Seminar 5 solutions
1. Read the following article and answer the following questions:
Which yield curve is higher in the US (2-year or 10-year) and why?
What signals about the future of the US economy do we get from yield curves?
For more details read also this article.
2. Suppose the market price of a 20-year pure discount bond with a face value of $1,000 is
$214.55. What is the spot interest rate for the 20-year maturity expressed in percentage per
annum?
Answer:
We know that the relationship between the price of a pure discount bond and the spot interest rate
at the 20/year maturity satisfies
Substituting the price of $214.55 and solving for i(t,20), we find
Therefore, the spot interest rate for the 20-year maturity expressed in percentage per annum is 8%.
3. Consider a 2-year euro-denominated bond that has a current market price of €970, a face
value of €1,000, and an annual coupon of 5%. Suppose the 1-year euro-denominated spot
interest rate is 5.5%. What is the 2-year euro-denominated spot interest rate?
Answer: The present value of a coupon paying bond is found by discounting each annual coupon
and the final principal payment at the appropriate spot interest rates for those maturities. Thus, to
find the 2-year euro-denominated spot interest rate we must solve for the two-period spot interest
rate in the following equation:
The answer is i(t,2) = 6.68%.
4. What should be the 2-year forward rate to prevent arbitrage? The spot exchange rate is
¥132.192/£.
U.K. Japan
1 year 1.105 0.370
2 year 1.770 0.430
What should be the 2-year forward rate to prevent arbitrage?
Answer:
FW = 132.192 x (1+ 0.00430)2
/ (1+0.0177)2.
= 127. 7435
( )
20
$1,000
P(t) =
1 + i(t,20)
1/20
$1,000
i(t,20) = - 1 = 0.08
$214.55
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ê ú
ë û
( )
2
€50 €1050
€970 = +
1.055 1+i(t,2)
5. Please, try to calculate EUR/USD 2 year forward rate based on the current market data.
Find the current EUR/USD spot rate, Germany 2-Year Bond Yield and U.S. 2 Year Treasury
Note. Compare your result to market forward rate.
Answer:
Spot rate EUR/USD 0.9753
2-year German bond yield 1.844
2-year US bond yield 4.47%
FW price 1.0568
FW points 431.59 indicate EURUSD 1.0185