Fixed Income Portfolio Management

Question 1

Discuss the criteria for selecting a benchmark bond index.

Answer 1

1. Market value risk varies directly with duration. The greater the risk aversion, the lower the acceptable market risk, and the shorter the appropriate duration of the portfolio and benchmark.
2. Income risk varies indirectly with maturity. The more dependent the client is upon a reliable income stream, the longer the appropriate maturity of the portfolio and benchmark.
3. Credit risk. The credit risk of the benchmark should closely match the credit risk of the the portfolio.
4. Liability framework risk is applicable only to portfolios managed to meet a liability structure and should ALWAYS be minimized.

Question 2

Describe stratified sampling.

Answer 2

Aka cell-matching. The manager first separates the bonds in the index into cells in a matrix according to risk factors, such as sector, quality rating, duration, callability, etc. Next the manager measures the total value of the bonds in each of the cells and determines each cell’s weight in the index. Finally, the manager selects a sample of bonds from each cell and purchases them in a n amount that produces the same weight in the portfolio as that cell’s weight in the index.

Question 3

Describe effective duration.

Answer 3

Effective duration represents the sensitivity of a bond’s (or portfolio’s) price to a 1% change in yield to maturity, a parallel shift in the yield curve. It takes into account changes in expected cash flow due to changes in yield. Due to it’s linear nature it underestimates the increase and overestimates the decrease in the value of the portfolio.

Question 4

Describe key rate duration.

Answer 4

Where as effective duration measures the portfolio’s sensitivity to parallel shifts in the yield curve, key rate duration measures the portfolio’s sensitivity to twist in the yield curve.

Question 5

Describe the Present value distribution (PVD) of cash flows.

Answer 5

PVD measures the proportion of the index’s total duration attributable to cash flows (both coupons and redemptions) falling within selected time periods.
1. Determine the PV of cash flows for every 6-month period.
2. Divide each PV by the PV of total cash flows from the benchmark to determine the percentage of the index’s total market value attributable to cash flows falling in each period. This will be the the weights of each period.
3. The Cash flow in each 6-month period can be considered a zero coupon bond with their duration being the end of the period.
4. Multiply the duration of each period by its weight to arrive at the duration contribution.
5. The duration contribution for each period is divided by the index duration. (i.e., the sum of all the periods’ duration contribution).
Thje resulting pattern across the time periods is the index’s PVD. If the manager duplicates the index PVD, the portfolio and the index will have the same sensitivities to both shifts and twists in the yield curve.PVD effectively describes how the total duration of the index (i.e., benchmark) is distributed across its total maturity.

Question 6

What is Classical Immunization?

Answer 6

The process of structuring a bond portfolio that balances any change in the value of the portfolio with the return from the reinvestment of the coupon and principal payments received throughout the period. The goal of classical immunization is to form a portfolio so that;

• If interest rates increase, the gain in reinvestment income >= loss in portfolio value.
• If interest rates decreases, the gain in portfolio value >= loss in reinvestment income.

To accomplish this we use effective duration.

Question 7

What are components of interest rate risk?

Answer 7

1. Price risk
2. Reinvestment risk
   It is important to note that price risk cause opposite effects. That is, as interest rates increase, prices fall but reinvestment rates rise.

Question 8

How do you effectively immunize a single liability?

Answer 8

1. Select a bond (or bond portfolio) with an effective duration equal to the duration of the liability. For any liability payable on a single date, the duration is taken to be the time horizon until payment.
2. Set the present value of the bond (or bond portfolio) equal to the present value of the liability.

The value of the portfolio is only immunized for an immediate, one-time parallel shift in the yield curve (ie.e, interest rates change one time, by the same amount, and in the same direction for all maturities).

Question 9

What does it mean if the duration a portfolio is not equal to the duration of the liability?

Answer 9

• If the portfolio duration is less than the liability duration, the portfolio is exposed to reinvestment risk.
• If portfolio duration is greater than liability duration, the portfolio is exposed to price risk.

Question 10

Why does a portfolio immunized using classic immunization need to be rebalanced?

Answer 10

Classical immunization only works for a one-time instantaneous change in interest rates.

Causes:

1. Passage of time causes the duration of both the portfolio and its target liabilities to change.
2. Interest rates fluctuate frequently, changing the duration of the portfolio and necessitating a change in the immunization strategy.

Classical immunization is not a buy and hold strategy.

Question 11

What is immunization risk?

Answer 11

Immunization risk can be thought of as the relative extent to which the terminal value of an immunized portfolio falls short of its target value as a result of arbitrary (nonparallel) changes in interest rates.

Question 12

What bond portfolio would best minimize immunization risk?

