Expected Risk Premium Research Articles

A Historical Perspective on US Treasuries Risk Premia

The uncontrolled growth of US public debt is causing some anxiety among investors in US Treasuries. It is therefore useful to estimate the current risk premia embedded in the US yield curve and assess the extent to which investors are pricing in potential future financing difficulties for the US government.In this paper, we provide both a theoretical and empirical explanation of the factors driving the US Treasuries yield curve and how it is possible to extract what market participants are currently pricing in.It is widely acknowledged that expectations about future US monetary policy play a crucial role in this market. However, there is a notable underestimation — even within academic literature — of the symmetrical role played by expectations regarding future risk premia. Through our original modeling of the US Treasuries yield curve, we document the history of these expected risk premia. Our findings indicate that from 2000 to 2022, investors consistently underestimated the strength of demandfor US Treasuries, which may explain the somewhat unusual behavior of this key market during that period.Since 2022, however, a new paradigm has emerged. Demand for longterm US treasuries has declined due to the resurgence of inflation, while debt issuance has surged, driven by substantial deficits and the Federal Reserve’s Quantitative Tightening policies. Consequently, risk premia have increased sharply.The future remains highly uncertain as lower inflation could once again bolster demand for US Treasuries while public debt is expected to continue its rapid expansion. In this volatile environment, our model will help investors manage their positions by enabling real-time comparisons between their own expectations and the actual market pricing.

Asset pricing with dividend surprises

In this paper, we derive an intertemporal dividend-surprise-augmented asset-pricing model and show that the expected risk premium compensates for stock returns’ exposure to (i) the market-wide dividend-surprise hedge portfolio based on dividend yield surprise and volatilities, in addition to (ii) the excess market return without dividend yield (as in the conventional CAPM) and (iii) the market-wide dividend yield factor without uncertainty. Our model implies that the uncertainty on dividend-surprise yield is attributable to systematic risk and should be priced at the cross-section, thereby theoretically supporting the existing empirical studies on the relation between dividend surprise and cross-sectional stock returns.

Startup Financing: Some Evidence from the Indian Venture Capital Industry

This study analyses the venture capitalists’ evaluation of startups in the Indian context by using primary data obtained from a survey study of representatives drawn from the industry. A distinguishing feature of the study is the categorization of venture capitalists on the basis of their stage of financing for analyzing the nature of diversification prevalent in the industry, the rank order of risks as perceived by the different categories of venture capitalists, and their expected risk premium. The findings of the study suggest the existence of two broad categories of venture capitalists; those involved in early-stage financing and those who invested across the life stages of startups. Furthermore, results indicate that each of these two categories of venture firms attaches varying importance to the broad considerations that are known to impact a startup’s value, they are differently diversified, their rank order of perceived risks is different and so is the expected risk premium.

The Return Expectations of Public Pension Funds

Abstract The return expectations of public pension funds are positively related to cross-sectional differences in past performance. This positive relation operates through the expected risk premium, rather than the expected risk-free rate or inflation rate. Pension funds act on their beliefs and adjust their portfolio composition accordingly. Persistent investment skills, risk taking, efforts to reduce costly rebalancing, and fiscal incentives from unfunded liabilities cannot fully explain the reliance of expectations on past performance. The results are consistent with extrapolative expectations, since the dependence on past returns is greater when executives have personally experienced longer performance histories with the fund. Authors have furnished an Internet Appendix, which is available on the Oxford University Press Web site next to the link to the final published paper online.

Asset pricing with heterogeneous agents and long-run risk

This paper shows that belief differences have strong effects on asset prices in consumption-based asset-pricing models with long-run risks. Belief heterogeneity leads to time-varying consumption and wealth shares of the agents. This time variation can resolve several asset-pricing puzzles, including the large countercyclical variation of expected risk premia, the volatility of the price-dividend ratio, the predictability of cash flows and returns, and the large predictability of returns in recessions. These findings show that belief differences, a widely observed attribute of investors, significantly improve the explanatory power of long-run risk asset-pricing models.

Asset Pricing with Heterogeneous Agents and Long-Run Risk

This paper shows that belief differences have strong effects on asset prices in consumption-based asset-pricing models with long-run risks. Belief heterogeneity leads to time-varying consumption and wealth shares of the agents. This time variation can resolve several asset-pricing puzzles, including the large countercyclical variation of expected risk premia, the volatility of the price--dividend ratio, the predictability of cash flows and returns, and the large predictability of returns in recessions. These findings show that belief differences, a widely observed attribute of investors, significantly improve the explanatory power of long-run risk asset-pricing models.

Extracting expected stock risk premia from option prices and the information contained in non-parametric-out-of-sample stochastic discount factors

This paper analyzes the factor structure and cross-sectional variability of a set of expected excess returns extracted from option prices and a non-parametric and out-of-sample stochastic discount factor. We argue that the existing potential segmentation between the equity and option markets makes it advisable to avoid using only option prices to extract expected equity risk premia. This set of expected risk premia significantly forecasts future realized returns, and the first two principal components explain 94.1% of the variability of expected returns. A multi-factor model with the market, quality, funding illiquidity, the default premium and the market-wide variance risk premium as factors significantly explains the cross-sectional variability of expected excess returns. The (asymptotically) different from zero adjusted cross-sectional R-squared statistic is 83.6%.

