FM for Actuaries

136 CHAPTER 4
Calculate the arithmetic mean rate of return and the geometric mean rate of
return of the stock.
4.13 The annual rate of return of a bond fund over the last 8 years are (in %) as
follows:
−0.53 15.29 32.68 23.96 −2.65 8.40 19.49 7.13
Calculate the arithmetic mean rate of return and the geometric mean rate of
return of the fund.
4.14 A fund has a value of $10,000 at the beginning of the year. A deposit of $300
was made at the end of every 4 months. A withdrawal of $200 was made at
the end of 9 months. At the end of the year, the fund balance after the final
deposit is $11,000. Find the DWRR earned by the fund. Also calculate the
approximate DWRR using equation (4.8).
4.15 A portfolio made up of two coupon bonds has an initial value of $20,000.
The fund records coupon payments in 6-month periods. For the 2-year period
2016 and 2017, the following fund values and coupon payments were
recorded:
Time Coupon payment Fund value
mm/dd/yy received before date
01/01/16 20,000
07/01/16 550 21,250
01/01/17 1,000 18,500
07/01/17 550 19,750
12/31/17 20,500
Calculate the TWRR and the DWRR of the fund.
4.16 A project requires investments of $1,000 and $1,176 at the end of the first
year and the third year, respectively, and generates income of $2,170 at the
end of 2 years. Find the internal rate of return of the project.
4.17 A project requires an initial cash outlay of $1,000 and a final investment of
$800 at the end of year 2, and is expected to generate $1,750 at the end of
the first year. Calculate the internal rate of return of the project.
4.18 A cash outlay of $600 generates incomes of $300 after 3 months and 9
months, and $50 after 1 year. Calculate the yield rate of the investment.