Answer 12

In general, the portfolio that has the lowest reinvestment risk is the portfolio that will do the best job of immunization.

• An immunized portfolio consisting entirely of zero-coupon bonds that mature at the investment horizon will have zero immunization risk because there is zero reinvestment risk.
• If cash flows are concentrated around the horizon (e.g., bullets with maturities near the liability date), reinvestment risk and immunization risk will be low.
• If there is a high dispersion of cash flows about the horizon date (as in a barbell strategy), reinvestment risk and immunization risk will be high.

Question 13

What is the effective duration of a portfolio?

Answer 13

A portfolio’s effective duration is the weighted average of the individual effective durations of the bonds in the portfolio.

Question 14

What is the portfolio dollar duration?

Answer 14

The dollar duration of the portfolio is the sum of the individual dollar durations.

Question 15

How do you rebalance a portfolio to a desired dollar duration?

Answer 15

1. Calculate the new dollar duration of the portfolio.
2. Calculate the rebalancing ratio and use it to determine the required percentage change (i.e., cash needed) in the value of the portfolio.
   2a. The rebalancing ratio equals the old DD divided by the new DD.
   2b. Subtract 1 from the rebalancing ratio to arrive at the necessary increase in value of each bond in the portfolio, and this the total increase in the portfolio value (i.e., required additional cash).

Question 16

Besides the rebalancing ratio, what is another method for returning a bond portfolio back to original dollar duration.

Answer 16

Select the bond in the portfolio with the highest duration and use it as a controlling to position. By using the bond with the highest duration, the manager could use less additional cash by increasing only one bond holding.

1. Calculate the decrease in the portfolio’s DD.
2. Add the change in the portfolio’s DD duration to the controlling position’s dollar duration. This will be the new desired DD of the controlling position.
3. Calculate the required new value of the controlling position by dividing the new desired DD of the controlling position by the current new DD of the controlling position. Multiply that ratio by the current value of the controlling position to get the required new value for the controlling position to have the new desired DD. This increase in the DD of the controlling position will return the portfolio DD back to its original DD.

Question 17

What does the spread duration measure?

Answer 17

Duration measures the sensitivity of a bond to a one-time parallel shift in the yield curve. Spread duration measures the sensitivity of non-Treasury issues to a change in their spread above Treasuries of the same maturity. (Remember that the amount of the spread is a function of perceived risk as well as market risk aversion).

Question 18

What is the nominal spread?

Answer 18

Nominal spread is the spread between the nominal yield on a non-Treasury bond and a Treasury of the same maturity.

Question 19

What is the zero-volatility (or static-spread)?

Answer 19

Zero-volatility spread (or static spread) is the spread that must be added to the Treasury spot rate curve to force equality between the present value of a bond’s cash flow (discounted at the Treasury spot rates plus the static spread) and the market price of the bond plus accrued interest.

Question 20

What is the option-adjusted spread (OAS)?

Answer 20

Option-adjusted spread (OAS) is determined using a binomial interest rate tree.

Question 21

What are the three spread duration measures used for fixed-rate bonds?

Answer 21

1. Nominal spread.
2. Zero-volatility (static) spread.
3. Option-adjusted spread (OAS).

Question 22

What is the spread duration of a portfolio?

Answer 22

The market value-weighted average of the individual sector spread durations.

Question 23

What are the four extensions to classical immunization that attempt to address the deficiencies of classical immunization?

Answer 23

1. Multifunctional duration (a.k.a. key rate duration)
2. Multi-liability immunization.
3. Relaxation of the minimum risk requirement.
4. Contingent immunization.

Question 24

Explain the risks associated with managing a portfolio against a liability structure.

Answer 24

There are three risks that the portfolio manager must be aware of:

1. Interest rate risk - Primary concern. Most fixed income move opposite to changes in interest rates. To help avoid, match duration and convexity of liability and portfolio. Convexity can be difficult to match, especially negative convexity seen in MBS and callable bonds.
2. Contingent claim risk (aka call risk or prepayment risk) - Callable bonds are called when interest rates fall. So there is a potential loss in higher stream of coupons and reinvesting at a lower interest rate. To adjust for this potential convexity must be considered when selecting bonds.
3. Cap risk. - Floating rate bonds may be subject to cap risk.If the coupon on the floating rate bond does not fully adjust upward for rising rates, the market value of the floating rate bond will adjust downward. The assets and liabilities will not adjust in sync and the surplus will deteriorate.

Question 25

Compare risk minimization with return maximization in immunized portfolios.

