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IAI Actuarial Core Principles · Business Finance · Key principles of finance

A one-year zero-coupon government bond with face value ₹1,000 is priced at ₹920, and the one-year risk-free rate implied by other instruments is 8% per annum. An investor can borrow and lend at 8%. Which action gives a risk-free profit with no net outlay today?

The bond's yield is about 8.70%, above the 8% borrowing rate, so borrow ₹920 and buy it. At maturity receive ₹1,000 and repay ₹993.60, locking in a risk-free profit of ₹6.40 without any initial outlay.

  1. ABorrow ₹920 at 8%, buy the bond; profit at maturity ₹6.4Correct
  2. BLend ₹920 at 8%, short the bond; profit ₹6.4
  3. CBorrow ₹920 at 8%, buy the bond; loss at maturity of ₹6.4
  4. DShort the bond and lend ₹920 at 8%; loss ₹6.4
  5. No arbitrage exists because the yield exceeds 8%

Explanation

The bond yields 1000/920 - 1 = 8.696%, above the 8% borrowing rate, so it is underpriced. Borrow ₹920 and buy the bond. At maturity receive ₹1,000 and repay 920 x 1.08 = ₹993.6, giving a profit of ₹6.4 with no initial outlay. Lending and shorting would lose money, and the yield exceeding 8% is exactly why arbitrage exists.

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