Question $4$

$($a$)$ A trader argues that monthly stock returns in a particular market exhibit return continuation. Stocks that have performed well in month $t$ continue to perform well in month $t+1$ and stocks that have performed poorly in month $t$ continue to perform poorly in month $t+1.$ You have access to historical monthly return data on each stock from an investable universe of $N$ stocks from this market.

$($i$)$ Propose an investment strategy that takes advantage of the above patterns.

$($ii$)$ Explain how you would evaluate whether the investment strategy you proposed in question $($i$)$ outperforms the broad market index.

$($b$)$ You are provided with historical monthly returns on the performance of a style index that follows a small$-$cap investment strategy. $($i$)$ Explain how you would assess whether the investment strategy has generated abnormal profits. $($ii$)$ Discuss the shortcomings of your proposed approach.

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