6.4 Fixed-Income risk and return Flashcards
The sources of return from a bond investment are:
All cash flows are received as scheduled
Coupons are reinvested at the YTM
The bond is either held to maturity or sold on the constant yield price trajectory
The constant yield price trajectory
the path that a bond’s price will follow as it approaches maturity if the YTM remains constant
The horizon yield
which is the internal rate of return on a bond over the investor’s holding period
The total return
the sum of reinvested coupon payments and the sale price (if the bond is sold before maturity) or redemption amount (if the bond is held to maturity).
Reinvestment risk
a greater concern for for investors with longer investment horizons.
Investors who intend to hold a bond until maturity have no exposure to price risk during the bond’s lifetime because, assuming no default, they will receive the bond’s par value at maturity regardless of how much its price fluctuates during its lifetime.
However, if the bond matures prior to the investor’s time horizon, the will be risk associated with reinvesting the principal repayment at maturity
greater for bonds with higher coupon rates
The Macaulay duration measure
the weighted average life of the cash flows, with the weights being the present value of the cash flows
mportant to considerations of the tradeoff between reinvestment risk and price risk because it represents the investment horizon that is immune to interest rate changes.
In other words, if a bond’s Macaulay duration is equal to an investor’s holding period, any losses in reinvestment income from a one-time parallel increase in yield will be matched by capital gains due to price appreciation (and vice versa for a decrease in yield).
a duration gap
An imbalance between investment horizon and Macaulay duration
Changes in interest rates will have more impact on bond prices than reinvesting returns, so the investor will suffer losses if interest rates rise.
An investor with a short time horizon relative to the Macaulay duration has a positive duration gap
a negative duration gap
means that price risk is dominated by reinvestment risk and investors are exposed to the risk of falling interest rates.
Macaulay duration > Investment horizon
Positive duration gap
Price risk dominates
Exposure to rising interest rates
Macaulay duration < Investment horizon
Negative duration gap
Reinvestment risk dominates
Exposure to falling interest rates
An option-free fixed-rate bond will always exhibit positive convexity and, all else equal, its convexity will be higher if it has:
a longer time to maturity
a lower coupon rate
a lower yield-to-maturity, and
more dispersed cash flows
Convexity is an attractive feature for investors because of
because of its impact on bond returns
Compared to a bond with less convexity, a more convex bond will experience greater price appreciation when interest rates fall and its price will depreciate at a lower rate when interest rates rise.
Money convexity
the quantified second-order effect of a change in yield in currency terms
For changes in yield-to-maturity, the convexity adjustment is most needed to account for the:
a) first-order effect on bond prices.
b) bond price risk due to small changes in yield-to-maturity.
c) non-linear relationship of bond prices and yield to maturity.
c) non-linear relationship of bond prices and yield to maturity.
The convexity adjustment is a complementary risk measure to duration. It accounts for the second-order (non-linear) effect of yield changes on price. It is most useful for large yield changes, because duration provides a good approximation for small yield changes.
One limitation as to why using the average duration of the bonds in a portfolio does not properly reflect that portfolio’s yield curve risk is that the approach assumes:
a) a parallel shift in the yield curve.
b) all the bonds have the same discount rate.
c) a non-parallel shift in the yield curve.
a) a parallel shift in the yield curve.
