“A fund with zero systematic risk (e.g., a market-neutral long-short equity fund) that uses the risk-free rate as its benchmark would have an information ratio that is equal to its Sharpe ratio. This is because active return will be equal to the portfolio’s return minus the risk-free rate, and active risk will be equal to total risk.”
My question is what is the significance of the zero systematic risk? Why does a portfolio need to have zero systematic risk for its Sharpe and Information ratio to be the same when the benchmark portfolio is the RF rate? Shouldn’t every portfolios Sharpe and Information ratio be the same when the benchmark used is the RF rate?
also if there is zero systematic risk, does it mean expected return is zero as well?
IMO- markets do not reward unsystematic risk and investors are rewarded only for taking systematic risk, risk that cannot be diversified. So if systematic risk is zero it implies that we have no exposure to equity markets, in which case our expected return would b risk free rate. Funds with zero systematic risk would then logically use risk free rate as benchmark.
a fund with zero systematic risk must necessarily be identical to the risk-free asset in both returns and standard deviation - substituting the risk free asset in place of benchmark portfolio in the equation for information ration gives us the sharpe ratio
That’s silly, of course. It’s a consequence of CAPM, but the risk-free asset has no idiosyncratic risk while an asset with a zero beta can have idiosyncratic risk.