Important Risk Ratios

by David Becker on September 12, 2012

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Risk adjusted returns are the backbone of many successful investment strategies. In addition to strong portfolio management techniques, which include determining the loss and profit levels prior to entering a trade and investor should understand the returns they will receive on a risk adjusted basis. To gauge how risky a strategy is, and investor can use a number of important statistical ratios, which will determine the risk associated with a specific strategy. This article will examine a number of important ratios which can assist an investor in determining the best risk adjusted returns.

Sharpe Ratio

The Sharpe ratio (created by William Sharpe) measures the efficiency of a portfolio. It quantifies the return received in exchange for the risk assumed. For evaluation purposes, the higher the ratio, the better the portfolio performance. The ratio determines risk adjusted returns by valuing risk in terms of the volatility of the returns. It is defined as:

  • Sharpe Ratio = (A – B) / C
  • Where A = return on the portfolio
  • B= Risk-free rate
  • C = Standard Deviation of the returns of the portfolio

The Sharpe ratio is the return of a portfolio minus a risk-free (cash or Treasury bill) rate of return, divided by the portfolio’s standard deviation. The ratio helps standardize the returns of managers within the same asset class so they can be compared on a risk-adjusted basis. The formula basically divides returns by the volatility of the returns (standard deviation).

A sharp ratio of 1 indicates that the returns on investment are proportional to the risk taken. A Sharpe ratio lower that is lower than 1 indicates that return on investment is less than the risk taken.

Negative Sharpe Ratios

If an investor generates returns that are less than the risk adjusted rate of return they will generate a negative average excess return. In these cases where the investor has a greater standard deviation and worse average performance may create a negative Sharpe Ratio.

Treynor Ratio:

William Sharpe’s work has been extended further by Jack Treynor where he proposed a new measure in 1965. Adopting the ideas from Sharpe, Treynor proposed the ratio equal to the return of the portfolio minus risk free rate divided by beta (a measure for systematic risk).

The beta of the market portfolio (which measures against a benchmark) is equal to one, while the betas of assets that are more volatile than a benchmark (such as the S&P 500 Index) have betas that are greater than.

The Treynor measure is very similar to the Sharpe ratio. The difference lies in examining the excess return of the asset to beta and not the standard deviation of the asset. The beta measures only the asset’s sensitivity to the market’s movements, while the standard deviation describes the volatility of the asset.

As a consequence, the Treynor measure addresses one of the drawbacks mentioned regarding the Sharpe ratio. The Treynor measure works well when adding assets to a portfolio as the betas determines how a new asset will change the dynamic of a portfolio.

Related: How to Minimize Investment Risk

Information Ratio:

This ratio is a revision of the Sharpe ratio as an extension of risk adjusted returns. Both are risk adjusted metrics but the only difference in the numerator of the Sharpe ratio and the Information ratio is the choice of benchmarks. The Sharpe ratio uses a risk-free asset such as Treasury bills, and the Information Ratio uses a well known benchmark, equity index or fixed income index.

The information ratio focuses on the residual return relative to residual risk. The information ratio can provide a measure of investment manager’s performance above a specific benchmark.

  • Information Ratio =     Excess Return / Active Risk

Where Active Risk = Std. Dev of Alpha

Since Treasury bills are generally passive, the information ratio gives investors value in relative performance.

Sortino Ratio:

The Sortino ratio focuses on downside movements and the importance of capital preservation as the theme toward risk for a number of investors. By definition, the Sortino ratio is closely related to the Sharpe Ratio.

The Sortino Ratio compares the return of a portfolio with the minimum acceptable return per an investor and divides it by the downside semi-standard deviation, which measures only the volatility of returns that are negative. In essence, the Sortino ratio only examines the standard deviation of the losing months within a time series of returns, and does not penalize a fund that has high volatility for positive months.

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This post was written by...

– who has written 5 posts on Excess Return.

David Becker is a consultant and portfolio manager who utilizes his 20 years’ experience trading and studying the capital markets to drive a consulting business that focuses on capital market analysis. Mr. Becker has significant experience managing risk in the commodity, equity, currency and fixed-income markets. Prior to founding Fortuity, Mr. Becker spent time as a portfolio manager at 2 Investment banks (London and New York), and three hedge funds. His LinkedIn profile.

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