Week 7 - Fixed-income portfolio management

Question 1

2 relationships between bond price and yield

Answer 1

1. INVERSE relationship
2. CONVEX & diminishing effect
   - effect of price change depends on whether the Y was high or low

Question 2

Forward rates

Answer 2

Rates AGREED TODAY for borrowing/lending in the future
- the forward rate equation should hold due to NO-ARBITRAGE RELATIONSHIP // law of one price

Question 3

What is the Term structure of interest rates?

Answer 3

A plot of zero-coupon yields rt against time to maturity t

Question 4

Explaining Term structure - EXPECTATIONS HYPOTHESIS

Answer 4

Forward rates are UNBIASED predictors {expectation} of FUTURE SPOT RATES
f_s,t = E[r_s,t]

This hypothesis can explain various shapes of the term structure
1.Upward sloping yield curve
- market expects future spot rates to increase compared to today
2. Downward sloping curve
- expects future spot rates to decrease
3. Flat yield curve
- expects future spot rates = current spot rates

Question 5

Explaining Term structure - LIQUIDITY PREMIUM HYPOTHESIS

(also from 2019 paper)

Answer 5

Lenders prefer liquidity (short-term) while borrowers prefer long-term
-> market provides a TERM PREMIUM: long-term bonds offer risk premium over short-term bonds…
… to incentivise lenders to lend money to borrowers for a LONGER TIME
-> HIGHER LONG-TERM RATES

1. this theory can ONLY explain an upward sloping yield curve!
   - Main prediction is we expect an upward sloping TERM STRUCTURE!

Question 6

Explaining Term structure - SEGMENTATION HYPOTHESIS

Answer 6

Every maturity has its own clientele (lender & borrower), and the yield curve is determined by demand for bonds with different maturities.
- There is no explicit relation between short-term and long-term rates

Lenders and borrowers in the long-term are DIFFERENT from those lending and borrowing in the short-term
- hence interest rates are determined by clientele supply and DEMAND for bonds with diff. maturities

1. Can explain any shape of yield curve - upward sloping/downward sloping/flat

Question 7

Modified duration, D*

Answer 7

• gives the APPROXIMATE CHANGE in BOND PRICE
• proportional to the small change
• D* = D/(1+r)

Question 8

Macaulay duration, D (or simply duration)

Answer 8

• WEIGHTED AVERAGE of payment dates
• weighted average of when we get paid by how much we get paid as a proportion of the total payment
• (weights sum to 1)

Question 9

Swaps & Interest rate swaps, specifically

Answer 9

1. An important tool for managing INTEREST RATE RISKS
2. A contract between 2 parties to EXCHANGE their CASH FLOWS in the FUTURE
3. 2 parties agree to exchange a stream of INTEREST PAYMENTS of one type (FIXED / FLOATING) for a stream of payments of another type
   eg. swapping a fixed rate k for a floating rate

Question 10

Why is the duration of a coupon bond lower than maturity?

Answer 10

Because a lot of the cash flows accrue before maturity

Question 11

As coupon rate rises, does duration increase or decrease? Why?

Answer 11

Duration falls as coupon rate rises
- the WEIGHT on the EARLY PAYMENTS is higher

Question 12

As yield rises, does duration increase or decrease? Why?

Answer 12

Duration falls as yield rises
- the value of LATER CASH FLOWS REDUCES by a greater proportional amount by a higher yield
– WEIGHTS of earlier cash flows in the total become greater.