The following data apply to CFA Problems $1$ through $3$: Hennessy & Associates manages a $$30$ million equity portfolio for the multimanager Wilstead Pension Fund. Jason Jones, financial vice president of Wilstead, noted that Hennessy had rather consistently of the S&P $500$ in four of the past five years. In the one less$-$favorable year, the shortfall was trivial.

Hennessy is a "bottom$-$up$"$ manager. The firm largely avoids any attempt to "time the market." It also focuses on selection of individual stocks, rather than the weighting of favored industries.

There is no apparent conformity of style among Wilstead's six equity managers. The five managers, other than Hennessy, manage portfolios aggregating $$250$ million made up of more than $150$ individual issues.

Jones is convinced that Hennessy is able to apply superior skill to stock selection, but the favorable returns are limited by the high degree of diversification in the portfolio. Over the years, the portfolio generally held about $40$ stocks, with about $2\%-3\%$ of total funds committed to each issue. The reason Hennessy seemed to do well most years was that the firm was able to identify each year about $10$ issues that registered particularly large gains.

On the basis of this overview, Jones outlined the following plan to the Wilstead pension committee:

Let's tell Hennessy to limit the portfolio to no more than $20$ stocks. Hennessy will double the commitments to the stocks that it really favors. and eliminate the remainder. Except for this one new restriction, Hennessy should be free to manage the portfolio exactly as before.

All the members of the pension committee generally supported Jones's proposal because all agreed that Hennessy had seemed to demonstrate superior skill in selecting stocks. Yet the proposal was a considerable departure from previous practice, and several committee members raised questions. Respond to each of the following questions.

a$.$ Will the limitation to $20$ stocks likely increase or