We observe the following annualized yields on four Treasury securities: The par
ID: 2612514 • Letter: W
Question
We observe the following annualized yields on four Treasury securities:
The par is $1000 for all the securities. The one with 0.5- year to maturity is a zero coupon bond. All other securities are coupon-bearing bonds selling at par. Note that, for par bonds, the coupon rate equals YTM.
1. Calculate the sport rates for the maturities of 0.5, 1, 1.5, and 2 years
2. What is the price of a 2-year bond with an 8% annual coupon rate (assume $1000 par)?
3. Suppose a 1-year zero-coupon bond with a par value of $1000 is selling at $900. Is there any arbitrage opportunity? If there is, construct an arbitrage portfolio and show the profit.
4. Calculate the one-period-ahead forward rates from 0 to 0.5, from 0.5 to 1, from 1 to 1.5, and from 1.5 to 2.
5. One year from now, you plan to purchase a then one-year bond with a 1000 par and an 8% annaul coupon rate. Waht is the expected price of the bond? Assume the expectation hypothesis holds. Under the expectation hypothesis, the expected future spot rate equals the forward rate.
*** Show All Work ***
Explanation / Answer
Answer 2
Answer 3
Yield from bond= (1000-900)/900=11.11%
Borrow money from market at price less than 11.11% say 10%
At maturity Redeem Bond=1000
Pay Borrowing with interest=900*1.10=990
Risk free return = 1000-990=10
Answer 4
Forward Rate=((1+Long Period Rate)^No of Long Period)/(((1+Short Period Rate)^No of Short Period)
Answer 5
B1=80/(1+0.08)+1000/1.08
=74+926
=1000
B0=1000/1.08=925.925
Spot Rates for the maturity 2*((1+yield on annual bond)to the 0.5 power-1) Maturity Yield Working Rate 0.5 4% 2*((1.02)^(1/(2*0.5))-1) 4.00% 1 4.50% 2*((1.045/1000)^(1/(2*1))-1) 4.45% 1.5 5% 2*((1.05)^(1/(2*1.5))-1) 3.28% 2 5.50% 2*((1.05)^(1/(2*2))-1) 2.45%Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.