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Assignment 1 for Econ 452 (2019) Penn State University

Due: before 1:18pm on January 31, 2019.

Please write your answers legibly.

Question 1. (32 pts) To answer this question, see the instructions on the course website for how to download data from FRED:

(1) (16 pts) Download seasonally adjusted real GDP (in billions of chained 2012 dollars), the real residential property price, and the effective FED funds rate. All three variables should be quarterly and cover only the period 1978-01-01 to 2018-01-01 for the U.S.. Put these data sets together in a new Excel sheet, where the first column (A) should be the quarterly dates. Transform each of the variables by dividing the variable by its average. Put the transformed variable in a new column. Submit the printed form of the Excel sheet that contains the original data and the transformed data. Clearly label each column.

(2) (8 pts) Plot the transformed GDP and the transformed housing price in one graph where the horizontal axis is time. Clearly label the plotted data. Use this graph to discuss the relationship and the contrast between the behavior of real GDP and the housing price.

(3) (8 pts) Plot the transformed housing price and the transformed effective federal funds rate in one graph where the horizontal axis is time. Clearly label the plotted data. Use this graph to discuss the relationship and the contrast between the housing price and the effective federal funds rate.

Question 2. (30 pts) Consider Treasury bills with a face value $100 (and zero coupon). All yields are annualized using 360 days for a year and expressed in percentage points.

(1) (8 pts) If T-bills have a yield 0:50 and a current maturity of 250 days, compute the actual interest rate of the T-bills in the current maturity (not annualized), express the result in percentage points, and round up the result to the fifth digit after the decimal point. Use this interest rate to compute the price of the T-bills, round up the result to the third digit after the decimal point, and then express the result in the quoted format.

(2) (6 pts) If the yield of the T-bills in part (1) increases by 30 basis points, with the current maturity being fixed, what is the percentage change in the price of the T-bills?

(3) (8 pts) If T-bills have a price quote 99 13 32 and a current maturity 350 days, compute the price of the T-bills in the decimal format first (round up the result to the third digit after the decimal point). Then, compute the yield on the T-bills and round up the result to the third digit after the decimal point. (Remember that all yields are expressed in percentage terms).

(4) (8 pts) If T-bills have a price quote 99 16 32 and a yield 0:8, what is the bills’ current maturity? (Round up the result to integer days.)

Question 3. (16 pts) In the following table, the first column is the maturity of bonds (in years). The second column is the yield on Treasury STRIPS of the face value $100 of each maturity. The third column is the price of zero-coupon bonds of the face value $100 issued by a municipal government TBN. Assume that the Treasury bonds have zero default probability.

Also assume that the only cause of the difference in the price between the Treasury STRIPS and TBN bonds of the same maturity is the default probability of TBN. maturity (years) yield on Treasury STRIPS of the face value (%) price of 0-coupon bonds TBN (face (value = $100) yield on TBN (%) implied default probability of TBN (%) 1 0.8 99 3 2.2 92 5 2.5 85 10 3.5 67 20 4.2 36 30 5.1 18

(1) (11 pts) Fill in the last two columns of the table, where the implied default probability is over the entire duration of the speci�ed maturity. (Keep the accuracy to the third digit after the decimal point). For the row with maturity = 5 years, demonstrate how you obtain the numbers in the last two columns.

(2) (5 pts) Plot the yield curves of the Treasury STRIPS and TBN bonds in the same graph. Clearly label the axes and curves.

Question 4. (2 pts each) For each statement below, answer whether the statement is true, false, or uncertain for the U.S economy. Briefly explain your answer.

(1) A fall in the prime mortgage rate occurred just before the GDP fell in every recession after 1970.

(2) Not all types of investments move in the same direction as real GDP.

(3) Over a long term, say, from 1982 to 2006, growth in the residential property price outpaced growth in real GDP. (4) Percentage changes in the unemployment rate and real GDP are similar.

(5) In the Great Recession, the U.S. Treasury and the FED bought only asset backed and mortgaged backed securities.

(6) TARP is a program that allowed the U.S. Treasury to sell its bonds to the Federal Reserve system at artificially high prices. 2

(7) In quantitative easing, the FED’s primary objective is to lower the FED funds rate.

(8) Buying in the Federal Funds market means that a depository institution uses reserves to buy Treasury securities. (9) Fed Funds are reserves that the Federal Reserve makes available at the discount window.

(10) The reserve requirement in the U.S. allows a U.S. bank to have the reserve ratio below the required ratio on some days.

(11) To borrow and lend in the Fed funds market, a bank puts up collateral.

 

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