A model of stock market moves

Changing the frame to see the big picture

TLDR:
- Stock prices move a lot whilst measures of the economy don’t change much
- I modeled the S&P 500 as a perpetual bond denominated in GDP to see if that explained it
- The coupon is earnings/NGDP - and this is stable through time but does move in recessions
- Moves in earnings/NGDP predict moves in the S&P 500 well
- The model predicts a big stock selloff if profits behave as in previous recessions
- If profits/NGDP move as in 2008, we should sell off 55%

Stock prices move a lot. Specifically, they move a lot compared to economic activity. In the case of an individual stock that might not be such a surprise - but the S&P 500 firms enjoy $12trio out of the $22trio of expenditure taking place in the US economy - around 55%. That number is reasonably stable through time :

Source: Bloomberg, SPX Total Revenues / NGDP

We might expect their price to change with that share - but the prices of stocks change far more and often in opposite directions. Here I’ve added S&P Market Cap as a proportion of NGDP on the left axis:

This is the sage of Omaha’s preferred indicator of stock valuation (though he uses the more expansive wilshire 5000), and it likes to move! Stocks have been valued as low as 0.5* NGDP, and as high as 1.25x despite companies share of output barely changing. NGDP itself is lucky to change by any more than +/- 5% in a year - not nearly enough to account for the variation either. So what is going on?

When I first heard about Buffet’s measure it had immediate appeal. Unlike a bond which is only a money contract, a stock is a claim on the output of real assets. Companies make stuff, not $. It might make sense to value a bond in $ but a stock’s value will change with the relationship of $ to stuff - and as I know from my prickly attitude to money - that relationship changes dramatically on every possible time frame. So if stocks are output contracts, we can change the frame from money to output to do some analysis.

If I’m anything, I’m a bond man. That’s given me a certain attitude to valuing stuff - make it look like a bond and do some bond maths. Applying that attitude to stocks, I reasoned that stocks are like a perpetual bond. They never mature, and they pay a ‘coupon’ of profits. For me, the coupon is profits and not dividends because profits are re-invested, the value from them accrues to shareholders over time even if the shareholders don’t see the cash from dividends. If profits are the coupon, what is the principal? Given that stocks return units of GDP - which you can sell for money if you like - I reasoned that nominal GDP would be the principal of my perpetual bond. The coupon then would be the percentage of profits in GDP.

The nice thing about a perpetual bond is that the maths is very simple. Without maturity to worry about, the yield is simply the coupon divided by the price. With the yield, we can determine the duration. Duration, for my non-bonders, is the time to recoup the present value of the price paid. In a perpetual, we’re never getting a principal payment, so its duration is how many coupons (discounted by the yield) recoups the price paid. The formula to calculate it is simple. Why do this? Because duration is also the sensitivity of price to yield. If we want to illuminate the puzzle of why stocks move so much in price, it’s great to know how sensitive prices should be.

So to work through an example - let’s take the S&P today. The level is 2830 as I write, giving a market cap of $24.4trio. That’s 1.13 times the 21.5trio first look at NGDP in Q1 of this year. Therefore, the price of our bond is 113. We have a 12 month EPS of 147, implying 1.27trio of earnings - 5.9% of NGDP - our coupon. Our yield, 5.9 / 113.1, is 5.2% - giving a duration of 20.25.

Now , the point of me doing this was to work out why stock prices move so much and we already have a big clue. The duration of 20.25 means - because duration is the sensitivity of price to yield - that small changes in the yield of the “bond” should mean big changes in the price. If investors expect the yield of today’s S&P in nominal GDP terms to move by 1%, they should only be happy to buy the index 20.25% lower than its current price. To see what kind of changes investors might expect, I looked at the history of the “coupon” - total S&P 500 trailing 12m earnings as a proportion of NGDP:

Source: Bloomberg.

If you weren’t looking at this too closely, you might well interpret it as a random walk. If investors believe that the “coupon” of their bond will be a random walk from the current value - they would have an expected coupon equal to whatever they see today. If we make that assumption, we can test the validity by looking at what changes investors saw in their coupon - and what the model predicts should be the price change of the bond. Running the numbers for the two big stock price falls of our recent experience gives the following results. Stock price moves are assessed on the high to low of the 14 week moving average:

These results are entirely consistent with investors viewing the S&P just as I’ve modeled it.

Back to the present day, we’ve had a decline in stock prices of 10%. Given the duration of the S&P in nominal GDP terms that we calculated earlier, 20.25, that would imply investors have experienced a 0.5% fall in the profit / gdp ratio. Indeed, since 2018, profits have fallen from 6.3% to 5.9% on a 12m trailing basis. From the 4th quarter of 2019 to the 1st of 2020, the ratio hasn’t moved at all. That’s to be expected. The measure of profits we must use is trailing by necessity. To believe that the selloff is appropriate, we must believe either that the 0.5% fall in the earnings/GDP ratio was already priced in and that profits will fall only another 0.5%, or that profits/gdp won’t fall, or that BCLMacro’s model is entirely wrong. With some trepidation, I look forward to seeing which turns out to be the case. A 2008 style fall in profits/ngdp would mean a sell off in the region of 55%.

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NB: This post is not investment advice and is not a trade recommendation. The views expressed here are my own and do not reflect those of my employer.