Asset Betas Research Articles

Deleveraging CAPM: Asset Betas vs. Equity Betas

The classic estimates of CAPM equity betas are notoriously unstable. We suppose that this is mainly due to changes of firm’s leverage over time. In order to take leverage into account, we propose a new approach where asset correlations among firms are pairwise constant, while equity correlations depend on the stochastic evolution of firms’ asset values.

Conic asset pricing and the costs of price fluctuations

Prudent upper and lower valuations from the literature on arbitrage free two price economies provide risk characteristics driving required returns. The risk characteristics assess the risk of price fluctuations. The difference between the upper and lower prudent valuations can be viewed as a capital charge. In addition the lower valuation assesses the down side tail risk. The required risk characteristics may be estimated on a daily basis from past data and we elaborate on how to perform such upper and lower valuations using distorted expectations. Details are provided for calculations using just the raw data, or by first fitting a probability distribution, or in terms of estimated arrival rates for jumps. The valuations are obtained with a dynamic calibration of a parametric distortion on the S&P 500 index options market. Results for required returns based on capital charges and down side risk compensation show an improvement when risk is represented by the arrival rates of jump sizes. For risk assessments based on arrival rates, capital charges constitute between 67 and 85% of the required return. The rest being a charge for downside risk exposures. After the introduction of risk characteristics into required returns there is little scope for covariation measures like asset betas. Different proposed constructions for required returns deliver differences in the value of an invested dollar and associated differences in asset rankings across time.

Finding The Beta For A Portfolio Isn't Obvious: An Educational Example

When a portfolio is not actively managed to maintain a fixed investment percentage in each asset but rather maintains a fixed number of shares for each asset, the portfolio weights will change over time because the market returns of the different assets will not be the same. Consequently, portfolio betas computed as a linear combination of asset betas, which is the usual practice, will be different from betas computed using regression techniques on portfolio returns as is done when evaluating individual assets and mutual funds. The alternative approaches can result in quite different beta statistics and, consequently, inconsistent decisions depending on which method is used.

Effects of IFRS-13 on the relevance of fair value adjusted by credit risk: Evidence from Europe

Accounting harmonization in Europe by International Financial Reporting Standard adoption is a recurrent object of study in the accounting literature. In this paper the consequences of the adoption of Standard-13 are analyzed. In particular, this research analyzes the effects on the implied volatility option (risk) for non-financial companies of three variables: financial leverage, own probability default (Debt Value Adjusted) and financial institutions credit risk (Credit Value Adjusted), before and after the adoption of the accounting standard on fair value. The empirical study focuses on member companies of the European Monetary Union zone to avoid other risk factors different to market risk (such as exchange rate or different risk free rate) and at the same time, easily identify the market portfolio (EUROSTOXX-50). To overcome the problems of endogeneity in the panel data, we use the technique System Generalized Method of Moments with instrumental variables to estimate the parameters. The results show that the leverage effect on excess risk does not change after adopting the Standard, however, its own and the financial institutions default probabilities become statistically significant. Furthermore, this novel methodology allows estimate industry asset betas and, in all cases the asset betas were lower than equity betas and, found an average debt beta of 0.4 for the sample period.

Conic Asset Pricing and the Costs of Price Fluctuations

Prudent upper and lower valuations from the literature on arbitrage free two price economies provide risk characteristics driving required returns. The risk characteristics assess the risk of price fluctuations. The difference between the upper and lower prudent valuations can be viewed as a capital charge. In addition the lower valuation assesses the down side tail risk. The required risk characteristics may be estimated on a daily basis from past data and we elaborate on how to perform such upper and lower valuations using distorted expectations. Details are provided for calculations using just the raw data, or by first fitting a probability distribution, or in terms of estimated arrival rates for jumps. The valuations are obtained with a dynamic calibration of a parameteric distortion on the S&P 500 index options market. Results for required returns based on capital charges and down side risk compensation show an improvement when risk is represented by the arrival rates of jump sizes. For risk assessments based on arrival rates, capital charges constitute between 67% to 85% of the required return. The rest being a charge for downside risk exposures. After the introduction of risk characteristics into required returns there is little scope for covariation measures like asset betas. Different proposed constructions for required returns deliver differences in the value of an invested dollar and associated differences in asset rankings across time.

