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# Beta

Beta is a measure of volatility of a stock's returns. It compares how much the stock's returns move relative to the returns of a known market or index, such as the S&P 500.

## Expanded Definition

Before discussing what the number means, let's look at how it is calculated. The movement of a stock's returns over time is compared to the movement of the returns of some comparable index. The average amount that the stock's return moves relative to the movement of the return of the index is the beta. By definition, when the two move in lockstep, the stock's beta is 1.0. For instance, the stock's return moves up 5% when the return of the index moves up 5% and down 3% when the return of the index moves down 3%.

Beta depends on two factors: the relative volatility of the stock's returns and the index's returns, and the correlation of stock's returns and the index's returns; the product of these two factors is the stock's beta. Thus, it may be that a stock with a beta of 1.0 has returns that are exactly as volatile as the index's returns and in perfect sync with the index's returns, but it is equally possible that a stock with a beta of 1.0 has returns that are 10 times as volatile as the index's returns, but out of sync with the index's returns (having a correlation of 0.1).

Stocks whose returns move by a lesser amount than the index's returns will have a beta lower than 1.0. Stocks whose returns move in larger steps on average than the index's returns, rising and falling rapidly, can have betas greater than 1.0; whether they will have betas greater than 1.0 depends on the correlation of returns between the stock and the index.

Beta values can be positive (which means the returns of the stock and index generally rise or fall together) or negative (which means the returns of the stock generally rise when the returns of the index fall, and vice versa). A beta of zero means that the correlation between the movement of the stock's returns and the index's returns is zero.

### Limitations of beta

The actual value calculated depends heavily on several things:

1. The length of time sampled. Three years will give a different result from five years.
2. The frequency at which the prices are sampled. Once weekly will give a different result from once daily.
3. When the prices are sampled. At close Monday will give a different result from at close Wednesday or at open Friday, for example.
4. The choice of index. A small cap should probably be compared to a small-cap index, like the Russell 2000, instead of the S&P 500, which is a large cap index.

Because of these differences in how beta is calculated, different sites which report beta will very often report (sometimes drastically) different numbers. Be sure that you understand how beta is calculated for the site you use as your source. For best results use beta to compare one stock with others and make sure the beta values used for all the stocks are from the same source (to be sure the values are comparable).

Also, because companies change over time, beta will also change.

### Beta as a proxy for risk

For many investors, the proxy for risk is price volatility. That is, if the price moves up or down a lot, it is often considered more risky than if the price does not move with as large jumps. But that view is flawed for a couple of reasons. First, even very large companies can see the price of their shares move a lot in a very short period of time. When GE or Berkshire Hathaway see their prices move by several percent, you can see that these relatively low-risk companies can still have volatile stock prices. Second, risk is the potential of losing your invested money. That comes about from investing in companies with poor management, lots of competition and poor products, and items such as that. It does not come about from the random fluctuations of the stock price.

Even if price volatility is a good proxy for risk, using beta as a measure is inappropriate: beta is calculated by comparing a stock's returns to the market's returns, not by comparing a stock's prices to the market's prices. As surprising as it may seem, comparing prices gives a very different result than comparing returns. In short, if price volatility is your definition of risk, beta won't help you assess it.