Book 4_Fixed_READING 58_INTEREST RATE RISK AND RETURN Flashcards
Sources of return from a bond investment
- Coupon and principal payments
- Reinvestment of coupon payments
- Capital gain or loss if bond is sold before maturity
Changes in yield to maturity (YTM) produce
- Price risk (uncertainty about a bond’s price)
- Reinvestment risk (uncertainty about income from reinvesting coupon payments)
An increase (a decrease) in YTM
decreases (increases) a bond’s price but increases (decreases) its reinvestment income.
Over a short investment horizon
price risk > reinvestment risk: a change in YTM affects price more than it affects reinvestment income
Over a long investment horizon
reinvestment risk > price risk: a change in YTM affects reinvestment income more than it affects price
A fixed-rate bond that has a reinvestment rate equal to the YTM
an investor who holds the bond until maturity will earn a rate of return equal to the YTM at purchase.
Unchanged YTM, Bond Sold Before Maturity
- The value of a bond at the same YTM as when it was purchased is its carrying value
Capital gains or losses at the time a bond is sold
= Price - the carrying value
Changed YTM, Bond Held to Maturity
- If rates rise (fall) before the first coupon date, an investor who holds a bond to maturity will earn a rate of return greater (less) than the YTM at purchase
Changed YTM, Bond Sold Before Maturity
The investor had bigger price risk, so an increase in yield decreased the rate of return over the one-year holding period because the sale price was lower
The Macaulay duration
may be interpreted as the investment horizon for which a bond’s price risk and reinvestment risk offset each other
Macaulay duration calculation
- is calculated as the weighted average of the number of years until each of the bond’s promised cash flows is to be paid,
- where the weights are the present values of each cash flow as a percentage of the bond’s full value.
duration gap
= Macaulay duration − investment horizon
- A positive duration gap: exposes the investor to price risk from increasing interest rates.
- A negative duration gap exposes the investor to reinvestment risk from decreasing interest rates.