Robust estimation with flexible parametric distributions: estimation of utility stock betas

The distributions of stock returns and capital asset pricing model (CAPM) regression residuals are typically characterized by skewness and kurtosis. We apply four flexible probability density functions (pdfs) to model possible skewness and kurtosis in estimating the parameters of the CAPM and compare the corresponding estimates with ordinary least squares (OLS) and other symmetric distribution estimates. Estimation using the flexible pdfs provides more efficient results than OLS when the errors are non-normal and similar results when the errors are normal. Large estimation differences correspond to clear departures from normality. Our results show that OLS is not the best estimator of betas using this type of data. Our results suggest that the use of OLS CAPM betas may lead to erroneous estimates of the cost of capital for public utility stocks.     

Industry Costs of Equity: Incorporating Prior Information

I examine whether incorporating economically motivated prior information yields more accurate forecasts of industry costs of equity. I find that incorporating the long‐run mean of the Capital Asset Pricing Model (CAPM) parameters and the industry characteristics in the cross section produces more accurate parameter estimates, which subsequently translate into more accurate out‐of‐sample forecasts of industry costs of equity. The outperformance of this method over rolling‐window estimates becomes larger as the forecast horizon extends into the future. These findings provide evidence that the CAPM parameters have a long‐run mean‐reversion property and correlate with the industry characteristics in a systematic way.     

CAPM for estimating the cost of equity capital: Interpreting the empirical evidence

We argue that the empirical evidence against the capital asset pricing model (CAPM) based on stock returns does not invalidate its use for estimating the cost of capital for projects in making capital budgeting decisions. Because stocks are backed not only by projects in place, but also by the options to modify current projects and undertake new ones, the expected returns on stocks need not satisfy the CAPM even when expected returns of projects do. We provide empirical support for our arguments by developing a method for estimating firms' project CAPM betas and project returns. Our findings justify the continued use of the CAPM by firms in spite of the mounting evidence against it based on the cross section of stock returns.     

Relationship between franking credits and the market risk premium: a comment

This paper examines two arguments presented in Gray and Hall (2006). First, that the generally used estimate of 0.06 for the market risk premium within the Officer version of the capital asset pricing model (CAPM) and the generally used estimate of 0.50 for the parameter ‘gamma’ within the Officer framework are jointly inconsistent with evidence concerning the market risk premium in the standard version of the CAPM. Second, that the first two of these parameter estimates are also jointly inconsistent with the observed cash dividend yield on the Australian market. To resolve these problems, Gray and Hall recommend setting gamma to zero. The present paper shows that the first argument does not account for the fact that imputation induces a reduction in the market risk premium as defined in the standard version of the CAPM. The present paper also shows that both arguments identify a problem that characterizes only parts of the Officer framework, and these parts are not generally used in Australia. Therefore, rather than suggesting that gamma should be zero, Gray and Hall's analysis identifies parts of the Officer framework that should be avoided.     

Does Money Explain Asset Returns? Theory and Empirical Analysis

A cash-in-advance model of a monetary economy is used to derive a money-based CAPM (M-CAPM), which allows us to implement tests of asset pricing restrictions without consumption data. A test as in Fama and MacBeth of the model suggests that the money betas have some explanatory power for the cross-sectional variation of expected returns; however, the model is rejected using conditional information. Consistent with our predictions, estimates of the curvature parameter are lower than those of the consumption CAPM (C-CAPM) and pricing errors of the M-CAPM tend to be smaller than those of the C-CAPM.     

In search of beta

Despite its limitations, the CAPM is a popular asset pricing model. However, the estimation of beta in the CAPM is affected by the choice of the returns frequency and firm characteristics. This study undertakes a detailed examination of the evidence for the UK and we find that the differences in beta computed from returns of various frequencies are related to size, liquidity, book-to-market and to some degree, opacity factors. One area where our conclusions might have important implications is in the regulatory use of the CAPM. Our results imply that low frequency beta estimates should, in most cases, be preferred to high frequency beta estimates.     

