Investing

By definition, the market itself has an underlying beta of 1.0, and individual stocks are ranked according to how much they deviate from the macro market (for simplicity purposes, the S&P 500 is usually used as a proxy for the market as a whole). A stock that swings more than the market (i.e. more volatile) over time has a beta whose absolute value is above 1.0. If a stock moves less than the market, the absolute value of the stock's beta is less than 1.0.

More specifically, a stock that has a beta of 2 follows the market in an overall decline or growth, but does so by a factor of 2; meaning when the market has an overall decline of 3% a stock with a beta of 2 will fall 6%. Betas can also be negative, meaning the stock moves in the opposite direction of the market: a stock with a beta of -3 would decline 9% when the market goes up 3% and conversely would climb 9% if the market fell by 3%.

Higher-beta stocks mean greater volatility and are therefore considered to be riskier, but are in turn supposed to provide a potential for higher returns; low-beta stocks pose less risk but also lower returns. In the same way a stock's beta shows its relation to market shifts, it also is used as an indicator for required returns on investment (ROI). If the market with a beta of 1 has an expected return increase of 8%, a stock with a beta of 1.5 should increase return by 12%.

This expected return on equity, or equivalently, a firm's cost of equity, can be estimated using the Capital Asset Pricing Model (CAPM). According to the model, the expected return on equity is a function of a firm's equity beta (β_E) which, in turn, is a function of both leverage and asset risk (β_A):

where:

• K_E = firm's cost of equity
• R_F = risk-free rate (the rate of return on a "risk free investment", e.g. U.S. Treasury Bonds)
• R_M = return on the market portfolio
• 

because:

and

Firm Value (V) = Debt Value (D) + Equity Value (E)

An indication of the systematic riskiness attaching to the returns on ordinary shares. It equates to the asset Beta for an ungeared firm, or is adjusted upwards to reflect the extra riskiness of shares in a geared firm., i.e. th Geared Beta.

Choice of benchmark

Published betas typically use a stock market index such as S&P 500 as a benchmark. The benchmark should be chosen to be similar to the other assets chosen by the investor. Other choices may be an international index such as the MSCI EAFE. The choice of the index need not reflect the portfolio under question: beta for e.g. gold bars compared to the S&P 500 may be low or negative carrying the information that gold does not track stocks and may provide a mechanism for reducing risk. The restriction to stocks as a benchmark is somewhat arbitrary. Sometimes the market is defined as "all investable assets" (see Roll's critique); unfortunately, this includes lots of things for which returns may be hard to measure.

Beta volatility and correlation

β = (σ / σ_m)r

That is, beta is a combination of volatility and correlation. For example, if one stock has low volatility and high correlation, and the other stock has low correlation and high volatility, beta can decide which is more "risky".

In other words, beta sets a floor on volatility. For example, if market volatility is 10%, any stock (or fund) with a beta of 1 must have volatility of at least 10%.

Another way of distinguishing between beta and correlation is to think about direction and magnitude. If the market is always up 10% and a stock is always up 20%, the correlation is one (correlation measures direction, not magnitude). However, beta takes into account both direction and magnitude, so in the same example the beta would be 2 (the stock is up twice as much as the market).

Definition

The formula for the beta of an asset within a portfolio is

,

where r_a measures the rate of return of the asset, r_p measures the rate of return of the portfolio, and Cov(r_a,r_p) is the covariance between the rates of return. In the CAPM formulation, the portfolio is the market portfolio that contains all risky assets, and so the r_p terms in the formula are replaced by r_m, the rate of return of the market.

Beta is also referred to as financial elasticity or correlated relative volatility, and can be referred to as a measure of the sensitivity of the asset's returns to market returns, its non-diversifiable risk, its systematic risk or market risk. On an individual asset level, measuring beta can give clues to volatility and liquidity in the marketplace. On a portfolio level, measuring beta is thought to separate a manager's skill from his or her willingness to take risk.

The beta coefficient was born out of linear regression analysis. It is linked to a regression analysis of the returns of a portfolio (such as a stock index) (x-axis) in a specific period versus the returns of an individual asset (y-axis) in a specific year. The regression line is then called the Security Characteristic Line (SCL).

α_a is called the asset's alpha coefficient and β_a is called the asset's beta coefficient. Both coefficients have an important role in Modern portfolio theory.

