Problem Set #1 SOLUTIONS
Prof. Wade Pfau
1. Rank the following assets from most liquid to least liquid. Provide a brief explanation
to explain your rankings.
a. checking account deposits
d. Washing machines
e. stocks from stock market
Most liquid to least liquid: a, c, e, d, b
It is okay if you switched the order of (a) and (c). Checking accounts are considered the
most liquid because it is easier to pay a large sum of money by check than by currency.
But currency is also quite liquid. Next, stocks are the easiest to sell in order to obtain
liquidity (just call your stock broker). Next, usually a washing machine would be easier
to sell in order to obtain liquidity than a house would be.
2. In ancient Greece, why was gold a more likely candidate for money than wine?
Wine is more difficult to transport than gold and is also more perishable. Gold is thus a
better store of value than wine and also leads to lower transaction costs. It is therefore a
better candidate for use as money.
3. a. What is the yield to maturity on a $1,000 face value discount bond maturing in one
year that sells for $750?
b. What is the yield to maturity on this same $1,000 face value discount bond if it
does not mature for two years and it sells for $750?
c. What is the intuition explaining why the yield to maturity is different in these two
(a) We can use our present value formula. The future value in one year is the face value
of the bond: $1,000. The present value is the price the bond is selling for: $750. The
length of time is one year:
PV = FV / (1+i)^n
750 = 1000 / (1+i)
i = 1000 / 750 – 1 = .3333 = 33.33%
(b) The length of time has increased to two years:
750 = 1000 / (1+i)^2
1+i = sqr (1000/750)
i = sqr(1000/750) – 1 = .1547 = 15.47%
(c) In both cases, the buyer pays $750 for a discount bond that will eventually return
$1,000. But in the second case, the buyer has to wait for two years to receive this
payment. This extra year of waiting lowers the yield to maturity (interest rate) received
for each year, because there are now two years for interest to accumulate.
4. Suppose the interest rate in the economy is 10%.
a. Calculate the present value of a security that pays you $550 next year, $605 the
year after, and $665.50 the year after that.
b. If this security is sold to you for $1,750, is the yield to maturity greater or less than
c. Assuming that you are looking to spend your money on a security, would you be
willing to buy this security for $1,750? Why?
d. Instead of 10%, what would the interest rate have to be in this economy to
convince you that spending $1,750 on this security is a good deal?
(a) PV = 550 / (1 +.1) + 605 / (1+.1)^2 + 665.50 / (1+.1)^3
PV = $1,500
(b) The price of the security is higher than the present value, so the yield to maturity is
(c) No, you should not be willing to buy this security for $1,750. Your yield to maturity
would less than the 10% that you could earn by purchasing a newly issued bond that has
the market interest rate of 10%.
(d) Now we know the present value ($1,750) but want to find the yield to maturity (i)
1750 = 550 / (1 +i) + 605 / (1+i)^2 + 665.50 / (1+i)^3
using a guess and check method: i = 1.95%
In order to convince you to spend $1,750 for this security, the interest rate in the
economy would have to be less than or equal to 1.95%.
5. If there is an increase in interest rates, which would you rather be holding, long-term
bonds or short-term bonds? Why? Which type of bond has the greater interest
When there is an increase in interest rates, you are better off holding short-term bonds.
The present value will fall more drastically for long-term bonds, leading to a much
smaller rate of return. With higher interest rates, you want to be able to buy new bonds
that offer the higher interest rates and not be stuck with long-term bonds offering the
lower interest rates. For these reasons, long-term bonds have more “interest rate risk.”
6. Read the following part of an article from Bloomberg.com on October 22, 2003.
Underline the statements in the column that explain bond price movements and draw the
appropriate supply and demand diagrams that support these statements.
U.S. Treasuries Advance on Indications That Growth
Rate Isn't Sustainable
Oct. 22 (Bloomberg) -- U.S. Treasuries rose for a fourth day in Asia on speculation the economy is
unlikely to create enough jobs to sustain the pace of growth.
Initial claims for jobless benefits were little changed at 385,000 last week, figures tomorrow will
probably show, according to the median forecast of 39 economists surveyed by Bloomberg News. A
Conference Board index of leading economic indicators in September fell for the first month since
The 4 1/4 percent note maturing in August 2013 rose 1/8, or $1.25 per $1,000 face amount, to 99
11/32 at 1:08 p.m. in Tokyo, pushing the yield down 1 basis point to 4.33 percent from as high as
4.47 percent Thursday. The yield on the 1 5/8 percent note due in September 2005 declined 2 basis
points to 1.82 percent. A basis point is 0.01 percentage point.
