Question

#3: Now, it is end of 2018, Ron has been investing with Bloom mutual fund for 4 years now. This morning, Ron was reviewing his investment statements and show the following information (Please ignore any fund expenses info. in solving this question)

Year	Beginning balance		Ending balance		Dividends per share
	No. Shares	Share price	No. Shares	Share price
2015	20,000	15	20,000	16	0.50
2016	20,625	16	20,625	13.75	0.60
2017	21,525	13.75	21,525	17	0.632
2018	22,325	17	22,325	18	0.80

(please notice that the dividends received at the end of each year have been used to purchase new shares at the beginning of the following year)

A. what is HPR of Ron in 2015?

1. 6.67%
2. 10%
3. 6.25%
4. 8.9%

B. What is the HPR of Ron during his entire investment horizon 2015-2018 (Please notice that Ron has been reinvesting his entire proceeds from dividends during years 2015,2016, and 2017 in the fund once they are received)?

1. 28%
2. 41.4%
3. 39.9%
4. 59.3%

C. What is the arithmetic average annual return of Ron during the period 2015-2018?

1. 8.54%
2. 5.53%
3. 6.52%
4. 9.63%

D. What is the Geometric average annual return of Ron during the period 2015-2018?

1. 2.8%
2. 8.76%
3. -8.77%
4. 8.52%

E. What is the dollar weighted average return of Ron during the period 215-2018?

1. 7.58%
2. 8.76%
3. 10.38%
4. 11.53%

F. Assuming that the dollar weighted return is Ron’s nominal rate of return, what is Ron’s real rate of return if the annual rate of inflation during the investment period is 3%?

1. 5.59%
2. 11.76%
3. 10.76%
4. 1.92%

Answer 1

Holding period return for years for 2015

Hpy = income +(value at the end fo period - value at the beginning for period)/value at the beginning of period

=[ 0.5*20000+(20000*16-20000*15)]/20000*15

= [10000+(320000-300000)]/300000

=30000/300000

= .1 or say 10%

So answer b is correct 10%

Holding period return during 2015 to 2018

Dividend for 2015, 2016,2017 are reinvented already included in shared

So

Hpy = [.8* 22325+(22325*18- 20000*15)]/20000*15

= [17860+(401850-300000)]/300000

= .399 or 39.9%

So return from 2015 to 2018 is 39.9%

So option is correct

C) arthemacte average annual return

Annual return

For 2015 = 10%

For 2016 =[.6*20625+(13.75*20625-16*20625)]/16*20625

= -10.31%

For 2017 = [.632*21525(17*21525-13.75*21525)]/13.75*21525

= 28.23 %

For 2018 = [.8*22325+(18*22325-17*22325)]/17*22325

=10.59%

Arthemacte average = return for (2015+2016+2017+2018)/4

=(10-10.31+28.23+10.59)/4

=.963 or 9.63% option d is correct

D) geometric return form 2015 to 2018

=N√a1*A2*A3..*an

=(4√1.10*.8969*1.2823*1.1059)-1

=(4√1.399)-1

=1.08758-1

=.876. Or 8.76 % so option b is correct.