The equations for the 3 measures are as follows:
Sharpe ratio = (R
P − R
F) / σ
P
Treynor measure = (RP − RF) / βP
Information ratio = (R
P − R
B) / (σ
P − B)
Since both portfolios are not well diversified most of their risk comes from unsystematic (company specific) risk and is not tied to the overall level of risk in the market thus in this case standard deviation is the best measure of risk to use. The Sharpe ratio is the best measure to use to compare the two portfolios which are undiversified since the Sharpe ratio uses standard deviation or total risk in the denominator of the equation as its measure of risk. The Treynor measure uses beta or systematic market risk as the measure of risk in the denominator and the information ratio is best to use when comparing a portfolio to a benchmark.
