Societe Generale’s Math Predicts Equity Market Chaos If Bond Yields Continue To Rise
Dean Brooke

Dean Brooke

Dean Brooke's economics & financial column brings you news, in-depth analysis, research, occasional gossip, and more. You can email him at dbrooke@rogueeconomics.net.
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Foreword/Disclaimer

I originally wrote this piece as part of a much broader essay back in 2018 during the last tightening cycle and things have changed - A LOT - since then. I have had to source this retrospectively from the notes I retained at the time because some of the source material seems to have since disappeared from the internet (though I notice that other writers have since referenced it and so research can be carried out if you have a care to google this information) so, apologies in advance for the rather loose referencing and as always you can feel free to submit questions/leave comments and of course DYOR always applies. I plan to update this in the near future (2022) as we are obviously beginning another tightening cycle and I will add to this piece sometime this year as the situation develops.

Introduction

The following chart is taken from Société Générale’s research into the sensitivity of US equities to a higher interest rate environment conducted in 2018.

Specifically, with respect to the rate on US government treasuries and how it affects equity markets.

Here are the notes from SocGen’s research, I’ll do my best to find an actual link to the source at a later date.

Fundamentally, Societe Generale research shows that the equity risk premium reduces exponentially for every 0.25% on the flagship 10year US treasury yield.

Furthermore, the equity risk premium moves further into negative territory past the 3.25% mark.

What Is The Equity Risk Premium?

To explain, the “equity risk premium” is a component of equity pricing which accounts for the percieved risk present in equity markets and is a premium over-and-above the so-called “risk free rate” (which is generally benchmarked against the yield on the 10 year US treasury).

That is to say, equity markets prices experience mark-ups of a certain percentage above-and-beyond bond yields due to the risk premium component of their valuations.

SocGen research shows that as treasury yields rise, the risk premium starts to weaken and in fact, can actually turn negative as we see above.

This is because as yields rise, the so-called “risk free rate” (indexed against the 10 year bond yield) moves closer to the excess returns from the S&P500.

Especially if the S&P500 flatlines or even starts an extended downmove, then the risk premium can actually go negative (and of course, we have to factor inflation adjustments into this formula as well).

Thus, SocGen research actually predicts that, once bond yields break a certain level, downside can manifest in the equity market in a reasonably predictable way relative to bond yields due to the way investors flip equities into bonds if they percieve a less-risky way of achieving the same yield for the same amount of principle investment capital.

In fact, one of the most interesting points about SocGen’s research is that the severity of an equity write-down is roughly projected to increase by 7% for every unit of 0.25% gained by rising bond yields.

We can thus extrapolate forwards from there.

Let us reflect on this and just take that on board for a moment.

The implication here is that equity markets in 2018 (when SocGen published their research) were nowhere near ready for interest rate normalisation and, on the contrary, were very sensitive to FED actions through the impacts which filter-through bond yields into the rest of the system.

We saw this in the way the S&P500 reacted to FED actions. For instance, during the so-called “taper tantrum” in in 2013 when equity markets became more volatile when the FED first announced their desire to taper-off QE.

We also saw a significant selloff in 2018 when the FED carried out a rate hoke.

We must translate this research into present times and ask ourselves:

Are equity markets more, or less robust in 2022?

We can speculatively say that equity markets are demonstrably more fragile due to the sheer fact of macroeconomic variables being demonstrably worse and of course, most S&P500 companies are more indebted in 2022 than they were in 2018 and the consumer is clearly in far worse shape as evidenced by the fact that inflation is running at 8% and consumer confidence is in the tank.

So, therefore, as the FED embarks on quantitative tightening, and the bond markets begin to respond by driving up yields, the risks inherent in the system due to the impact of rising yields upon the risk premium will begin to manifest through greater downside risks on stocks.

A Basic Calculation Of The Risk Premium

Lets try a basic calculation:

  • The 10 Year Treasury has a yield of about 2.93 as of present.

  • We can see that the 1 year range of the S&P500 is roughly 20%

  • We can see that inflation is running at roughly 8.30%.

So, therefore we can calculate this forwards:

  • The 1 year return of the S&P500 can be said to be around 20%.
  • Inflation is 8.30%.
  • Therefore the inflation-adjusted return for the S&P500 is more like 11.70%.
  • The 10 Year Treasury yield is currently 2.93% and this can also be referred to as the so-called “risk free rate”.
  • Subtracting this from the inflation-adjusted 1 year return for the S&P gives the S&P500 a risk premium of 8.77%.

We can therefore see, how rising yields in combination with high inflation suppress the risk-premium on equities because if you are able to earn a high-enough return from bond-yields, the premium you receive for taking risks on equities reduces.

After all, why take risks on equities if you can earn an annual return from yields alone?

 

Conclusion & Afterthought

The basis of Societe Generale’s research is a simple concept. It simple describes a situation where people who currently take risks on equities tend to switch to percieved safer options (US government treasuries) if the yield from government treasury bonds rise.

The more yields rise, the more impetus there is for investors to sell their stocks into bonds to earn the same return which equities deliver without the risk of holding equities. Especially if equity prices continue to stay confined within a range or even fall.

Societe Generale’s paper argues that this occurs in a fairly predictable way.

Every 0.25 on the 10 Year US government bond yield translates to a downside potential expansion of 7% on the S&P500.

I believe we can already see evidence for this in S&P pricing.

In this example we can see that the TNX index which tracks the yield of the 10 year US treasury bond actually is a mirror-image of recent S&P500 performance.

This inverse-correlation appears to have been in-place since October 2021.

Presuming yields are going to continue to rise due to the Federal Reserve beginning quantitative tightening in combination with raising interest rates, we can being to see how yields are going to have very direct impacts upon equity valuations.

In fact I believe that yields and interest rates are on the verge of a historic breakout.

We can see here how the 10-year treasury yield is currnetly pushing through the upper-boundary of it’s long-term downtrend.

This could open up the upside to a trend of higher yields and higher interest rates especially if inflation is going to become entrenched as a countercurrent to asset markets because of course nobody is going to lend money for below inflation returns over the long-run.

The issue for central banks and investors alike is that nobody is going to tolerate negligible risk premium returns in return to investing their money in the fundamentally risky stock market over the long run either.

As such, I believe we can expect volatility to skyrocket from here as the risk-premium declines and inflation continues to erode the worthiness of investment returns in equity markets.

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