Answer 25

Risk minimization is one standard condition for classical immunization. It refers to the many tools used to minimize exposure to risk faced when immunizing a portfolio to meet a liability.
Return maximization is the concept behind contingent immunization. Given a manager that has the ability to lock in an immunized rate of return equal to or greater than the required safety net return. If he feels he can generate even greater returns, he should pursue active management in hopes of generating excess value.

Question 26

What is cash flow matching?

Answer 26

Cash flow matching is used to construct a portfolio that will fund a stream of liabilities with portfolio coupons and maturity values. Cash flow matching will also cause the durations to be matched, but it is more stringent than immunization by matching duration. The timing and amounts of asset cash flows must also correspond to the liabilities. Because of this, the durations will stay matched as time passes and rebalancing should not be needed.

Question 27

What are the differences between cash flow matching and multiple-liability immunization?

Answer 27

Cash flow matching is more restrictive, simpler to understand, and safer (though both are very safe when done correctly) but generally makes the purchase price of the required portfolio higher.

Question 28

What are the advantages of combination matching over multiple-liability immunization?

Answer 28

• Provides liquidity in the initial period
• Reduces the risk associated with nonparallel shifts in the yield curve. The initial cash needs are met with asset cash flows. There is no rebalancing needed to meet initial cash requirements.

Question 29

What is the primary disadvantage of combination matching?

Answer 29

It is more expensive.

Question 30

With respect to the investment objectives, compare the use of liabilities as a benchmark vs. a bond index.

Answer 30

The investment objective:
Using liabilities as a benchmark would be to maintain sufficient portfolio value to meet the liabilities.
Using a bond index as a benchmark depends on whether the manager follows a passive or active approach. If passive, it would be to mimic the index. If active, it would be to consistently outperform the index.

Question 31

List the bond portfolio strategies from passive to active.

Answer 31

1. Pure bond indexing (PBI).
2. Enhanced indexing by matching primary risk factors (sampling).
3. Enhanced indexing by small risk factor mismatches.
4. Active management by larger risk factor mismatches.
5. Full-blown active management.

Question 32

What is the equation for the change in value of a bond given the decimal change in interest rates?

Answer 32

-(effective duration)(decimal change in interest rates)(price)

Question 33

What is the equation for the dollar duration?

Answer 33

-(effective duration)(.01)(price)

Question 34

What is the bond rebalancing ratio?

Answer 34

old Dollar Duration / new Dollar Duration

Question 35

What is contingent immunization?

Answer 35

A combination of active management strategies and passive management techniques (immunization). As long as the rate of return on the portfolio exceeds a prespecified safety net return, the portfolio is managed actively.

Question 36

What are the implications of cyclical supply and demand changes in the primary corporate bond market?

Answer 36

Supply and demand analysis can be used to understand bond price and resulting spread changes. Even though it seems counter-intuitive, corporate bonds often perform best during periods of heavy supply. Increases in the number of new corporate bond issues are sometimes associated with narrower spreads and relatively strong returns. Possible reasons: Valuation of new issues validates prices of outstanding issues, relieving price uncertainty and reduces all spreads. Increase in supply attracts attention and could be associated with an even larger increase in demand. That demand raises the corporate bond prices relative to Treasury bonds, resulting in lower relative corporate bond yields and spreads associated with the increase in supply.

Question 37

What is the impact of secular changes in the market’s dominant product structures?

Answer 37

In all but the high-yield market, intermediate-term and bullet maturity bonds have come to dominate the corporate bond market. Callable issues still dominate the high-yield segment, but this situation is expected is expected to change as credit quality improves with lower interest financing and refinancing. There are three implications associated with these product structures:

1. Securities with embedded options may trade at a premium due to their scarcity.
2. Credit managers seeking longer durations will pay a premium price for longer duration securities because of the tendency toward intermediate maturities.
3. Credit-based derivatives will be increasingly used to take advantage of return and/or diversification benefits across sectors, structures, and so forth.

Question 38

What are some of the common rationales why managers actively trade in the secondary bond markets?

Answer 38

1. Yield/spread pickup trades - Pick up additional yield - most common.
2. Credit-upside trades
3. Credit-downside trades
4. New issue swaps
5. Sector rotation
6. Yield curve-adjustment trades
7. Structure trades
8. Cash flow reinvestment trades

Question 39

What is a swap spread?

Answer 39

A swap spread spread is the spread paid by the fixed-rate payer over the rate on the on-the-run Treasury with the same maturity as the swap. Swap spreads are widely used in Europe as an indication of credit spreads.

Question 40

What are the affects of leverage on portfolio duration and investment returns for a fixed-income portfolio?

Answer 40

• As leverage increases, the variability of returns increases.
• As the investment return increases, the variability of returns increases.
• As leverage increases, duration increases, given that the duration of borrowed funds is typically less than the duration of invested funds.

