GLOBAL EVIDENCE ON THE EQUITY RISK PREMIUM

The size of the equity risk premium—the incremental return that shareholders require to hold risky equities rather than risk-free securities—is a key issue in corporate finance. Financial economists generally measure the equity premium over long periods of time in order to obtain reliable estimates. These estimates are widely used by investors, finance professionals, corporate executives, regulators, lawyers, and consultants. But because the 20th century proved to be a period of such remarkable growth in the U.S. economy, estimates of the risk premium that rely on past market performance may be too high to serve as a reliable guide to the future.
The authors analyze a 103-year history of risk premiums in 16 countries and conclude that the U.S. risk premium relative to Treasury bills was 5.3% for that period—lower than previous studies suggest—as compared to 4.2% for the U.K. and 4.5% for a world index. But the article goes on to observe that the historical record may still overstate expectations of the future risk premium, partly because market volatility in the future may be lower than in the past, and partly because of a general decline in risk resulting from new technological advances and increased diversification opportunities for investors. After adjusting for the expected impact of these factors, the authors calculate forward-looking equity risk premiums of 4.3% for the U.S., 3.9% for the U.K., and 3.5% for the world index. At the same time, however, they caution that the risk premium can fluctuate over time and that managers should make appropriate adjustments when there are compelling economic reasons to think that expected premiums are unusually high or low.     

ESTIMATING THE EQUITY RISK PREMIUM AND EQUITY COSTS: NEW WAYS OF LOOKING AT OLD DATA

This article examines three alternative ways of estimating the expected return on the equity market in using the CAPM or some other risk premium model. The three techniques are (1) direct estimation of the average nominal equity return for use as a forecast nominal equity return; (2) estimation of the average real equity return, which can then be added to a forecast inflation rate; and (3) estimation of an average equity risk premium, which is then added to a current risk-free rate. Ibbotson and Sinquefeld's data on annual holding period returns are used to test the validity of their assumption that the equity risk premium follows a random walk and that the third of these approaches is thus the best method.
The paper reaches three major conclusions. First, each of these three techniques involves a "bias" of some kind. The use of average equity returns as a forecast is subject to "risk-free rate" and "inflation rate" biases, while the use of an average equity risk premium is subject to a "term premium" bias. As a result, only the data can tell us which approach is best. Second, from analyzing equity and bond return data and the trend in interest rates, the author concludes that the term premium bias when using average historic equity risk premium is by far the largest of the three sources of bias. Indeed, the popular practice of adding an historic average equity risk premium to the 30-year Treasury bond rate significantly overstates equity costs. Third, after examining equity rates of return back to 1871, the author concludes that the real equity return seems to follow a process that is close to a random walk and is thus the "best" of the three techniques to use as a "naive" forecast.     

International asset pricing under segmentation and PPP deviations

We analyze the impact of both purchasing power parity (PPP) deviations and market segmentation on asset pricing and investor's portfolio holdings. The freely traded securities command a world market risk premium and an inflation risk premium. The securities that can be held by only a subset of investors command two additional premiums: a conditional market risk premium and a segflation risk premium. Our model is empirically supported with important implications for tests of international asset pricing.     

Who makes on-the-run Treasuries special?

The most recently issued, on-the-run, Treasuries are extremely liquid and frequently trade at a premium in both the cash and repo, or financing, markets. Previous research suggests that both the cash and repo premiums reflect demand from buy-and-hold investors who value the superior liquidity of these securities and are reluctant to lend them in the repo market. We find evidence that premiums in the repo market are also closely related to market participants’ demand to hedge interest rate risk associated with their holdings of fixed income securities.     

Pricing factors in multiple-term structures from interbank rates

This article analyzes the reward for the risk embedded in interbank derivatives, seeking to characterize the size and economic sources of the components of this risk premium in interbank spread quotes. The basis swap (BS) spreads – floating-to-floating interest rate swaps – are employed as a vehicle used by investors to express their views concerning the risk of borrowing on the interbank market. Our results show that the size of the risk premium ranges from 20 to 60 basis points, depending on the tenor, during periods of financial distress. Moreover, the evolution of this risk premium increases dramatically after August 2007, primarily due to the evolution of credit variables such as sovereign and financial sector risks. Finally, we also document important sources of commonality between risk premiums at different tenors. An analysis of the determinants of risk premia reveal that investors’ compensation relates to financial sector credit and liquidity uncertainty, and risk aversion.     

