An asset's beta is a metric describing how likely it is to change in value as broader financial markets change. You can measure the beta of an individual asset, such as a stock, with this formula: **Asset Beta = Covariance/Variance**.

Covariance is the joint variability of two variables, such as an individual stock and a market index. Variance measures how far a set of values spreads out from the average value. Its square root is the standard deviation. In symbols, the formula is:

**β = Cov(r _{i}, r_{m}) / Var(r_{m})**

where:

Cov(r_{i}, r_{m}) = [∑(r_{i}- r_{iA}) (r_{m} - r_{mA})] / (n-1)

Var(r_{m}) = [∑(r_{m} - r_{mA})^{2}] / (n-1)

**r _{i}** = expected return on an individual asset

**r _{m}** = average expected return on the market portfolio

**A** = the average return of the asset or portfolio

**n** = number of observations

The return on an asset or portfolio equals ((opening price – closing price)/opening price).

## Example Calculation for the Beta of an Asset

You can use Microsoft Excel or Google Sheets for calculating beta. You can calculate a stock's beta by constructing arrays of prices (usually daily closing prices) and stock returns ((closing stock price – previous closing)/previous closing) of the stock and an overall market index for a set number of consecutive observations.

For example, you could create a table where each row contains the daily closing price, the returns for stock X and the stock market returns of the S&P 500 benchmark index. According to the U.S. Securities and Exchange Commission, the S&P 500 index represents a sample of leading companies in leading industries within the U.S. economy.

| | | | |
---|---|---|---|---|

| | | | |

1 | $10.20 | 3,845.53 | ||

2 | $10.35 | 1.47% | 3,899.22 | 1.40% |

3 | $9.98 | -3.57% | 3,814.57 | -2.17% |

4 | $10.45 | 4.74% | 3,965.69 | 3.96% |

5 | $10.69 | 2.30% | 3,789.55 | -4.44% |

6 | $11.22 | 4.94% | 3,954.56 | 4.35% |

7 | $12.28 | 9.47% | 3,920.44 | -0.86% |

8 | $11.30 | -7.99% | 3,968.50 | 1.23% |

9 | $9.54 | -15.59% | 4,009.30 | 1.03% |

10 | $9.09 | -4.71% | 3,956.17 | -1.33% |

11 | $12.84 | 41.21% | 3,870.60 | -2.16% |

12 | $10.22 | -20.35% | 3,788.88 | -2.11% |

The spreadsheet returns a covariance of 0.002629 and a variance of 0.001504. Dividing the variance into the covariance gives a beta of 1.748.

## Example Calculation for the Beta of an Investment Portfolio

To calculate the beta of a portfolio you have through a brokerage, you sum the weighted betas of each stock inside the portfolio. The portfolio beta formula is:

**βₚ = W₁β₁+W₂ β₂+W₃ β ₃…W _{n} β_{n}**

where:

**β _{p}** = portfolio beta

**n** = asset number

**W _{n}** = weight of asset n

**β _{n }**

*=* beta of asset n

In this example, the allocation of the portfolio consists of stocks X, Y and Z, with the indicated values and betas:

| ||||
---|---|---|---|---|

| | | | |

X | $10,894 | 32.98% | 1.748 | 0.577 |

Y | $14,099 | 42.69% | 0.897 | 0.383 |

Z | $8,037 | 24.33% | 0.551 | 0.134 |

Total | $33,030 | 100.00% | 1.093 |

The 1.093 value resulting from the weighted beta calculation indicates a positively correlated portfolio with slightly higher volatility than the market.

## Interpreting Beta Values

As with individual assets, understanding a portfolio's risk and possible returns is key to making informed investment decisions. Measurements such as portfolio beta provide data that can help an investor reshape a portfolio in changing economic times or ensure that a group of investments has a high probability of performing as expected.

Aswath Damodaran explains in a New York University paper that the Capital Asset Pricing Model (CAPM) postulates a linear relationship between the expected return for an asset and its beta – the slope of a linear regression. When an asset has a beta of zero, it changes independently of fluctuations in the market. A positive value indicates that an asset rises when the markets rise and falls when markets fall. Conversely, a negative beta indicates that an asset moves in the opposite direction of the financial market.

The market has a beta of 1.0, so an asset or portfolio with a high beta (greater than 1.0) is more volatile than the market, while it would be less volatile if the beta of a stock is under 1.0. Low-beta stocks are only weakly correlated to the market.

Portfolio beta shows how closely a portfolio follows more general market trends. This allows an investor to take advantage of projected market growth or hedge against market downtrends through diversification into negative-beta assets that will move contrary to a market. Portfolio beta measures also provide a reference point for comparing projected returns for markets, individual assets and portfolios.

| | | | |
---|---|---|---|---|

| | | | |

1 | $10.20 | 3,845.53 | ||

2 | $10.35 | 1.47% | 3,899.22 | 1.40% |

3 | $9.98 | -3.57% | 3,814.57 | -2.17% |

4 | $10.45 | 4.74% | 3,965.69 | 3.96% |

5 | $10.69 | 2.30% | 3,789.55 | -4.44% |

6 | $11.22 | 4.94% | 3,954.56 | 4.35% |

7 | $12.28 | 9.47% | 3,920.44 | -0.86% |

8 | $11.30 | -7.99% | 3,968.50 | 1.23% |

9 | $9.54 | -15.59% | 4,009.30 | 1.03% |

10 | $9.09 | -4.71% | 3,956.17 | -1.33% |

11 | $12.84 | 41.21% | 3,870.60 | -2.16% |

12 | $10.22 | -20.35% | 3,788.88 | -2.11% |

References

Writer Bio

Eric Bank is a senior business, finance and real estate writer, freelancing since 2002. He has written thousands of articles about business, finance, insurance, real estate, investing, annuities, taxes, credit repair, accounting and student loans. Eric writes articles, blogs and SEO-friendly website content for dozens of clients worldwide, including get.com, badcredit.org and valuepenguin.com. Eric holds two Master's Degrees -- in Business Administration and in Finance. His website is ericbank.com.