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Investing/Strategies / Mechanical Investing
|Subject: Re: The Best Measure for the Best Blend||Date: 11/16/2007 2:10 AM|
|Author: Zeelotes||Number: 203947 of 251824|
Treynor Index -- Treynor developed the first composite measure. This measure postulates two components of risk:
*Risk resulting from unique fluctuations in markets
*Risk resulting from unique fluctuations in portfolios
In order to identify risk due to market fluctuations, Treynor introduced the Characteristic Line. This line defines the relationship between rates of return for a portfolio over time and the rates of return for an appropriate market portfolio.
Treynor noted that the Characteristic Line's slope measures the relative volatility of the portfolio's returns in relation to returns for the aggregate market -- the Portfolio's Beta.
Deviations from the Characteristic Line indicate unique returns for the portfolio relative to the market.
Treynor suggested that risk averse investors would always prefer portfolio possibility lines with larger slopes, because such high-slope lines would place investors on higher indifference curves.
What is measured by the Treynor Index?
It measures the portfolio's Risk Premium Return per Unit of Risk
All investors would prefer to maximize this value
Beta measures systematic risk, but says nothing about diversification. It implicitly assumes a completely diversified portfolio.
The Treynor Index (T) is a measure of the stock's excess return per unit of risk. The excess return is defined as the difference between the stock’s return and the 1-Year Treasury Bill rate over the same period of time. The risk measure here is the market risk evaluated by the stock's beta.
How should the Treynor's values be Interpreted?
Positive T Values: The larger the T value, the more preferable the stock is for all investors, regardless of their risk preference. Normally, a stock with a negative beta should experience a rate of return below the Treasury Bill rate, so both the excess return and beta would be negative, and the T values would be positive.
Negative T Values: Stock has a return below the 1-Year Treasury Bill rate and a positive beta; indicates extremely poor stock performance and selection.
Stock beta is negative with a positive excess return; indicates very good stock performance.
Treynor Index Calculation
Treynor Index = (Average ROI of Investment - Average ROI of Risk Free Investment) / Slope of Fund's Characteristic Line (Volatility) i.e., Beta
Jensen Performance Measure
What is measured by the Jensen Performance Measure? Superior portfolio managers who accurately predict market turns or who identify undervalued investments earn higher returns. Each of them have consistently positive random error terms. Jensen's alpha represents the ability of the fund manager to achieve a return that is above what could be expected, given the risk in the fund. It is a statistical measure of performance similar to the Sharpe Ratio.
This indicator was developed to determine the success of a fund manager in stock selection by providing a basis of comparison for portfolios that have different risk exposures. It is generally used for portfolio performance measurement and to identify the part of the performance that can be attributed solely to the portfolio (in other words, the result of superior performance and not luck).
How should Jensen index's values be Interpreted?
Positive alphas represent good performance by the fund manager. Negative alphas reflect poorly on the performance of the fund manager. The alpha should be calculated based on an extended period of time - usually three years.
Jensen Index Calculation
Jensen Index = ((Average ROI of Investment - Average ROI of Risk Free Investment) - (Beta * (Average ROI of Index i.e. S&P 500 - Average ROI of Risk Free Investment))) * 0.10
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