Question

Bonus Problem 1 (30 marks) There are two investment funds available in the market at time 0. Fund A -It earns interest at a force of interest o4 0.04 0.04(1 -2t)2 = 0.16t - 0.16t2, where 0 sts1 Fund B -It earns interest at a force of interest 80.03, where 0 ts1 Recently, a fund manager has developed a new fund which lasts for 1 year. At time 0, an investor invests $10000 into this new fund. The fund manager invests 20 % of the money in fund A (with smaller force of interest initially) and invests 80 % of the money in fund B (with larger force of interest initially) At some time when 8f first equals to 8, the investor invests an additional amount of $3000 into the fund. At the same time, the fund manager invests all wealth (including the wealth invested previously) into fund A Some time later when 8 equals to 8 again, the investor withdraws an amount of $2000 from the fund. At the same time, the fund manager changes the strategy by investing all wealth (including the wealth invested previously) into fund B until time 1 Questions (a) Calculate the dollar-weighted rate of return for this invest ment over this year. (b) Calculate the time-weighted rate of return for this invest ment over this year.

Answer 1

=) 0:166 - 0.66% = 0.03. 0.16+ - 0.16+ 0.03 : 0 :) - t = 0.16+ J -0.16) - 4 0.16 0.03 ANDNR THE Super 00290° fo.25, 0.753 .. The investment Time timeline is as follows :- A Propor Non - 0207. A and 807 B ₃ oct 20.25 - Ant 100.00 0.25 Lt Lots - 100% in A → 13000 0.75 lt L - 100% in B → 11000 3400 (А) ... сомго км Kon (pus Evr) = { Amat Rate Ś Ant. ' e for fond A olt(0.25 Do 0.167 -0.164)dx 0.4669 % 0.25 C 20.75 sets (0.167 -0.46tº) at - to 1.4334%.

... DWROR = 20. 41667 7. + ROM * 0.03 2008 90 al 0.41667). + 34000 + a 1.8354 7. 13ooox 0.75 0.25 34000 + 11000 0.03 34000 = DWROR = 3.176476 (6) Time weighted RoR (TWROR) • Timex Rate { Time - oop po.(0.260.41662.9.) + 02 €0.03 20:25) + [ (0.75 -0.25) 1.83347] 2.350034).