Question

please show work! ASAP!

Question 3. Simple Bootstrapping You have fives bonds as shown in the below. Three are zero coupon bonds and the other two are coupon bonds. By applying bootstrapping you would like to compute each spot rate for each bond and figure out the spot rate curve. Bond Coupon Zero Rates Principal 100 100 Maturity 0.25 0.50 1.00 OO 100 1.50 2.00 FERUAWN- Bond Price 97.5 96.9 95.0 94.7 100.6 100.9 101.3 101.9 102.3 102.6 103.5 2.50 3.00 3.50 ees 400 12.4 a. Compute the spot rate using the bootstrapping method. b. Draw the yield curve of spot rates (i.e. term structure of spot rates). c. Is that an upward slope or downward slope? d. What is the spread between a 5 year bond rate and a 6month yield? e. Based on the answer of d, do you think the slope is steep? If yes, why? If not, why not?

can you please help me out? I can't figure out.

Answer 1

a. Computation of spot rate using bootstrapping method:

Present Value = Future Value/(1+Interest Rate)^Period

Where, Interest rate is the Yield or the "Spot Rate"

Therefore, 97.5 = 100/(1 + Yield)^0.25

(1 + Yield) ^ 0.25 = 1.025641

(1 + Yield) = 1.025641 ^ (1/0.25)

1 + Yield = 1.106577

Therefore, Yield or Spot Rate = .106577 or 10.6577%

Refer attachment following screenshot for the rest of the yields.

X fac =(C8/C4)^(1/03)-1 C D E F G H I J K L M 0.00% 12.40% 15.00% PARTA Coupon (X) Maturity (Y) Bond Price (Z) 0.00% 0.25 97.5 0.00% 0.5 96. 9 8.00% 1.5 94.7 9.00% 2 100.6 9.50% 2.5 100. 9 10.20% 3 101.3 11.80% 3.5 101.9 13.60% 4.5 102.6 9 5 102.3 103.5 100 100 100 Principal (A) Total Interest (B) = (X)*() * (A) Total Maturity Value (C) = (A) + (B) 100 12.00 112 100 18.00 118 100 23.75 123.75 100 30.60 130.6 100 41.30 141.3 100 49.60 149.6 100 61.20 161.2 100 75.00 175 100 100 100 Yield (C)/(Z)* (1/(Y)) 10.66% 6.50% 5.26% 11.84% 8.30% 8.51% 8.84% 9.79% 9.97% 10.56% 11.08% PART B Yield Curve) 14.00% 12.00% 10.00% 8.00% 6.00% 2.00% 0.00% 1 2 3 4 5 6 7 8 9 10 11

b. Term Structure of Spot Rates:

Refer above screenshot for Yield Curve for all the Bonds above.

c. The Slope is an upward curve.

d. Spread between a 5 Year Bond and a 6-Month Bond:

Yield of 5 Year bond = 11.08%

Yield of 6 Month bond = 6.5%

Spread = 4.58%

e. Steepness of Curve:

Yes the curve is fairly steep. Following are the reasons for the steepness:

1. Higher spreads over longer periods generally reflect higher risk. This is due to the fact that the uncertainty over longer period is much more than the uncertainty during shorter periods.

2. Different credit risks of the underlying borrower could also cause spreads to widen. As the default risk rises for a borrower, the yield will move up.

3. Liquidity can also cause a widening spread between tenures. Investors may tend to buy shorter term bonds when there is expected to be volatility in the markets. This can cause shorter terms yields to move down. But this is a temporary phenomenon.

Refer following screenshot for the formula used.

Calculation.xlsx - Excel 0 x & Share Formulas Data Review View Power Pivot Tell me what you want to do... BSSY Jabe = File Home Insert Page Layout Cut Arial E Copy - Paste B I U O Format Painter Clipboard Font 11 - A A === Wrap Text Η General 0 - Sign in Σ AutoSum : Α Ο Fill - Sort & Find & Clear Filter Select Editing - A Merge & Center - $ % 48.08 Insert Delete Format Conditional Format as Formatting Table Styles Cell Styles Alignment Number Cells B1 - fic PARTA C D E F G 0.09 1 PARTA 2 Coupon (X) 3 Maturity (Y) 4 Bond Price (2) 0.102 0.124 0.15 0 0.5 96.9 0.25 97.5 0.08 1.5 94.7 1 95 3 0.095 2.5 100.9 0.118 3.5 101.9 0.136 4.5 102.6 100.6 101.3 102.3 103.5 100 100 100 6 7 8 Principal (A) 100 Total Interest (B) = (x) * (Y) * (A) =C2°C3*C6 Total Maturity Value (C) = (A) + (B) =SUM(C6:07) 100 =D2 D34D6 =SUM(D6:07) 100 =E2 E3 E6 ESUM(E6:E7) 100 =F2*F3*F6 =SUM(F6:F7) 100 =G2 G3*G6 = SUM(G6:G7) 100 =H2H3*H6 =SUM(H6:H7) =12*13*16 = SUM(16:17) 100 = J2*J3*J6 =SUM(J6:37) 100 =K2*K3*K6 =SUM(K6:7) =L2*L3*L6 =SUM(L6:L7) =M2 M3 M6 =SUM(M6:M7) 10 Yield (C)/(Z)* (1/(Y)) = (C8/C4)^(1/C3)-1 = (D8/D4)^(1/D3)-1 = (E8/E4)^(1/E3)-1 = (F8/F4)^(1/F3)-1 =(G8/G4)^(1/3)-1 =(H8/H4)^(1/H3)-1 =(18/14)^(1/13)-1 =(J8/J4)^(1/J3)-1 =(K8/K4)^(1/K3)-1 =(L8/L4)^(1/L3)-1 = (M8/M4)^(1/M3)-1 11 12 PART B Yield Curve) 16 14.00% 12.00% 10.00% 8.00% 6.00% 4.00% 2.00% 0.00% 1 2 3 4 5 6 7 8 9 10 11 Part A and B + 1 Ready @ J -- + H 4:27 PM A x 28/03/2020 19