Tests of the hypothesis of the existence of risk premium in the foreign exchange market

This paper tests for a risk premium in the foreign exchange market. The null hypothesis of the test is the random walk hypothesis in the foreign exchange market. The alternative hypothesis is that biases of current spot rates (or forward rates) from future spot rates are systematically related to a set of economic variables on which a risk premium may depend. This paper provides firm evidence for a risk premium in the foreign exchange market. The risk premium explains 10–20% of the total variance in future spot rates when the US dollar/mark quarterly rates are used. The magnitudes are smaller (less than 10%) for monthly rates.     

交易所国债期限风险溢价的实证研究

本文考察了上海证券交易所国债期限风险溢价的时间变化特征及决定因素。实证结果显示，债券剩余期限越长，平均风险溢价越高；通过对不同期限债券组合的风险溢价序列建立回归模型，发现长短期利差及风险溢价的前期值对中长期债券期限风险溢价的时变性具有明显的解释能力。     

Can hedging tell the full story? Reconciling differences in United States aggregate- and industry-level exchange rate risk premium

While the importance of currency movements to industry competitiveness is theoretically well established, there is little evidence that currency risk impacts US industries. Applying a conditional asset pricing model to 36 US industries, we find that all industries have a significant currency premium that adds about 2.47 percentage points to the cost of equity and accounts for approximately 11.7% of total risk premium in absolute value. Cross-industry variation in the currency premium is explained by foreign income, industry competitiveness, leverage, liquidity, and other industry characteristics, while its time variation is explained by US aggregate foreign trade, monetary policy, growth opportunities, and other macro variables. The results indicate that methodological weakness, not hedging, explains the insignificant industry currency risk premium found in previous work, thus resolving the puzzle that currency risk premium is important at the aggregate stock market level, but not at the industry level.     

Term premium dynamics in an emerging market: Risk,liquidity, and behavioral factors

This paper contributes to the fixed income research by identifying determinants of term premium in an emerging market’s treasury bond yields with particular attention on ambiguity. We use Nelson–Siegel yield curves generated from daily bond price quotes as input to construct a three-factor affine term structure model which decomposes observed yields into risk-neutral and term premium components. We also construct an ambiguity index using intraday FX return data following Brenner and Izhakian (2018). Our analyses suggest that a combination of factors representing market risk, credit risk, liquidity, ambiguity, and investor sentiments can explain majority of the variation in term premia. Explanatory power of credit risk measures are found to increase while those of volatility, ambiguity, and sentiment measures diminish with the maturity horizon. The results imply that ambiguity aversion of bond investors is a major determinant of the shape of the yield curve as it drives the premia for short end of the yield curve lower in line with the expectation of flight-to-safety behavior.     

Rare disaster risk and the expected equity risk premium

Consistent with the predictions of rare disaster models, we find that a proxy for the time‐varying probability of rare disasters helps to explain fluctuations in expectations of the equity risk premium. Our proxy for disaster risk is a recently developed measure of global political instability, and the expected market risk premium is from Value Line analysts' expected stock returns. Consistent with long‐run risk models, uncertainty about expected GDP growth and expected consumption growth is also significantly positively related to the expected market risk premium. We obtain similar results when we use the earnings–price ratio and the dividend–price ratio as proxies for the expected market risk premium.     

Consumption risk and the cross-section of government bond returns

In this paper we provide a consumption-based explanation of risk in nominal US Treasury bond portfolios. We use a consumption-CAPM with Epstein–Zin–Weil recursive preferences. Our model introduces two sources of risk: uncertainty about current consumption (reflected in contemporaneous consumption growth) and uncertainty about prospects of consumption in a long run (reflected in innovations to expectations about future consumption growth). We use a novel approach to estimate pricing factors in our model: we employ a factor-augmented VAR model with common factors, extracted from a large panel of macroeconomic and financial data, as state variables. We find that the important source of risk in US bonds is related to uncertainty in prospects in future consumption and it induces a positive and significant risk premium. We find as well that covariance risk related to innovations in expectations about future consumption growth is greater for long term bond portfolios than for short term bond portfolios, which is consistent with a duration measure of risk and justifies why long term bonds require greater premium than short term bonds. Our model explains well the cross-sectional variation in average excess returns of bonds with different maturities over the period 1975–2011 and compares favorably with competing models.     

