gives about a 40% increase in the stock market, as a handy rule of thumb. No wonder the stock market loves QE!

If we take the EMH seriously, we must conclude that the combination of low TIPS spreads predicting low inflation, and a booming stock market predicting high NGDP, means that we can expect productivity/RGDP to come roaring back any minute now. A market Monetarist argument for Supply Side Optimism. Yes, I’m looking at You Britmouse. 🙂