Suppose I bought a $1000 ten-year treasury note (2031) with 4% yield. After one year, the yield decreased to 1%. If I sell it, how much premium will I get? Will I get (3% * 1000)? If the calculation is more complicated, how much approximately will the premium be (between $10-$50 or $50-$100 or $100-$500 or ...)?
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2What is the coupon rate?– DJohnMCommented Jul 5, 2021 at 1:36
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1 Answer
Let's assume you bought the bond at par for $1,0000 to avoid DJohnM's comment, which is spot on. Price at par, we know the coupon rate equals the yield of 4%. (If that's not the case, just can change the coupon rate in the following calculation.)
The value of the bond one-year from today at a 1% yield is computed as
Value_1 = 20/(1+.01/2)^1 + 20/(1+.01/2)^2 + ... + 1020/(1+.01/2)^18 = $1,257.59
The cash flows are the periodic (6-month) coupons at a 4% coupon rate. This is will be the price at which you can sell. Computing your return is more complicated because you need to know the reinvestment rate of your first two coupons.