``We are bullish on bonds,'' said Tokyo-based Kazuyuki Takigawa, who helps oversee $913 million
of debt at Fuji Investment Management Co., a unit of Mizuho Financial Group Inc., Japan's largest
lender. ``The growth that appeared in the last quarter will not be sustained. It will slow down'' and
10-year yields ``will go down towards 4 percent.'' …
The situation here is that the growth rate will not be sustained, which means that stocks
could not be expected to do as well. Thus the relative return of stocks compared to bonds
falls and so bonds become more attractive. This increases the demand for bonds, which
increases the price of bonds and decreases their yield to maturity. Any possible decrease
in the supply of bonds, which could occur because of fewer investment opportunities,
would contribute to the same effect.
Note, the interpretation of the information about Bond #1: It matures in August 2013. It
is a 4.25% note, which is in terms of its face value. It rose 1/8, which means that its price
rose by 1/8 out of $100, or 10/8 out of $1000, or $1.25 per $1000 face value. The price
rose to 99 11/32, or $99.34 per $100 of face value. Thus, the yield drops.
7. Here is part of an article entitled “Japan Ministry Hopes Bond Sales Won’t Jolt
Market” by Asako Tanabe from The Asian Wall Street Journal on October 21, 2003:
“Japan will attempt to place a record 120 trillion yen ($1.097 trillion) of government
bonds in financial markets during the fiscal year starting April 1, requiring the Ministry
of Finance to plan its move carefully to avoid disrupting the market, analysts say…. ‘The
[Ministry of Finance] will talk with the market so the issuance won’t be surprising,’ said
Shuichiro Natori, economist at Mizuho Research Institute. ‘The MOF wants to avoid
causing [bond prices] to drop sharply.’”
Use supply and demand diagrams to explain why bond prices could drop sharply with
such a situation. What could happen to interest rates in such a situation?
An increase in supply of bonds could lower their price and increase interest rates.
8. Why might giving politicians a larger role in central bank operations lead to a stronger
political business cycle?
Politicians interested in achieving re-election will be more likely to use expansionary
economic policies prior to an election which will require contractionary economic
policies after the election to lower inflation. This could lead to more ups and downs in
the business cycle.
9. How independent from politicians do you think the central bank in your home country?
Or are there special circumstances that make this question hard to answer?
A variety of unique answers are possible
10. If the Federal Reserve sells $2 million of bonds to the First Commercial Bank, what
happens to reserves and the monetary base? Use T-accounts to explain your answer.
Reserves and the monetary base fall by $2 million, as the following T-accounts indicate:
First National Bank Federal Reserve System
Assets Liabilities Assets Liabilities
Reserves –$2 million Securities –$2 million Reserves –$2 million
Securities +$2 million
11. Why might the procyclical behavior of interest rates (rising during business cycle
expansions and falling during recessions) lead to procyclical movements in the
The rise in interest rates in a boom increases the cost of holding excess reserves and
the incentives to borrow from the Fed. Therefore, e falls, which increases the amount
of reserves available to support checkable deposits, and the volume of discount loans
increases, which raises the monetary base. The result is a higher money supply
during a boom. Similarly, when interest rates fall during a recession, the money
supply also has a tendency to fall because e rises and the volume of discount loans
12. Bank reserves are a liability of the central bank, but they are an asset of a private
bank. Why is this?
When a private bank holds reserves, it is holding a financial claim against the central
bank. Thus, the reserves represent assets of the private bank. On the other hand, the
central bank is obliged to accept reserves as payment and the reserves represent
something the central bank owes to the private bank. Thus, reserves are a liability of
the central bank.
13. Suppose that the required reserve ratio is a constant fraction of deposits, r. Suppose
also that the currency depositors hold grows steadily with the amount of their
deposits, such that c = C/D. Also, suppose that the amount of excess reserves a bank
holds is inversely related to the ratio of bank deposits to currency, such that e =n(
D/C ), where n is a constant scaling term. In other words, suppose that as people
hold more currency relative to their deposits, banks feel more comfortable that
depositors will not withdraw a lot of currency and so decide to hold fewer excess
reserves. Find an expression for the money supply’s money multiplier in terms of r,
n, and c. Show your calculations to receive full credit.
First let us write out some of the definitions we know.
The money supply can be written as:
M = m ⋅ MB or M = D + C
and the monetary base is: MB = R + C
we also know that R = RR + ER and RR = r ⋅ D and ER = e ⋅ D
C D n
and we defined c and e as c = and e = n =
D C c
using these definitions, we can obtain an express for MB:
MB = R + C
= RR + ER + C
D + c⋅D = r + + cD
Then, D = and since M = D + C = D + c ⋅ D , we get:
MB 1 + c
+ c = MB and thus we have our multiplier.
r+ +c r + +c
n n n
c c c
14. If a central bank has an interest-rate target, why will an increase in money demand
lead to an increase in the money supply? Illustrate your explanation with a supply-
An increase in money demand will create
upward pressure on the interest rates. The
only way to maintain an interest-rate
target is to further increase the money
supply to match the increase in money
demand. The central bank could buy
bonds, which bids up their price and
lowers their yield to maturity, helping to
get interest rates back down to the desired