Fin 322: Chapter 11 -- Managing Bond Portfolios

Front 1

Macaulay's duration

Back 1

A measure of the effective maturity of a bond, defined as the weighted average of the times until each payment, with weights proportional to the present value of the payment.

Front 2

Modified duration

Back 2

Macaulay's duration divided by 1 + yield to maturity. Measures interest rate sensitivity of bond.

Front 3

Immunization

Back 3

A strategy to shield net worth from interest rate movements.

Front 4

Rebalancing

Back 4

Realigning the proportions of assets in a portfolio as needed.

Front 5

Cash flow matching

Back 5

Matching cash flows from a fixed-income portfolio with those of an obligation.

Front 6

Dedication strategy

Back 6

Refers to multiperiod cash flow matching.

Front 7

Convexity

Back 7

The curvature of the price-yield relationship of a bond.

Front 8

Substitution swap

Back 8

Exchange of one bond for a bond with similar attributes but more attractively priced.

Front 9

Intermarket spread swap

Back 9

Switching from one segment of the bond market to another.

Front 10

Rate anticipation swap

Back 10

A switch made in response to forecasts of interest rate changes.

Front 11

Pure yield pickup swap

Back 11

Moving to higher yield bonds, usually with longer maturities.

Front 12

Tax swap

Back 12

Swapping two similar bonds to receive a tax benefit.

Front 13

Horizon analysis

Back 13

Forecast of bond returns based largely on a prediction of the yield curve at the end of the investment horizon.

Front 14

Even ______ such as Treasury issues are subject to interest rate risk.

Back 14

default-free bonds (What are they also subject to?)

Front 15

Duration

Back 15

A direct measure of the sensitivity of a bond's price to a change in its yield.

Front 16

The proportional change in a bond's price approximately equals the negative of duration times the _____.

Back 16

Proportional change in 1+y. (What should this be multiplied with to get the proportional change in a bond's price?)

Front 17

Immunization strategies

Back 17

Strategies that are characteristic of passive bond portfolio management. They attempt to render the individual or firm immune from movements in interest rates.

Front 18

Immunization strategies can take form of ___.

Back 18

Immunizing net worth or, in stead, immunizing the future accumulated value of a bond portfolio. (What type of strategy does this describe?)

Front 19

Immunization of a fully funded plan is accomplished by matching _____ and ____.

Back 19

the durations of assets, liabilities. (What do these two characteristics accomplish?)

Front 20

To maintain an immunized position as time passes and interest rates change, the portfolio ___.

Back 20

Must be periodically rebalanced. (Why should we periodically rebalance portfolios?)

Front 21

Accounting for convexity can substantially improve on the accuracy of the _____ for bond-price sensitivity to changes in _____.

Back 21

duration approximation, yields. (What concept do these features generally relate to?)

Front 22

Dedication, or Cash flow matching

Back 22

A more direct form of immunization. If a portfolio is perfectly matched in cash flow with projected liabilities, rebalancing will be unnecessary. (What type of matching does this describe?)

Front 23

Active bond management can be decomposed into ____ forecasting techniques and ____ analysis.

Back 23

interest rate, intermarket spread. (What type of management do these two techniques make up?)

Front 24

Active strategies are popularly classified as ____.

Back 24

Substitution swaps, intermarket spread swaps, rate anticipation swaps, or pure yield pickup swaps. (What strategy do these classifications describe?)

Front 25

Macaulay's formula for duration, denoted D

Back 25

D = Σ (T, t=1) t x w(subt)

Front 26

Macaulay's formula for duration written out

Back 26

D = W₁ + 2w₂ + 3w₃ + 4w₄ + ... + Twsubt

Coefficient: time until nth cash flow

wsubn : weight of nth Cash Flow (CF)

Front 27

Proportional change in a bond price can be related to the change in maturity, y, by the mathematical rule:

Back 27

ΔP/P= -D x [Δ(1+y)/1+y]

Front 28

The proportional price change equals the ___.

Back 28

proportional change in (1 + bond’s yield times the bond’s duration) Bond price volatility is proportional the bond’s duration, and the duration becomes a natural measure of interest rate exposure. (What does this measure?)

