8. Managing Bond Portfolios

Question 1

YTM

Answer 1

YTM assumes that all coupons can be reinvested at YTM rate, takes into account expected drop/rise in price

Question 2

Current yield

Answer 2

Annual coupon / bond price

If coupon rate > current yield > YTM, bond is trading at premium

Question 3

Realised yield

Answer 3

Not equal to YTM if hold to maturity, depends if you reinvest and at what rate

Question 4

Yield

Answer 4

Yield is only thing that is not fixed, but varies with market.

Question 5

Duration

Answer 5

Effective maturity (average of maturities of all CF’s, each payment has own maturity) or interest-rate sensitivity

Question 6

Interest rate sensitivity

Answer 6

Price changes proportionally to duration, high duration is risky.

1. Prices and yields are inversely related: yields increase -> bond prices fall
2. Price curve is convex: increase in bond’s YTM -> smaller price change than decrease in yield of equal magnitude
3. Prices of LT bonds are more sensitive to interest rate changes than of ST bonds
4. As maturity increases, price sensitivity increases at decreasing rate
5. Duration is inversely related coupon rate: if coupons are high -> duration is low (lot of weight on first years)
6. Duration is inversely related to yield: higher yield -> less weight for later payments -> lower
   duration

Question 7

Pension funds

Answer 7

Have liabilities similar to bond (difference: pension payments are not fixed), all future cash outflows discounted

Question 8

Coverage ratio

Answer 8

(A/L) is most important measure, decreases if yield drops -> pension funds want low duration liabilities (less sensitive to change in yield)

Question 9

Like bond

Answer 9

Get money now and payout in future.

Discount rate (yield) is important in determining value of liability (yield ↓, liability ↑ a lot)

Not possible to match, since duration is higher than longest zero-coupon bond (30 years)

Question 10

Price change in duration

Answer 10

Proportional to duration, not to maturity

Question 11

Modified duration

Answer 11

• For small changes in yield, approximation of duration is good
• Overestimation of losses and underestimation of gains -> good for bondholder

Question 12

Correction for convexity

Answer 12

• For small changes, convexity part close to zero

- ∆𝑦 and convexity always positive, so conservative

Question 13

Rules for duration

Answer 13

1. Duration zero-coupon bond = time to maturity (all weights on payoff last payment)
2. Duration is higher when coupon rate is lower
3. Duration is higher with longer time to maturity
   - Exception: deep discount bond duration does not increase with maturity
4. Duration is higher when YTM is lower (more weight on earlier payments)
5. Duration of perpetuity = 1+𝑦 / 𝑦

Question 14

Callable bonds

Answer 14

Negative convexity (concavity), ceiling on bond’s market price (cannot rise above call price

Question 15

MBS

Answer 15

Negative convexity, based on portfolio of callable amortising loans (home owners have right to refinance at any time)

Call price isn’t as ceiling, home owners won’t directly refinance when yield is below rate

Question 16

Tranches

Answer 16

Underlying mortgage pool is divided into set of derivative securities (short-term payment is safest, long-term is riskiest)

• Nobody knew what was in the pool of mortgages (loss of transparency)
  + Able to pool risk

Question 17

Passive management

Two strategies that see market price as being correct, but have very different risks:

Answer 17

1. Indexing (hold index of bonds)

2. Immunization (hedge away pre-defined risk)

Question 18

Indexing (hold index of bonds)

Answer 18

a. Difficult because compositions changes continuously (bonds expire)
b. Stratification of bonds into cells (term and bond): is a simplification
i. Disadvantage: you don’t buy bond that’s on your balance sheet, there might be other risks that are not reflected (currency risk, default risk)

Question 19

Immunization (hedge away pre-defined risk)

Answer 19

Matching interest rate exposure of assets and liabilities (duration matching), price risk and reinvestment rate risk exactly cancel out

a. Sell asset if bond that has to be paid back matures. If yield drops, reinvestment return is lower, but price of bond increases. Always get same value (risks cancel out). Actually, little bit more value, because convexity of coupon bond is higher than convexity from zero-coupon bond.

Result: value of assets will track value of liabilities whether rates rise or fall. Yield increases -> drop in price, but higher reinvestment rates makes up for this.

b. GIC: guaranteed investment contract (has guaranteed interest rate)

Question 20

Active investment strategy

Answer 20

Achieve returns greater than commensurate with risk borne.

1. Use interest rate forecasts to predict movements in entire bond market.
2. Some form of intramarket analysis to identify particular sectors of market or particular bonds that are relatively mispriced.