How Taxes on Firms Reduce the Risk of After-Tax Cash Flows

Most firms make decisions based on one discount rate applied to expected net aftertax cash flows. The need to adjust for differences in risk, other than leverage, is most often neglected. One source of risk differences is the tax system. Even for fully equity-financed firms there can be substantial effects of taxation on after-tax risk when there are depreciation deductions. Among the few studies of these effects, even fewer identify all effects correctly. Some claim to characterize the cost of capital, but fail to identify the marginal investment. When this is taxed together with inframarginal investment, marginal beta differs from average. To find asset betas, observed equity betas should not only be unlevered, but also “unaveraged” and “untaxed.” The problems identified here imply that currently suggested tax reforms may fail. Tax neutrality results rely on firms correctly discounting for risk,

Index-tracking optimal portfolio selection

This paper considers a portfolio selection problem with multiple risky assets where the portfolio is managed to track a benchmark market barometer, such as the S&P 500 index. A tracking optimization model is formulated and the tracking-efficient (TE) portfolios are shown to inherit interesting properties compared with Markowitz mean-variance (MV) optimal portfolios. In comparison to an MV-portfolio, both the beta and the variance of a TE-portfolio are higher by fixed amounts that are independent of the expected portfolio return. These differences increase with index variance, are convex quadratic in the asset betas, and depend on the asset means and covariance matrix. Furthermore, a TE portfolio is obtained by simply extending an MV portfolio by constant adjustments to portfolio weights, independent of the specified mean return of the portfolio, but dependent on the index variance and asset return parameters. Consequently, at lower thresholds of risk, TE portfolios are better-diversified than MV portfolios.

What Drives the Value Premium?: The Role of Asset Risk and Leverage

This paper shows empirically how asset risk and financial leverage interact to explain the equity risk dynamics of value versus growth stocks. During economic downturns, the asset betas and leverage of value firms increase, contributing to a sharp rise in equity betas. Asset betas of growth firms are much less sensitive to economic conditions, and, consistent with the tradeoff theory of capital structure, growth firms are also less levered, contributing to the relative stability of their equity betas. By incorporating instruments that better capture beta dynamics, I show that the interactions of conditional betas with the market risk premium and volatility explain approximately 40% of the unconditional value premium. The Author 2013. Published by Oxford University Press on behalf of The Society for Financial Studies. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com., Oxford University Press.

WACC Calculations in Practice: Incorrect Results due to Inconsistent Assumptions - Status Quo and Improvements

This paper argues that in practical applications the weighted average cost of capital (WACC) is often incorrectly estimated due to the simultaneous use of two inconsistent input parameters: (i) a beta of debt equal to zero when transforming asset betas into equity betas (beta levering) and (ii) a cost of debt above the risk-free interest rate when calculating the WACC. The paper discusses and quantifies the consequences of this inconsistency and offers viable solutions. By replacing the cost of debt with the risk-free rate, a more accurate WACC is calculated and the estimation of the cost of debt becomes obsolete. Furthermore, the paper presents a solution to obtain the correct WACC without increasing the calculation’s complexity.

What Drives the Value Premium: The Role of Asset Risk and Leverage

This paper shows empirically how asset risk and financial leverage interact to explain the equity risk dynamics of value versus growth stocks. During economic downturns, the asset betas and leverage of value firms increase, contributing to a sharp rise in equity betas. Asset betas of growth firms are much less sensitive to economic conditions, and, consistent with the tradeoff theory of capital structure, growth firms are also less levered, contributing to the relative stability of their equity betas. By incorporating instruments that better capture beta dynamics, I show that the interactions of conditional betas with the market risk premium and volatility explain approximately 40% of the unconditional value premium.

Would Stricter Capital Requirements Raise the Cost of Capital? Bank Capital Regulation and the Low Risk Anomaly

Capital requirements for banks must balance a number of factors, including any effects on the cost of capital and in turn the rates available to borrowers. Standard theory predicts that, in perfect and efficient capital markets, reducing banks’ leverage would reduce the risk and cost of their equity but leave the overall weighted average cost of capital unchanged. We test these two predictions empirically. We confirm that the equity of better-capitalized banks has both lower systematic risk (beta) and lower idiosyncratic risk. However, over the last 40 years in the United States, lower risk banks have higher stock returns on a risk-adjusted or even a raw basis, a pattern consistent with a stock market anomaly previously documented in other samples. A simple calibration using historical data suggests that a ten percentage-point increase in Tier 1 capital to risk-weighted assets would have increased the weighted average cost of capital by between 60 and 90 basis points per year. In competitive lending markets, a change of this magnitude would have doubled or tripled spreads, because bank asset betas implied an average risk premium of only 40 basis points above Treasury yields over that same period.

Accounting-based Risk Measurement: An Alternative to Capital Asset Pricing Model Derived Discount Factors

Discount factors have a long tradition of being computed using capital market inputs for the estimation of systematic risk. They are of increasing importance in financial accounting, including the valuation of goodwill and other intangibles. In view of the volatility of stock market returns and their inaccuracy and disjunction from the underlying cash flows of the firm, this paper proposes an alternative accounting-based approach: accountingbased risk measurement. Alternatives to beta are computed from planning and budgeting metrics at firm level to produce consistent risk estimates factoring patterns of revenue and cost behaviour weighted according to their impact on the accounting rate of return. This approach is contrasted with the analysis and interpretation of asset betas in the corporate finance literature.