Front 29

Practitioners often rewrite the bond price proportional change mathematically as ____, defining modified duration as D*=D/(1+y).

Back 29

ΔP/P= -D x Δy

Front 30

The percentage change in bond price is just the product of ___ and the change in the bond's ____.

Back 30

modified duration, yield to maturity.

Front 31

Because the percentage change in the bond price is proportional to modified duration, modified duration is natural measure of the bond's ______.

Back 31

exposure to interest rate volatility. (What type of bond duration is this a natural measure of?

Front 32

Duration

Back 32

Allows us to quantify the sensitivity of Malkiel's bond price relations to enhance the ability to formulate investment strategies.

Front 33

What does the % change in bond value equation assert?

Back 33

This equation asserts that the percentage price change is directly proportional to the change in the bond's yield.

Front 34

The % change in bond value equation suggests a graph of the percentage change in the bond price as a function of the change in its would would plot a straight line, with slope equal to D*. What does this not account for?

Back 34

According to the second of Malkiel's five bond-pricing relationships, bond price and yield relationships are NOT linear. (What is the assumption of the % change in bond value equation?)

Front 35

Convexity equation

Back 35

ΔP/P= -D x Δy + ½ x Convexity x (Δy)^2

Front 36

The duration rule always underestimates the ___ following a change in its yield. What formula remedies this?

Back 36

new value of a bond. The duration approximation for bond price changes, accounting for convexity, changes this. (What rule always underestimates this?)

Front 37

Convexity is more important as a practice matter when ____

Back 37

potential interest rate changes are large. (What concept are these changes more important to?)

Front 38

Convexity is generally considered a desirable trait because ___.

Back 38

bonds with a greater curvature gain more in price when yields fall than they lose when yields rise (This desirable trait is usually found in what concept?)

Front 39

Duration of perpetuity =

Back 39

(1+y)/y

Front 40

Rule #1 of Malkiel's bond price relations

Back 40

The duration of a zero-coupon bond equals its time to maturity. (What rule number of Malkiel's bond price relations is this?)

Front 41

Rule #2 of Malkiel's bond price relations

Back 41

With time to maturity and yield o maturity held constant, a bond's duration and interest rate sensitivity are higher hen the coupon rate is lower. (What rule number of Malkiel's bond price relations is this?)

Front 42

Rule #3 of Malkiel's bond price relations

Back 42

With the coupon rate held constant, a bond's duration and interest rate sensitivity generally increase with time to maturity. Duration always increases with maturity for bonds selling at par or at a premium to par. (What rule number of Malkiel's bond price relations is this?)

Front 43

Rule #4 of Malkiel's bond price relations

Back 43

With other factors held constant, the duration and interest rate sensitivity of a coupon bond are higher when the bond's yield to maturity is lower. (What rule number of Malkiel's bond price relations is this?)

Front 44

Rule #5 of Malkiel's bond price relations

Back 44

The duration of a level perpetuity is (1+y)/y. (What rule number of Malkiel's bond price relations is this?)

Front 45

Duration matching balances the difference between the ____ of the coupon payments (reinvestment rate risk) and the ___ (price risk).

Back 45

accumulated value, sale value of the bond. (What type of matching balances these two features?) When interest rates fall, the coupons grow less than the base case, but the higher value of the bond offsets this. When interest rates rise, the value of the bond falls, but the coupons more than make up for this loss because they are reinvested at the higher rate.

Front 46

Immunization can be analyzed both n terms of ____ and ____.

Back 46

Present value and future value

Front 47

Fixed-income investors face two offsetting types of interest rate risk:

Back 47

Price risk and reinvestment rate risk. (Who faces these two offsetting types of interest rate risk?) Increases in reinvestment income will grow. If the portfolio duration is chosen appropriately, these two effects will cancel out exactly. When the portfolio duration is set equal to the investor's horizon date, the accumulated value of the investment fund at the horizon will be unaffected by interest rate fluctuations.

Front 48

For a horizon equal to the portfolio's duration, ____ and ___ have to exactly cancel out, thereby immunizing the obligation.

