- Arbitrage. With perfect foresight and no risk premium the return one-year bond should be equal to the interest rate on a six-month bond bought today, reinvested in a six-month bond bought six months from now. (1+i1)(1+i2)=(1+yr) reflects compounding. Now rates are quoted as one-year rates, so if the six-month rate is quoted as 0.6% then the actual return is (1+x)(1+x)=1.006 so sqrt(1.006)=(1+x)=1.0029955 or 1.003. That is, half the one-year rate is a very close approximation when rates are low. So if the one year rate is 1.0082, then the implied return for the second six months is 1.0083/1.003 = 1.0052. That is, markets expect the 6-month interest rate six months from now to be 1.04%. In other words, the FOMC will continue boosting rates at a steady pace.
- Here is what has happened since 1990 to long rates. I used the average of 20-year and 30-year bond rates, in part because there are years in which only one or the other was available. Just to check, I downloaded the excel spreadsheet as an .xml file (Excel 2004 format), imported into Stata, and regressed interest rate = constant + a*date + b*date2. That’s the trend line in the graph. (I forgot to convert the date sequence to give the proper x-axis labels. The series starts Jan 2, 1990 and runs to yesterday.)
- I also calculated the implied yield on long bonds, using the same approach as in (1) above, by comparing the yields on 7 year bonds and 10 year bonds, and 20 year bonds versus 30 year bonds. That graph shows that markets have built in somewhat higher yields.
- Is it sensible that over the next 30 years inflation will never top 2%? In other words, if I were to factor in a risk premium, what would change?
- Back out from that what markets “believe” growth will be 20-odd years from now.
- What questions does that raise? (Many, I trust!)
For your reference I’ve written about this on Autos and Economics.