How Taxes on Firms Reduce the Risk of After-Tax Cash Flows

Most firms make decisions based on one discount rate applied to expected net after tax cash flows. The need to adjust for differences in risk, other than leverage, is most often neglected. One source of risk differences is the tax system. Even for fully equity-financed firms there can be substantial effects of taxation on after-tax risk when there are depreciation deductions. Among the few studies of these effects, even fewer identify all effects correctly. Some claim to characterize the cost of capital, but fail to identify the marginal investment. When this is taxed together with inframarginal investment, marginal beta differs from average. To find asset betas, observed equity betas should not only be unlevered, but also “unaveraged” and “untaxed.” The problems identified here imply that currently suggested tax reforms may fail. Tax neutrality results rely on firms correctly discounting for risk, in particular the risk of tax deductions.

Assessing Project Risk

Finding the appropriate discount rate, or cost of capital, for evaluating investment projects requires an accurate estimate of project risk. This can be challenging because project risk cannot be estimated directly using the CAPM, but must instead be inferred from a set of traded securities, typically the equity betas of comparable firms in the same industry. These equity betas are then unlevered to undo the effect of comparable companies' financial leverage and obtain estimates of “asset” betas, which are then used to estimate project risk.The authors show that asset betas estimated in this way are likely to overestimate project risk. The equity returns of companies are risky not only because of their existing projects but also because of their growth opportunities. Such growth opportunities often include embedded “real options,” such as the option to delay, expand, or abandon a project. Because such real options are similar to leveraged positions in the underlying project, a company's growth opportunities are typically riskier than its existing projects. Therefore, to properly assess project risk, analysts must also unlever the asset betas derived from comparable company stock returns for the leverage contributed by their growth options.The authors derive a simple method for unlevering asset betas for growth options leverage in order to properly assess project risk. They then show that standard methods for assessing project risk significantly overestimate project costs of capital—by as much as 2–3% in industries such as healthcare, pharmaceuticals, communications, medical equipment, and entertainment. Their method should also be applied to stock return volatility to derive project volatility, an important input for determining the value of a firm's growth opportunities and the appropriate time for investing in these opportunities.

Accounting Based Risk Measurement: An Alternative to CAPM Derived Discount Factors

Discount factors have a long tradition of being computed using capital market inputs for the estimation of systematic risk. They are of increasing importance in financial accounting, including the valuation of goodwill and other intangibles. In view of the volatility of stock market returns and their inaccuracy and disjunction from the underlying cash flows of the firm, this paper proposes an alternative accounting based approach: accounting based risk measurement (ABRM). Alternatives to beta are computed from planning and budgeting metrics at firm level to produce consistent risk estimates factoring patterns of revenue and cost behaviour weighted according to their impact on the accounting rate of return. This approach is contrasted with the analysis and interpretation of asset betas in the corporate finance literature.

Ambiguous Information, Portfolio Inertia, and Excess Volatility

ABSTRACTI study the effects of risk and ambiguity (Knightian uncertainty) on optimal portfolios and equilibrium asset prices when investors receive information that is difficult to link to fundamentals. I show that the desire of investors to hedge ambiguity leads to portfolio inertia and excess volatility. Specifically, when news is surprising, investors may not react to price changes even if there are no transaction costs or other market frictions. Moreover, I show that small shocks to cash flow news, asset betas, or market risk premia may lead to drastic changes in the stock price and hence to excess volatility.

Conditional beta pricing models: A nonparametric approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama–MacBeth procedure with betas estimated under several alternative parametric specifications.

Conditional Beta Pricing Models: A Nonparametric Approach

We propose a two-stage procedure to estimate conditional beta pricing models that allows for flexibility in the dynamics of asset betas and market prices of risk (MPR). First, conditional betas are estimated nonparametrically for each asset and period using the time-series of previous data. Then, time-varying MPR are estimated from the cross-section of returns and betas. We prove the consistency and asymptotic normality of the estimators. We also perform Monte Carlo simulations for the conditional version of the three-factor model of Fama and French (1993) and show that nonparametrically estimated betas outperform rolling betas under different specifications of beta dynamics. Using return data on the 25 size and book-to-market sorted portfolios, we find that the nonparametric procedure produces a better fit of the three-factor model to the data, less biased estimates of MPR and lower pricing errors than the Fama-MacBeth procedure with betas estimated under several alternative parametric specifications.

Risk Changes around Calls of Convertible Bonds

AbstractWe examine changes in equity and asset betas around convertible bond calls and report two major findings. First, calling firms exhibit an increase in asset betas following the call. We argue that the finding is consistent with the implications of the sequential financing theory but not of the backdoor equity financing theory. Second, abnormal returns at call announcements are negative only for the subsample of firms that also exhibit an increase in equity beta. We conclude that risk changes help explain the market reaction to convertible bond calls.

Informed traders and limit order markets

We consider a dynamic limit order market in which traders optimally choose whether to acquire information about the asset and the type of order to submit. We numerically solve for the equilibrium and demonstrate that the market is a “volatility multiplier”: prices are more volatile than the fundamental value of the asset. This effect increases when the fundamental value has high volatility and with asymmetric information across traders. Changes in the microstructure noise are negatively correlated with changes in the estimated fundamental value, implying that asset betas estimated from high-frequency data will be incorrect.