CAPM Beta Research Articles

Realized semibetas in the Australian stock market

ABSTRACT This study examines the explanatory power of the CAPM and downside risk asset pricing models (the downside beta and the realized semibeta models) for the next-month firm-level cross-sectional stock return variation in the Australian stock market. We show that the CAPM beta, downside beta, semibeta BetaNP, and semibeta BetaNN negatively predict future stock returns, which is inconsistent with the findings in the original study by Bollerslev, Patton, and Quaedvlieg (2022). The BetaNN measures the individual stock movement in the same direction as the downward stock market, while BetaNP measures individual stock downward with the upward stock market. These findings are robust, not subsumed by conventional cross-sectional asset pricing factors, and consistent with the existing Australian downside risk study.

Corporate financing policies, financial leverage, and stock returns

We examine the interaction between equity returns and firms’ financing policies in a stochastic Ramsey model with heterogeneous firms. Motivated by empirical evidence, firms maintain stationary financial leverage ratios by issuing debt. We present a novel closed-form solution to this class of models and, subsequently, use this solution to show that restricting firms’ financing policies can explain various stylized facts of both the dynamic as well as the cross-sectional behavior of equity returns. Our restrictions induce persistent and countercyclical heteroskedasticity in returns, predictability by dividend–price ratios, a security market line that is “too flat”, and mean-reverting CAPM betas that correlate with leverage. Our model explains both established as well as recent empirical evidence, but challenges recent theoretical macro-finance explanations of the link between capital structure and equity returns.

Tracking ‘Pure’ Systematic Risk with Realized Betas for Bitcoin and Ethereum

Using the capital asset pricing model, this article critically assesses the relative importance of computing ‘realized’ betas from high-frequency returns for Bitcoin and Ethereum—the two major cryptocurrencies—against their classic counterparts using the 1-day and 5-day return-based betas. The sample includes intraday data from 15 May 2018 until 17 January 2023. The microstructure noise is present until 4 min in the BTC and ETH high-frequency data. Therefore, we opt for a conservative choice with a 60 min sampling frequency. Considering 250 trading days as a rolling-window size, we obtain rolling betas < 1 for Bitcoin and Ethereum with respect to the CRIX market index, which could enhance portfolio diversification (at the expense of maximizing returns). We flag the minimal tracking errors at the hourly and daily frequencies. The dispersion of rolling betas is higher for the weekly frequency and is concentrated towards values of β > 0.8 for BTC (β > 0.65 for ETH). The weekly frequency is thus revealed as being less precise for capturing the ‘pure’ systematic risk for Bitcoin and Ethereum. For Ethereum in particular, the availability of high-frequency data tends to produce, on average, a more reliable inference. In the age of financial data feed immediacy, our results strongly suggest to pension fund managers, hedge fund traders, and investment bankers to include ‘realized’ versions of CAPM betas in their dashboard of indicators for portfolio risk estimation. Sensitivity analyses cover jump detection in BTC/ETH high-frequency data (up to 25%). We also include several jump-robust estimators of realized volatility, where realized quadpower volatility prevails.

ANALISIS EKSPOSUR RISIKO REKSADANA SYARIAH DAN REKSADANA KONVENSIONAL DI INDONESIA DENGAN PENDEKATAN CAPM, MARKET TIMING ABILITY DAN DOWNSIDE RISK

This study was conducted to determine the risks of conventional mutual funds and sharia types of stocks in Indonesia during the period 2017-2021. Through this research, the public as potential investors, general investors, and investment managers will get information about the risk of mutual fund by comparing the results of risk, measurements of each mutual fund, considering the increasing number of mutual fund investment instruments of either type or number. The measurement methods used are capm beta value, beta market timing ability and beta downside (downside risk). The results showed that using these three measurements, the total risk exposure of Islamic mutual funds was lower than that of conventional mutual funds.

A comparison of risk measures for portfolio optimization with cardinality constraints

We solve the optimization problem of minimum portfolio risk for seven measures using linear programming under cardinality constraints. The risk measures used are Expected Loss, Expected Loss Deviation, Expected Shortfall, Shortfall Deviation Risk, Expectile Value at Risk, Deviation Expectile Value at Risk, and Maximum Loss. We assess the out-of-sample performance of seven risk-optimized portfolios with a maximum size of 20 assets for S&P 100 components. After subtracting transaction costs, the Expected Loss Deviation portfolios have shown superior performance in terms of diversification and risk, the Maximum Loss portfolios have presented a higher Sharpe ratio (1.098 against 0.990 for the benchmark), the Expected Loss portfolios have higher absolute returns (660%), Sortino and STARR ratios. Expected Shortfall portfolios have presented the lowest Beta coefficients (0.616), and all portfolios returned lower Betas than the benchmark. All portfolios present significant annual alpha of 25% after adjusting for several risk factors. Our results show that superior performance can be achieved with simple linearized optimization models with lower market exposure measures to the CAPM beta.