Testing asset pricing models with changing expectations and an unobservable market portfolio

When the assumption of constant risk premiums is relaxed, financial valuation models may be tested, and risk measures estimated without specifying a market index or state variables. This is accomplished by examining the behavior of conditional expected returns. The approach is developed using a single risk premium asset pricing model as an example and then extended to models with multiple risk premiums. The methodology is illustrated using daily return data on the common stocks of the Dow Jones 30. The tests indicate that these returns are consistent with a single, time-varying risk premium.     

Does the equity premium puzzle persist during financial crisis? The case of the French equity market

This paper examines the effects of the financial crisis that began in 2008 on the equity premium of 6 French sector indices. Since the systematic risk coefficient beta remains the most common explanatory element of risk premium in most asset pricing models, we investigate the impact of the crisis on the time-varying beta of the six sector indices cited. We selected daily data from January 2003 to December 2012 and we applied the bivariate MA-GARCH model (BEKK) to estimate time-varying betas for the sector indices. The crisis was marked by increased volatility of the sector indices and the market. This rise in volatility led to an increase in the systematic risk coefficient during the crisis and first post-crisis period for all the major indices. The results are intuitive and corroborate findings in the empirical literature. The increase of the time-varying beta is considered by investors as an additional risk. Therefore, as expected, investors tend to increase their equity premiums to b ear the impact of financial crisis.     

International capital asset pricing: Evidence from options

We study the risk dynamics and pricing in international economies through a joint analysis of the time-series returns and option prices on three equity indexes underlying three economies: the S&P 500 Index of the United States, the FTSE 100 Index of the United Kingdom, and the Nikkei-225 Stock Average of Japan. We develop an international capital asset pricing model, under which the return on each equity index is decomposed into two orthogonal jump-diffusion components: a global component and a country-specific component. We apply separate stochastic time changes to the two components so that stochastic volatility can come from both global and country-specific risks. For each economy, we assign separate market prices for the two return risk components and the two volatility risk components. Under this specification, we obtain tractable option pricing solutions. Model estimation reveals several interesting insights. First, global and country-specific return and volatility risks show different dynamics. Global return movements contain a larger discontinuous component, and global return volatility is more persistent than the country-specific counterparts. Second, investors charge positive prices for global return risk and negative prices for volatility risk, suggesting that investors are willing to pay positive premiums to hedge against downside global return movements and upside volatility movements. Third, the three economies contain different risk profiles and also price risks differently. Japan contains the largest idiosyncratic risk component and smallest global risk component. Investors in the Japanese market also price more heavily against future volatility increases than against future market downfalls.     

Original-Issue Systematic and Default Risk Pricing Efficiency of Speculative-Grade Bonds

We investigate whether primary market, original‐issue risk premiums on speculative‐grade debt are justified solely by expected defaults or whether these risk premiums also include other orthogonal risk components. Studies of secondary‐market holding period risk and return have hypothesized that risk premiums on speculative‐grade debt may be explained by bond‐ and equity‐related systematic risk and possibly other types of risk. Using an actuarial approach that considers contemporaneous correlation between default frequency and severity and first‐order serial correlation, we cannot reject the hypothesis that the entire original‐issue risk premium can be explained by expected default losses. This suggests that speculative‐grade bond primary markets efficiently price default risk and that other types of risk are priced as coincident as opposed to orthogonal risks.     

Stochastic risk premiums,stochastic skewness in currency options,and stochastic discount factors in international economies

We develop models of stochastic discount factors in international economies that produce stochastic risk premiums and stochastic skewness in currency options. We estimate the models using time-series returns and option prices on three currency pairs that form a triangular relation. Estimation shows that the average risk premium in Japan is larger than that in the US or the UK, the global risk premium is more persistent and volatile than the country-specific risk premiums, and investors respond differently to different shocks. We also identify high-frequency jumps in each economy but find that only downside jumps are priced. Finally, our analysis shows that the risk premiums are economically compatible with movements in stock and bond market fundamentals.     

