U.S. Treasury Yields: The 10-Year Probabilities
Summary
- It's more important to understand that the probability of heads in a coin-flip is 50% than it is to guess heads or tails.
- The same is true for interest rates, a lesson learned the hard way by many including the author.
- We present this week's 10-year distribution for future 3-month Treasury bill yields for 20 points in time.
- Looking for more investing ideas like this one? Get them exclusively at Corporate Bond Investor. Learn More »
One of the most fruitless exercises in finance is trying to predict interest rates. Most investors have proven this to themselves over the years by learning from their mistakes. In addition to my own mistakes, I learned this lesson from various wise and not-so-wise teachers and co-workers. Some of the most valuable ways of making this point about interest rate forecasting are hard to forget:
Key Maxim of the Harvard Economics Department
“Give ‘em a rate, or give ‘em a date, but never give ‘em both.”
Lehman Brothers
“Yeah, the head of fixed income is a genius. He’s the only one in the firm that has positioned us right for rate moves over the last 5 years. A year ago, there were two guys like that. And the year before that, there were 4 guys. And the year before that, there were 8 guys, and…well, you’ve got the message.”
Bank of America
From the legendary Wm. Mack Terry, who invented “funds transfer pricing,” the basic foundation of interest rate risk management in banking: “The reason we had to develop transfer pricing was that senior management was always betting the bank on interest rates. When they were right, they claimed credit. When they were wrong, they blamed it on someone else. This system shows, after the fact, who should get the blame.”
Legendary Finance Professor and Member of the RISK Hall of Fame
“Macro economists don’t really know what they are doing.”
Dean of Professors of Monetary Economics
“It is a good thing you are going to see the central bank of [that G7 country], because they need a lot of help.”
Forecasting the Odds of Getting Heads, Not Predicting Whether the Next Flip is Heads or Tails
The moral of these stories from wise men and women is that the interest rate risk focus should be on understanding the distribution of possible courses of interest rates, rather than betting the bank on a point forecast that predicts whether rates go up or down.
The graph below does just that for the 3-month Treasury bill rate for the next 10 years in semi-annual time steps.
Each cell of the table gives the probability, rounded to the nearest 10th of 1 percent, that the 3-month T-bill rate will fall in that cell at the point in time at the top of the column. For example, the red square in the column labeled with a 2 says that there is a 54.2% chance that the 3-month Treasury bill rate will be between 0% (the label on the y-axis) and 1% in 2 years. The probability that the 3-month Treasury bill rate will be negative in 2 years is the sum of the probabilities in the cells below the red cell: 20.3% plus 1.5% = 21.8%. Using this table, one can make an informed choice about the investment strategy to pursue.
Where did these numbers come from? At Kamakura Corporation we do interest rate risk and other risk management simulations for clients daily, but the most intensive simulations we do each weekend for this “Monday Forecast.”
We go through these steps on a fully automated basis:
We get the history of U.S. Treasury rates all the way back to January 2, 1962, daily, from the U.S. Department of the Treasury. We create a daily history of the present value of $1 for each day for each daily maturity out to the longest maturity reported by the Treasury. During this period, the longest maturity has varied among 10 years, 20 years, and 30 years. Using the approach outlined by Heath, Jarrow and Morton, we derive the average rate of change in yields and the volatility of yields that best explains the movements of Treasuries over this historical period. An example can be found at this link. We extract from this history the points on the yield curve whose movements drive the rest of the yield curve. 40 years ago, the three shocks were often called “level, slope and bend” in the yield curve. Using more modern techniques, we find that 10 points on the yield curve explain 99.99% of movements in the other yield curve segments. We use 120 quarterly segments to span the 30-year length of the curve. We then shock these factors N times for as many time steps as we need for the purpose at hand. The table shows 20 6-month time steps out to 10 years, but we actually used 120 time steps out 30 years for the full simulation. Because computers work for free on weekends, we took 1 million samples of these random shocks for all ten factors at each time step. Finally, after getting the results you see above, we double-checked that our simulation correctly priced the Treasury curve we used as input (shown below). Of course, it did.
We look forward to keeping investors up to date on the best estimate of the distribution for future interest rates in the weeks ahead.
For a daily ranking of the best risk-adjusted value of corporate bonds traded in the U.S. market, please check out a free trial of The Corporate Bond Investor. Subscribers are actively arbitraging 160-year-old legacy credit ratings using modern big data default probabilities from Kamakura Corporation. Remember, the Pony Express and credit ratings were both invented in 1860. Are you still using the Pony Express?
This article was written by
Dr. Donald R. van Deventer has been in the risk management business since completing his Ph.D. in Business Economics at Harvard University in 1977. He founded the Kamakura Corporation in 1990 after 13 years with two of the 10 largest banks in the US and a stint as investment banker in Tokyo. He joined SAS Institute Inc. as co-head, of the Center for Applied Quantitative Finance in 2022 when SAS acquired Kamakura Corporation. At the time Kamakura was acquired by SAS, Kamakura's institutional clients had total assets or assets under management of 48 trillion dollars.
He leads the investing group Corporate Bond Investor to bring Kamakura's state-of-the-art risk analytics to individual investors. The analytical processes underlying the Corporate Bond Investor are identical to those provided to institutional investors by SAS Institute Inc. He also provides a daily ranking of corporate bonds by best risk-adjusted return. His investing group is currently the only one on Seeking Alpha to focus exclusively on corporate bonds.
Analyst’s Disclosure: I am/we are long TLT. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.
The author owns a portfolio of Treasuries and Corporate Bonds disclosed quarterly to subscribers to The Corporate Bond Investor.
Seeking Alpha's Disclosure: Past performance is no guarantee of future results. No recommendation or advice is being given as to whether any investment is suitable for a particular investor. Any views or opinions expressed above may not reflect those of Seeking Alpha as a whole. Seeking Alpha is not a licensed securities dealer, broker or US investment adviser or investment bank. Our analysts are third party authors that include both professional investors and individual investors who may not be licensed or certified by any institute or regulatory body.
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