# Study On The Ratios Of Different Stocks Finance Essay

In finance, Jensen's alpha is used to determine the abnormal return of a security or portfolio of securities over the theoretical expected return. The theoretical return is predicted by a market model, most commonly the Capital Asset Pricing Model (CAPM) model. The market model uses statistical methods to predict the appropriate risk-adjusted return of an asset. The CAPM for instance uses beta as a multiplier.Jensen's alpha was first used as a measure in the evaluation of mutual fund managers by Michael Jensen in 1968. The CAPM return is supposed to be 'risk adjusted', which means it takes account of the relative riskiness of the asset. After all, riskier assets will have higher expected returns than less risky assets. If an asset's return is even higher than the risk adjusted return, that asset is said to have "positive alpha" or "abnormal returns". Investors are constantly seeking investments that have higher alpha.

Since Eugene Fama, many academics believe financial markets are too efficient to allow for repeatedly earning positive Alpha, unless by chance. To the contrary, empirical studies of mutual funds spearheaded by Russ Wermers usually confirm managers' stock-picking talent, finding positive Alpha. However, they also show that after fees and expenses are deducted, the effective Alpha for investors is negative. (These results also explain why passive investing is increasingly popular.)Nevertheless, Alpha is still widely used to evaluate mutual fund and portfolio manager performance, often in conjunction with the Sharpe ratio and the Treynor ratio.in this case ,only Tesco have a positive Alpha, indicating that investing in Tesco can allow investor for repeatedly earning abnormal return.

The Sharpe ratio is a measure of the excess return (or Risk Premium) per unit of risk in an investment asset or a trading strategy, named after William Forsyth Sharpe. Since its revision by the original author in 1994, it is defined as:

S = \frac{R-R_f}{\sigma} = \frac{E[R-R_f]}{\sqrt{\mathrm{var}[R-R_f]}},

where R is the asset return, Rf is the return on a benchmark asset, such as the risk free rate of return, E[R − Rf] is the expected value of the excess of the asset return over the benchmark return, and σ is the standard deviation of the excess of the asset return over the benchmark return.[1] In practice, σ is often incorrectly calculated as the standard deviation of the asset return, as opposed to the standard deviation of the numerator. However, this typically doesn't materially affect results or conclusions based on those results.

Strengths and weaknesses

The Sharpe ratio has as its principal advantage that it is directly computable from any observed series of returns without need for additional information surrounding the source of profitability. Other ratios such as while the Treynor ratio works only with systematic risk of a portfolio, the Sharpe ratio observes both systematic and idiosyncratic risks. The returns measured can be of any frequency (i.e. daily, weekly, monthly or annually), as long as they are normally distributed, as the returns can always be annualized. Herein lies the underlying weakness of the ratio - not all asset returns are normally distributed. Abnormalities like kurtosis, fatter tails and higher peaks, or skewness on the distribution can be a problematic for the ratio, as standard deviation doesn't have the same effectiveness when these problems exist. Sometimes it can be downright dangerous to use this formula when returns are not normally distributed.

In this case, only the TESCO have a positive SHARP ratio, another have negative ratio. The Tesco is still worthwhile for investing. Because it is a dimensionless ratio, lay people find it difficult to interpret Sharpe Ratios of different investments. For example, how much better is an investment with a Sharpe Ratio of 0.5 than one with a Sharpe Ratio of -0.2? This weakness was well addressed by the development of the Modigliani Risk-Adjusted Performance measure, which is in units of percent return -- universally understandable by virtually all investors.

Treynor ratio

The Treynor ratio named after Jack L. Treynor,[2] is a measurement of the returns earned in excess of that which could have been earned on an investment that has no diversifiable risk (e.g., Treasury Bills or a completely diversified portfolio), per each unit of market risk assumed. The Treynor ratio relates excess return over the risk-free rate to the additional risk taken; however, systematic risk is used instead of total risk. The higher the Treynor ratio, the better the performance of the portfolio under analysis.There is some limitation when using the treynor rato as a measurement of portfolio. Like the Sharpe ratio, the Treynor ratio (T) does not quantify the value added, if any, of active portfolio management. It is a ranking criterion only. A ranking of portfolios based on the Treynor Ratio is only useful if the portfolios under consideration are sub-portfolios of a broader, fully diversified portfolio. If this is not the case, portfolios with identical systematic risk, but different total risk, will be rated the same. But the portfolio with a higher total risk is less diversified and therefore has a higher unsystematic risk which is not priced in the market. An alternative method of ranking portfolio management is Jensen's alpha, which quantifies the added return as the excess return above the security market line in the capital asset pricing model. As they two both determine rankings based on systematic risk alone, they will rank portfolios identically.in this case, when using the treynor rato to measure the stock, Tesco have a biggest ratio then rank 1, all of four companies have relatively small ratio, indicating that investing in Tesco can make a high return compared to the another four at a certain risk.

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