From the treasury page( http://wwws.publicdebt.treas.gov/AI/OFNtebnd):
type: 10-YEAR NOTE
maturity: 07-15-2013
coupon: 1.875
yield: 1.999
price: 98.881
CUSIP: 912828BD1
This means that you pay $98.881 for each $100 of face value of the note. The yield of 1.999 is the yield to maturity. That is the yield given an investment of $98.881, a return of annual coupons, and a return of $100 after 10 years.
I believe there is a yield to maturity formula, which I don't have. However the yield to maturity is basically the sum of two components: The average coupon yield on investment, plus the yield from the increase in 'price'.
So an approximation is: the first year coupon yield on investment is 1.875/98.881 (times 100) or 1.896. For the last year the coupon yield is 1.875/100. Since for later years, the value of the bond goes up, a close approximation is the average of 98.881 (first year) and 100 (last year) or 1.875/((100+98.881)/2) or 1.886. Then the yield from the increase in price is simply (from excel) RATE(100, 98.881, 10) or 0.113. That is, the interest rate needed to get $100 from an initial investment of $98.881 after 10 years. When these two components are added together, you get 1.886+0.113 or 1.999.
This ignores the inflation adjustments, and I believe that is correct.
Maybe someone has the real formulas that are used. The above are an approximation based on my understanding of the bond market.
Wayne
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