ps1 (1)

B8306 Fall 2023 Professor Xuelin Li Due Date: Fri, Sept 29 3 c) Calculate the yield of the bond in part (b). How does the yield of this bond compare to the spot rates? d) Now assume that you are pricing a risky (i.e. there is a small chance this bond will default) 2-year bond with an annual 2.75% coupon. You believe the risk of this bond warrants that it trade at a 200 basis point spread to the comparable Treasury yield. What will be the price of this risky 2-year bond? Question 4. 2s10s curve and economic growth The 2s10s curve measures the difference in yields between the 10- and the 2-year US Treasury bonds; 2s10s is positive when the 10-year yield is above the 2-year yield. It is common Wall Street folk wisdom that an inverted yield curve (i.e. when the 10-year yield is less than the 2-year yield, or the 2s10s is negative) forecasts recessions. We will measure the extent to which the US economy is near a recession by the year-over-year growth rate of real GDP. The purpose of this question is to test whether the 2s10s curve forecasts year-ahead GDP growth. a) Go to the fred.stlouisfed.org (FRED) website and download the 2s10s curve (search for the series called “ 10-Year Treasury Constant Maturity Minus 2-Year Treasury Constant Maturity ”). Make sure to choose the “Edit Graph” option and specify that you want this series to have quarterly end-of-period values. b) Now choose the “Add Line” options and search for “Real Gross Domestic Product.” Then choose “Edit Line 2” and under units choose the option “Percent Change from Year Ago.” Make sure this is also at a quarterly frequency. c) Now go to FRED’s “Download” butt on and download these two data series as an Excel or CSV file. When you download the raw data, replace the “.” (period) with a blank cell in Excel, to allow for plotting of the data. d) Now create a new column called “GDP +4” which for every date should hav e the 4-quarter ahead year-over-year percent GDP growth. Now plot a scatter plot of year-ahead GDP growth against the current 2s10s curve. e) Now add the best-fitting regression line to this scatter plot, and show the regression equation as well as the R-sq uared. Go to “Add Chart Element” → “Trend Line” → “Linear”. To add the regression equation and the R - squared, go to “Add Chart Element” → “Trend Line” → “More Trendline Options” and click on “Display Equation on chart” and “Display R -squared value on cha rt.” You may need to click on and drag the resulting legend box to a more visible part of the figure. f) Interpret the resulting graph. Is there evidence that an inverted 2s10s curve forecasts recessions as measured by GDP growth?