The Return Expectations of Institutional Investors

Analysis of required expected return disclosures by public pension funds in individual asset classes reveals a reliance on past performance in setting return expectations. These extrapolative expectations operate through the expected risk premium and occur across all risky asset classes. Pension plans act on their extrapolated expectations by adjusting their target asset allocations. Pension funds extrapolate performance more when executives have personally experienced a longer performance history with the fund, and when employing certain investment consultants. The results cannot be explained by differential risk-taking, persistent investment skill, efforts to reduce costly rebalancing, or fiscal pressure from unfunded liabilities.

Skewness Preference and Asset Pricing: Evidence from the Japanese Stock Market

Previous studies have shown that investor preference for positive skewness creates a potential premium on negatively skewed assets. In this paper, we attempt to explore the connection between investors’ skewness preferences and corresponding demand for a risk premium on asset returns. Using data from the Japanese stock market, we empirically study the significance of risk aversion with skewness preference that potentially delivers a premium. Compared to studies on other stock markets, our finding suggests that Japanese investors exhibit preference for positively skewed assets, but do not display dislike for ones that are negatively skewed. This implies that investors from different countries having dissimilar attitudes toward risk may possess different preferences toward positive skewness, which would result in a different magnitude of expected risk premium on negatively skewed assets.

Portfolio Scoring by Expected Risk Premium

In this article, the authors discuss a general method for ranking portfolios that places few limitations on the portfolio constituents other than using publicly traded assets. The ranking scores reflect the expected reward investors would require for accepting the risks of the portfolio in the context of an asset pricing framework. The scores are computed through a factor model that acknowledges the factor return correlations. The authors illustrate the approach with a large universe of exchange-traded funds assuming a linear model with Fama–French–Carhart factors wherein factor premiums (i.e., expected returns) are proportional to factor volatilities. The empirical analysis implies that the most significant factors from the Fama–French–Carhart factor set driving the premiums are the market and the momentum factors.

Effect of credit supply constraint on labour productivity in Sub-Saharan Africa

This paper investigates the effect of credit supply constraint of risk on labour productivity in 33 Sub-Saharan Africa (SSA) countries spanning 1990-2013. It estimates the long run effect of credit supply constraints on labour productivity using the pooled mean group (PMG) estimator. The results revealed that a reduction in both actual and expected risk premiums increased labour productivity in SSA. The findings suggest that in order to relax the credit supply constraints with the intent to improving labour productivity, domestic interest rate should account for changes in foreign interest rate to enhance the needed capital inflows.

Risk-Neutral Cumulants, Expected Risk Premia, and Future Stock Returns

This paper builds an empirical model to connect option-implied cumulants with expected risk premia through latent risk factors. Expected risk premia on individual stocks are estimated by applying a new partial least squares-based method on risk-neutral cumulants at different orders and various maturities. The filtered expected risk premia based on the second and third order risk-neutral cumulants exhibit a considerably large dispersion across stocks, which further generates a wide cross-sectional variation in future realized risk premia. I find a positive relationship between the ex-ante filtered expected risk premium and future realized risk premium during the period of 1996-2017. A strategy that goes long the decile portfolio with the largest filtered expected risk premium and short the decile portfolio with the smallest filtered expected risk premium yields a Fama-French-Carhart alpha of 1.06% per month (t-stat 3.75). The filtered expected risk premium of the above trading strategy is correlated (Corr: 51.5%) with the equal-weighted stock's expected excess return in Martin and Wagner (2018). Moreover, I show that the predictability of the filtered expected risk premium can be potentially explained by informed trading driven by short-selling constraints.

A Re-Interpretation of 'Significant' Empirical Financial Research

Currently, the use and interpretation of t statistics and p-values is under scrutiny in various scientific fields for several reasons: p-hacking, data dredging, misinterpretation, multiple testing, or selective reporting, among others. To the best of our knowledge, this discussion has hardly reached the empirical finance community. Thus, the aim of this paper is to show how the typical p-value based analysis of empirical findings in finance can be fruitfully enriched by the supplemental use of further statistical tools. We revisit popular studies regarding the validity of the CAPM and determine Bayesian measures for hypothesis testing. In comparison to the typical yes and no decisions made under frequentist approaches, these measures allow a direct interpretation regarding the strength of the empirical finding. For instance, while Fama and MacBeth (1973) find an expected risk premium that is significantly different from zero for systematic risk, we observe that the likelihood for an expected risk premium to be zero is approximately 43% at the same time.

