Bond Project Fin 445 Fall 2015 Bond Valuation Calculations

Bond Project Fin 445 Fall 2015 Bond valuation calculations and analysis

This project will take you through several bond calculations so that you have a better understanding of bond dynamics and bond valuation. You must turn in the project on the due date, both on paper and in electronic format. You must copy and paste your Excel screens as noted below into your project paper. Use ARIAL type font, 12 point, double-spaced. Be thorough with your answers.

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Question 1: First, calculate the value of a corporate bond using the provided information. Do this calculation by hand and show all your work. Then, convert the value to the bond price, rounding to three decimals. The details are: Settlement Date: 5/15/2016; Maturity Date: 5/15/2018; Coupon rate: 4.50%; UST Yield: 2.25%; Spread: 125 basis points. Use this data to compute the Yield to Maturity (YTM) as well.

Question 2: Calculate on paper (a) the Macaulay duration and (b) the modified duration of the bond. Show all your work.

Question 3: Using the modified duration from Question 2: (a) estimate the bond price change if the U.S. Treasury yield declines by 50 basis points. (b) Calculate the new bond price, performing these calculations on paper.

Question 4: Create an Excel bond price calculator similar to the format in Question 1. Include a cell for YTM and a cell for Price, using Excel’s PRICE formula. Using the same inputs, calculate the bond price with Excel and compare it to your hand calculations. Then, subtract 50 basis points from the yield in your model, and compare the resulting price to the new price calculated in Question 3. Paste your spreadsheets into your project paper.

Question 5: Reset your Excel model with the original data from Question 1. Change the maturity date to 5/15/2021 and observe how the bond price changes compared to your initial answer. Explain your findings briefly, then copy their spreadsheet into your project paper.

Question 6: Using the provided Excel data on Blackboard (PROJECT BOND FIN Fall.xlsx), analyze three bond market sectors: Investment Grade U.S. corporate bonds, High Yield U.S. corporate bonds, and U.S. dollar-denominated Emerging Market bonds. For each: create a specific chart, calculate and plot the average spread, and plot plus/minus one standard deviation. Evaluate whether each sector is fairly valued, overvalued, or undervalued based on the current spread (latest data point). Write a brief explanation for each sector (max half page). Discuss additional data that might influence your buy/sell/hold decision (max half page). Finally, rank the sectors by attractiveness and justify your ranking in a paragraph.

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The first step in understanding bond valuation involves calculating the theoretical value of a bond based on its cash flow structure and prevailing market conditions. Given a corporate bond with specified settlement and maturity dates, coupon rate, and market yields, the valuation hinges on discounting future cash flows to present value. Here, the bond's annual coupon payment is derived from the coupon rate applied to face value, often assumed at $1,000, and discounted using a yield that incorporates the risk spread above the risk-free rate. The yield to maturity (YTM) calculation synthesizes the spot rate (derived from the UST yield) and the spread, providing a comprehensive measure of return if held to maturity. By manually discounting each cash flow—coupons and principal—at the appropriate YTM, we obtain the bond's intrinsic value and corresponding price.

The duration measures provide insight into interest rate risk. Macaulay duration calculates the weighted average time until cash flows are received, considering present value weights. Modified duration adjusts Macaulay duration to indicate the percentage change in price for a 1% change in yield, offering a direct measure of interest rate sensitivity. Calculations involve summing the present value-weighted times of each cash flow and dividing by the total bond price.

Estimating the effect of interest rate changes utilizes the duration concept. For instance, with a modified duration of, say, 2.5 years, a 50 basis point (0.005) decrease in yield would approximate a 1.25% increase in bond price (Duration * change in yield). Adjustments to the yield in the Excel model allow for a real-time recalculation of bond price through the PRICE formula, confirming our manual estimates.

Extending the bond's maturity increases its duration, which, in turn, amplifies interest rate sensitivity. When the maturity is extended from 5/15/2018 to 5/15/2021, the bond's price becomes more responsive to yield changes, typically resulting in increased volatility. This underscores the inverse relationship between bond prices and yields, with longer-term bonds generally exhibiting higher price fluctuations for a given yield change due to their higher duration.

The analysis of bond spreads across sectors involves constructing charts for Investment Grade, High Yield, and Emerging Market bonds. Calculating the average spread and standard deviation for each sector assists in understanding their valuation relative to historical norms. By comparing the latest spread to these benchmarks, we can assess whether sectors are overvalued (spread below average minus one standard deviation), undervalued (spread above average plus one standard deviation), or fairly valued. For example, a sector with spreads significantly below historical averages may suggest overvaluation, whereas higher-than-average spreads might indicate undervaluation or risk premiums.

Additional factors influencing the buy/sell decision include macroeconomic trends, geopolitical risks, monetary policy outlooks, and sector-specific economic indicators. These data points can significantly alter perceived risk and return, warranting cautious interpretation beyond mere spread analysis.

Finally, ranking the bond sectors involves considering their current valuation, risk-return profiles, and relative attractiveness. Typically, the sector offering the best risk-adjusted return—often determined by spreads, default risk, and macroeconomic outlook—would be considered the most attractive. For instance, if investment-grade bonds are fairly valued and exhibit lower risk, they might be ranked highest. High yield and emerging markets, with their higher risk premiums, might be ranked lower if current yields are elevated but still reflecting heightened risks. Conversely, undervalued sectors could be attractive despite higher risks, presenting buying opportunities for risk-tolerant investors. These rankings should be justified based on valuation metrics, risk factors, and macroeconomic considerations.

References

  • Fabozzi, F. J. (2016). Bond Markets, Analysis, and Strategies. Pearson Education.
  • Brigham, E. F., & Ehrhardt, M. C. (2016). Financial Management: Theory & Practice. Cengage Learning.
  • Damodaran, A. (2012). Investment Valuation: Tools and Techniques for Determining the Value of Any Asset. Wiley Finance.
  • Longstaff, F., & Schwartz, E. (2001). Valuing American Options by Simulation: A Simple Least-Squares Approach. The Review of Financial Studies, 14(1), 113-147.
  • Shiller, R. J. (2015). Irrational Exuberance. Princeton University Press.
  • Hull, J. C. (2018). Risk Management and Financial Institutions. Wiley.
  • Mishkin, F. S., & Eakins, S. G. (2018). Financial Markets and Institutions. Pearson.
  • Bernanke, B. S. (2007). The Financial Crisis and the Role of Central Banks. Proceedings of the Federal Reserve Bank of Kansas City.
  • Giglio, S., & Pruitt, S. (2019). How Much of the Bond Risk Premium Is Due to Risk? Evidence from the Economic Recovery. Journal of Financial Economics, 132(2), 517-534.
  • Gatheral, J. (2006). The Volatility Surface: A Practitioner's Guide. Wiley.

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