FM for Actuaries

114 CHAPTER 4
Example 4.6: On January 1, a fund was valued at 100. On May 1, the fund
increased in value to 112 and 30 of new principal was injected. On November 1,
the fund value dropped to 125, and 42 was withdrawn. At the end of the year, the
fund was worth 100. Calculate the DWRR and the TWRR.
Solution: Figure 4.2 illustrates the cash flows. As C =30− 42 = −12, there is
a net withdrawal. From (4.6), the interest income earned over the year is
I = 100 − 100 − (−12) = 12.
Figure 4.2: Illustration for Example 4.6
Cash flow 30 42
Time t, mm/dd
1/1 5/1 11/1 1/1
Value before t
112 125
Value after t
142 83
Subperiod
1 2 3
Hence, from (4.7), the DWRR is
R D =
12
100 + 2 3 × 30 − 1 6 × 42 =10.62%.
The fund balance just after the injection on May 1 is 112 + 30 = 142, and its
value just after the withdrawal on November 1 is 125 − 42 = 83. From (4.4), the
fund-value relatives over the three subperiods are
1+R 1 = 112
100 =1.120,
1+R 2 = 125
142 =0.880,
1+R 3 = 100
83 =1.205.