Question

A closed-end fund starts the year with a net asset value of $12.00. By year-end, NAV equals $12.10. At the beginning of the year, the fund was selling at a 2% premium to NAV. By the end of the year, the fund is selling at a 7% discount to NAV. The fund paid year-end distributions of income and capital gains of $1.50.

a. What is the rate of return to an investor in the fund during the year?

b. What would have been the rate of return to an investor who held the same securities as the fund manager during the year?

Answer 1

Part a:

Answer:
Suppose that NAV0 denotes the net asset value of the fund at the beginning of the year and NAV1 denotes the fund's net asset value at the end of the year.
Then the return on the fund is calculated as:

[(1 − 0.07)NAV1 − (1 + 0.02)NAV0 + 1.5]/[(1 + 0.02)NAV0]
= [.93 × 12.10 − 1.02 × 12 + 1.5]/[1.02 × 12]
= 4.2%

Part b:

Answer: An investor holding the securities directly would have avoided the premium at the beginning of the year and the discount at the year-end. The return, in this case, should be higher. This is because there was a premium at the time of the purchase and a discount at the sale.
The return in this case would have been:

[NAV1 − NAV0 + 1.5]/[NAV0]
= [12.10 − 12 + 1.5]/12
= 13.3%