Investment Theory - Note 11

What is interest rate risk?

The risk that changes in market yields affect bond values and returns.

What happens to bond prices when interest rates rise?

Bond prices fall.

Which bonds are generally more rate-sensitive: long or short maturity?

Long-maturity bonds.

Which bonds have greater rate sensitivity: low or high coupon?

Low-coupon bonds, other factors held constant.

How does a lower YTM generally affect bond rate sensitivity?

It increases interest rate sensitivity.

Why does receiving cash flows sooner reduce rate sensitivity?

Earlier payments are less affected by discount-rate changes.

Why is maturity alone insufficient to measure interest rate risk?

Coupon rate and YTM also affect price sensitivity.

What is price risk?

The risk of selling a bond for less than anticipated.

What is reinvestment risk?

The risk of reinvesting coupons at lower-than-anticipated rates.

How do rising rates affect price risk and reinvestment returns?

Prices fall, while future coupon reinvestment rates rise.

What is Macaulay duration?

The present-value-weighted average time until a bond's payments.

What does duration measure economically?

A bond's effective maturity and interest-rate exposure.

How are cash flow weights calculated for Macaulay duration?

Present value of each cash flow divided by bond price.

What is the Macaulay duration formula?

D = Σ[t × PV(CFt)] / Bond price.

How does bond duration compare with its maturity?

Duration is less than or equal to maturity.

What is the duration of a zero-coupon bond?

Exactly its time to maturity.

Why does a coupon bond have duration below its maturity?

It pays some cash flows before the final maturity date.

How does a lower coupon affect duration?

It increases duration, holding other factors constant.

How does increasing maturity generally affect duration?

It generally increases duration.

How does a lower YTM affect coupon-bond duration?

It increases duration, other factors held constant.

What is the duration of a perpetuity with yield y?

D = (1+y)/y.

What is modified duration?

Macaulay duration divided by 1 plus the per-period yield.

What is the modified duration formula?

D* = D/(1+y), with consistent yield and time units.

What is the duration price-change approximation?

ΔP/P ≈ −D* × Δy.

Why is there a negative sign in the duration formula?

Bond prices and yields move in opposite directions.

Modified duration 5, yield rises 1 percentage point: price change?

Approximately −5%.

Modified duration 7, yield falls 0.5 percentage point: price change?

Approximately +3.5%.

Note 11 Example 11.1: price $897.26, D=11.37, yield 9%→9.1%. ΔP?

Approximately −$9.36.

When using Δy, how do you express 0.1 percentage point?

0.001 in decimal form.

What is passive bond management?

Managing fixed-income risk without trying to exploit mispriced bonds.

What is immunization?

A strategy protecting an investment objective against interest-rate changes.

What are the two immunization methods named in Note 11?

Target-date immunization and net-worth immunization.

What is target-date immunization?

Matching bond duration to a future investment horizon.

Why can matching duration to the investment horizon work?

Price changes and coupon reinvestment effects tend to offset.

If the investment horizon is five years, what duration is targeted?

Five years.

What is net-worth immunization?

Matching asset and liability interest-rate exposures to protect net worth.

Why does duration matching help protect net worth?

Assets and liabilities respond similarly to small yield changes.

For exact first-order asset/liability protection, what exposures must match?

Present-value-weighted duration, or dollar duration.

Does immunization perfectly protect against every interest-rate change?

No. The simple approximation is most reliable for small yield changes.

Why must an immunized portfolio be rebalanced?

Durations change as time passes and market yields move.

What is rebalancing in an immunized bond portfolio?

Adjusting holdings to restore the target duration exposure.

What is cash-flow matching?

Matching bond cash payments directly to future obligations.

Give a simple cash-flow-matching example.

Buying a zero-coupon bond paying exactly when a liability is due.

What is a dedication strategy?

Constructing a bond portfolio whose cash flows cover specified liabilities.

Why can cash-flow matching restrict portfolio choice?

It requires securities with suitable payment dates and amounts.

Why is duration only an approximation?

The bond price-yield relationship is curved, not linear.

What is bond convexity?

The curvature of the relationship between bond prices and yields.

What is the duration-plus-convexity price-change formula?

ΔP/P ≈ −D*Δy + 0.5×Convexity×(Δy)².

What is the annual-coupon bond convexity formula?

C = Σ[t(t+1)×PV(CFt)]/[P(1+y)²].

Why is positive convexity desirable?

It improves gains when yields fall and reduces losses when yields rise.

For a standard positive-convexity bond, what does duration-only pricing do?

It underestimates the bond's new value relative to the tangent approximation.

What happens to the bond price gain when yields fall with positive convexity?

The gain is larger than the duration-only prediction.

What happens to the bond price loss when yields rise with positive convexity?

The loss is smaller than the duration-only prediction.

Why is convexity especially useful for larger yield changes?

The nonlinearity makes duration-only estimates less accurate.

In the convexity formula, what happens to (Δy)² when Δy is negative?

It remains positive.

Note 11 Example 11.4: D*=11.26, C=212.4, Δy=+2%. Estimated ΔP/P?

−18.272%.

Note 11 Example 11.4: initial price $1,000. Estimated dollar change?

−$182.72.

What actual price change is reported in Example 11.4?

−$188.54, giving an actual price of $811.46.

What is active bond management?

Trying to outperform by forecasting rates or identifying mispriced bonds.

What are two sources of value in active bond management?

Interest-rate forecasts and identification of relative mispricing.

What might an active manager do if interest rates are expected to fall?

Increase portfolio duration.

Why increase duration before an expected fall in yields?

Longer-duration bonds tend to gain more when yields decline.

What is a substitution swap?

Exchanging a bond for a similarly risky but more attractively priced bond.

What is an intermarket spread swap?

Switching between different fixed-income market sectors.

What is a rate anticipation swap?

Changing bond holdings based on interest-rate forecasts.

What is a tax swap?

Exchanging similar bonds to obtain a tax benefit.

When can active bond strategies generate abnormal returns?

When the manager has information or insight superior to the market.

Why is interest-rate forecasting risky for active managers?

Incorrect timing can erase profits from security selection.

What approach does the Sanford Bernstein example emphasize?

Combining many small mispricing opportunities instead of one large bet.