Bond Yields and Stock Prices
Post hoc ergo propter hoc?
September was a difficult month for the US stock market, with the S&P down by 5% or so. A number of market pundits have suggested that the fall in the stock market was attributable to the coincident rise in bond yields, as reflected in the 10-year US Treasury yield which increased from 1.30% to 1.50% during this same period. The relationship between bond yields and the price of equities is a strong one, but we can’t say for sure that the 20bp rise in 10-year UST yields in fact caused the fall in equity prices. There may be something to this argument, possibly a lot, or this may be just another case of fallacious post hoc ergo proper hoc reasoning. [If you don’t know the expression post hoc ergo propter hoc, please watch this short video clip from The West Wing. It’s a classic.]
Other people may attribute the fall in equities to some variant of the September effect. It may be true that September is often a bad month for equities, and that October is even worse. Again there may be something to this argument, as Mark Twain allegedly said (I paraphrase): “It is dangerous to speculate in the stock market during the month of September.” But we should recall the rest of his statement: “And the other dangerous months are October, January, June, November….”
I don’t know what caused the September fall in equities, but I know how a former boss of mine would have explained this: “More sellers than buyers”. But of course for every buyer there has to be a seller (and vice versa). In September, the market clearing price which matched equity sellers and buyers was 5% lower at the end of the month than at the beginning of the month. But why?
As you will have learned in your core finance course, the intrinsic value of equities (stocks) is determined by two factors: expected future equity cash flows (including the expected future growth in corporate profits) and the discount rate used to convert those future cash flows into present value terms. And the discount rate used to value equities is determined in part (though not exclusively) by the so-called “risk free (interest) rate”, with the 10-year UST bond yield often used as a proxy for the risk-free rate. So yes, there is a strong theoretical relationship between bond yields and equity prices.
There is also substantial empirical support for this relationship, but the relationship between stock prices and bond yields is often changing and difficult to estimate reliably, as explained in this 2013 research piece from Pimco.
To test our understanding of this stock price-bond yield relationship, let’s ask ourselves a simple question: How much should we pay for a one-time guaranteed (risk free) payment of $100 to be received 10-years from now? The answer of course depends entirely on the discount rate we use to value the future cash flow, in this case the current yield on a 10-year UST bond. (Theoretically, a zero-coupon UST bond.) At a discount rate of 1.00%, the present value of that single $100 cash payment due in 10-years equals $90.53; but at a rate of 1.5% the PV of the payment falls to $86.17. This is a fall in value (bond price) of about 5%, for a single payment due in 10-years, resulting from a 50bp change in the discount rate from 1% to 1.5%.
Of course equities generate cash flows over more than a single period and they are not in any sense “risk free”. But it is still true that for any given set of expected (probability-adjusted) future cash flows, the value of those cash flows will fall when the discount rate goes up. When we value equities, we don’t use the risk-free rate as our discount rate, but we do use the risk-free rate to estimate the appropriate equity discount rate. The model we often use to determine the equity discount rate (cost of capital) is the Capital Asset Pricing Model (CAPM), but I won’t go into that here. [Read here if you would like to learn more about CAPM.]
As an example, consider a stream of annual equity cash flows beginning at $10 and growing at a consistent and sustainable annual rate of 2%, which is discounted at a rate of 5%. The present value of these future cash flows equals $333.33. [I did this using the Gordon Growth Model: V = CF/(r-g)]. But if we leave the cash flows unchanged and increase the discount rate by just 20bp, attributable perhaps to an underlying change in the risk-free rate, then the PV of those same expected future equity cash flows falls to $312.50, a change in value of about 6.25%.
And so, ceteris paribus (more Latin!), a rise in the risk-free rate of even just 20bp could in theory account for much or all of a 5% fall in the value of the stock market, given the current level of interest rates. [A change of 20bp equals 15% of a 1.3% interest rate, but a much lower percentage of a higher rate.] And this may in fact be what happened in September, although I am not sure. I didn’t actually attempt to value the US stock market using this methodology, so my numbers may be off. But hopefully you can see the logic I would have used had I done so.
Of course, few things in finance are quite this simple. Changes in the risk-free rate do not always flow through basis point for basis point into the cost of equity, and it may be the case that expected future equity cash flows also change with the change in interest rates, either due to changes in operational cash flows (particularly in interest rate sensitive sectors of the economy) or due to other factors, including equity risk premiums, a topic we won’t go into in this post.
Having said that, there is great merit in the KISS principal (Keep it Simple, Stupid), whether or not this is what Fr. William of Ockham really had in mind. And intuitively at least, it makes sense that September’s fall in equity values might have been due in large part (if not entirely) to changing conditions in the bond market, and in particular in the market for UST bonds.
But think about the implications of this observation.
Ten-year maturity UST bonds currently yield 1.5%, but three years ago the yield was 3% and in June 2007 the yield was 5%. June 2007 was before the financial crisis really took root, which triggered a big Fed cut in short-term rates and massive Fed intervention in the UST bond market, totaling over $7tn (yes, trillion!) in UST bond purchases by the Fed. This unprecedented buying of UST bonds by the Fed (so-called quantitative easing) drove down the yield on UST bonds and drove up the value of other financial assets, including stocks. [By way of reference, the total outstanding value of all UST and US agency bonds is currently around $25tn (including the increase in value resulting from lower bond yields) and the current value of the total US stock market is about $50tn, up 3x from the value in June 2007.] It is of course true that the outlook for future equity cash flows has also changed significantly over this period, but if a 20bp (0.20%) move in UST yields during one month can cause a 5% correction in the value of the entire US stock market, what will happen if and when rates go up by 100bp or more?
I have no idea, of course, but it could make September 2021 look like a pretty benign month.
For more on this topic, read here:
The Market is Right to be Spooked by Rising Bond Yields, WSJ, October 2, 2021
The Stock Market’s Hot Summer Became a Swoon, NY Times, October 4, 2021
The Stock-Bond Correlation, Pimco Research, November 2013