The efficiency of inflation expectations in treasury bill markets: The Brazilian evidence

In the recent past Brazilian inflation has varied within broad limits, from 0.4% to 5.12% on a monthly basis, and in a very volatile way. In such an economic environment investors should demand a risk premium to bear pure inflation uncertainty. After generalizing the methodology of Fama to the case of multiple periods explicitly considering the risk premiums demanded by investors this paper proceeds to examine the efficiency of inflation expectations in the Brazilian Treasury Bills market. The empirical results for the 1972–1976 period suggest that risk premiums are relevant and they do not appear to follow a random-walk process.     

业绩对赌协议对并购溢价和市场反应的影响

在推进并购市场契约创新背景下,研究业绩对赌协议有重要的理论和实践意义。本文构建了并购双方在信息不对称市场上的理论效用模型,并以2006—2020年收购方为上市公司的资产收购为样本,得到以下结论：第一,业绩对赌协议中对未来承诺期限规定越严格,溢价规模越大,且业绩对赌相对规模与溢价呈倒U形关系;第二,通过在模型中引入股价异常回报情况,发现业绩对赌协议和市场反应之间为正向关系,在此基础上验证了并购溢价在两者关系中的中间遮掩效用和门槛效用;第三,进一步研究发现,并购溢价会对合约细节与对赌结果、市场反应与对赌结果之间的关系产生影响。本文研究有助于企业避免由过度保护、代理问题和信息不对称造成的估值溢价偏差,进而合理利用并购溢价和协议细节调动市场投资者的积极情绪与信心。     

The Discount Rate in Emerging Markets: A Guide

There is considerable controversy about the correct discount (or "hurdle") rate to use when performing valuations of investments in real assets in emerging markets. The topic is particularly relevant because of the growing need to evaluate privatizations, direct private acquisitions, and greenfield investments in new productive facilities throughout the world.
This article argues that the traditional practitioners' approach of building a country risk premium into the discount rate is generally inappropriate, mainly because country risk is not the same for all projects nor is it totally systematic. Moreover, there is no reason for the discount rate to be closely related to the spread on the government bonds of the country concerned. The author also points out that, in determining the appropriate discount rate, what is important is not the segmentation of the market, but the extent to which the investor is locally or globally diversified. The article accordingly reviews a selected group of models for calculating discount rates for both segmented and integrated markets. Adjustments to the valuation procedure are also suggested for cases in which investors are not well diversified or the investment is illiquid.     

Stock Returns and Volatility under Market Segmentation: The Case of Chinese A and B Shares

In most countries where firms list separate shares for trading by foreign and domestic investors, the prices of the foreign shares tend to be higher. In China, the reverse tends to be true. In this paper, we would like to focus on the information content in lagged premiums of Chinese A over B traded shares. The lagged premiums are found to have certain predictive power over the future returns and volatility of both A and B shares, with some interesting patterns. Specifically, an increase in the premium ratio of A shares will be followed by a rise in the return of A shares and a fall in the return of B shares. It is found that both of the investors in Chinese A- and B-share markets reveal positive feedback trading behavior. Moreover, the liquidity and information availability will affect the magnitude of such behavior especially in B-share markets. By using multivariate GARCH model, it is also demonstrated that the unexpected changes in the premium ratio of A-share price over B-share price contribute to the return volatility of both A shares and B shares. These patterns may provide foundations for the development of pricing models for equity shares under market segmentation.     

Currency returns, market regimes and behavioral biases

Covered interest rate parity assumes that there is no risk premium on the hedged returns on currencies. However, empirical evidence indicates that risk premiums are not identically zero, and this is referred to as the forward premium puzzle. We show that there exist market regimes, within which behavioral biases affect decisions, and a type of parity holds within regimes. The foreign exchange market switches between regimes where there is a premium. This paper presents various tests for the hypotheses of currency regimes and regime dependent risk premiums. Based on the existence of regimes, a diversified currency portfolio is created with a mean-variance criterion. Using the Federal Exchange Rate Index as a proxy for the currency benchmark and the U.S. T-Bill as the risk free asset, the similarity between the benchmarks and the implied equilibrium hedged and unhedged portfolios provides evidence for regimes and decision bias. Within each regime interest rate parity is appropriate for modeling currency returns.     

