Question

5.You invest $100 in a mutual fund that grows 12 percent annually for three years. Then the fund experiences an exceptionally bad year and declines by 40 percent. After the bad year, the fund resumes its 12 percent annual return for the next three years. a. What is the average percentage change for the seven years? b. If you liquidate the fund after nine years, how much do you receive? c. What is the annualized return on this investment using a dollar-weighted calculation and using a time-weighted calculation?

Answer 1

Solution a) Average Return = (12% + 12% + 12% - 40% + 12% + 12% + 12%)/7 = 4.57%

Solution b) The fund would be liquidated after seven years not nine years here.

The value received end of the year =  Previous year ending value*(1+growth rate for the year)

= P0*(1 + r)

The values are calculated as follows:

Solution c) Dollar-weighted return = Sum of returns/Number of years

= (12% + 12% + 12% -40% + 12% + 12% + 12%)/7

= 4.57%

Time-weighted return = Geometric mean of the individual returns

= [(1 + r1)*(1+r2)*...........*(1+rn)]^(1/n) - 1

= [(1 +12%)*(1 +12%)*(1 +12%)*(1-40%)*(1 +12%)*(1 +12%)*(1 +12%)]^(1/7)-1

= 1.024458 - 1

= 0.024485

= 2.4458%

= 2.45%

Alternatively, time-weighted return can be calculated as = (Final Value/Initial Value)^(1/n) - 1

= (118.4294/100)^(1/7)-1

= 0.024458

= 2.4458%

= 2.45%

Please comment in case of any doubts or clarifications required. Please Thumbs Up!!