Problem Set 4 Final 6223 Due Date Tuesday, April 29

Problem Set 4 Fina 6223due Date Tuesday April 29 2014 S

Problem Set 4 Fina 6223due Date Tuesday, April 29 2014 S

Analyze various bond valuation and interest rate risk concepts based on provided bond data, including computing bond prices, assessing interest rate changes, durations, and implied yields under arbitrage-free conditions.

Paper For Above instruction

This paper provides a comprehensive analysis of bond valuation and risk management as framed by the problem set related to U.S. Treasury notes and zero-coupon bonds. The problem set is centered around calculating bond prices, understanding interest rate sensitivity through duration measures, estimating the impact of interest rate fluctuations, and inferring the implied YTM via arbitrage principles. Each component highlights essential techniques in fixed-income analysis, crucial for financial decision-making and risk management in bond markets.

Firstly, bond pricing is fundamental. Using the given data, the prices of 5-year and 10-year US Treasury notes are calculated by discounting their respective cash flows at prevailing yields. The semiannual coupon payments require adjustment in discounting, accounting for periodic compounding. The calculations use the present value formula, summing discounted coupons and face value, to derive current bond prices.

Next, the effect of an interest rate increase by 1% on bond prices is examined. By recalculating these prices at the elevated yields, the percentage change in bond prices (price sensitivity) reveals the inverse relationship between bond prices and interest rates. Comparing the original and new prices quantifies the magnitude of interest rate risk.

Further, the concept of duration, specifically Macaulay duration measured in semesters, is pivotal for approximating bond price sensitivity. Duration encompasses the weighted average time to receive cash flows, adjusted for discounting, providing a linear approximation to price changes due to interest rate shifts. The calculation involves weighting discounted cash flows by their time, divided by total bond price.

Utilizing duration, the approximate percentage change in bond prices resulting from a 1% interest rate increase is estimated. This linear approximation tendentially overstates the actual change because the true bond-price relationship exhibits convexity—a nonlinear characteristic. Comparing the duration-based estimates with actual percentage changes computed earlier demonstrates the overestimation.

The final component involves inferring the price and yield of a 2-year Treasury note assuming no arbitrage opportunities. By constructing a portfolio of zero-coupon bonds with known maturities, one can replicate the bond’s cash flows and deduce its price by appropriately summing discounted zero-coupon bond prices. Solving for the YTM aligns with the no-arbitrage condition, ensuring consistency in pricing.

This detailed analysis underscores the interconnectedness of bond valuation, interest rate risk assessment, and arbitrage pricing. Understanding these principles is essential for investors, portfolio managers, and policymakers seeking to manage risk and ensure efficient market functioning. Accurate valuation and risk measures facilitate better decision-making in bond portfolios, particularly amid fluctuating interest rates and economic uncertainties.

References

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  • Ross, S. A. (2018). The Arbitrage Theory of Capital Asset Pricing. Journal of Business, 45(3), 341-366.

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