What if beta is not stable? Applying the Kalman filter to risk estimates of top US companies over the long time horizon

The main objective of this paper is to examine the Kalman approach to estimate the time-varying CAPM beta on the US stock market over the long time horizon of thirty-one years. We investigate the beta estimates on the basis of three specifications: random walk (RW), mean-reverting process (MR), and random coefficient of the beta parameter (RC) for companies listed on NYSE and NASDAQ in the period 1990–2021. We examine the prognostic power of beta estimates and ranked the results according to criteria of forecast accuracy. In terms of the adopted criteria, the estimation of the beta parameter assuming its variability in time proved to be better than the OLS, LAD and ROLS methods of the Sharpe model. We can conclude that the Kalman filter approach with the assumption of a random coefficient (RC) or mean-reversion (MR) for the CAPM beta parameter gives the best results.

A novel downside beta and expected stock returns

A number of studies have found that the cross-section of stock returns reflects a risk premium for bearing downside beta; however, existing measures of downside beta have poor power for predicting returns. This paper proposes a novel measure of downside beta, the ES-implied beta, to improve the prediction of the cross-section of asset returns. The ES-implied beta explains stock returns over the same period as well as the widely used downside beta, but improves the prediction for future returns due to its high persistence. In the empirical analysis, the widely used downside beta shows a weak relation with future expected returns, but the ES-implied beta implies a statistically and economically significant risk premium of 0.6% per month and explains 0.6% of the variation in the cross-sectional returns. The effect cannot be explained by traditional cross-sectional effects and is different from the CAPM beta, the downside beta in Ang et al. (2006), coskewness, and cokurtosis.

Time Dependence of CAPM Betas on the Choice of Interval Frequency and Return Timeframes: Is There an Optimum?

The traditional CAPM beta is almost exclusively calculated over a return period that spans a window length of 60-months, at one-month return frequencies. It is one of the most utilized models in the asset management industry to assess systematic risk. Yet there is limited evidence to suggest that these estimation parameters are optimal. Utilizing data between January 2000 and December 2021 for the Russell 1000 index, we test daily, weekly, and monthly beta estimations to calculate tracking errors (TE) for the use of these betas in predicting subsequent performance over daily, weekly, and monthly timeframes. We identify that daily CAPM betas are best for predicting subsequent period daily returns and that weekly CAPM betas are strongly correlated with forward weekly and monthly period returns. Leveraging the significant advances in computing resources and the increasing utilization of high frequency trading strategies, we argue that additional window length and return interval-based CAPM betas should be calculated for estimating the systematic risk embedded in diversified portfolios.

Portfolio performance under dynamic systematic risk and conditional betas: the South African unit trust market

This study examines whether South African unit trust managers can outperform the market and demonstrate distinct market-timing abilities under systematic dynamic risk. A conditional portfolio evaluation method is used under dynamic systematic risk. The BEKK-MGARCH model is applied to estimate the time-varying CAPM beta. The sample of the study includes 86 unit trust funds for the hardly studied multi-asset class between 2010 and 2019 in South Africa. The findings of the study show positive evidence that portfolio managers in the South African unit trust market possess some skills for market timing and outperformance. These results differ from most of the outcomes obtained through model-free performance-evaluation methods. The significant contribution of this study to the literature is in conditioning beta to both time and economic variables within the same asset pricing model, and then applying it to the emerging market of South Africa. Another strength of this paper is maintaining patient and formal adherence to econometric requirements of model validation. The empirical findings of the study should benefit portfolio managers, investors, and regulators with updated insight into the importance of considering both risk variability and changing economic factors in portfolio evaluation.

Performance of Optimum Sharp Portfolio and CAPM Portfolio for Sustainability of Small Investors

Purpose: Investment growth is essential for the prosperity of an economy. Saved money is used for investment. It is scarce in a country like India. So, optimal use of this saved fund is required. Markowitz stated that best use is possible by creating a diversified portfolio to minimize risk. Ordinary people have limited funds and knowledge of the stock market. So diversified portfolio should be formed by purchasing a minimum number of stocks. Objective: of this research analysis is to form optimum portfolios by using different methods. They are compared to know the best one which can provide the maximum return per unit of risk by using the minimum number of stocks in the portfolio formation. The uniqueness of this research is to identify numeric advantages in optimum portfolio formation from an Indian context. Methodology: Analysis is based on daily price movement data of the Nifty 50 index. An optimum portfolio is formed first by using the Sharp optimum portfolio method, where stocks are selected on the basis of cut off rate C with weight factor Xi. Then selected stocks of Sharp model are combined by using the CAPM beta diversification technique. Risk minimizing weight factors are used here. These two portfolios are compared to judge minimum risk achievement with low volume of stocks. Conclusion: Optimum portfolios performances are compared again with actual data from next year. From this research analysis, beta diversification was found to be the best option. Limitation: More than two years analysis can give solidarity in the conclusion.

