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- Short term T.Bill rates and the Fed Funds rate move together strongly: The result backs up the intuition that the Fed Funds rate and the short term treasury rate are connected strongly, with an R-squared of 56.5%; a 1% increase in the Fed Funds rate is accompanied by a 0.62% increase in the T.Bill rate, in the same month. Note, though, that this regression, by itself, tells you nothing about the direction of the effect, i.e., whether higher Fed funds rates lead to higher short term treasury rates or whether higher rates in the short term treasury bill market lead the Fed to push up the Fed Funds rate.
- T.Bond rates move with the Fed Funds rate, but more weakly: The link between the Fed Funds rate and the 10-year treasury bond rate is mush weaker, with an R-squared of 6.7%; a 1% increase in the Fed Funds rate is accompanied by a 0.19% increase in the 10-year treasury bond rate.
- T. Bill rates lead, Fed Funds rates lag: Regressing changes in Fed funds rates against changes in T.Bill rates in the following period, and then reversing direction and regressing changes in T.Bill rates against changes in the Fed Funds rate in the following period, provide clues to the direction of the relationship. At least over this time period, and using monthly changes, it is changes in T.Bill rates that lead changes in Fed Funds rates more strongly, with an R squared of 23.7%, as opposed to an R-squared of 9% for the alternate hypothesis. With treasury bond rates, there is no lagged effect of Fed funds rate changes (R squared of zero), while changes in T.Bond rates do predict changes in the Fed Funds rate in the subsequent period. The Fed is more a follower of markets, than a leader.
Note that almost any macro economic change, whether it be a surge in inflation, an increase in real growth or a global crisis (political or economic) affects earnings growth, T.Bond rates and the equity risk premiums, making the impact on value indeterminate, until you have worked through the net effect. To illustrate the interconnections between earnings growth rates, equity risk premiums and macroeconomic fundamentals, I looked at data on all of the variables going back to 1961:
- In the bearish version, which I call the Interest Rate Apocalypse, all of the inputs (earnings growth for the next five years and beyond, equity risk premiums) into value are held constant, while raising the treasury bond rate to 4% or 4.5%. Not surprisingly, the effect on value is calamitous, with the value dropping about 20%. While that may alarm you, it is unclear how the analysts who tell this story explain why the forces that push interest rates upwards have no effect on earnings growth, in the next 5 years or beyond, oron equity risk premiums.
- In the bullish version, which I will term the Real Growth Fantasy, all of the inputs into value are left untouched, while higher growth in the US economy causes earnings growth rates to pop up. The effect again is unsurprising, with value increasing proportionately.
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- More of the same: In this narrative, you can argue that, as has been so often the case in the last decade, the breakout in the US economy will be short lived and that we will revert back the low growth, low inflation environment that developed economies have been mired in since 2008. In this story, the treasury bond rate will stay low (2.5%), earnings growth will revert back to the low levels of the last decade (3.03%) after the one-time boost from lower taxes fades, and equity risk premiums will stay at post-2008 levels (5.5%). The index value that you obtain is about 2250, about 16.4% below March 2nd levels.
- The Return of Inflation: In this story line, inflation returns, though how the story plays out will depend upon how much inflation you foresee. That higher inflation rate will translate into higher earnings growth, though the effect will vary across companies, depending upon their pricing power, but it will also cause T. Bond rates to rise. If the inflation rate in the story is a high one (3% or higher), the equity risk premium may also rise, if history is any guide. With an inflation rate of 3% and an equity risk premium of 6%, the index value that you obtain is about 2133, about 20.7% below March 2nd levels.
- The Growth Engine Revs Up: In this telling, it is real growth in the US economy that surges, creating tailwinds for growth in the rest of the world. That higher real growth rate, while pushing up earnings growth for US companies (to 8% for the near term), will also increase treasury bond rates (to 3.5%), as in the inflation story, but unlike it, equity risk premiums will drift back to pre-2008 levels (closer to 4.5%). The index value that you obtain is about 3031, about 12.7% above March 2nd levels.
- A Melded Version: I believe in a melded version of these stories, where inflation returns (but stays around 2%) and real growth in the economy increases, but only moderately. That will translate into higher treasury bond rates (my guess would be 3.5%), with a proportionate increase in earnings growth (at least in steady state) and an equity risk premium of 5%, splitting the difference between pre-crisis and post-crisis periods. The index value that I obtain, with these assumptions, is about 2610, about 3.1% below March 2nd levels.
- T.Bond Rates, Inflation and Real GDP Growth – 1954-2017
- Fed Funds Rate and Treasury Rates – 1962-2017
- T.Bond Rates, Earnings Growth Rates and ERP – 1961- 2017
- Intrinsic Valuation Spreadsheet for S&P 500
- More of the Same: Spreadsheet
- The Return of Inflation: Spreadsheet
- The Growth Engine Revs Up: Spreadsheet
- The Melded Version: Spreadsheet