Some Tests of the Risk-Return Relationship Using Alternative Asset Pricing Models and Observed Expected Returns

This study examines the performance of three asset pricing models: the CAPM, the APT and the UAPT using observed expected returns from a three-phase dividend discount model with Value Line analyst estimates of future company-level earnings, dividends and growth rates. Our study is the first we know of to test the three major asset pricing models using observed expected returns. Our results are similar to prior research using ex post (realized) returns in that we find that the UAPT using macroeconomic factors is the best performing model, followed by the APT and the CAPM. However, our results also suggest that the importance of macroeconomic factors is much greater to expected returns than to realized returns, and the corresponding R2 values for models using expected returns are much higher than for models using realized returns. Combining our results for the UAPT with those of Marston and Harris (1993) for the CAPM suggests that these models are more successful in tests using observed expected returns than in tests using realized returns as proxies for expected returns. Unit root tests suggest that monthly observed expected returns follow the classic random walk without drift model while monthly realized returns do not.     

The CAPM and value at risk at different time-scales

By resorting to wavelet analysis, we estimate the capital asset pricing model (CAPM) at different time-scales for the Chilean stock market. Our sample comprises 24 stocks that were actively traded on the Santiago Stock Exchange over 1997-2002. We find evidence in support of the CAPM at a medium-term horizon. We extend the literature in this area to analyze the impact of time scaling on the computation of value at risk. We conclude that risk is concentrated at higher frequencies of the data.     

Cross‐sectional Tests of Conditional Asset Pricing Models: Evidence from the German Stock Market

We study the performance of conditional asset pricing models and multifactor models in explaining the German cross‐section of stock returns. We focus on several variables, which (according to previous research) are associated with market expectations on future market excess returns or business cycle conditions. Our results suggest that the empirical performance of the Capital Asset Pricing Model (CAPM) can be improved when allowing for time‐varying parameters of the stochastic discount factor. A conditional CAPM using the term spread explains the returns on our size and book‐to‐market sorted portfolios about as well as the Fama‐French three‐factor model and performs best in terms of the Hansen‐Jagannathan distance. Structural break tests do not necessarily indicate parameter instability of conditional model specifications. Another major finding of the paper is that the Fama‐French model – despite its generally good cross‐sectional performance – is subject to model instability. Unconditional models, however, do a better job than conditional ones at capturing time‐series predictability of the test portfolio returns.     

International Asset Pricing and Portfolio Diversification with Time-Varying Risk

We test the conditional capital asset pricing model (CAPM) for the world's eight largest equity markets using a parsimonious generalized autoregressive conditional heteroskedasticity (GARCH) parameterization. Our methodology can be applied simultaneously to many assets and, at the same time, accommodate general dynamics of the conditional moments. The evidence supports most of the pricing restrictions of the model, but some of the variation in risk-adjusted excess returns remains predictable during periods of high interest rates. Our estimates indicate that, although severe market declines are contagious, the expected gains from international diversification for a U.S. investor average 2.11 percent per year and have not significantly declined over the last two decades.     

Estimating the Cost of Equity Capital for Property-Liability Insurers

This article presents new evidence on the cost of equity capital by line of insurance for the property‐liability insurance industry. To do so we obtain firm beta estimates and then use the full‐information industry beta (FIB) methodology to decompose the cost of capital by line. We obtain full‐information beta estimates using the standard one‐factor capital asset pricing model and extend the FIB methodology to incorporate the Fama–French three‐factor cost of capital model. The analysis suggests the cost of capital for insurers using the Fama–French model is significantly higher than the estimates based upon the CAPM. In addition, we find evidence of significant differences in the cost of equity capital across lines.     

