Loading the player...

What is 'R-Squared'

R-squared is a statistical measure that represents the percentage of a fund or security's movements that can be explained by movements in a benchmark index. For example, an R-squared for a fixed-income security versus the Barclays Aggregate Index identifies the security's proportion of variance that is predictable from the variance of the Barclays Aggregate Index. The same can be applied to an equity security versus the Standard and Poor's 500 or any other relevant index.

BREAKING DOWN 'R-Squared'

R-squared values range from 0 to 1 and are commonly stated as percentages from 0 to 100%. An R-squared of 100% means all movements of a security are completely explained by movements in the index. A high R-squared, between 85% and 100%, indicates the fund's performance patterns have been in line with the index. A fund with a low R-squared, at 70% or less, indicates the security does not act much like the index. A higher R-squared value indicates a more useful beta figure. For example, if a fund has an R-squared value of close to 100% but has a beta below 1, it is most likely offering higher risk-adjusted returns.

R-Squared Calculation Example

The calculation of R-squared requires several steps. First, assume the following set of (x, y) data points: (3, 40), (10, 35), (11, 30), (15, 32), (22, 19), (22, 26), (23, 24), (28, 22), (28, 18) and (35, 6).

To calculate the R-squared, an analyst needs to have a "line of best fit" equation. This equation, based on the unique date, is an equation that predicts a Y value based on a given X value. In this example, assume the line of best fit is: y = 0.94x + 43.7

With that, an analyst could compute predicted Y values. As an example, the predicted Y value for the first data point is:

y = 0.94(3) + 43.7 = 40.88

The entire set of predicted Y values is: 40.88, 34.3, 33.36, 29.6, 23.02, 23.02, 22.08, 17.38, 17.38 and 10.8. Next, the analyst takes each data point's predicted Y value, subtracts the actual Y value and squares the result. For example, using the first data point:

Error squared = (40.88 - 40) ^ 2 = 0.77

The entire list of error's squared is: 0.77, 0.49, 11.29, 5.76, 16.16, 8.88, 3.69, 21.34, 0.38 and 23.04. The sum of these errors is 91.81. Next, the analyst takes the predicted Y value and subtracts the average actual value, which is 25.2. Using the first data point, this is:

(40.88 - 25.2) ^ 2 = 14.8 ^ 2 = 219.04. The analyst sums up all these differences, which in this example, equals 855.6.

Lastly, to find the R-squared, the analyst takes the first sum of errors, divides it by the second sum of errors and subtracts this result from 1. In this example it is:

R-squared = 1 - (91.81 / 855.6) = 1 - 0.11 = 0.8

RELATED TERMS
  1. Coefficient of Determination

    A measure used in statistical model analysis to assess how well ...
  2. Risk Measures

    Statistical measures that are historical predictors of investment ...
  3. Beta

    Beta is a measure of the volatility, or systematic risk, of a ...
  4. Covariance

    A measure of the degree to which returns on two risky assets ...
  5. Covered Interest Arbitrage

    The practice of using favorable interest rate differentials to ...
  6. Index Hugger

    A managed mutual fund that tends to perform much like a benchmark ...
Related Articles
  1. Investing

    R-Squared

    Learn more about this statistical measurement used to represent movement between a security and its benchmark.
  2. Investing

    How to Pick the Best Stocks? Listen to Customers (AMZN, PZZA)

    Rated top in customer service, these companies have delivered impressive stock performance over the past year.
  3. Investing

    How This New ETF Tracks Millennial Consumer Habits

    A recently launched ETF aims to track Millennial consumer habits.
  4. Investing

    Understanding Volatility Measurements

    How do you choose a fund with an optimal risk-reward combination? We teach you about standard deviation, beta and more!
  5. Financial Advisor

    Does Your Investment Manager Measure Up?

    These key stats will reveal whether your advisor is a league leader or a benchwarmer.
  6. Investing

    Consumer Defensive Stocks: Are These 2016's Best?

    These eight consumer defensive stocks meet strict objective parameters for top-tier investment potential in 2016.
  7. Investing

    5 Ways To Measure Mutual Fund Risk

    These statistical measurements highlight how to mitigate risk and increase rewards.
  8. Investing

    PTTRX: A Risk Statistics Case Study

    Analyze the risk metrics of the mutual fund PTTRX. Find out what standard deviation, capture ratios and R-squared indicate about correlation and volatility.
  9. Financial Advisor

    Are High-Multiple Tech Stocks Winners or Losers?

    Are high-multiple tech stocks a good investment right now?
  10. Investing

    PRHSX: Risk Statistics of Health Sciences Mutual Fund

    Examine the risk metric of the T. Rowe Price Health Sciences Fund. Analyze beta, capture ratios and standard deviation to assess volatility and systematic risk.
RELATED FAQS
  1. What's the difference between r-squared and adjusted r-squared?

    Learn how R-squared and adjusted R-squared values differ, how they are calculated, the relationship between them and how ... Read Answer >>
  2. Where do funds report their r-squared?

    Learn where to find R-squared calculations for mutual funds. Explore R-squared, Alpha and Beta and how these calculations ... Read Answer >>
  3. What's the difference between r-squared and correlation?

    Discover how R-squared calculations determine the practical usefulness of beta and alpha correlations between individual ... Read Answer >>
  4. What's the relationship between r squared and beta?

    Learn about the relationship between R-squared and Beta. Explore how the concepts are related and often used in conjunction ... Read Answer >>
  5. How do you calculate r-squared in Excel?

    Calculate R-squared in Microsoft Excel by creating two data ranges to correlate. Use the Correlate formula to correlate both ... Read Answer >>
Hot Definitions
  1. Magna Cum Laude

    An academic level of distinction used by educational institutions to signify an academic degree which was received "with ...
  2. Cover Letter

    A written document submitted with a job application explaining the applicant's credentials and interest in the open position. ...
  3. 403(b) Plan

    A retirement plan for certain employees of public schools, tax-exempt organizations and certain ministers. Generally, retirement ...
  4. Master Of Business Administration - MBA

    A graduate degree achieved at a university or college that provides theoretical and practical training to help graduates ...
  5. Liquidity Event

    An event that allows initial investors in a company to cash out some or all of their ownership shares and is considered an ...
  6. Job Market

    A market in which employers search for employees and employees search for jobs. The job market is not a physical place as ...
Trading Center