Answer-first summary for fast verification
Answer: undervalued.
## Explanation **Step 1: Calculate arbitrage-free price using spot rates** The bond pays: - Year 1: 5 - Year 2: 5 - Year 3: 105 Arbitrage-free price = 5/(1.015) + 5/(1.02)² + 105/(1.0425)³ = 5/1.015 + 5/1.0404 + 105/1.1331 = 4.9261 + 4.8058 + 92.6662 = 102.3981 **Step 2: Calculate price using YTM of 4.25%** Price using YTM = 5/(1.0425) + 5/(1.0425)² + 105/(1.0425)³ = 4.7962 + 4.6004 + 92.6662 = 102.0628 **Step 3: Compare prices** - Arbitrage-free price: 102.3981 - Market price (using YTM): 102.0628 The market price is **lower** than the arbitrage-free price, indicating the bond is **undervalued**. **Key Insight**: When the YTM equals the 3-year spot rate but the spot rate curve is upward sloping (1.50% < 2.00% < 4.25%), the bond will be undervalued because the YTM calculation uses a single discount rate that is too high for the earlier cash flows.
Author: LeetQuiz Editorial Team
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An analyst gathers the following information about spot rates:
A 3-year, 5% annual coupon bond with similar risk as the benchmark is trading at a yield-to-maturity of 4.25%. Compared to the arbitrage-free price, the bond is currently:
A
undervalued.
B
fairly valued.
C
overvalued.
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