In: Finance
1. A fund had the following annual prices and dividends (beginning of the year): 2002 2003 2004 2005* 2006 2007 $50 $55 $63 $20 $24 $23 $1 $1 $.40 $.40 $.40 * Price reflects a three for one split.
a. Compute each year return.
b. Compute the four years holding period return.
c. Compute the annualized rate of return
a. Return for year 2003 = [(annual price of the year + dividend)/annual price of previous year] - 1
= [($55+$1)/$50] - 1 = ($56/$50) - 1 = 1.12 -1 = 0.12 or 12%
Return for year 2004 = [($63+$1)/$55] - 1 = ($64/$55) -1 = 1.164 -1 = 0.164 or 16.4%
Return for year 2005 = [($20+$0.40)/$63] - 1 = ($20.4/$63) -1 = 0.32 -1 = -0.68 or -68%
Return for year 2006 = [($24+$0.4)/$20] - 1 = ($24.4/$20) -1 = 1.22 -1 = 0.22 or 22%
Return for year 2007 = [($23+$0.4)/$24] - 1 = ($23.4/$24) -1 = 0.975 -1 = -0.025 or -2.5%
b. 4 years holding period return for period 2004 to 2007 = [(ending value + dividend)/beginning value] - 1
= [($23+$1+$0.4+$0.4+$0.4)/$63] - 1 = ($25.2/$63) -1 = 0.4 - 1 = -0.6 or -60%
4 years holding period return for period 2002 to 2005 = [($20+$1+$1+$0.4)/$50] - 1 = ($22.4/$50) -1 = 0.448 -1 = -0.552 or -55.2%
4 years holding period return for period 2003 to 2006 = [($24+$1+$0.4+$0.4+$0.4)/$55] - 1 = ($26.2/$55) -1 = 0.476 = -0.524 or -52.4%
c. Annualized rate of return = (ending value of investment/beginning value of investment)1/n - 1
=($23+$1+$1+$0.4+$0.4+$0.4)/$50]1/6 -1
= ($26.2/$50)0.17 - 1 = (0.524)0.17 - 1 = 0.8960 - 1 = -0.104 or -10.4%