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Question $1$

Portfolio management is concerned with making decisions about investment mix and policy, matching investments to objectives, asset allocation for individuals and institutions, and balancing risk against performance.

$($i$)$ Explain the difference between Active and Passive portfolio management.

$($ii$)$ Explain the two main strategies in passive portfolio management and comment on the effectiveness of the strategies in achieving the desired outcome.

$($i$)$ Suppose two investors have formed portfolios, A and B $,$ designed to track a particular benchmark. Over a period of three years, the returns to the portfolios as well as the index returns were as follows:

$\backslash$table$[[$Year$,$Quarter,Managed portfolio A $(\%),$Managed portfolio B $(\%),$Benchmark $(\%)],[2022,1,3\mathrm{.}9,4,4\mathrm{.}2],[,2,-3\mathrm{.}9,-4\mathrm{.}9,-4\mathrm{.}7],[,3,11,10\mathrm{.}6,10],[,4,2\mathrm{.}3,3\mathrm{.}2,2\mathrm{.}7],[2023,1,1\mathrm{.}1,0\mathrm{.}8,0\mathrm{.}2],[,2,3\mathrm{.}5,3\mathrm{.}7,4\mathrm{.}8],[,3,9\mathrm{.}9,9\mathrm{.}1,9\mathrm{.}3],[,4,-0\mathrm{.}7,1\mathrm{.}8,0\mathrm{.}9],[2024,1,8\mathrm{.}2,7\mathrm{.}9,6\mathrm{.}2],[,2,4\mathrm{.}2,4\mathrm{.}7,8],[,3,4,2\mathrm{.}8,7],[,4,0\mathrm{.}2,0\mathrm{.}4,5]]$

Calculate the annualised tracking errors for the managed portfolios. Which portfolio performed better over the period and why?

$2$