Back 48

Price risk and reinvestment risk exactly cancel out.

Front 49

Many banks and thrift institutions have a natural mismatch between the maturities of assets and liabilities. Give an example.

Back 49

For example of this mismatch, bank liabilities are primarily the deposits owed to customers; these liabilities are short-term in nature and consequently of low duration. Assets largely comprise commercial and consumer loans or mortgagees. These assets are of longer duration than deposits, which means their values are correspondingly more sensitive than deposits to interest rate fluctuations. When interest rates increase unexpectantly, banks can suffer serious decreases in net worth--their assets fall in value by more than their liabilities.

Front 50

When interest rates change, the present value (PV) of the fund's ____ change.

Back 50

Liabilities. (What does interest change in response to for a fund?)

Front 51

Any institution with a future fixed obligation might consider ____ as a reasonable risk policy. This notion was introduced by an actuary, whose idea was that duration-matched assets and liabilities let the asset portfolio meet the firm's obligations despite interest rate movements.

Back 51

immunization. (Who might consider this as a reasonable risk policy?)

Front 52

As interest rates and asset durations continually change, managers must rebalance and change the composition of a portfolio of fixed-income assets to realign ____.

Back 52

its duration with the duration of the obligation. (This change in portfolio composition should continually rebalanced with respect to what?)

Front 53

Rebalancing the portfolio entails ____ as assets are bought or sold, so continuous rebalancing is not feasible.

Back 53

Transaction costs. (When does this happen?)

Front 54

Why can a manager not rest even when a position is immunized?

Back 54

The need for rebalancing is continuously needed in response to interest rate changes. Even if rates do not change, the passage of time will also affect duration and require rebalancing. (Why is this important?)

Front 55

Macaulay's duration equals ___ (in words).

Back 55

the weight average of the times to each coupon or principal payment made by the bond.

Front 56

For Macaulay's duration, what should the weight applied to each time to payment be related to?

Back 56

The weight applied to each time to payment clearly should be related to the "importance" of that payment to the value of the bond. In fact, the weight for each payment time is the proportion of the total value of the bond accounted for by that payment, the present value of the payment divided by the bond price. (What concept is this for?)

Front 57

Interest rate sensitivity rule #1, confirming that maturity is a major determinant of interest rate risk:

Back 57

Bond prices are yields are inversely related: As yields increase, bond prices falls; as yields fall, bond prices rise.

Front 58

Interest rate sensitivity rule #2, confirming that maturity is a major determinant of interest rate risk:

Back 58

As increase in a bond's yield to maturity results in a smaller price change than a decrease in yield of equal magnitude.

Front 59

Interest rate sensitivity rule #3, confirming that maturity is a major determinant of interest rate risk:

Back 59

Prices of long-term bonds tend to be more sensitive to interest rate changes than prices of short-term bonds.

Front 60

Interest rate sensitivity rule #4, confirming that maturity is a major determinant of interest rate risk:

Back 60

The sensitivity of bond prices to changes in yeilds increases at a decreasing rate as maturity increases. In other words, interest rate risk is less than proportional to bond maturity.

Front 61

Interest rate sensitivity rule #5, confirming that maturity is a major determinant of interest rate risk:

Back 61

Interest rate risk is inversely related to the bond's coupon rate. Prices of low-coupon bonds are more sensitive to changes in interest rates than prices of high-coupon bonds.

Front 62

Interest rate sensitivity rule #6, confirming that maturity is a major determinant of interest rate risk:

Back 62

The sensitivity of a bond's price to a change in its yield is inversely related to the yield to maturity at which the bond currently is selling.

Front 63

The "effective" maturity of a bond should be measure as ___ paid out by the bond.

Back 63

some sort of average of the maturities of all the cash flows paid out by the bond. (What should this measure?)

Front 64

Since a a zero-coupon bond makes only one payment at maturity, it's _____ is a well-defined concept.

Back 64

time to maturity. (What type of bond is time to maturity well-defined for?)

Front 65

Equal duration assets are ___ to interest rate movements.

Back 65

equally sensitive. (What assets are equally sensitive to interest rate movements?)