The equations for the 3 measures are as follows:
Treynor measure = (R
P − R
F) / β
P
Sharpe ratio = (RP − RF) / σP
Information ratio = (R
P − R
B) / (σ
P − B)
Since both portfolios are well diversified most of their risk comes from systematic risk or beta and is tied to the general level of overall risk in the market. In this case the best measure to use would be the Treynor measure since this uses beta or systematic risk as the measure of risk. The Sharpe ratio uses standard deviation as the measure of risk in the denominator and the information ratio is best to use when comparing a portfolio to a benchmark.
