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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.)

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Answer:

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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