Question

The S&P 500, a benchmark index, tracking the performance of large U.S. equities has historically returned 8.5% per annum. The average active fund manager typically earns approximately 75% of the S&P 500 and charges higher annual fees. For reference, +90% of individual, non-professional investors lose money. Calculate the accumulated account balance in 20 years based on the following assumptions.

• S&P 500 index fund generates 8.5% annual return and charges a 0.25% annual fee
• Active manager generates 75% of S&P 500 fund annual return and charges a 1.25% annual fee
• Initial investment balance = $25,000
• No additional investment after initial investment

1. What is the expected annual rate of return for the S&P 500 index fund and the actively managed fund?

2. What excel formula would you use to calculate the accumulated asset value? Fill in the relevant inputs below.

Rate =

Nper =

Pmt =

[pv] =

[fv] =

[type] =

Accumulated Asset Value _________________

3. What is the difference of the accumulated asset value between the two investment alternatives?

Answer 1

a)expected return on S&P50==8.5%+0.25%=8.75%
actively managed fund=(75%*8.5%)+1.25%=7.625%
b)accumulated asset value for S&P:
=fv(rate,nper,pmt,pv,type)
=fv(8.75%,20,0,-25000,0)
=133821.32
for actively managed fund:
=fv(7.625%,20,0,-25000,0)
=108693.43
c)difference is 133821.32-108693.43=25127.89