A 10-year, 8% coupon bond currently sells for $90. A 10-year, 4% coupon bond currently sells for $80. What is the 10-year zero rate? (Hint: Consider taking a long position in two of the 4% coupon bonds and a short position in one of the 8% coupon bonds.)

3.57% per Annum or 0.0357

Explanation:

Recall that,

By Taking a long position in two of the 4% coupon bonds and a short position in one of the 8% coupon bonds it results in the following

The Year 0: 90 - 2 x 80 = - 70

The Year 10: 200 - 100 = 100

Since both coupons cancel each other.

In 10 years time a $100 will be the same to $70 today.

The 10-year rate, R, (10-year-rate) is given as,

The rate is 1/10 in 100/70 = 0.0357 or 3.57% per year.

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