A closed-end fund starts the year with a net asset value of $29. By year-end, NAV equals $30.80. At the beginning of the year, the fund is selling at a 4% premium to NAV. By the end of the year, the fund is selling at a 9% discount to NAV. The fund paid year-end distributions of income and capital gains of $3.20. a. What is the rate of return to an investor in the fund during the year? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Rate of return % b. What would have been the rate of return to an investor who held the same securities as the fund manager during the year? (Round your answer to 2 decimal places.) Rate of return %
P0 = NAV0 x (1 + Premium) = $29.00 x 1.04 = $30.16
P1 = NAV1 x (1 – Discount) = $30.80 x 0.91 = $28.03
The NAV increased by $1.80 but the price of the fund decreased by $2.13
Return = (P1 + Distributions)/P0 – 1 = ($28.03 + $3.20)/$30.16 – 1 = 3.55%
An investor holding the same securities as the fund manager would have earned a rate of return of the NAV and not been subject to the change from premium to discount.
Return = (NAV 1 + Distributions)/NAV 0 – 1 = ($30.80 + $3.20)/$29.00 – 1 = 17.24%
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