Topic Quiz 8 Flashcards
How does Macaulay’s duration measure the effective maturity of a bond?”
a. It is the weighted average of the times until each payment.
b. It is the sum of the weights on the bond payments.
c. It strips the face value from a zero coupon bond.
d. It adds the term of the coupons to the term of the face value.
a. It is the weighted average of the times until each payment.
“What is a rule of duration?”
a. With the YTM and the coupon rate of a bond held constant, a bond’s duration will decrease the longer the term of the bond.
b. With time-to-maturity and the coupon rate of a bond held constant, a bond’s duration will decrease the lower the bond’s YTM.
c. The duration of a zero coupon bond is its maturity.
d. With time-to-maturity and YTM held constant, a bond’s duration will decrease the smaller the bond’s coupons.
c. The duration of a zero coupon bond is its maturity.
The duration of a portfolio of bonds with
a. an infinite life will be the weighted average of durations of individual bonds.
b. longer terms to maturity will be the weighted average of durations of individual bonds.
c. equal coupon rates will be the weighted average of durations of individual bonds.
d. equal yields will be the weighted average of durations of individual bonds.
d. equal yields will be the weighted average of durations of individual bonds.
Why is duration a good approximation for small changes in the YTM but not with large changes in the YTM?
a. When YTM decreases, duration overestimates the change in a bond’s price.
b. Duration explains the long term changes in price.
c. When YTM increases, duration underestimates the change in a bond’s price.
d. Duration explains a linear relationship.
d. Duration explains a linear relationship.
An inter-market spread swap can be used when rebalancing a bond portfolio. How would you trade in an inter-market spread swap?
a. Sell a bond that is currently trading at a YTM that is too high and buy bonds with similar characteristics that are trading at the correct yield.
b. If you expect a yield increase you would buy higher duration bonds and sell lower duration bonds.
c. If you expect a yield decrease you adopt a passive management strategy.
d. If you expect the yield gap between 10 year Treasury bonds and 10 year AA rated corporate bonds to narrow you would buy corporate bonds.
d. If you expect the yield gap between 10 year Treasury bonds and 10 year AA rated corporate bonds to narrow you would buy corporate bonds.
What will be the Macaulay’s Duration of a zero coupon bond?
It will be the same as the zero coupon bond’s maturity term as the only payment made by a zero coupon bond is on its maturity date.
Will the prices of bonds trading at lower yields to maturity (YTM) be more or less sensitive to changes in interest rates than bonds trading at higher YTM?
More sensitive.
Test this by pricing a two year bond that has coupon rate of 5% and is trading at a YTM of 1% and a two year bond that has a coupon rate of 5% and is trading at a YTM of 10%. Then calculate the prices of these bonds when the YTMs increase by 1%. The price change for the two year bond trading at a YTM of 1% will be a lot bigger than the price change for the other two year bond. Another way to think about it is that a 1% increase from a YTM of 1% to 2% doubles the YTM. However, a 1% increase from a YTM of 10% to 11% is an increase of only 0.1%.
Would bonds with higher coupon rates be less or more sensitive to interest rate changes than bonds with lower coupon rates?
Bonds with lower coupon rates would be more sensitive as they will pay smaller amounts earlier than bonds with higher coupon rates.
How is modified duration different from duration?
Modified duration is simply duration divided by 1 plus the YTM.
Are shorter term or longer term bonds more sensitive to interest rate changes?
Longer term bonds will be more sensitive to changes in interest rates than shorter term bonds.
What active trading strategy should you use when you expect the yield gap between government and corporate bonds to widen?
You would use an inter-market spread swap where you short sell corporate bonds.
An increase in the corporate bond yield relative to the yield on government bonds will see corporate bond prices fall. This is profitable for the short sale of bonds.
How can the duration of a bond portfolio be measured?
The bond portfolio’s duration is the weighted average of the durations on the individual bonds in the portfolio.The weights will be determined by how much of the total funds had been invested in each of the bonds.
Why is the convexity of a bond important?
Duration measures the linear relationship between changes in yield to maturity (YTM) and changes in bond prices. However, the relationship between bond prices and YTM is non-linear. For a non-callable bond there will be positive convexity.between bond prices and YTMs. A callable bond will have positive convexity as YTM decreases but this will change to negative convexity as the YTM approaches the YTM where the bonds price equals the price at which the issuer will exercise the right to buy back the bond (the call value),
What would you use to compare the yield sensitivities of bonds with different maturities and coupon rates? Actual maturity or effective maturity?
You would use effective maturity, as the yield sensitivity of longer term bonds with lower coupon rates will be higher than the yield sensitivity of bonds with the same maturity with higher coupon rates.
If a corporate bond’s credit rating is increased from A to AA by Standard and Poors, what will happen to its duration?
The bond’s duration will increase as the bond’s higher credit rating will mean investors will regard it to be a safer investment. So it will now trade at a lower yield to maturity (YTM). Lower YTM bonds are more sensitive to interest changes than bonds trading at a higher YTM.
