MPA 620
Finance Toolkit
Key Homework #9
1. US National Debt and Deficit. Use the data available at FRED to analyze the Federal debt
and deficit.
a. Comment about the trends in the Federal Government Debt (GFDEBTN). Use an
annual frequency and end of period aggregation.
i. Overall level.
During the more recent times, the debt has been increasing rapidly, which is especially true
during the Great Recession.
ii. Change in annual level.
The deficit was especially large during the Great Recession and continues at almost $600 billion
a year. During the end of the Clinton administration, we actually had a budget surplus, which is
extreme rare.
iii. Percentage change in the annual level.
The percentage growth in the debt has been constant over the last 50 years. The pattern follows
the business cycle.
b. Comment about the trends in the Federal Government Deficit (FYFSD).
The absolute size the federal deficit has increased significantly since 1970. The
federal deficit increases most rapidly during economic downturns. This happens as a
natural consequence of federal spending mandates. Recessions mean that workers
lose their jobs. This increases unemployment compensation. Also, the federal
government increases expenditures during recessions to stimulate the economy.
Economic growth generates additional tax revenues and this reduces the deficit. In
general, the government almost always seems to spend more that it collects in
taxes. This causes the almost $20 trillion in borrowing that the US Treasury must
accomplish.
c. How are the graphs of the change in the annual level of debt and the deficit similar?
Illustrate your answer with appropriate graphs.
The change in the debt graphs and the deficit graphs are mirror images of each
other since they are measuring the same thing. The change is the negative of the
deficit. They look a little difference because the change in the debt graph is annual
and the deficit graph is for quarterly data.
2. Treasury Yield Curve. The US Treasury publishes information about yield curves on their
website. Use this chart to answer the following:
a. Explain how the US Treasury constructs their yield curve chart.
The US Treasury has issued securities which have a big variety of times to maturity.
To construct the yield curve shown on the US Treasury website, it simply finds the
securities whose maturities correspond most closely to 1 month, 3 months, 6
months, 1 year, 5 years, 10 years, 20 years, and 30 years. The yields to maturity of
these securities along with the time to maturity gives the information that is
necessary to construct a yield curve.
b. Explain how the US Treasury yield curve incorporates many of the ideas inherent in
the term structure of interest rates.
The term structure of interest rates holds the following factors constant:
i. Default Risk
ii. Liquidity
iii. Tax treatment
The term structure takes into consideration
i.
ii.
Interest rate risk
Inflation risk
All the securities reported in the Treasury yield curve have the same default risk,
liquidity, and tax treatment. This means that the yield curve reflects interest rate
and inflation risk.
c. Compare today’s yield curve with the one that existed on January 2, 2007 which was
about a year before the Great Recession began.
The yield curve before the Great Recession show high interest rates. The yield curve
was also very flat. We actually say that this yield curve is inverted and it is predicting
the recession.
d. How could you use the US Treasury yield curve chart to determine the expected
rates of inflation?
The YTMs for Treasury Bonds, Notes, and Bills are all nominal interest rates. The
YTMs for TIPS are real interest rates. We can calculate the expected rate of inflation
by simply subtracting the real rates from the nominal rates of Treasuries with similar
maturities.
3. Expected Rate of Inflation from Treasury Bonds and TIPS from Corresponding Bonds. Use
the quotations from the Wall Street Journal to find the current YTM’s for
a. Treasury Bond maturing February 15, 2025. Explain why this is a nominal interest
rate. Why is this bond trading at a premium?
These are nominal interest rates because their face value isn’t adjusted for inflation.
Holding these type of bonds means that investors will receive less buying power
when the bonds maturity than when the bonds were purchased.
There are two Treasuries maturity on February 15, 2025. The bond with a coupon
rate of 7.625% is trading at a premium because the coupon rate exceeds the yield to
maturity. Receiving annual coupon payments of $7.625 per $100 of face value is
much better than $2.30 which corresponds to the market YTM.
The second Treasury has a coupon rate of 2.00% which is less than the market rate.
Therefore, traders don’t want this bond but can be induced to buy it by offering it at
a discounted price. Hence, we see the price of 97.125.
b. TIPS maturing January 15, 2025. Explain why this is a real interest rate. What is this
bond trading at a premium?
The face value of Treasury Inflation Protected Securities is adjusted month for
inflation by using the CPI. The face value of the bond increases enough to keep its
purchasing power constant. Because the coupon payments are the coupon rate
multiplied by the face value of the bond, the coupon payments are also adjusted for
inflation. This means that the rate of return on these bonds is a real rate because it
has been adjusted for inflation.
This bond is trading at a premium because of the high coupon rate of 2.375 which
far exceeds the real YTM of 0.387.
c. Use the Fischer equation to calculate the average expected inflation rate between
now and January\February 2025.
We can calculate the expected rate of inflation by subtracting the real YTM of TIPS
from the nominal YTM of the regular Treasury. In this case, we subtract 0.4% from
2.3% to get and expected inflation rate of 1.9%.
d. How would you calculate the expected average inflation rate between now and
January\February 2045?
We would find a Treasury Bond that matures January\February 2045 and TIPS that
mature in the same time frame. We would then use the Fischer equation as we did
in part (c).