## Reference Materials

## Treynor Ratio

## How Is it Useful?

The Treynor ratio is similar to the Sharpe ratio. In both cases the measure of return is the excess over the risk-free investment. The two differ in their definitions of risk. The Sharpe ratio uses standard deviation to define volatility risk, whereas the Treynor ratio uses beta as a measure of market or systematic risk. The Treynor ratio is useful in determining how a particular investment contributes to a diversified portfolio.

## What Is a Good Number?

Generally speaking the higher the Treynor ratio the better. One hopes the excess return over the risk-free rate is large. However, one should be cautious of Treynor ratios that appear abnormally high. If a Treynor ratio is too large, it could be the result of the beta in the denominator being very small. Such a scenario might indicate an incorrectly specified benchmark.

## What Are the Limitations?

Like all benchmark-relative metrics, choosing the proper benchmark as a reference point is key. However, this creates a bit of a quandary if the Treynor ratio seeks to measure how the addition of the investment impacts the risk of the portfolio. If one has a broadly diversified portfolio covering many different asset classes, what would the appropriate benchmark be for the portfolio?

Perhaps the best use for the Treynor ratio lies in evaluating a multi-manager line-up. If the investor is planning to have several managers representing each Treynor Ratio of the major asset classes, then one can first specify the correct benchmark for each given asset class, then calculate Treynor ratios for each of the managers within each asset class, and then examine how different combinations of similar managers work together.

## What Do the Graphs Show Me?

Below are graphs representing the two halves of the Treynor ratio. The upper graph shows the rolling excess return above the risk-free rate. The lower graph shows the risk metric, which is the rolling-period beta versus the appropriate benchmark. The Treynor ratio rolls both of these measures into a single metric. However, one should be aware of the impact that low betas might have on the calculation of a Treynor ratio. If the benchmark chosen isn’t a good fit to the manager, the beta might be low, resulting in a misleadingly high Treynor ratio.

## What Are Typical Values?

The table below displays 10-year Treynor ratios for separately managed account composites covering six asset classes, calculated relative to the appropriate benchmarks for each category. Across all six asset classes, the median manager exhibits roughly the same Treynor ratio as the benchmark. Overall the Treynor ratios are highest for emerging markets, as emerging markets have had the best performance relative to the risk-free rate over the last 10 years with modest ranges of beta (see also the beta StatFACT for ranges).

The Treynor ratio actually pre-dates its more famous cousin, the Sharpe ratio. The first version appeared in early 1965 in the Harvard Business Review under the title “How to Rate Management of Investment Funds.” Treynor originally wanted to examine portfolio performance with the market impact neutralized. Eventually the formula below became that standard definition of Treynor ratio.