FM for Actuaries

278 CHAPTER 8
state the benchmark index it attempts to replicate. Depending on the investors’ risk
appetites, they may select funds that benchmark an aggressive or conservative market.
The discrepancy between the fund’s performance and the benchmark index
is called the tracking error. Managers will attempt to reduce the tracking errors
using quantitative techniques that minimize the error variance. Thus, the focus is
on reducing the tracking errors at low costs without worrying about active asset
selection and buy-sell timing.
On the other hand, an active bond management strategy may involve some form
of interest-rate forecasting. The fund manager would consider different scenarios
of interest-rate movements in the future and predict the holding-period yield for
different bonds accordingly. As bonds with different characteristics may be affected
by interest-rate changes differently, the holding-period yield discussed in
Section 7.4 under various scenarios will generally be different. The manager will
then choose the bond with the highest holding-period yield under the most likely
scenario. If the manager’s forecast for the interest-rate movement is correct, she
will be able to outperform the benchmark return. Example 7.6 illustrates the use of
horizon analysis to enhance the performance of a fund.
A broader active management framework would take a quantitative approach
in assessing the value of a bond, taking into account all embedded options and
structures of the bond. A proper application of relative-value analysis includes
assessment of the sector of the bond issuer and its credit profile.
8.9 Summary
1. The Macaulay duration of a bond measures the average period of the investment.
The modified duration is the Macaulay duration divided by 1 plus
the yield rate per payment period. When measured in terms of the number of
payment periods, the modified duration is the percentage increase in the bond
price per one percentage point decrease in the yield per payment period.
2. The modified duration and the Macaulay duration can be used to approximate
the change in the bond price for small changes in interest rate. If higher
accuracy is desired, the convexity may also be incorporated in the bond price
correction.
3. Duration varies with the coupon rate of interest, the yield to maturity and
the time to maturity of a bond. The duration of a portfolio of bonds is the
weighted average of the individual bonds in the portfolio.
4. Cash-flow matching and dedication strategy are methods of funding liability
obligations by matching them with specific payments generated from a
portfolio of bonds. These strategies are not subject to interest-rate risk.