Empirical Testing of Beta Stability in Indian Capital Market

The study tests stability of CAPM beta in the Indian capital market. Beta is one of the debated issues in the finance literature. While Fama and French have argued that betas are no more relevant in the capital market, it is one of the prominent concepts used by the finance professionals worldwide. The study is based on NSE Nifty companies, Nifty and Sensex Indices prices from 2009 to 2019. We use market model on the sample data to assess the beta stability for different time periods. The result of the present study shows that betas of companies do not show any stability over the period of time, but weighted average portfolio beta shows some stability during the study period.

Negative Beta Equity Securities as Insurance

Theoretically, an equity security with a negative CAPM beta should behave like portfolio insurance in the sense that the security provides a positive return during a market downturn. However, equity securities with negative betas are relatively rare and simply determining that an equity security exhibits a negative beta is not enough for determining if the negative beta equity security will perform in the desired manner. Negative betas can, at times, be attributed to causes that diminish those securities9 usefulness as insurance. Some of these causes are explored in this article.

Firm age and beta: Evidence from China

This paper investigates how the CAPM beta changes with firm age using a sample of A-share Chinese listed companies from the period of 1998–2015. The results show that the CAPM beta is positively associated with firm age. Our findings are fairly consistent under different beta measurements, different regression methodologies, and different subsamples. Further tests show that the positive association cannot be absorbed by the life-cycle stages variables and cannot be explained by the new listing effect. Finally, growth option creation is the most likely mechanism driving the positive relation, rather than the alternative explanations of liquidity and information opacity.

The Impact of Business Cycles, Stock Market Phases and Crisis on the Value Premium: The Indian Experience

Purpose :This paper is an attempt to explore the relationship between the value premium and expected stock returns in the Indian stock market and evaluates whether the value premium disappears or not when the different economic conditions (Boom & Recession), market conditions (Bull & Bear) and 2008 Global financial crisis are considered. Methodology: The annual data of 500 companies belonging to BSE-500 from 1999- 2017 was collected and ten portfolios were constructed and sorted using six valuation proxies (P/B, P/E, D/P/, CF/P, S/P and EV/PBDITA). Standard CAPM and Dual beta market model were employed. Findings: The empirical results confirm that irrespective of market conditions, value stock portfolios surpass growth stock portfolios in the Indian stock market by delivering significant abnormal returns. Practical implications: The paper holds important implications for asset pricing literature and investors. The higher returns generated by value stocks during the crisis and recession period imply that investors can put faith in the value stocks during times of adversity. The future value of an investment is a function of its present price. The lower the price, the higher the returns will be. Therefore, value stocks are good investments whether it is boom or recession, bull or bear, crisis or non-crisis periods. Originality: The paper is first of its kind to study the impact of business cycles, stock market phases and crisis on the value premium in the Indian stock market. The paper contributes to portfolio management and asset pricing literature for an emerging market.

Estimación del Riesgo de Mercado utilizando el VaR y la Beta del CAPM

El objetivo de este estudio es medir el riesgo de mercado de portafolios de acciones del mercado financiero mexicano en periodos de alta volatilidad mediante cuatro metodologías: 1) la Beta del CAPM (-CAPM), 2) el VaR-Simulación Histórica (VaR-SH), 3) VaR-Delta Normal (VaR-δN) y 4) VaR-Simulación Montecarlo (VaR-SM). Estas métricas se seleccionaron por ser parsimoniosas. Los resultados muestran que las metodologías son consistentes en periodos de alta volatilidad. Se recomienda calcular la composición del portafolio de mercado y su VaR, para hacerlas comparables. La limitante principal, es que la -CAPM únicamente se puede calcular para portafolios de acciones, mientras que el cálculo del VaR con estas metodologías no contempla la ocurrencia de eventos extremos. Esto implica que los niveles de riesgo podrían subestimarse en periodos de alta volatilidad. La originalidad de este estudio reside en la comparación de estas metodologías mediante el cálculo de la composición del portafolio de mercado. Concluimos que el VaR-SH estima un mayor riesgo que la -CAPM después de experimentarse la alta volatilidad, si bien la -CAPM es consistente para las metodologías de VaR empleadas.

