Question

Calculation Problem 2. The table below provides returns on a portfolio along with returns for the corresponding benchmark index for the past eight quarters. The table also provides the difference between portfolio returns and the benchmark index, the average of these differences over the past eight quarters and the standard deviation of these differences. What is the annualized tracking error for this period? All rights reserved Difference 0.023 Period Portfolio 0.05 0.036 Index 0.027 0.046 0.010 0.019 0.003 0.022 0.010 0.022 0.012 0.002 0.001 0.003 0.007 0.03 0.081 0.023 0.008 7 0.089 0.014 0.003 0.011789 0.006 0.008 Average SD 8

Answer 1

Annualized tracking error can be calculated with the help of following formula -

Annualized tracking error = Standard deviation of the difference between portfolio return and benchmark index   *sqrt. (number of quarter in a year)

Where,

Standard deviation of the difference between portfolio return and benchmark index = 0.011789 (given in table)

Sqrt. (number of quarter in a year) = sqrt. (4) (As the given portfolio and benchmark returns are quarterly return and a year has 4 quarters)

Therefore,

Annualized tracking error = 0.011789 * sqrt (4)

= 0.011789 * 2

= 0.023578

Therefore annualized tracking error is 0.023578