The pricing of capital assets in a multiperiod world

This paper proposes a general framework for the pricing of capital assets in a multiperiod world. Under quite general conditions, the analysis shows that the equilibrium expected nominal return on any asset can always be expressed as the sum of the risk-free rate and various risk premiums. The first risk premium is identical to the usual risk premium in the Sharpe-Lintner-Mossin capital asset pricing model. The mathematical forms of all the remaining risk premiums are identical even though each individual risk premium may be present for a different reason.     

Contrarian flows,consumption and expected stock returns

We investigate the relation between contrarian flows, consumption growth, and market risk premium. We construct a contrarian flows measure by summing up the capital flows to stocks that go against the total flow of the aggregate market. We show that the contrarian flows are negatively influenced by the same-quarter consumption growth. During bad times, the majority of investors who are affected by the negative shock reduce their equity exposure, and these extra supplies of risky assets are absorbed by contrarian investors who are least affected by the consumption shock. Using quarterly stock market data, we find that the contrarian flows forecast market returns at short-to-intermediate horizons. The predictability stems from the component that is explained by the consumption growth, and therefore the consumption growth contains valuable information about the market risk premium. Moreover, the predictability is stronger for growth stocks than for value stocks, and hence it negatively predicts the value premium. This is because the contrarian flows measure the market risk premium and growth stocks bear more discount rate risk than value stocks. Out-of-sample tests show that the main results are robust to data-snooping bias.     

The skewness risk premium in equilibrium and stock return predictability

In this study, we investigate the skewness risk premium in the financial market under a general equilibrium setting. Extending the long-run risks (LRR) model proposed by Bansal and Yaron (J Financ 59:1481–1509, 2004) by introducing a stochastic jump intensity for jumps in the LRR factor and the variance of consumption growth rate, we provide an explicit representation for the skewness risk premium, as well as the volatility risk premium, in equilibrium. On the basis of the representation for the skewness risk premium, we propose a possible reason for the empirical facts of time-varying and negative risk-neutral skewness. Moreover, we also provide an equity risk premium representation of a linear factor pricing model with the variance and skewness risk premiums. The empirical results imply that the skewness risk premium, as well as the variance risk premium, has superior predictive power for future aggregate stock market index returns, which are consistent with the theoretical implication derived by our model. Compared with the variance risk premium, the results show that the skewness risk premium plays an independent and essential role for predicting the market index returns.     

The Variation of Economic Risk Premiums in Real Estate Returns

We examine the predictable components of returns on stocks, bonds, and real estate investment trusts (REITs). We employ a multiple-beta asset pricing model and find that there are varying degrees of predictability among stocks, bonds, and REITs. Furthermore, we find that most of the predictability of returns is associated with the economic variables employed in the asset pricing model. The stock market risk premium is highly important in capturing the predictable variation in stock portfolios, and the bond market risk premiums (term and risk structure of interest rates) are important in capturing the predictable variation in bond portfolios. For REITs, however, both the stock and bond market risk premiums capture the predictable variation in returns. REITs have comparable return predictability to stock portfolios. We conclude that there is an important economic risk premium for REITs that are not captured by traditional multiple-beta asset pricing models.     

The high-volume return premium: evidence from the Chinese stock market

Extreme trading activity contains valuable information about the future evolution of stock prices in the Chinese stock market. Over the next 30 trading days after the initial volume shocks, a high-low volume portfolio earns a net average cumulate return of 2.08% and a high-low volume and size portfolio earns 3.37%, suggesting that there exists a high-volume return premium and that Chinese investors favor high-volume small-size stocks. However, a volume momentum portfolio earns a −1.65% net average cumulative return, indicating that Chinese stocks exhibit a short-run reversal. Portfolio construction, market risk, and firm size do not seem to explain the results.