Alternative measures of the Federal Reserve Banks’ cost of equity capital

The Monetary Control Act of 1980 requires the Federal Reserve System to provide payment services to depository institutions through the 12 Federal Reserve Banks at prices that fully reflect the costs a private-sector provider would incur, including a cost of equity capital (COE). Although Fama and French [Fama, E.F., French, K.R., 1997. Industry costs of equity. Journal of Financial Economics 43, 153–193] conclude that COE estimates are “woefully” and “unavoidably” imprecise, the Reserve Banks require such an estimate every year. We examine several COE estimates based on the CAPM model and compare them using econometric and materiality criteria. Our results suggest that the benchmark CAPM model applied to a large peer group of competing firms provides a COE estimate that is not clearly improved upon by using a narrow peer group, introducing additional factors into the model, or taking account of additional firm-level data, such as leverage and line-of-business concentration. Thus, a standard implementation of the benchmark CAPM model provides a reasonable COE estimate, which is needed to impute costs and set prices for the Reserve Banks’ payments business.     

What's your real cost of capital?

In valuing any investment project or corporate acquisition, executives must decide what discount rate to use in their estimates of future cash flows. The traditional approach is to apply the capital asset pricing model (CAPM), which has remained fundamentally unchanged for 40 years. But the formula--in particular, its beta element--has long been a source of frustration. In fact, corporate executives and investment bankers routinely fudge their CAPM estimates, say the authors, because experience and intuition tell them the model produces inappropriate discount rates. CAPM has three main problems: First, beta is a measure of both a stock's correlation and its volatility; second, beta is based on historical data; and third, CAPM rates don't take into account the term of the investment. These factors together result in discount rates that defy common sense. As an alternative to CAPM and its beta element, the authors developed a forward-looking approach to calculating a company's cost of capital, the market-derived capital pricing model (MCPM). It does not incorporate any measure of historical stock-to-market correlation, relying instead on estimates of future volatility derived from the options market. This is helpful since investor expectations from the options market are built into a company's current stock price. Using GE as an example, the authors give step-by-step instructions for how to calculate discount rates with MCPM. They also offer evidence from a range of industries to show that MCPM's discount rates are more realistic--especially from the corporate investor's perspective--than are CAPM's.     

The performance of cross-sectional regression tests of the CAPM with non-zero pricing errors

We show that in the presence of non-zero pricing errors, the Fama–MacBeth (FM) cross-sectional regression test is very likely to either reject the Capital Asset Pricing Model (CAPM) when it (almost) holds or accept the model when it grossly fails. We investigate the case when pricing errors are correlated with betas and demonstrate that the test performance depends crucially on the correlation, cross-sectional distribution of betas, and several other parameter values. Even when the CAPM holds exactly (pricing errors are zero) the FM test is equally likely to either reject or accept the model when typical sample sizes are used.     

APT VS. CAPM ESTIMATES OF THE RETURN-GENERATING FUNCTION PARAMETERS FOR REGULATED PUBLIC UTILITIES

In public utility rate hearings, there are extensive arguments concerning the most appropriate model of the return-generating function. Bower, Bower, and Logue (1984) suggest that the APT is superior to the CAPM, but their results have troublesome ranking differences between the two models when applied to returns from electric versus natural gas utilities. The purposes of this paper are to develop forward estimates of the parameters for both of these models applied to five different utility portfolios of electric and natural gas companies at a point in time, and to test whether these estimates are valid during a subsequent or future period. Also, forecasting errors for each model are compared to determine which model is best and to ascertain if there are any ranking conflicts. There are no ranking conflicts with the models as the market model consistently underestimates the actual return. Thus, the analysis suggests that the arbitrage model is a superior representation of the return-generating process of these utilities.     

Testing the CAPM revisited

This paper re-examines the tests of the Sharpe–Lintner Capital Asset Pricing Model (CAPM). The null that the CAPM intercepts are zero is tested for ten size-based stock portfolios and for twenty five book-to-market sorted portfolios using five-year, ten-year and longer sub-periods during 1965–2004. The paper shows that the evidence for rejecting the CAPM on statistical grounds is weaker than the consensus view suggests, and highlights the pitfalls of testing multiple hypotheses with the conventional heteroskedasticity and autocorrelation robust (HAR) test with asymptotic P-values. The conventional test rejects the null for almost all sub-periods, which is consistent with the evidence in the literature. By contrast, the null is not rejected for most of the sub-periods by the new HAR tests developed by Kiefer et al. (2000), Kiefer and Vogelsang (2005), and Sun et al. (2008).     