For an example, in a year where the broad market or benchmark index returns 25% above the risk free rate, suppose two managers gain 50% above the risk free rate. Since this higher return is theoretically possible merely by taking a leveraged position in the broad market to double the beta so it is exactly 2.0, we would expect a skilled portfolio manager to have built the outperforming portfolio with a beta somewhat less than 2, such that the excess return not explained by the beta is positive. If one of the managers' portfolios has an average beta of 3.0, and the other's has a beta of only 1.5, then the CAPM simply states that the extra return of the first manager is not sufficient to compensate us for that manager's risk, whereas the second manager has done more than expected given the risk. Whether investors can expect the second manager to duplicate that performance in future periods is of course a different question.

Beta (finance)

The beta coefficient, in terms of finance and investing, describes how the expected return of a stock or portfolio is correlated to the return of the financial market as a whole.

An asset with a beta of 0 means that its price is not at all correlated with the market; that asset is independent. A positive beta means that the asset generally follows the market. A negative beta shows that the asset inversely follows the market; the asset generally decreases in value if the market goes up and vice versa (as is common with precious metals).

Correlations are evident between companies within the same industry, or even within the same asset class (such as equities), as was demonstrated in the Wall Street crash of 1929. This correlated risk, measured by Beta, creates almost all of the risk in a diversified portfolio.

The beta coefficient is a key parameter in the capital asset pricing model (CAPM). It measures the part of the asset's statistical variance that cannot be mitigated by the diversification provided by the portfolio of many risky assets, because it is correlated with the return of the other assets that are in the portfolio. Beta can be estimated for individual companies using regression analysis against a stock market index.

Earnings yield

Earnings yield is the quotient of earnings per share divided by the share price. It is the reciprocal of the P/E ratio.

The earnings yield is quoted as a percentage, allowing an easy comparison to going bond rates.

Applications

The earnings yield can be used to compare the earnings of a stock, sector or the whole market against bond yields. Generally, the earnings yields of equities are higher than the yield of risk-free treasury bonds reflecting the additional risk involved in equity investments. The average P/E ratio for U.S. stocks from 1900 to 2005 is 14,^{[citation needed]} which equates to an earnings yield of over 7%.

The earnings yield is also the cost to a publicly traded company of raising expansion capital through the issuance of stock.

Other uses

Earnings yield is one of the factors discussed in Joel Greenblatt's The Little Book That Beats the Market. However, Greenblatt uses an adjusted earnings yield formula to account for the fact that different companies have different debt levels and tax rates.

Stock pricing book value

To clearly distinguish the market price of shares from the core ownership equity or shareholders' equity, the term 'book value' is often used since it focuses on the values that have been added and subtracted in the accounting books of a business (assets - liabilities). The term is also used to distinguish between the market price of any asset and its accounting value which depends more on historical cost and depreciation. It may be used interchangeably with carrying value. While it can be used to refer to the business' total equity, it is most often used:

• as a 'per share' value': The balance sheet Equity value is divided by the number of shares outstanding at the date of the balance sheet (not the average o/s in the period).
• as a 'diluted per share value': The Equity is bumped up by the exercise price of the options, warrants or preferred shares. Then it is divided by the number of shares that has been increased by those added.

Uses

1. Book value is used in the financial ratio price/book. It is a valuation metric that sets the floor for stock prices under a worst-case scenario. When a business is liquidated, the book value is what may be left over for the owners after all the debts are paid. Paying only a price/book = 1 means the investor will get all his investment back. Shares of capital intensive industries trade at lower price/book ratios because they generate lower earnings per dollar of assets. Business depending on human capital will generate higher earnings per dollar of assets, so will trade at higher price/book ratios.
2. Book value per share can be used to generate a measure of comprehensive earnings, when the opening and closing values are reconciled. BookValuePerShare, beginning of year - Dividends + ShareIssuePremium + Comprehensive EPS = BookValuePerShare, end of year.

Changes are caused by

1. The sale of shares/units by the business increases the total book value. Book/sh will increase if the additional shares are issued at a price higher than the pre-existing book/sh.
2. The purchase of its own shares by the business will decrease total book value. Book/sh will decrease if more is paid for them than was received when originally issued (pre-existing book/sh).
3. Dividends paid out will decrease book value and book/sh.
4. Comprehensive earnings/losses will increase/decrease book value and book/sh. Comprehensive earnings, in this case, includes net income from the Income Statement, foreign exchange translation changes to Balance Sheet items, accounting changes applied retroactively, and the opportunity cost of options exercised.

New share issues and dilution

The issue of more shares does not necessarily decrease the value of the current owner. While it is correct that when the number of shares is doubled the EPS will be cut in half, it is too simple to be the full story. It all depends on how much was paid for the new shares and what return the new capital earns once invested. See the discussion at stock dilution.

Net book value of long term assets

Book value is often used interchangeably with "net book value" or "carrying value", which is the original acquisition cost less accumulated depreciation, depletion or amortization.