Question

In: Finance

1. A fund had the following annual prices and dividends (beginning of the year): 2002 2003...

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

Solutions

Expert Solution

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%


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