Incentive Effects of Community Rating in Insurance Markets: Evidence from Massachusetts Automobile Insurance

Rate regulations in insurance markets often impose cross-subsidies in insurance premiums from low-risk consumers to high-risk consumers. This paper develops the hypothesis that premium cross-subsidies affect risk taking by insurance consumers, and tests this hypothesis by examining the marginal impact of premium subsidies and overcharges on future insurance costs. The empirical analysis uses 1990–2003 rating cell-level data from the Massachusetts automobile insurance market, in which regulation produced large cross-subsidies across cells. Consistent with the hypothesized effects, premium subsidies are found to be significantly related to higher future insurance costs, and the opposite effects are found for premium overcharges.     

Credibilistic risk aversion

In the probabilistic risk aversion approach, risks are presumed as random variables with known probability distributions. However, in some practical cases, for example, due to the absence of historical data, the inherent uncertain characteristic of risks or different subject judgements from the decision-makers, risks may be hard or not appropriate to be estimated with probability distributions. Therefore, the traditional probabilistic risk aversion theory is ineffective. Thus, in order to deal with these cases, we suggest measuring these kinds of risks as fuzzy variables, and accordingly to present an alternative risk aversion approach by employing credibility theory. In the present paper, first, the definition of credibilistic risk premium proposed by Georgescu and Kinnunen [Fuzzy Inf. Eng., 2013, 5, 399–416] is revised by taking the initial wealth into consideration, and then a general method to compute the credibilistic risk premium is provided. Secondly, regarding the risks represented with the commonly used LR fuzzy intervals, a simple calculation formula of the local credibilistic risk premium is put forward. Finally, in a global sense, several equivalent propositions for comparative risk aversion under the credibility measurement are provided. Illustrated examples are presented to show the applicability of the theoretical findings.     

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.     

A note on Mossin’s theorem for deductible insurance given random initial wealth

Mossin’s theorem for deductible insurance given random initial wealth is re-examined. For a fair premium, it is shown that a necessary and sufficient condition, in the spirit of the Generalized Mossin Theorem for coinsurance, is impossible using the notion of expectation dependence. Next, it is established that for a fair premium, full insurance will be optimal for a risk-averse individual if the random loss and the random initial wealth are negative quadrant dependent, improving upon an extant result in the literature. In view of a set of examples given in this paper, such a sufficient condition cannot be obtained using the notion of expectation dependence. Finally, for an unfair premium, it is shown that partial insurance will always be optimal, irrespective of the risk preference of the individual as well as the dependence structure between the random loss and the random initial wealth.     

Expected returns and expected dividend growth

We investigate a consumption-based present-value relation that is a function of future dividend growth and find that changing forecasts of dividend growth are an important feature of the post-war U.S. stock market, despite the failure of the dividend–price ratio to uncover such variation. In addition, dividend forecasts are found to covary with changing forecasts of excess stock returns over business cycle frequencies. This covariation is important because positively correlated fluctuations in expected dividend growth and expected returns have offsetting effects on the log dividend–price ratio. The market risk premium and expected dividend growth thus vary considerably more than is apparent using the log divided–price ratio alone as a predictive variable.     

The joint cross-sectional variation of equity returns and volatilities

This paper analyzes the determinants of the simultaneous cross-sectional variation of return and volatility risk premia. Independently of the model specification employed, the estimated risk premium associated with the default premium beta is always positive and statistically different from zero. Moreover, the risk premium of the market volatility risk premium beta is negative and statistically significant. However, both risk factors are priced economically and statistically differently in the volatility and return segments of the market. On average, common factors in both segments explain 90% of the variability of volatility risk premium portfolios, but only 65% of the variability of equity return portfolios.     

