By: Steve Sosnick, Chief Strategist at Interactive Brokers
Yesterday we asserted that the 50 basis point spread between 2-year and 10-year US Treasury yields showed that bond traders viewed the current inflationary pressures as transitory. I based that assertion on the nature of interest rate calculations. If 2-year rates are about 1.5%, 5-year rates are about 1.9% and 10-year rates are about 2%, it implies that forward rates will be very modest as we proceed out the yield curve. Today we’ll explain the basics of the mathematics behind this.
I first became familiar with interpolating forward rates as a summer intern in Sales and Trading at Salomon Brothers in 1985.[i]One of my rotations was at the money markets desk. Armed with my finance studies and a reasonable facility with Excel (or was it VisiCalc?), I came up with the idea of entering the various Eurodollar rates into a spreadsheet in order to see if there were anomalies in the market’s pricing of forward rates. We didn’t spot all that many arbitrage opportunities – those markets were efficient even then – but it was a fairly novel way to look at markets at the time.
The logic depends on compound interest rate formulas.The standard formula is this:
FV = PV (1 + r/n) ^ nt
Where:
FV = future value
PV = present value
r = interest rate (usually annualized)
n = number of times interest is compounded per period (say 12 for monthly, 4 for quarterly, etc)
t = time (usually years)
If you lent me $100 for 1 year at a 2% rate, then you would expect to receive $102 in a year. If you lent it to me for 2 years at a 2% rate, compounded annually, then you would expect to receive $104.04.You see that is more than $104, which would be the case if it were simple interest. The formula shows that 100 * 1.02^2 = 104.04.
If you offer me the choice of lending me the money for a year at 2% or for two years at 3%, we can figure out the implied interest rate for the second year if we break apart the formula. We know that 1 year at 2% yields $102, and after 2 years at 3% it would be $106.09 (100*1.03^2). That means that the implied 1 year interest rate for the second year is greater than 2% – it’s just over 4%.
106.09 = 100 * (1 + r1) * (1 + r2)
Since we know that the first year rate, r1, is 2%, we can solve algebraically:
106.09 = 100 * 1.02 * (1+ r2)
106.09 / 102 = 1.0401, so r2 = 4.01%
Why are you demanding a near-doubling of rates in year two? Do you expect me to suddenly become a much worse credit risk in that time period, or do you expect inflation to greatly erode your purchasing power in that second year?
This is an oversimplified example, of course, but this is the logic we employed in asserting that bond markets are anticipating very low inflation over the longer term. Remember that US Treasury traders are relatively unconcerned about credit risk. They believe that the US government can simply print sufficient dollars to pay its debts. The bigger worry is about the purchasing power of those future payments. In other words, they are almost exclusively concerned with inflationary expectations.
If bond investors were expecting inflation to kick up in years 2-10, or 5-10, we would expect to see them demand much higher yields for longer-term debt. Quite frankly, they’re not. If they expected inflation to kick in meaningfully over that time period, they would demand more than 50bp more for 10-year rates than they do for the ensuing eight years after the 2-year notes mature. Or, they would demand more than 10bp for the five-year period after the 5-year note matures. The implication is that after the initial jolt that we see over the coming two years, inflation will stabilize shortly after and then cease to be an issue as we look further out.
That’s quite an implicit assertion. As we noted yesterday, this shows an incredible faith in the Fed’s powers to fight inflation – “Don’t Fight the Fed”, indeed. Investors became quite used to exogenous deflationary pressures over the past decade or more, and perhaps they expect those pressures to resume in the near future. I’m less certain of that, since much of that deflationary force came from supply-chain globalization, particularly utilizing Chinese labor, and those price considerations may be ebbing.
Or there is a more basic issue at hand. Despite their rhetoric otherwise, the Fed is continuing to add to its holdings of securities at something approaching their pre-taper rate. According to Federal Reserve H.4.1 reports, the holdings of securities on the Fed’s balance sheet on February 9th, 2022 were $8.395 trillion. On January 5th they were $8.279 trillion. For those of you keeping score at home, that’s an increase of $116 billion in just over a month. It is entirely possible that the message of the bond market is being distorted by central bank activity.
[i] For those of you who are fans of the book Liar’s Poker, I was finishing up my program when Michael Lewis was arriving for training class.
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