How to Calculate the Beta of a Stock and Portfolio

Beta is the 2nd letter in the Greek alphabet, and the financial world uses it to refer to the sensitivity of an asset’s price compared to a specific index or benchmark. Beta is also used as a measure of an asset’s risk relative to that benchmark. The beta of a stock tells an investor how much a stock moves compared to the general stock market it trades in. Read on to find out more about this very important asset risk metric and how to use it.

Beta Calculation

The beta can readily be computed for a stock or portfolio in a spreadsheet like Excel using opening and closing stock price data for each stock and the relevant stock market index. Three methods for calculating the beta on an individual stock are described below.

Variance/Covariance Method

Calculating beta using the covariance/variance formula is probably the most common method of calculating the beta of a stock. This formula takes the covariance of the return of the market and the return of the asset and then divides that by the market return’s variance over a given timeframe.

To calculate beta for a stock using this method, you first need to understand the following terms:

• Variance (σ2): The spread between numbers in a specific data set. In finance, the variance is commonly used to calculate how each asset in a portfolio performs in relation to the other assets in the portfolio. It can also be used to determine the amount the market moves in relation to its mean.
• Covariance: A measure used in finance to determine the similarity and degree of the directional relationship between the returns on two assets. If two stocks move in the same direction, then they have a positive covariance of an amount proportional to the degree they do so. If they move in opposite directions, the covariance is negative in an amount related to their divergance.

Furthermore, given that:

Return = closing price – opening price/opening price

The formula for the beta calculation could then be written:

Beta = Covariance of market and asset returns / Variance of the market’s returns

or

Covariance (ri , rm) = Σ ( ri , n – ri , avg ) multiplied by ( rm , n – rm , avg ) / (n-1)

Variance (rm) = Σ (rm , n – rm , avg ) ^2 / n

Therefore:

Beta = Covariance (ri , rm) / Variance (rm)

Where:

Σ = standard deviation of stock returns

ri = average expected return on asset i

rm = average expected rate of return on the general market

The Correlation Method

This method of calculating beta involves dividing the standard deviation of an asset’s returns by the standard deviation of the market’s returns and then multiplying the result by the correlation of the asset’s and the market’s returns:

?i = (σi / σm)*Correlation (ri, rm)

Where:

?i= beta of asset i

ri = average expected return on asset i

rm = average expected rate of return on the general market

σi = standard deviation of the asset’s returns

σm= standard deviation of the market’s returns

The Slope Method

Beta can also be calculated for an asset using the SLOPE function in Microsoft Excel. This function computes the slope of a regression line based on two sets of data points. To compute the beta, these data point sets should correspond to the set of percent changes in a market index and the set of percent changes in the specific asset’s price observed over the same time period.

You would enter this formula into a cell to compute beta from market and stock returns:

beta value = SLOPE (Market returns range, Stock returns range)

Where:

Market returns range = Rows and columns of 1st market return and last market return separated by a colon (:), as in A1:A500 where column A contains 500 daily returns of the market.

Stock returns range = Rows and columns of first stock return and last stock return separated by a colon (:), as in B1:B500 where column B contains 500 daily returns of the stock.

As before, returns are calculated for each period for the stock and the market by subtracting the open from the close and then dividing by the open.

Calculating Beta Example

To calculate the beta of Apple Inc. (NASDAQ: AAPL) as a specific example using the covariance/variance method, you would take the covariance of the expected return on AAPL stock to the average expected return on the S&P 500 index and then divide that number by the variance in the overall S&P 500 market’s average expected return.

Let’s say the covariance of the S&P 500’s return to AAPL’s returns is 0.032, which is then divided by the average market return’s variance of 0.0235 to give a beta of 1.36. The formula would look like this:

AAPL beta value = 0.032 / 0.0235 = 1.36

In practice, a beta of 1.36 means that the returns involved in holding Apple stock are about 36% more volatile than those derived from the S&P 500 index. Holding Apple stock presents a greater degree of investment risk than holding a portfolio of stocks conforming to the overall S&P 500 market.

In general, a stock that moves in tandem with the market would have a beta of 1.0. If the stock moves less than the general market, the beta would be below 1.0, while a stock that moves more than the general market would have a beta of more than 1.0.

Calculate Beta of a Portfolio

As seasoned investors and portfolio managers know, an important consideration when building a portfolio consists of the level of diversification. Diversifying stocks in your portfolio lowers investment risk — owning stocks in a wide range of companies and industries tends to reduce the overall volatility of the portfolio.

Accordingly, when you own stocks in a broad number of companies, your exposure to market events generally decreases because some stocks remain unaffected or are affected either positively or negatively by an event. This is one good reason that portfolio managers give importance to the beta of a portfolio.

To calculate the beta of a portfolio, follow the steps outlined below:

• Calculate the value of each stock you own in your portfolio by listing the number of shares you have multiplied by the current stock price.
• After you’ve determined the value of each stock holding in the portfolio, calculate what proportion or share each stock represents in the portfolio.
• Multiply those proportions by the beta of each stock. For example, if Apple makes up 0.30 of the portfolio and has a beta of 1.36, then its weighted beta in the portfolio would be 1.36 x 0.30 = 0.408.
• Add up the weighted beta numbers of each stock. The sum of the weighted betas of all the stocks in the portfolio will give you the portfolio’s overall beta.

In the table above, the value of the stock in the portfolio and the proportion or share of the portfolio of each stock can be seen in the first two columns. The sum of the weighted betas in the furthest column to the right gives you the overall beta of the portfolio.

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Using Beta to Evaluate Risk

If you’ve been trading or investing in recent times, then you probably already understand how vital assessing the risk involved in a stock or market is before taking a position. By diversifying your portfolio, you’ll probably reduce the risk of the portfolio against general market moves.

Since beta is based on price and determined relative to the market; however, it may not be the best assessment of risk for some stocks. To accurately determine the risk of a stock, take into account the company’s fundamentals, its earnings and business prospects and the future market for its products or services. Other factors that can indicate risk include the firm’s level of debt, the cost of servicing that debt and the value of assets.

Remember that if the overall volatility of the market increases, then a stock with a beta of one would also experience the same higher volatility levels. While the beta of a stock can be useful as a risk assessment, it is relative and can change with market volatility. Make sure you research your investments thoroughly and have a suitable risk appetite before committing your funds to a particular stock.

Frequently Asked Questions