In your calculations, please round computed prices to the second decimal place (
ID: 2719238 • Letter: I
Question
In your calculations, please round computed prices to the second decimal place (e.g., 220.78 instead of 220.7765). A risk-free annuity A pays two annual payments of $100 (the first payment is made in a year). If the term structure of interest rates is flat and the interest rate is 61.80%/year, what is the price of the annuity? What is the yield to maturity of the annuity? The term structure suddenly changes and now the spot interest rate for one year (r1) is 80%/year and the spot interest rate for two years (r2) is 50%/year. As it turns out. the price of the annuity stays the same as in part (a). What is the yield to maturity of the annuity now? Suppose that there are two annuities on the market: annuity A from before and annuity B, which will make 3 annual payments of $100, with the first payment in one year. The price of annuity B is $100. Is there an arbitrage opportunity here? If so, create a table that presents the cash flows of your trading strategy to take advantage of tills arbitrage opportunity. Your trading strategy should only use annuities A and B.Explanation / Answer
a) Price of Annuity = R [(1+i)*n - 1] /i
= 100 [(1+.6180)*2 - 1] / .618 0
= 261.80
b) Yeild to maturity = Interest / price of bond
= 61.8 / 261.8 = 23.6%
c) (1 + s1) * (1 + f) = (1+ s2)*2
= ( 1 + .8) * ( 1 + f) = ( 1 + .5)*2
= 25%