Q4) (1 point) Assume that you observe the following term structure: STRIPS 1-yea

Question

Q4) (1 point) Assume that you observe the following term structure: STRIPS 1-year zero-coupon bond 2-year zero-coupon bond 3-year zero-coupon bond 4-year zero-coupon bond Yield-to-Maturity 4.0% 5.0% 6.0% 7.0% Assume your annual income will be $200,000 two years from now. You think it might be a good idea to save your future income (2 years from now) using today's interest rates, because you find interest rates attractive. A bond broker, who knows that you will make $200K two years from now, is willing to let you short these bonds as long as you can pay back with your income in the future. (a) What is the maximum amount you can borrow today by shorting 2-year zero-coupon bonds? (b) Assume you already have borrowed from (a) to 4 years from now? money as in (a). You plan to use all of your proceeds buy 4-year zero-coupon bonds, and hold them for four years. How much will you get ate in- 2-year" for "l-year-forward-rate and in-"3-year" for "I-year" forward rate. mutile two forward rates and $200.000 and compare with your answer in (b). (c) Calculate

Explanation / Answer

(a) Given for a zero coupon bond: FV (Future Value) = $200,000 , T = 2 years, r = YTM (for 2 years) = 5%,

Then PV (Present Value) = FV/(1+r)T = 200,000/1.052 = 181405.8957

Thus we will receive (by borrowing) maximum of $181,405.90 if we short a bond and pay $ 200,000 in 2 years from now.

(b) Given for a zero coupon bond: PV (Present Value) = $1,81,405.8957 , T = 4 years, r = YTM (for 4 years) = 7%,

Then FV (Present Value) = PV * (1+r)T = 181405.8957 * 1.074 = 2,37,786.1243

Thus our proceeds from the 4 year bond would be $ 2,37,786.12

{Note: Since we will also have to return back $ 2,00,000 after 2 years, our net proceeds (from short 2 year bond & long 4 year bond) would be $ 2,37,786.12 - $ 2,00,000 = $ 37,786.12 }

(c) 1 year forward rate, 2 years from now = f(2,1) can be calculated as-

(1+r3)3 = (1+r2)2 * (1+f2,1)

f2,1 = [(1+r3)3 / (1+r2)2 ] - 1 = [1.063/1.052] - 1 = 8.028662132%

{for above we have used from given table r3=6%, r2=5%}

1 year forward rate, 3 years from now = f(3,1) can be calculated as-

(1+r4)4 = (1+r3)3 * (1+f3,1)

f3,1 = [(1+r4)4 / (1+r3)3 ] - 1 = [1.074/1.063] - 1 = 10.05696061%

{for above we have used from given table r4=7%, r3=6%}

$200,000 * (1+f3,1) * (1+f4,1)  = 200000 * 1.08028662132 * 1.1005696061 = $ 2,37,786.12 (same as the value we get in part b)

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