Assignment 2 International financial market and korean economy Solution

IFM&KE
CAU MBA
Fall 2015

Answers to Problem Set 2
(Due on October 13th, 2015)

1.

Suppose that a Cadillac costs E 45,000 in Germany and that the current USD/EUR
exchange rate is 0.7624. Calculate the dollar price of the Cadillac.

2.

45,000 × 0.7624 = $34,308

Consider the following exchange rates:
EUR/USD = 1.2500 ($/Euro)
USD/CAD = 1.1000 (CAD/$)
EUR/CAD = 1.3550 (CAD/Euro)

How could you use this information to make money in the currency markets?
EUR



USD

×

USD

= 1.25 × 1.10 = 1.375 > 1.3550 = EUR/CAD
CAD
EUR

USD

×

USD CAD
1.375
×
=
>1
CAD 𝐸𝐸𝑈𝑈𝑈𝑈 1.3550

The above calculations tell that we can get arbitrage profits by converting 1Euro as follows.
EuroCADUSDEUR
Hence, the FX markets are not in equilibrium now.
3. Suppose that you took a short position on 12,500,000 Japanese Yen future (remember, a
short position involves selling Yen) at a price of 104.5 Yen/$. If the spot rate on the
contract's expiration date was 103.45 Yen/$, calculate your profit/loss from the futures
contract.

1


IFM&KE
CAU MBA
Fall 2015

This is the case in which Yen is appreciated contrary to your anticipation. Compared with
the current exchange rate, you should sell yen at a cheaper price. So, you will suffer loss
amounting to
USD 1,214.095 = 12,500,000 × (

1
1
−
)
103.45 104.5

4. Suppose that the annualized inflation in the US is 3% while annual inflation in Europe is
1%. If the current exchange rate is $1.40 per Euro, what would you expect the exchange
rate to be in one year? If the exchange rate one year from now turns out to be $1.50 per
Euro, what has happened to the real exchange rate?
From the UIP,

iUS = 𝑖𝑖𝐸𝐸𝐸𝐸𝑅𝑅 +

𝐸𝐸 𝑒𝑒 $ −𝐸𝐸$/𝐸𝐸𝐸𝐸𝐸𝐸
𝐸𝐸𝐸𝐸𝐸𝐸

𝐸𝐸$/𝐸𝐸𝐸𝐸𝐸𝐸

0.03 = 0.01 +

𝐸𝐸 𝑒𝑒 −1.4
1.4

 𝐸𝐸 𝑒𝑒 = 1.428.

Next, the real exchange rate is defined as follows.
𝜀𝜀 =
𝜀𝜀𝑃𝑃𝑈𝑈𝑈𝑈

Rearranging the above, 𝐸𝐸$/𝐸𝐸𝐸𝐸𝐸𝐸 = 𝑃𝑃

𝐸𝐸𝑈𝑈𝑈𝑈

𝐸𝐸$/𝐸𝐸𝐸𝐸𝐸𝐸 × 𝑃𝑃𝐸𝐸𝑈𝑈𝑈𝑈
𝑃𝑃𝑈𝑈𝑈𝑈

. So, assuming there is no change in the price levels of

the two countries, the appreciation (depreciation) of the Euro (USD) exceeding the

expectation (1.50>1.40) is in line with real appreciation (real depreciation) of the Euro(USD).
5. (From the textbook) Consider two countries, Japan and Korea. In 1996, Japan experienced
relatively slow output growth (1%), whereas Korea had relatively robust output growth
(6%). Suppose the Bank of Japan allowed the money supply to grow by 2% each year, whereas
the Bank of Korea chose to maintain relatively high money growth of 12% per year. For the
following questions, use the simple monetary model (where L is constant). It will be easier to
treat Korea as the home country and Japan as the foreign country.
A. What is the inflation rate in Korea? In Japan?
πKor = 𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 − 𝑔𝑔𝐾𝐾𝐾𝐾𝐾𝐾 = 12% − 6% = 6%
πJap = 𝜇𝜇𝐽𝐽𝐽𝐽𝐽𝐽 − 𝑔𝑔𝐽𝐽𝑎𝑎𝑎𝑎 = 2% − 1% = 1%
2


IFM&KE

CAU MBA
Fall 2015

B. What is the expected rate of depreciation in the Korean won relative to the
Japanese yen?
According to the PPP, E𝐾𝐾𝐾𝐾/𝑌𝑌𝑌𝑌𝑌𝑌 =

𝑃𝑃𝐾𝐾𝐾𝐾𝐾𝐾
𝑃𝑃𝐽𝐽𝐽𝐽𝐽𝐽

. Hence,

∆E𝐾𝐾𝐾𝐾

𝑌𝑌𝑌𝑌𝑌𝑌

E𝐾𝐾𝐾𝐾

𝑌𝑌𝑌𝑌𝑌𝑌

Hence, 5% depreciation of Korean Won is expected.

