Portfolio returns can be measured in many ways. Generating profitable returns is one aspect that is key to success, but the costs associated with generating those returns is an aspect of market analysis that sometime goes unnoticed. For many investors, risk- adjusted returns are extremely important as creating a roller coaster return environment in which the volatility of the returns are problematic, can mitigate the attractiveness of a portfolio manager.
In addition to strong risk management techniques, which are imperative to generating successful returns, traders need to consider the extent of the volatility associated with a specific strategy which can be evaluated by using a number of statistical metric which can help determine robustness of the risk-adjusted returns. Some of the more well-known statistical ratios are; the Sharpe Ratio, the Information-ratio, the Sortino Ratio, M2/M3, and the Treynor Ratio. Each of these ratios supplies an investor with a benchmark to judge the risk-adjusted returns of their portfolio.
Sharpe Ratio
William Sharpe created a metric in an effort to measure the accuracy of a portfolio relative to the volatility of the underlying returns. Sharpe created this ratio in an effort to measure the returns garnered as a relationship to the risk untaken. The Sharpe ratio measures risk-adjusted returns and divide this metrics by the standard deviation of the average-returns. When examining this metrics, an analyst should consider that the higher the ratio, the better the portfolio performance.
- Sharpe Ratio = (X – Y) / Z
- Where X = The average return on the portfolio
- Y = Risk-free rate
- Z = Volatility of Returns
The Sharpe ratio measures the average-return after subtracting the risk free rate, divided by the portfolio’s standard deviation. The ratio creates metrics that can be used to evaluate returns within the same sector and across a spectrum of disciplines.
The index uses a level of one to specify a neutral rating. An index level of one means that the returns produced by a portfolio equal the risk assumed to produce the returns. An index level below 1 indicates that returns on an investment are worse than the risk assumed to generate that return. Additional, a Share ratio above one indicates that the portfolio is returning more than the risk taken by the portfolio manager to produce those returns.
Information-ratio:
The Information-ratio is also an attempt to improve on the Sharpe ratio. The difference within the ratios lies in the numerator which is average return minus a rate. The Sharpe ratio uses a risk free rate while the Information-ratio uses a benchmark that is more closely associated with the portfolio such as the S&P 500 in the case of a long only equity portfolio.
The Information-ratio is considered an active risk metrics, as the ratio gives investors a gauge of relative performance.
Sortino Ratio:
The Sortino attempts to improve upon the Sharpe ratio by removing the penalty associated with upside volatility. Sortino created a ratio that focused solely on downside standard deviations while still keeping the basic premise of the Sharpe ratio. The Ratio examines the average return minus the risk free rate of return (identical to the Sharpe ratio) but then divides it by the negative standard deviation, which measures only negative volatility.
M Squared
The M-Square ratio was developed by Franco Modigliani and his granddaughter Leah Modigliani in 1997, as an extension of Sharpe Ratio to create risk-adjusted portfolios by using risk-free rate.
The M-Square ratio allows the portfolios to be compared simply by looking at the resulting returns. The fund with highest M-Square ratio will have the highest return for a given amount of risk. When M-Square ratio is used, investor’s measure of risk is the tracking error as opposed to relative risk / volatility.
M-Cube ratio is an extension of M-Square ratio and it gives investor allocation information as to allocate cash, the benchmark and the potential active strategy. The M-Cube ratio calculation would give same results as M-Square ratio but the target tracking error is not present.
The M3 measure recognizes that the investor has to consider basis points of risk-adjusted performance after ensuring that correlations of various funds versus the benchmark are also equal. In effect, all tracking errors are normalized to the same value.
Treynor Ratio:
Jack Treynor altered the Sharpe ratio in an effort to compare the average return on a portfolio to a benchmark. Treynor designed a metrics to examine risk-adjusted returns by subtracting the risk free rate from the average return and then dividing by the beta of the portfolio to a benchmark.
The beta of the market portfolio is a measurement in which the number one reflects a neutral measure. A portfolio that is less than one is less volatile than its market benchmark, while beta’s that are greater than 1 are more volatile than their benchmark.
The difference between the Sharpe and Treynor ratio is the analysis of excess return in the Treynor compared to the volatility of the portfolio in the Sharpe. The beta measures portfolios sensitivity to returns, while the standard deviation describes the volatility of the portfolio.
As a standalone measure the Treynor ratio has the drawback of not addressing risk-adjusted returns as it relate to volatile, the metrics works well when adding assets to a portfolio.