Question

• Ron decided to go with Bloom mutual fund. And he wants to simulate his returns had he invested in Bloom fund during the previous year. Ron was provided with the following information from Bloom regarding the previous year: Bloom started last year with a net asset value of $13 per share. And net asset value is $15 by year end. At the beginning of the year, the fund was selling at a premium of 5%, while by the end of the year the fund was selling at a 15% discount of the NAV. Bloom paid year end distributions of income and capital gains of $1.40.

10. What would be Ron’s rate of return had he purchased bloom’s fund last year?

1. 16%
2. 3.9%
3. -6.6%
4. 3.66%

• 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)

11. what is HPR of Ron in 2015?

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

12. 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%

13) 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%

14. 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%

15. 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%

16. 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

Ron has invested in mutual fund last year

He started with nav 13$ trading at 5% primium mean per unit cost of mutual fund is 13$*1.05 = 13.65 $

And at the end of year nav of unit of mutual fund was 15 $ trading at discount of 15% means market value of a unit of mutual fund =15(1-.15) I.e. 15(.85) =12.75$

Income per unit of mutual fund= 1.4$

Return = income +(value at end- value at beginning)/value at beginning

={1.4+12.75-13.65}/13.65

=.5/13.65

=.0366 or say 3.66%

Option d is correct

A)Holding period return for 2015

Income =income +( value at the end of period - value at the beginning of period)/value at the beginning of period

=[.5*20000+(16*20000-15*20000)]/15*20000

=30000/300000

=.1 or say 10%

So option b is correct

B) holding period return during 2015 to 2018

Dividend for 2015,16,17 are reinvented. Already included in no& value of share.

Value of intial investment = 20000share @15 =300000$

Value at the end of 2018 = 22325 share @ 18each = 401850$ (also includes income for 2015,16,17 reinvented)

Income for 2018 = 0.8$ per share on 22325. Share = 17860$

Return = (17860+401850-300000)/300000

= .399 or say 39.9% so answer c is correct

C) arthematic average annual return

Annual return for 2015 = 10%

For 2016 =[0.6*20625+ (13.75*20625-16*30625)]/30625*13.75

=-10.31%

For 2017 ={.632*21525+(21525*17-21525*13.75)}/21575*13.75

=.2823 or say 20.23%

For 2018={.8*22325+(22325*18-17*22325)}/17*22325

=.1059 or 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

Geometric return form 2015 to 2018

Geometric return =n√a1*a2*a3 ....an

={4√(1.1*.8969*1.2823*1.1059)}-1

=(4√1.399)-1

=1.08758 -1

= 0.0876 or say 8.76 %

Option b is correct.