Mutual Fund Unlocked: R-squared, Beta and Standard Deviation
To analyse the relationship between portfolio and index as well as its volatility, statistical tools like R-squared, Beta and Standard deviation are used. These tools analyse the risk involved in the schemes and assists investor to choose the best suited investment.
Standard Deviation (SD)
Standard deviation is the tool used to evaluate the volatility in the fund's returns relative to its average. That is, it states the deviation of funds return from the historical average returns of the fund.
Formula for Standard Deviation is
Standard Deviation= Square Root of variance
Where
Variance= (Sum of difference between monthly return(squared) and its average / number of monthly return data points – 1)
Higher the SD higher the volatility in funds returns so investors are advised to prefer funds with lower SD that is volatility.
R-squared
R-squared is the statistical tool used to determine the relationship between portfolio and its index. It is expressed as a percentage range of 1-100%.
R-squared is calculated by squaring the correlation, where correlation is division of covariance between index and the portfolio and standard deviation of both index and portfolio.
So, the formula for the calculation of R-squared is
R-squared= Square of correlation
Where
Correlation = Covariance between Benchmark(Index) and Portfolio/ (SD of Portfolio*SD of the benchmark)
SD= standard Deviation
Range of R-Squared
1-40%- This range shows the low correlation between portfolio returns and Index returns.
40-70%- This range shows the average correlation between portfolio returns and Index returns.
70-100%- This range shows the good correlation between portfolio returns and Index returns.
Usually Index Funds have the R-squared close to 100.
Beta
Beta is a tool which measures fund’s volatility compared to its index. It states the possibility of swing in funds performance in comparison to its index.
Beta is calculated by multiplying the R-square with division of SD of fund and SD of the index
So, formula for Beta is
Beta= Standard deviation of Fund/Standard deviation of benchmark * R-square
When the stock price movement is same as per market then resultant Beta will be equal to 1.
When the stock price movement beats market then resultant Beta will exceed 1.
When the stock price moves less as per market then resultant Beta will be less than 1.
To unlock more insights regarding mutual fund and its analysis, Stay Tuned to Mutual Funds Unlocked.
Mutual Fund Unlocked: Basics of Mutual Funds (Part I)
Mutual Fund Unlocked: Basics of Mutual Funds (Part II)
Mutual Fund Unlocked: NAV and Mutual Fund Costs
Mutual Fund Unlocked: Understanding the Ratios of Mutual Funds
Mutual Fund Unlocked: Information Ratio and Sortino Ratio