Session 8 - Fixed Income (II)

Question 1

Describe the major type of yield curves

Answer 1

• yield curve = representation of the yields available to investors at different maturities within the market
• three types of curves: spot, forward, and par

Question 2

Definition of the carry trade

Answer 2

• borrowing at the lower interest rate and investing at the higher interest rate
• earn the spread

Question 3

Exploit a stable upward sloping yield curve of one currency Intramarket with

Answer 3

a Buy a bond and finance it in the repo market.
b Received fixed and pay floating on an interest rate swap.
c Take a long position in a bond (or note) futures contract

Question 4

Exploit a stable upward sloping yield curve of two currency Intermarket with

Answer 4

a. borrow in the lower rate currency, exchange to higher rate currency, invest the higher rate currency
b. enter currency swaps, receive higher currency, pay lower rate currency
c. borrow in the higher rate currency, invest higher rate currency, convert the financing position to the lower rate currency via the FX forward market

Question 5

Carry Trade with upward sloping yield curves / steep market

Answer 5

• invest in the long end and borrow at the short end on the relatively steep curve
• receive fixed and pay floating
• take a long position in the bond/note future

Question 6

Carry Trade with upward sloping yield curves / steep market

Answer 6

• borrow at the long end and lend at the short end
• pay fixed and receive floating
• take short future positions

Question 7

Explain why a fixed-income portfolio manager might choose to alter portfolio convexity

Answer 7

• sell convexity if believe no movement in the yield curve, increase yield
• increase/long convexity if believe huge movement but not sure what direction, giving up yield
• • to benefit from convexity, decline/increases in yield must occur within a short window of time as the lower yield creates a drag on yield and the yield sacrificed can be larger than the price effect

Question 8

Explain how a fixed-income portfolio manager might choose to alter portfolio convexity

Answer 8

• buying and selling options
• when the UL price decrease, the option value decrease at a slower rate than the UL
• when the intrinsic value reaches 0, UL’s price will not affect the option’s value
• when the UL price increase, increases at a similar rate as the UL

Question 9

Formulate a portfolio positioning strategy given forward interest rates and an interest rate view

Answer 9

1. Parallel Upward Shifts in the Yield Curve
2. Changes in interest rates, direction uncertain
3. Duration - Neutral Bullets, Barbells, and Butterflies
4. Using Options

Question 10

Expand on Parallel Upward Shifts in the Yield Curve

Answer 10

• if expect stable yield curve, one will own as much of the longer maturity as possible
• expect parallel shift, one would choose the bond that offers the highest return given the change in yields

Question 11

Expand on Changes in interest rates, direction uncertain

Answer 11

• if expect huge movements and direction not sure, increase convexity
• sell convexity if the stable yield curve

Question 12

Expand on Duration-Neutral Bullets, Barbells, and Butterflies

Answer 12

• in a parallel shift, more convexity portfolio (barbell) > less convexity (bullet) portfolio
• flattening, barbell > bullet
• steepening, bullet > barbell
• long wings + short body for more volatile environments
• short wings + long wings for more stable environments

Question 13

Definition of duration neutral weight for butterfly

Answer 13

• duration of the wings = duration of body
• MV of the wings = MV of the body (also $duration neutral)
• 50/50 shorting the body and allocating the proceeds to equal long positions in each wing

Question 14

Expand on using Options

Answer 14

• reduce convexity by selling options or buying MBS
• • sell convexity if the view = stable yield
• • short maturity at or near the money options has the most convexity

Question 15

Evaluate a portfolio’s sensitivity to a change in curve slope using key rate durations of the portfolio and its benchmark

Answer 15

• curve = steeper and less curvature, –> portfolio with more partial duration at the intermediate maturities and less partial duration at the shorter and longer maturities (more bullet structure)
• curve = flatten and more curved, –> portfolio with more partial duration at the shorter and longer maturities and less partial duration at the intermediate maturity (more barbell structure)
• Predicted change = Portfolio par amount × Partial PVBP × (–Curve shift)

Question 16

Discuss inter-market curve strategies

Answer 16

• Intermarket trades involve more than one yield curve and require investors to accept or hedge currency risks
• inter-market asset decisions made on the basis of prospective hedged returns (based on forward FX rates rather than projected spot FX rates)
• • When all assets are hedged into a common currency, the portfolio’s base currency becomes irrelevant for inter-market decisions

Question 17

Under what conditions would two markets share a yield curve? And what does it mean if it doesn’t?

Answer 17

1. Perfect Capital Mobility between the markets so that risk-adjusted expected return will be equalized
2. The Exchange Rate will be fixed forever
   - - investors must believe there is no risk that the currencies will exchange at a different rate in the future

• Or else:
• yield differentials will emerge and lead to differential risk and return expectations in the two markets and allowing each market to trade on its own fundamentals

Question 18

What does Covered Interest Arbitrage imply?

Answer 18

• each of the bond’s cash flows was hedged in the forward FX market to the date it will be received, then exposure to both the foreign yield curve and the foreign currency will have been eliminated
• cash flows from the foreign bond and its hedges will behave as if the foreign bond were denominated in the domestic currency and trading off the domestic yield curve”

Question 19

Construct a duration-neutral government bond portfolio to profit from a change in yield curve curvature (extreme bullet, barbell, less extreme barbell)

Answer 19

• extreme barbell - consists of 2 bonds which are the shortest maturity and longest maturity bond, weighted to get the same effective duration as the benchmark portfolio
• • outperform in a parallel move, flatten slope change, increased curvature, increase rate volatility
• extreme bullet - consist of two bonds (with target durations that are the closest to the BM duration) or with one bond if there is a bond with duration = BM duration
• • outperform in steepening, loses/decrease curation (as middle perform well when losing curvature), decrease interest rate volatility
• less extreme barbell consists of four securities instead of two, having some exposure to the middle of the yield curve
• • when the risk of underperformance of the extreme barbell is too high during steepening and less curvature scenarios

Question 20

Evaluate the expected return and risks of a yield curve strategy.

Answer 20

• Expected returns can be decomposed into
  1) yield income
  2) rolldown return
  3) Expected changed in price based on investor’s views of yields and yield spreads
  4) Expected change in credit losses
  5) Expected currency gains or losses (usually given)
• • yield income and rolldown return do not contribute to risk since they can be determined with certainty in advance

Question 21

What would a negative yield mean?

Answer 21

• may start seeing new-issue bond with a negative coupon
• If the coupon rate is negative, we now have two- way credit exposure—the bond owner now owes regular payments to the issue
• the modified duration on those bonds will be larger than the maturity