SHOW FORMULAS & WORK !!! For this homework assume that current prices on Zero co
ID: 2790680 • Letter: S
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SHOW FORMULAS & WORK !!!
For this homework assume that current prices on Zero coupon treasury bonds of the following times to maturity (in years) are 98.6 97.0 95.2 93.3 91.3 Question 1. (a) Determine the spot rates based on these prices. That is, find the yield curve for 1,2 3,4 and 5 year ZC bonds based on these prices (b) Determine the forward rates for 1,2,3 and 4 year ZC Bonds, that are implied by the above table to hold i (c) What are the expected prices of 1, 2, 3 and 4 year ZC Bonds in 1 years time? (d) What will be the expected value of this portfolio in one years time based on these forward rates? (e) What are the modifed durations of these bonds in 1 years time? (f) Based on this data, should an investor expect (short-term) interest rates to be lower or higher in 1 years time? If so, by how much on average? one vears time.Explanation / Answer
Time 1 2 3 4 5 Price in $ 98.6 97 95.2 93.3 91.3 Assume that the bond is issued for $100. Since Zero coupon bond it is issued at a discount to par value Zero coupon bond value = face value /((1+rate)^ period) % Yield = [(face value/price)^(1/no of period) -1]*100% 1) Time 1 2 3 4 5 YTM 1.42% 1.53% 1.65% 1.75% 1.84% Here yield is Increasign, so fwd rate and spot rates also increase. Assuming 1.42% as the spot rate then forward rates for 1,2,3 & 4 are calcualted as below. ie. F1 = 1.42% & 2 yr yield is 3.09%. Hence the formula is (1+f1)*(1+f2)=(y2^2) ie. (1+1.42%)*(1+f2)=((1.309^2) Solving f2 we get 4.79% 2) Generalising the formual fn=[((1+YTMn)^n / (1+YTMn-1)^(n-1)]-1 f1=((1.0153^2)/(1.0142^1))-1 === 1.65% f2 =((1.0165^3)/(1.0153^2))-1 == 1.89% f3=((1.0175^4)/(1.0165^3))-1==2.04% f4=((1.0184^5)/(1.0715^4))-1==2.19% f0 f1 f2 f3 f4 1.42% 1.65% 1.89% 2.04% 2.19% YTM 1 =(((1+1.42%)*(1+1.65%))^(1/2))-1 YTM 2 =(((1+1.42%)*(1+1.65%)*(1+1.89%))^(1/3))-1 YTM 3 =((((1+1.42%)*(1+1.65%)*(1+1.89%)*(1+2.04%)))^(1/4))-1 YTM 4 =(((1+1.42%)*(1+1.65%)*(1+1.89%)*(1+2.04%)*(1+2.19%))^(1/5))-1 Price as of Year n = parvalue / ((1+fn)^n) 3) Price as of Year 98.38 $ Price as of Year 96.32 $ Price as of Year 94.12 $ Price as of Year 91.70 $ 4) Cost =98.6+98.38+96.32+94.12+91.7 Cost 479.12 $
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