Answer: Suzuki tells her client that although she can certainly double the portfolio’s tracking risk to 4 percent, the portfolio’s alpha will increase but not double. The problem is that as an investor increases a portfolio’s tracking risk, the long-only constraint increasingly limits the portfolio manager from taking full advantage of her investment insight.
‾‾‾‾‾√If the breadth is constant but the IC falls because a smaller portion of the manager’s insight is translated into the portfolio, then the IR must also fall.
The answer may not be clear … but it needs to be looked at with regards to
a) the type of client suzuki is supporting (pension fund) - so long only constraint applies.
b) if investor wants to take advantage of the extra information he has - to increase alpha - he would short (sell) the part of his portfolio he does not like - and add on to the investment on the long side (-30, +130 kind of deal) - but the long only constraint prevents that.
c) just because you doubled active risk - does not mean doubling up on the alpha (excess return).