펀드 분석 지표

● Standard Deviation

   Standard deviation is a random variable, or population or multiset of values is a measure of the spread of its values. It is usually denoted with the letter σ (lower case sigma). It is defined as the square root of the variance. In other words, the standard deviation is the root mean square (RMS) deviation of values from their arithmetic mean.

 

The standard deviation of variable X is defined as :

   In finance, standard deviation is a representation of the risk associated with a given security (stocks, bonds, property, etc.), or the risk of a portfolio of securities. Risk is an important factor in determining how to efficiently manage a portfolio of investments because it determines the variation in returns on the asset and/or portfolio and gives investors a mathematical basis for investment decisions. The overall concept of risk is that as it increases, the expected return on the asset will increase as a result of the risk premium earned - in other words, investors should expect a higher return on an investment when said investment carries a higher level of risk.

● Beta Coefficient

   The Beta coefficient, in terms of finance and investing, is a measure of a stock (or portfolio)’s volatility in relation to the rest of the market. Beta is calculated for individual companies using regression analysis.

   The beta coefficient is a key parameter in the capital asset pricing model. It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio.

 

The formula for the Beta of an asset within a portfolio is

● Jensens Alpha

   Jensen's alpha (or Jensen's Performance Index) is used to determine the excess return of a stock, other security, or portfolio over the security's required rate of return as determined by the Capital Asset Pricing Model. This model is used to adjust for the level of beta risk, so that riskier securities are expected to have higher returns. The measure was first used in the evaluation of mutual fund managers by Michael Jensen in the 1970's.

Jensen's alpha = Portfolio Return - (Risk free return + (Market Return - Risk free Return) * Beta)

● Sharpe Ratio

   The Sharpe ratio is a measure of the mean excess return per unit of risk in an investment asset or a trading strategy. Since its revision by the original author made in 1994, it is defined as:

           

   
   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 return.

   The Sharpe ratio is used to characterize how well the return of an asset compensates the investor for the risk taken. When comparing two assets each with the expected return E[R] against the same benchmark with return Rf, the asset with the higher Sharpe ratio gives more return for the same risk. Investors are often advised to pick investments with high Sharpe ratios.

● Treynor Ratio

   The Treynor ratio is a measurement of the returns earned in excess of that which could have been earned on a riskless investment (i.e. Treasury Bill) (per each unit of market risk assumed).

   The Treynor ratio (sometimes called reward-to-volatility ratio) relates excess return over the risk-free rate to the additional risk taken; however systematic risk instead of total risk is used. The higher the Treynor ratio, the better the performance under analysis.

                                             

   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.

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