Understanding Housing Market Volatility

The Campbell–Shiller present value formula implies a factor structure for the price–rent ratio of housing market. Using a dynamic factor model, we decompose the price–rent ratios of 23 major housing markets into a national factor and independent local factors, and we link these factors to the economic fundamentals of the housing markets. We find that a large fraction of housing market volatility is local and that the national factor has become more important than local factors in driving housing market volatility since 1999, consistent with the findings in Del Negro and Otrok (2007). The local volatilities mostly are due to time variations of idiosyncratic housing market risk premia, not local growth. At the aggregate level, the growth and interest rate factors jointly account for less than half of the total variation in the price–rent ratio. The rest is due to the aggregate housing market risk premium and a pricing error. We find evidence that the pricing error is related to money illusion, especially at the onset of the recent housing market bubble. The rapid rise in housing prices prior to the 2008 financial crisis was accompanied by both a large increase in the pricing error and a large decrease in the housing market risk premium.     

FORWARD RISK PREMIA AND THE MATURITY OF CONTRACTS: A NOTE

This paper examines the behavior of the risk premium component of currency forward rates. Analyzing forward rates of one, two and three-month maturity, we find that the power of forward rate as a predictor of future spot rate decreases with the length of contract maturity. Further, we find that the proportion of the variance of the forward premium which is due to the variation of the risk premium is larger than the proportion due to the expected spot rate change for all currencies except for the Canadian dollar. This proportion also increases with the length of maturity.     

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.     

Is the Market Portfolio a Dynamic Factor? Evidence from Individual Stock Returns

This paper uses a factor model to test whether the market portfolio is a dynamic factor in the sense that individual stock returns contain a premium linked to the conditional risk of the market portfolio. The market conditional risk is based on a decomposition of the market variance into a time-varying trend component and a transitory component. The evidence shows that the conditional market premium is rising when the permanent trend rises relative to the conditional variance. The evidence for individual stock returns supports the notion that the market portfolio is a dynamic factor. Individual stock return autocorrelations are fully explained by the time variation in the market premium. The risk premia attributed to static factors are statistically insignificant.     

Mortgage timing

We study how the term structure of interest rates relates to mortgage choice at both household and aggregate levels. A simple utility framework of mortgage choice points to the long-term bond risk premium as distinct from the yield spread and the long yield as a theoretical determinant of mortgage choice: when the bond risk premium is high, fixed-rate mortgage payments are high, making adjustable-rate mortgages more attractive. We confirm empirically that the bulk of the time variation in both aggregate and loan-level mortgage choice can be explained by time variation in the bond risk premium, whether bond risk premia are measured using forecasters’ data, a vector autoregressive (VAR) term structure model, or a simple household decision rule based on adaptive expectations. The household decision rule moves in lock-step with mortgage choice, lending credibility to a theory of strategic mortgage timing by households.     

The pricing of sentiment risk in European stock markets

This paper studies whether sentiment is rewarded with a significant risk premium in the European stock markets. We examine several sentiment proxies and identify the Economic Sentiment Indicator from the EU Commission as the most relevant sentiment proxy for our sample. The analysis is performed for the contemporaneous excess returns of EA-11 stock markets in the period from February 1999 to September 2015. We apply a conditional multi-beta pricing model in order to track the variation of the sentiment risk premium over time. The results demonstrate a positive significant relationship between sentiment and contemporaneous excess returns which is consistent with previous studies. The calculated sentiment risk premium is significant as well but negative implying that an investment in EA-11 countries over the examined time period – that is bearing sentiment risk – would have been unattractive to the investors on average.     

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.     

偏度风险溢酬及其预测能力研究——基于人民币对外汇期权的实证分析

基于无模型方法,利用在岸人民币对美元期权的市场价格数据,通过提取风险中性三阶矩和已实现三阶矩估算偏度风险溢酬,并考察其时变特征、与波动率风险溢酬的关系和对汇率尾部风险的预测能力。结果表明,外汇期权市场上存在显著为负的时变偏度风险溢酬;偏度风险溢酬与波动率风险溢酬存在共同的驱动因子。此外,偏度风险溢酬在短期内对汇率暴涨的尾部风险事件具备一定的预测能力。当偏度风险溢酬增加时,投资者对偏度风险的厌恶加剧,预期未来人民币大幅贬值的概率上升。