SRP2=SRB2+IR2" id=“MathJax-Element-15-Frame” role=“presentation” style=“display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.16px; letter-spacing: normal; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;” tabindex=“0”>SR2P=SR2B+IR2SRP2=SRB2+SRP2=SRB2+IR2" id=“MathJax-Element-15-Frame” role=“presentation” style=“display: inline-table; line-height: 0; text-indent: 0px; text-align: left; text-transform: none; font-style: normal; font-weight: normal; font-size: 16.16px; letter-spacing: normal; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;” tabindex=“0”>IR2The book says the equation implies that the active portfolio with the highest information ratio will also have the highest Sharpe ratio.
But, if the information ratio is a large negative amount, the sharp ratio can also be highest. Therefore, the expected information ratio is NOT the best criterion for assessing active performance among various actively managed funds with the same benchmark.