Beta (finance) - Academic Theory

Academic Theory

Academic theory claims that higher-risk investments should have higher returns over the long-term. Wall Street has a saying that "higher return requires higher risk", not that a risky investment will automatically do better. Some things may just be poor investments (e.g., playing roulette). Further, highly rational investors should consider correlated volatility (beta) instead of simple volatility (sigma). Theoretically, a negative beta equity is possible; for example, an inverse ETF should have negative beta to the relevant index. Also, a short position should have opposite beta.

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) + Cash and Risk-Free Securities = 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. the Geared Beta.