You have the following information:

Years to Maturity   Zero coupon bond yield Zero coupon bond price

       1                               5%                                  0.952381

       2                              4.75%                             0.911364

       3                              4.5%                                0.882616

What is the forward implied rate from year 1 to 2?

Question

You have the following information:

Years to Maturity   Zero coupon bond yield  Zero coupon bond price

1                               5%                                  0.952381

2                              4.75%                             0.911364

3                              4.5%                                0.882616

What is the forward implied rate from year 1 to 2?

BlackTom AI · Accepted Answer

We’re given zero-coupon bond data and asked for the forward rate from year 1 to year 2.
First, confirm the annual compounding convention from the data: a 1-year zero yield of 5% has price 0.952381, which is (1+0.05)^{-1} as expected. Similarly, the 2-year zero yield of 4.75% has price 0.911364, which matches (1+0.0475)^{-2}.
To find the 1-year forward rate starting 1 year from now (f1,2), use the no-arbitrage relationship with annual compounding:
(1+z2)^2 = (1+z1) * (1+f1,2).
Here, z1 = 0.05 and z2 = 0.0475.
Compute (1+z2)^2: (1.0475)^2 ≈ 1.097256.
Compute (1+z1): 1.05.
Solve for (1+f1,2): (1+f1,2) = (1.097256) / (1.05) ≈ 1.0450.
Thus f1,2 ≈ 0.0450, or about 4.50%.
Now evaluate the answer choices:
- 4.75%: This would imply (1+f1,2) ≈ 1.0475, which is larger than the computed value; it ignores the carry from A1 to A2 implied by z1 being higher than z2.
- 4.5%: This matches the calculation precisely, giving (1+f1,2) ≈ 1.0450.
- 5%: This would set (1+f1,2) equal to 1.05, which is too high relative to the ratio (1+z2)^2/(1+z1).
- 4.25%: This would yield (1+f1,2) ≈ 1.0425, which is too low compared to the actual ratio.
In summary, the forward rate is derived from the ratio of the squared 2-year discount factor to the 1-year discount factor, reflecting the no-arbitrage condition between consecutive maturities.

fin_412_120258_251367 Mid-term Test 2

You have the following information: Years to Maturity Zero coupon bond yield Zero coupon bond price 1 5% 0.952381 2 4.75% 0.911364 3 4.5% 0.882616 What is the forward implied rate from year 1 to 2?

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