8.1) Term Structure interest rates & Bootstrapping (Chapter 15)

Question 1

What is Term Structure of Interest Rates (TSI)?

Answer 1

The relationship between the yields to maturity and term to maturity of a sample of similar bonds

Question 2

What characteristics of bonds need to be similar for term structure of interest rates? (5)

Answer 2

-risk
-liquidity
-tax rates
-coupon rates
-credit quality

Question 3

Doesn’t need to be similar → time to _________
o Additional ____________that investor want for additional time on securities is the time ____________

Answer 3

maturity
Return
spread

Question 4

What does the ‘time factor’/time premium/ time spread/price of time show?

Answer 4

What the market is thinking of the future of the economy, inflation, future interest rates

Question 5

What bond or category fits the criteria of term structure interest rates? (2)

Answer 5

• Government (The risk factor stays the same with government bonds)
• Zero-coupon bonds (No reinvestment risk and don’t contaminate this pure price of time)

Question 6

What is the importance of TSI? (3)

Answer 6

• Used to extract spot rates* which are applied in:
  o Pricing bonds
  o Extracting forward rates
  ▪ Predict future interest rates and use them to formulate active bond strategies.
  ▪ Predicting future economic activity and make investment decisions
  o Other uses (i.e., estimating inflation, monetary policies)

Question 7

• Shape of curve changes with changes in __________ rates
• Yields generally move together with ______
• Shape of curve is important to _____________ & economists

Answer 7

interest
time
investors

Question 8

What is the meaning of the different TSI yield curves? (4)

Answer 8

• Flat yield curve : Investors want the same return for all instruments.
• Upward-sloping yield curve : Investors want higher return for long-term instruments & lower return for short-term instruments.
• Downward-sloping yield curve : Investors want a higher return for short-term instruments and a lower-return for long-term instruments.
• Hump-shaped yield curve : Investors want a lower return for short & long-term instruments and a higher return for medium-term instruments.

Question 9

What are the two methods of deriving spot rates? (2)

Answer 9

1) Direct observation
2) Bootstrapping

Question 10

how does the direct observation method work? (3)

Answer 10

1) Works if given a pure yield curve, made of stripped treasury zero-coupon bonds
2) YTM of a ZCB is the spot rate
3) Observe bond yields in the TSI → those are your spot rates

Question 11

What are the spot rates and how are they calculated?

Answer 11

The YTM of a Zero-coupon bond is the spot rate

Question 12

What are the characteristics of bootstrapping? (3)

Answer 12

• Only used if not possible to observe the TSI
• Extract spot rates from the dirty curve
• Can’t directly observe spot rates for maturities greater than 1-year and 6 months in South Africa (This is why you have to do bootstrapping)

Question 13

What are the assumptions of bootstrapping? (2)

Answer 13

1) Assumes an efficient market
2) the market price of a Treasury coupon security (bond) should be equal to the value of the package of zero-coupon Treasury securities (bonds) that duplicates the coupon bond’s
cash flows

Question 14

What does bootstrapping assume about an efficient market? (1x2)

Answer 14

• Assumes an efficient market:

1) Market prices for bonds are arbitrage free.
2) Arbitrage free means you cannot make profit from reconstituting or stripping.

(From this assumption you can take the formula and derive the spot rate)

Question 15

What does bootstrapping assume about the market price of a Treasury bond being equal to the value of the package of zero-coupon treasury bonds that duplicates the coupon bond’s cash flows?

Answer 15

Where the yield used for discounting is the spot rate corresponding to the cash flow.

Question 16

Clarify assumtion 2 of bootstrapping

Answer 16

the price of a bond is the present value of its future cash flows, and you can calculate this present value by summing the prices of the corresponding zero-coupon bonds.

rooted in the concept of arbitrage

Question 17

What are the inputs for a 3 ear annual coupon bond (using bootstrapping)? (3)

Note → bootstrapping the spot rates for 3yrs using annual coupon bonds

Answer 17

o 1-year spot rate
o 2-year spot rate
o Price of a 3-year annual coupon treasury bond

Question 18

Price the following bond: 5-year, 8% coupon bond, FV R,1000, discount @ 10% (YTM of similar 5-year
bonds)

Answer 18

Question 19

What are the key assumptions of pricing a bond (recap)? (2)

Answer 19

• Assume a flat yield curve (Yields required by investors are the same for different maturities)
• Assume the bond is viewed as one block of cashflows (Viewed as one instrument)

Question 20

Why are the assumptions of bond pricing flawed? (2x3)

Answer 20

• The curve isn’t flat
  o Investors don’t require the same yield for different maturities
  o Using the wrong discount rate
  o Therefore, mispricing bond (over/under paying & arbitrage opportunities)
• Can break the bond down into multiple pieces (strip the coupons)
  o Best to view bond as a package of cash flows
  o Discount each cf at its unique interest rate that matches its’ time to maturity

Question 21

What is the Arbitrage-Free valuation technique?

Answer 21

Bond pricing technique, in which you view the bond as a pakcage of zero-coupon bonds than can be stripped and sold separately

Question 22

What is the implication of Aribtrage-Free Valuation technique?

Answer 22

The implication is that each ZCB should be discounted separately using a unique YTM to match the time period in which each cash flow will be received

Question 23

True or false, YTM of ZCB = spot rate

Answer 23

True

Question 24

What should the FV of a coupon bond equal?

Answer 24

The FV of a coupon bond should = the value of all the package of ZCBs that duplicates the coupon bond’s cash flow

Question 25

What is the Bond pricing AFV formula?

Answer 25

Question 26

What is the key point of the Arbitrage-Free pricing technique? (2)

Answer 26

• The fair value of a coupon bond (P𝐵) should equal the value of all the package of zero coupons bonds that duplicates the coupon bond’s cash flow.
• If it fails an arbitrage opportunity exists

Question 27

What if the bonds Market Price < AFV price?

Answer 27

Bond is under-priced

Question 28

If the bond is underpriced what can the investor do? (2)

Answer 28

• Bond stripping: Investor can sell the cash flows as individual ZCBs on the market and make a profit
• Buy → Strip → sell
• i.e. a bond is trading at a price of R800. The price based on the AFV is R990
  o Buy bond at R800 → strip the coupons → sell at R990

Question 29

What if the bonds market price > AFV price?

Answer 29

Bond is over-priced

Question 30

If the bond is over-priced what can the investor do? (2)

Answer 30

• Bond reconstitution: Investor can buy the individual ZCBs in the market, reconstitute the
  cashflows into a coupon bond and sell this bond at a profit
• Buy separate ZCBs → reconstitute → sell
• i.e. a bond is trading at a price of R1200, your price based on AFV is R990
  o Buy separate zero-coupon bonds at R990 → Reconstitute the bond → sell for R1 200