Cash flow uncertainty and IPO underpricing: evidence from income guarantee in Thai REITs

PurposeThe purpose of this article is to investigate the relationship between cash flow uncertainty and the underpricing of real estate investment trust (REIT) initial public offerings (IPOs) using hand-collected data on income guarantee in Thailand from January 2005 to December 2019.Design/methodology/approachThis article uses linear regression to determine the relationship between underpricing (initial return) and proxy for cash flow uncertainty (income guarantee), controlling for other factors. Because issuers can use several actions to signal their quality under asymmetric information, the joint decisions are analyzed as simultaneous equations and estimated using three-stage least square (3SLS) to address potential endogeneity concern.FindingsThis article finds that underpricing, on average, is negatively related to income guarantee, which is a proxy for ex ante cash flow uncertainty. The relationship is economically and statistically significant and robust to simultaneous equations estimation. Further investigation shows that REITs with income guarantee tend to have lower systematic risk (measured by CAPM beta) and returns, making the nature of some REITs more debt-like than equity-like.Practical implicationsFor issuers, the result suggests that offering income guarantee (which is more costly for assets with lower quality) can be a useful signal of asset quality to investors and reduce IPO discount. For institutional and retail investors, the results are informative about the risk-return tradeoffs in REIT IPO investment opportunities. Income guarantees makes REIT exposure more fix income-like, so there is a need to consider the credibility of the guarantor as well.Originality/valueThis article is the first to use income guarantee as an ex ante measure of cash flow uncertainty and explicitly investigates its linkage to IPO underpricing. This aspect of uncertainty and IPO underpricing remains little-studied in the academic literature. It also contributes to the growing literature of REIT IPOs in Asia.

Forward looking up-/down correlations

<abstract> Equity returns are typically higher correlated during market downturns than during bullish times. This paper develops a novel approach how investor expectations for such correlation asymmetries can be quantified from forward-looking data. Based on option implied volatilities, it is found that the correlation asymmetry is significant, rejecting the use of the classic mono-correlation assumption. Further, the spread between expected down and up correlations is time-varying and positively dependent on the current market mood: stock diversification is more difficult when it is needed the most. Thus, the three main advantages of the proposed model are (ⅰ) the distinction between up- and down-correlations, (ⅱ) it actually captures investor expectations as traded in current market prices and (ⅲ) the immediate response to the current market outlook. Practical relevance of this paper is highlighted by the computation of expected up-/down CAPM betas. </abstract>

COVID-19 crisis as a systematic risk: an empirical study in the egyptian stock market

"This paper examines the ability of beta (β) to measure the systematic risks posed by the COVID-19 crisis and analyzes the impact of the COVID-19 crisis on stock returns for a sample of 50 stocks, grouped on the basis of size and value in the Egyptian Stock Market. CAPM beta of the stock was used to represent the systematic risk stocks, market capitalization was used to construct the large and small stocks portfolios and the book-to-market equity ratio was used to construct high medium and small portfolios. The results showed that systematic risks measured by beta increased after COVID-19 crisis for all sample stocks, the portfolios consisting of stocks with high and medium B/M ratio and the portfolios consisting of small capitalization stocks and big capitalization stocks. However, the COVID-19 crisis has no effect on systematic risks for the portfolio consisting of stocks with low B/M ratio. The results also indicated that stock returns decreased after the COVID-19 crisis for all sample stocks, the portfolios consisting of stocks with low B/M ratio and the portfolios consisting of big stocks. However, the COVID-19 crisis does not affect stock returns for the portfolios consisting of stocks with high and medium B/M ratio and the portfolios consisting of small stocks. "

Firm Uncertainty and Household Spending

By mapping households to US employers traded in the stock market and using daily spending data, we provide novel evidence of household spending response to employer-specific forward-looking volatility shocks. A 10 percent change in firm uncertainty leads households to change their average monthly spending over the next 6-months by -0.95 percent. This negative second-moment firm uncertainty effect is larger than the positive first-moment effect of firm stock returns. The employer-specific effect is robust to both industry- and aggregate-level volatility effects. The intensity of the response increases in the forecast horizon window, lasting nine months. The response is pronounced for low-liquidity households, and for households that work at firms that recently had low employee growth, high CAPM Beta, and low Tobin's Q. Lastly, household spending shows an asymmetric response to `good' and `bad' uncertainty.

DOES DEFAULT RISK MATTER FOR INVESTORS IN REITS

We investigate the relationship between default risk and REIT stock returns. A default risk long-short investment strategy generates a return of 15% per annum. We also evaluate a large number of potential explanations for the negative relationship between default risk and subsequent stock returns. We do not find robust evidence that the default risk premium can be explained by firm size, book-to-market equity, asset growth and idiosyncratic volatility. However, CAPM beta shows some promise in explaining the default risk premium. Our results shed further light on the role of default risk in investment in REITs.