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Ratios



Treynor Ratio

This is another risk-adjusted performance measure, similar in calculation and application to the Sharpe Ratio. The difference is that while Sharpe weighs a fund's returns against total risk (standard deviation, or volatility), Treynor looks at excess return for each unit of systemic risk (the volatility, inherent in the market, that cannot be diversified). The Treynor calculation, then, takes the fund's excess return over a notional risk-free rate (what would be earned from, say, cash on deposit, or Government bonds), then divides it by the fund's Beta. A Treynor Ratio greater than 1 shows that the fund has produced more units of return than of risk. So, in basing on market risk alone, the ratio assumes that non-systemic risk is capable of being eliminated by diversification across a wide range of investments, and measures whether the systemic risk has been rewarded.
Also known as the Volatility to Reward ratio, Treynor is useful in comparing funds that invest in similar market sectors and achieve similar returns. For example, when assessing a range of UK Equity funds, it is the one with the highest Treynor Ratio that is taking on the least market risk to achieve its level of performance. Also, since it factors out the manager's ability from movements in the fund's sector, Treynor may be used to compare fund performances adjusted for systemic risks in different market sectors - because, although intuitively the ratio should be higher for bond funds than for those investing entirely in equities, this is not necessarily true in every case. While not perfect, and not to be taken in isolation, the Treynor Ratio can be a pointer to the optimum risk- and sector-adjusted fund for a particular risk-aversion profile.

Worked Example: Treynor Ratio
Treynor works on the assumption that non-systemic risk – that which is associated with the manager's activities, rather than endemic to the market itself – can be mitigated or eliminated by a combination of investment skill and diversification.
Systemic risk – conditions and movements in the market – cannot be affected by the manager's decisions, and so Treynor measures how much loss or gain has been taken for each unit of this 'unavoidable' risk that attaches to the fund.
In our examples below we look at some funds with good R-Squared correlations to their benchmark, and with differing degrees of sensitivity to its movements (Beta), over a three-year period.

Table 1. Total Return - Ratios table against benchmark "UT Cautious Managed" (risk free rate at 3.5%) from Unit Trust/OEIC universe
Name Alpha Beta R-Squared Treynor
Capita Financial - Miton Extra Income -3.9 1.36 0.89 -1.68
Jupiter - Distribution TR 2.31 0.73 0.86 2.48
Midas Balanced Income TR 2.7 1.30 0.87 3.39
MLC Trust Mgt - Conservative TR 0.06 0.70 0.87 -0.90
UT Cautious Managed TR 0 1 1 0.50

The Higher Betas
Both Capita and Midas have higher Betas – for every 1 point of change in the benchmark, these funds moved 1.36 and 1.30 points respectively. These suggest that both managers are making bets away from the benchmark's composition, and investors will want to see good positive Alphas, indicating that active management is being rewarded.
Capita's negative result fails this particular test, while Midas has generated positive Alpha. However, the point is that both funds are taking on much the same degree of market risk, and the results as measured by Treynor are very different. Capita does not do well from its heightened sensitivity to market movements, and in fact is losing almost 2.2 points more than the benchmark risk would demand. This is reflected in a Treynor nearly 40% lower than that of the Midas offering, which is making 3.39% for every unit of systemic risk.

The Lower Betas
Another contrasting picture is presented by the Treynors of the Jupiter and MLC funds. Their lower Betas are comparable to each other, indicating that the funds have taken on only 70-73% of the movements in the benchmark. Jupiter has turned this to advantage, with a Treynor showing that they generated 2.48% for each unit of market risk. MLC is working with virtually the same degree of systemic risk, but returning a negative Treynor 1.6% below what the benchmark would have offered. To see how this translates into performance, we can examine the next table, which charts the funds' total returns over the same three-year period.

Table 2. Total return performance from Unit Trust/OEIC universe
Name 3y
Capita Financial Miton Extra Income TR 3.1
Jupiter Distribution TR 17.56
Midas Balanced Income TR 25.39
MLC Trust Management Conservative TR 9.39
Sector: UT Cautious Managed TR 11.93

Much as expected, the Jupiter and Midas funds comfortably outperform both the benchmark and their peers, despite the funds' very different Beta relationship to movements in the sector. Where we do see comparable profiles – Capita and Midas, Jupiter and MLC – the negative Treynors point up the funds that are operating in similar conditions to their rivals, but being punished by the systemic risk.
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