Question

The YTM on a 2 year zero coupon bond is 5% and the YTM on a 1 year zero coupon bond is 3%. What does the no-arbitrage condition tell you about the rate you can lock in today on a 1 year safe loan that starts next year (the one-year forward rate)?

Answer 1

Answer:

$111.11 or 111.11% of face value

Explanation:

Assuming the face value of $100 for all bonds (without loss of generality)

If the two year coupon bond is repackaged as a one year zero coupon bond paying $12 after one year and another two year bond paying $112 after 2 years, the price of the two zero coupon bonds are given as

Price of one year Zero coupon bond = 12/1.05 = $11.43 (one year ZCB has YTM of 5%)

Price of two year Zero coupon bond = 112/1.06^2 = $99.68 (two year ZCB has YTM of 6%)

So, one can sell the repackaged bonds at a price = $11.43+ $99.68 = $111.11 or 111.11% of face value