问题如下：
Gertrude Fischer mentions two properties of the Sharpe ratio and the information ratio that she says are very useful.
Property 1: The Sharpe ratio is unaffected by the addition of cash or leverage in a portfolio.
Property 2: The information ratio for an unconstrained portfolio is unaffected by the aggressiveness of the active weights.
Are Fischer’s two properties correct?
选项：
A.Yes.
B.No. Only Property 1 is correct.
C.No. Only Property 2 is correct.
解释：
A is correct.
Both properties are correct. For Property 1, if is the weight of an actively managed portfolio and (1 – ) is the weight on risk-free cash, changing does not change the Sharpe ratio, as can be seen in this equation.
{$table1}For Property 2, the information ratio of an unconstrained portfolio is unaffected by multiplying the active security weights, by a constant.
考点：Sharpe ratio & information ratio
解析：两个结论：1. Sharpe ratio不受现金份额以及杠杆变化的影响。即，无论基金经理是更多投资无风险组合、更少投资基金，还是通过杠杆以无风险利率举债的方式来更多投资基金、更少投资无风险组合，该投资基金的夏普比率始终不会发生变化。
2.对于没有限制的投资基金，信息比率不会受到基金超额权重激进程度的影响。
这个题，查阅完讲义。还是有区分度的。
确实是IR没有给constraint和unconstrained限制都不受aggressiveness of active weight影响。
但是如果是equity的话只有unconstrained不受aggressiveness of active weight影响
而这道题没有加equity限制，只提到portfolio而已。故我认为第二句话虽说是没错，但是不是很严谨。