≈ πKor − πJap = 6% − 1% = 5%.

C. Suppose the BOK increases the money growth rate from 12% to 15%. If nothing
in Japan changes, what is the new inflation rate in Korea? Using time series
diagrams, illustrate how this increase in the money growth rate affects the money
supply, Korea’s interest rate, prices, real money supply, and the exchange
rate over time. (Plot each variable on the vertical axis and time on the horizontal
axis.)

πKor = 𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 − 𝑔𝑔𝐾𝐾𝐾𝐾𝐾𝐾 = 15% − 6% = 9%

For diagrams, see Appendix A.

D. Suppose the BOK wants to maintain an exchange rate peg with the Japanese yen.
What money growth rate would the Bank of Korea have to choose to keep the value
of the won fixed relative to the yen?
To keep the exchange rate constant, the Bank of Korea must lower its money growth rate. We
can figure out exactly which money growth rate will keep the exchange rate fixed by using
the fundamental equation for the simple monetary model.
πKor − πJap = (𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 − 𝑔𝑔𝐾𝐾𝐾𝐾𝐾𝐾 ) − �𝜇𝜇𝐽𝐽𝐽𝐽𝐽𝐽 − 𝑔𝑔𝐽𝐽𝑎𝑎𝑎𝑎 � = (𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 − 6%) − 1% = 0

𝜇𝜇𝐾𝐾𝐾𝐾𝐾𝐾 = 7%

Therefore, if the Bank of Korea sets its money growth rate to 7%, its exchange rate with Japan
will remain unchanged.
E. Suppose the Bank of Korea sought to implement policy that would cause the
Korean won to appreciate relative to the Japanese yen. What ranges of the money
growth rate (assuming positive values) would allow the Bank of Korea to achieve
this objective.
Using the same reasoning as previously, the objective is for the won to appreciate:

∆E𝐾𝐾𝐾𝐾

𝑌𝑌𝑌𝑌𝑌𝑌

E 𝐾𝐾𝐾𝐾

𝑌𝑌𝑌𝑌𝑌𝑌

< 0.

This can be achieved if the Bank of Korea allows the money supply to grow by less than 7%
3


IFM&KE
CAU MBA
Fall 2015

each year.

6. (From the textbook) This question uses the general monetary model, in which L is no
longer assumed constant and money demand is inversely related to the nominal interest
rate. Consider the same scenario described in the beginning of the previous question. In
addition, the bank deposits in Japan pay 3% interest.
A. Compute the interest rate paid on Korean deposits.
Fisher effect: iKor − iJap = πKor − πJap iKor − 3% = 6% − 1% iKor = 8%
B. Using the definition of the real interest rate (nominal interest rate adjusted for
inflation), show that the real interest rate in Korea is equal to the real interest rate in
Japan. (Note that the inflation rates you calculated in the previous question will
apply here.)
𝑟𝑟𝐾𝐾𝐾𝐾𝐾𝐾 = iKor − πKor = 8% − 6% = 2%,

𝑟𝑟𝐽𝐽𝐽𝐽𝐽𝐽 = iJap − πJap = 2% − 1% = 1%

C. Suppose the Bank of Korea increases the money growth rate from 12% to 15% and
the inflation rate rises proportionately (one for one) with this increase. If the nominal
interest rate in Japan remains unchanged, what happens to the interest rate paid
on Korean deposits?

We know that the inflation rate in Korea will increase to 9%. We also know that the real
interest rate will remain unchanged. Therefore: iKor = 𝑟𝑟𝐾𝐾𝐾𝐾𝐾𝐾 + πKor = 1% + (6% + 3%) =
10%

D. Using time series diagrams, illustrate how this increase in the money growth rate
affects the money supply, Korea’s interest rate; prices, real money supply; and
the exchange rate over time. (Plot each variable on the vertical axis and time on
the horizontal axis.).

See the Appendix for diagrams.

4


IFM&KE
CAU MBA
Fall 2015

<Appendix>
Diagrams for Q5-C

5


IFM&KE
CAU MBA
Fall 2015

Diagrams for Q6-D

6