Is Mean-Variance Analysis Vacuous: Or was Beta Still Born?

We show in any economy trading options, with investors havingmean-variance preferences, that there are arbitrage opportunitiesresulting from negative prices for out of the money call options.The theoretical implication of this inconsistency is that mean-varianceanalysis is vacuous. The practical implications of this inconsistencyare investigated by developing an option pricing model for aCAPM type economy. It is observed that negative call pricesbegin to appear at strikes that are two standard deviationsout of the money. Such out-of-the money options often trade.For near money options, the CAPM option pricing model is shownto permit estimation of the mean return on the underlying asset,its volatility and the length of the planning horizon. The model is estimated on S&P 500 futures options data coveringthe period January 1992–September 1994. It is found thatthe mean rate of return though positive, is poorly identified.The estimates for the volatility are stable and average 11%,while those for the planning horizon average 0.95. The hypothesisthat the planning horizon is a year can not be rejected. Theone parameter Black–Scholes model also marginally outperformsthe three parameter CAPM model with average percentage errorsbeing respectively, 3.74% and 4.5%. This out performance ofthe Black–Scholes model is taken as evidence consistentwith the mean-variance analysis being vacuous in a practicalsense as well.     

The Market Value of UK Dividends From Shares With Differing Entitlements

Abstract:   This paper determines the market value of dividends in the UK during periods before and after 1997. Previous studies, which use the ex‐dividend day method, tend to provide noisy and potentially biased measures of dividend value. We estimate the value of dividends from the prices of shares that are identical except for their dividend entitlements, and are traded concurrently (within the same hour). We argue that our estimates of dividend value are the cleanest yet available for the UK. Our evidence suggests that ex‐dividend day estimates are biased downwards, but that this bias may be mitigated by the use of robust regression. Dividend values are heterogeneous and are not explained by the tax‐clientele hypothesis.     

A Comparison of the Efficacy of Liquidity,Momentum, Size and Book‐to‐Market Value Factors in Equity Pricing on a Heterogeneous Sample: Evidence from Asia

This paper compares the size and book‐to‐market value factors of Fama and French (1993) alongside Momentum of Jagadeesh and Titman ( 1993 ) with two Liu ( 2006 ) liquidity factors formed from 1 year rebalancing and 1 month rebalancing respectively. A heterogeneous and comprehensive sample of the top blue chip stocks of all national Asian equity markets with further differentiation undertaken between sub samples formed for Japan only and Asia excluding Japan for period January 2000 to August 2014. Our empirical results suggest that multifactor time invariant pricing models based on augmented capital asset pricing model (CAPM) framework are ineffective in explaining the cross section of stock returns in the presence of significant inter and intra‐market segmentation. However an alternative model specification based on a time varying parameter specification and using same sets of factors yields significant enhancements in explaining cross section of stock returns across universe. We find that momentum factor largely lacks significance while a time varying two factor model, based on CAPM plus liquidity factor, is optimal. The liquidity factor being that of Liu (2006) and annually rebalanced. Our findings are important for investment managers seeking appropriate factors and modelling techniques to hedge against risks as well as firm's financial managers seeking to reduce costs of equity capital.     

Currency risk premia and uncovered interest parity in the International CAPM

Zero-investment uncovered interest parity (UIP) portfolio positions provide perfect factor-mimicking portfolios for currency risk in the International CAPM context. Their returns are the currency risk premia. Since the UIP positions on average provide low returns, the currency risk premia must be low so that currency risk appears not to be priced in an unconditional model. However, previous research has shown that UIP returns are predictable and may be quite substantial conditionally. We use this observation to generate a specific conditional version of the International CAPM. A GMM approach shows that the conditional model performs well, while the unconditional International CAPM is (marginally) rejected. The paper thus argues that previous rejections of the International CAPM stem from the fact that currency risk premia are by nature low over extended periods of time and do not provide evidence against the International CAPM.