Question 41

What are the factors that affect the repo rate?

Answer 41

1. The repo rate increases as the credit risk of the borrower increases.
2. As the quality of the collateral increases, the repo rate declines.
3. As the term of the repo increases, the repo rate increases. Please note: The repo rate is a function of the repo term, not the maturity of the collateral security.
4. Delivery. If collateral is physically delivered, the repo rate will be lower. If the repo is held by the borrower’s bank, the rate will be higher. If no delivery takes place, the rate will be even higher.
5. Collateral. If the availability of the collateral is limited, the repo rate will be lower. The lender may be willing to accept a lower rate in order to obtain a security they need to make delivery on another agreement.
6. The federal funds rate, the rate at which banks borrow funds from one another, is a benchmark for repo rates. The higher the federal funds rate, the higher the repo rate.
7. As the demand for funds at financial institutions change due to seasonal factors, so will the repo rate.

Question 42

What are the advantages of using futures instead of cash market instruments to alter portfolio risk?

Answer 42

Futures are:

1. More liquid.
2. Less expensive.
3. Make short positions more readily available, because the contracts can be more easily shorted than an actual bond.

Question 43

What is price basis?

Answer 43

Price basis refers to the difference between the spot price and the futures prices delivery.

Question 44

What is Basis risk and why is it important?

Answer 44

Basis risk is the variability of the basis. It is an important consideration for hedges that will be lifted in the intermediate term (i.e., before delivery). Basis can change unexpectedly due to difference in the underlying bond and the futures contract.

Question 45

What are the 3 basic sources of hedging error?

Answer 45

1. Forecast of the basis at the time the hedge is lifted.
2. Estimated durations.
3. Estimated yield beta.

Question 46

What are the drawbacks of Standard Deviation and Variance?

Answer 46

• Bond returns are often not normally distributed around the mean.
• The number of inputs increase significantly with larger portfolios.
• Obtaining estimates for the inputs can be problematic.

Question 47

What is semivariance?

Answer 47

Semivariance measures the dispersion of returns below a target.

Question 48

What are the drawbacks of Semivariance?

Answer 48

• It is difficult to compute for a large bond portfolio.
• If investment returns are symmetric, it yields the same ranking as the variance and the variance is better understood.
• If investment returns are not symmetric, it can be difficult to forecast.
• Because the semivariance is estimated with only half the distribution, it is estimated with less statistical accuracy.

Question 49

Describe the Shortfall risk measure.

Answer 49

Shortfall risk measures the probability that the actual return or value will be less than the target return or value.Shortfall risk is the ratio of number of observations that fall below the target return to the total number of observations.

Question 50

What is the drawback of Shortfall risk?

Answer 50

Shortfall risk does not consider the impact of outliers so the magnitude (dollar amount) of the shortfall below the target return is ignored.

Question 51

What does value at risk (VaR) measure?

Answer 51

The value at risk (VaR) provides the probability of a return less than a given amount over a specific time period.

Question 52

What is the drawback of VaR?

Answer 52

VaR does not provide the magnitude of losses that may exceed the loss specified by VaR.

Question 53

What is the general rule for using futures contracts to control interest rate risk?

Answer 53

Long futures - increase duration

Short futures - decrease duration

Question 54

What are the potential sources of excess return for an international bond portfolio?

Answer 54

1. Market selection.
2. Currency selection.
3. Duration management.
4. Sector selection.
5. Credit analysis.
6. Markets outside of the benchmark.

Question 55

What are the advantages of investing in emerging market debt (EMD) include:

Answer 55

1. Increased quality in emerging market sovereign bonds.
2. Increased resiliency; the ability to recover from value-siphoning events.
3. Lack of diversification in major EMD index offers return-enhancing potential.

Question 56

What are the risks associated with emerging market debt (EMD)?

Answer 56

1. Unlike emerging market governments, emerging market companies do not have the tools to offset negative events.
2. Highly volatile returns with negatively skewed distributions.
3. A lack of transparency and regulations.
4. Underdeveloped legal systems that do not protect against actions taken by governments.
5. A lack of standardized covenants.
6. Political risk.

Question 57

Describe the criteria for selecting a fixed-income manager?

Answer 57

1. Style analysis - The majority of active returns are explained by a manager’s style.
   2, Selection bets - Credit spread analysis and over/under valued securities.
2. Investment process - Investigating the total investment process of the manager.
3. Alpha correlations - Alphas should be diversified. Correlated alphas will lead to significant volatility.

Question 58

How do you calculate the cushion spread in a fixed-income portfolio?

Answer 58

The cushion spread or excess achievable return is the difference between the current immunization rate and minimum acceptable return.