Understanding beta

Beta or CAPM beta was introduced by William Sharp, who won a Nobel Prize for developing CAPM, capital asset pricing model. Sharp argued that only that part of the risk associated with an investment that cannot be diversified away should be priced on the market. This kind of risk is known as systematic risk which arises from market structure or dynamics which produce shocks or uncertainty faced by all agents in the market. In the financial field variance is used to measure the deviations of returns around mean and it is used as an absolute measure of risk. Beta on the other hand is a relative risk measure that captures the co-movement of an investment relative to the market.

The betas that serve as a risk measure in number of risk models in finance have two basic characteristics that we need to keep in mind before estimating the parameter. The first key assumption is that betas measure the risk added to a well-diversified portfolio, rather than total risk. It means that it is entirely possible that an investment with high individual risk has a low risk, in terms of market risk. The second key characteristic is that betas measure the relative risk of an asset and are consequently standardized around one. Other investments are then ranked according to how much they deviate from the market. It is intuitive that market capitalization weighted average of beta across all investments should be equal to one. Meaning that a market portfolio in theory should include all investable assets and the beta of this market portfolio is exactly one.

There is a simple approach to estimate beta by regressing the returns on any asset against the market returns. It is clear that there is no possible way that one can obtain the data on market portfolio, which consists of all investable assets. In order to estimate beta parameter a proxy for market returns must be used. In most cases analysts use most relevant stock index as a proxy for market movement. It is important to understand that, although the estimation of the parameter is not mathematically complex, the estimated parameter can vary significantly depending on the inputs of the estimation procedure.

Factors that impact beta

There are three choices regarding the data that need to be made before estimating and all of them have meaningful impact on the results.

First is a choice of the length of the estimation period. Most of the estimations are done using periods between two years and five years, but there is no recipe for choosing the optimal estimation period. In selecting the time period for beta estimation there is trade off involved. By going back further in time there is an advantage of having more observations in the regression analysis, but this could be offset by the fact that the firm itself might have changed its characteristics over that period. Keep in mind that we are not looking for the most accurate estimation of beta over the last period, our goal is to obtain best possible beta for the future. The choice regarding the time period clearly depends on the company that is being examined. We can go further back in time for firms which have remained fairly stable in terms of business mix and leverage. In contrast shorter time period should be used for firms that have restructured, acquired or divested business, or changed their financial leverage over the last couple of years.

The second important decision to make is to decide on return interval, used to measure historical returns. Most of the specialists use monthly or weekly returns to estimate betas. Using shorter (daily) returns would increase the number of observations in the regression, but on the other hand it can result in bias estimates of beta. There are numerous stocks on the market that are not traded daily, which means that their data include a significant number of days with zero returns. This can decrease the measured correlation with the market index and directly impacts the estimated beta. For some stocks even weekly returns can result in biased estimations of beta, in such cases the monthly returns should be used. Annual returns are evidently not appropriate for regression analysis, because of the small number of observations.

The final decision that needs to be made has to do with the proxy used to best imitate the market movement. Equity indices are most commonly used as a proxy for market return. Usually indices include only a specific subset of companies, which are not the best representation of market movements. Nevertheless financial analysts still use them mainly because of the data availability. For comparison there are no indices reported on weekly basis that include numerous asset classes, such as real estate and fixed income assets. What is the most appropriate index to use for estimation? Indices that include more securities should yield better estimates than indices that include less.