protagonist wrote: ↑Sat Mar 30, 2024 6:06 pm
Thanks again, Kevin! One more question.

Kevin M wrote: ↑Sat Mar 30, 2024 1:16 pm
excluding any term-premium, which could be positive or negative, rolling 1-year TIPS for 10 years has the same expected return as holding a 10-year TIPS to maturity.

I get that now. Except...

What do you mean by "term premium"? Is that synonymous with the discount/premium at which you purchased the bond, or something else?

And does it influence which ones you sell? And if so, how and why?

(That was more than one question. Sorry.)

The New York Fed has a web page related to this:

Treasury Term Premia. From that page:

In standard economic theory, yields on Treasury securities are composed of two components: expectations of the future path of short-term Treasury yields and the Treasury term premium. The term premium is defined as the compensation that investors require for bearing the risk that interest rates may change over the life of the bond. Since the term premium is not directly observable, it must be estimated, most often from financial and macroeconomic variables.

The first part, "expectations of the future path of short-term Treasury yields" means that, other than the term premium, the expected return of a 10-year Treasury is the same as that of rolling a 1-year (or 1m or 3m or 6m) Treasury for 10 years. With the current inverted yield curve, this means that the shorter-term yields are expected to decline.

For example, on Thursday the 1y CMT yield was 5.03% and the 10y was 4.20%, so over the next 10 years the 1y yield is expected to decline so that you'd end up earning an annualized 4.20% if you rolled the 1y annually for 10 years.

The term premium is the extra yield, above what the expectations part implies, that is compensation for taking the risk of going long, given that the path of short-term yields is uncertain.

Next on the page:

Current and former New York Fed economists Tobias Adrian, Richard K. Crump, and Emanuel Moench developed a statistical model to describe the joint evolution of Treasury yields and term premia across time and maturities, described in detail in Adrian, Crump, and Moench (2013).

Here's the term premium chart that's linked on that page:

Note that the term premium usually is positive, which is what we'd expect, since investors should be compensated for the risk of the uncertainty of forward short-term rates, but it has been negative at times in recent years, and the most recent value, for Feb 2024, is -0.162 (negative).

What is the implication of a negative term premium? It seems to indicate that investors view shorter-term Treasuries as riskier than longer-term Treasuries. One way to look at that might be that reinvestment risk is getting more weight in investment decisions than price risk. Ben Bernanke wrote an article about this in 2015:

Why are interest rates so low, part 4: Term premiums | Brookings.

The economic conditions were different when he wrote the article, so some of the ideas don't apply to the current environment, but he did say this:

If longer-term bonds are a hedge against risk, then investors should be willing to accept low or even negative compensation for holding bonds rather than short-term securities.

At any rate, like the liquidity and unexpected inflation premia that apply to breakeven inflation, the term premium is not observable, so the best we can do is use models to estimate it. That's why I expressed uncertainty as to what term premium is embedded in the present yield curve.

In terms of the investment decisions we've been discussing, I brought it up in pondering whether to sell shorter-term TIPS with higher yields, or not quite as short-term TIPS with lower yields to buy longer-term TIPS with even lower yields.

If we assume that the term premium is 0, then the expected return of rolling a 1y TIPS into another 1y TIPS has the same expected return as holding a 2y TIPS; i.e., the 1y yield 1y from now is expected to be lower by an amount that can be determined from this equation:

(1+y1) * (1+y1_1) = (1+y2)^2,

where y1 = 1y yield now, y1_1 = 1y yield one year from now, and y2 = 2y yield. We can solve for y1_1 as follows:

y1_1 = (1+y2)^2/(1+y1) - 1

Plugging in the 1y and 2y CMT yields from Thursdsay:

y1_1 = (1+4.59%)^2/(1+5.03%)-1 = 4.15%

Which means that with a term premium of 0, the expected 1y yield one year from now is 4.15%.

So if the term premium is 0, I should be indifferent to rolling a 1y bond for two years or holding a 2y bond to maturity. If I were to sell my 2y TIPS to buy longer-term TIPS, I am expressing a preference for holding some shorter-term TIPS, which implies I would roll the 1y TIPS into another 1y TIPS at maturity. Rather than do that, I might as well just sell the 1y TIPS, even though the yield is higher, especially since it is functioning more like a nominal bond than the 2y TIPS.

Since the term premium is not observable, and it might even be slightly negative now, I just assume it's zero.

If I make a calculation error, #Cruncher probably will let me know.