Question

You are the manager of the Mighty Fine mutual fund. The following table reflects the activity of the fund during the last quarter. The fund started the quarter on January 1 with a balance of $100 million.

Mighty Fine Mutual Fund
Monthly Data (measured at end of month)
	January	February	March
Net inflows ($ million)	5.5	-4.3	0
HPR (%)	-4.30	6.20	1.80

a. Calculate the quarterly arithmetic average return on the fund. (Round your answer to 2 decimal places.)

Arithmetic average              %

b. Calculate the quarterly geometric (time-weighted) average return on the fund. (Round your answer to 2 decimal places.)

Geometric average              %

c. Calculate the quarterly dollar-weighted average return on the fund. (Round your answer to 2 decimal places.)

Dollar-weighted average return              %

Answer 1

a. Arithmetic monthly average return= (-4.3%+6.2%+1.8%)/3=1.23%

Hence, quarterly return = (1+1.23%)^3-1=3.74%

b. Monthly geometric return= ((1-4.3%)*(1+6.2%)*(1+1.8%))^(1/3)-1=1.14%

Hence, quarterly return= (1+1.14%)^3-1=3.45%

c. Fund value at period 0=5.5 million

Fund value after January=5.5*(1-4.3%)=$5.2635 million

Fund value after February=(5.2635-4.3)*(1+6.2%)=$1.023

Fund Value after March= 1.023*(1+1.8%)=$1.0414

Hence quarterly dollar weighted return= (1-2.4%)^3-1=-7.07%