Putting the present value model into practice: a comparison of two alternative approaches

ABSTRACTA key issue around putting the present-value model into practice is how to construct the unobserved future expectations of the fundamental variables related to an asset. One approach is to fit a vector autoregression (VAR) for the fundamental variables and deduce their future expectations from the estimated VAR. An alternative is to directly specify the future expectations as unobserved components (UC) and use the Kalman filter to extract their estimates from the realized data. This article examines whether the predictions of the present-value model are consistent across the two approaches. Constructing the VAR and UC versions of the standard present-value model, we examine how the two versions compare in identifying the main driver of the US and UK housing markets. For the UK, the two approaches consistently attribute most variations in the price–rent ratio to the expected future risk premium for housing investment. For the US, however, the two approaches deliver considerably different results: the VAR version marks the expected risk-free rate of return, whereas the UC version singles out the expected risk premium as the main driver of the ratio. We conclude that the choice between the VAR and UC approaches is not a trivial issue related to utilizing the present-value model.

A Financially Motivated Extension of the Heston Model for a Joint ℙ- and ℚ-Dynamics Analysis of Variance

The empirical, or “ℙ,” distribution determines profits and losses from market price changes, while the risk- neutral “ℚ” distribution is what is embedded in derivatives prices. Expected returns under the ℙ distribution include expected risk premia, while under the ℚ, those risk premia are embedded in the probabilities. Risk-neutral probabilities, and hence market prices for derivatives, move randomly because expectations about true (ℙ-density) probabilities change and also because risk premia are variable too. While changes in the ℚ density are observable in option prices, the breakdown between true expectations and risk premia is not. Although evidence suggests that risk premia may fluctuate as much as probability beliefs do, it is rare for their dynamics to be formally modeled. That is what Rebonato and Ng do in this article looking at exchange rates. Starting with the assumption of a standard Heston model for dynamics under the P measure, they construct a corresponding volatility process under the ℚ measure by modifying the long-term variance level and the reversion speed. Rather than modeling these as constant parameters, they introduce mean-reverting diffusions for both parameters. The effects of these generalizations are explored by holding one constant while the other is varied. After showing the extra flexibility that the “complex Heston” formulation allows, they devise an analytic approximation formula using the average projected parameter values from the dynamic model as the constant parameters in the standard Heston specification and show that the approach works very well. Finally, they take the model to the data for the EURUSD, JPYUSD, and GBPUSD exchange rates and demonstrate that the new model can fit well over time without the need to refit parameter values.

Equity Risk Premiums (ERP): Determinants, Estimation and Implications The 2018 Edition

Equity risk premiums are a central component of every risk and return model in finance and are a key input into estimating costs of equity and capital in both corporate finance and valuation. Given their importance, it is surprising how haphazard the estimation of equity risk premiums remains in practice. We begin this paper by looking at the economic determinants of equity risk premiums, including investor risk aversion, information uncertainty and perceptions of macroeconomic risk. In the standard approach to estimating equity risk premiums, historical returns are used, with the difference in annual returns on stocks versus bonds over a long time period comprising the expected risk premium. We note the limitations of this approach, even in markets like the United States, which have long periods of historical data available, and its complete failure in emerging markets, where the historical data tends to be limited and volatile. We look at two other approaches to estimating equity risk premiums – the survey approach, where investors and managers are asked to assess the risk premium and the implied approach, where a forward-looking estimate of the premium is estimated using either current equity prices or risk premiums in non-equity markets. We also look at the relationship between the equity risk premium and risk premiums in the bond market (default spreads) and in real estate (cap rates) and how that relationship can be mined to generated expected equity risk premiums. We close the paper by examining why different approaches yield different values for the equity risk premium, and how to choose the “right” number to use in analysis.

Comparing Entropy and Beta as Measures of Risk in Asset Pricing

The paper establishes entropy as a measure of risk in asset pricing models by comparing its explanatory power with that of classic capital asset pricing model’s beta to describe the diversity in expected risk premiums. Three different non‑parametric estimation procedures are considered to evaluate financial entropy, namely kernel density estimated Shannon entropy, kernel density estimated Rényi entropy and maximum likelihood Miller‑Madow estimated Shannon entropy. The comparison is provided based on the European stock market data, for which the basic risk‑return trade‑off is generally negative. Kernel density estimated Shannon entropy provides the most efficient results not dependent on the choice of the market benchmark and without imposing any prior model restrictions.

Macroeconomic Fundamentals to the Commodity Risk Premium

This chapter aims to build a connection between commodities’ price movements and the growth level in industrial production in different economic regions. Commodities should only be incorporated in a diversified strategy as long they either have a poor correlation to standard assets such as equities, or offer an attractive risk premium. We demonstrate that the part of commodity return not attributed to the roll yield is related to economic activities in the U.S. and China. 40 to 50% of variation in commodities returns are explained by industrial production growth in those both regions. The slow-down of economic activity implies lower excess returns on commodities. Similar to the risk premium on equities and credit, the commodity risk premium is dependent on the economic environment. This finding casts doubt on both commodities’ diversification potential, and investor’s interest in this asset class in terms of expected risk premium, given the current low world structural growth.

Momentum and Mean-Reversion in Commodity Spot and Futures Markets

We study momentum and mean-reversion strategies in commodity futures prices and their relationship to momentum and mean reversion in commodity spot prices. We find that momentum performs well in futures markets, but not in spot markets, and that mean-reversion performs well in spot markets, but not in futures markets. A decomposition of the basis (the slope of the term-structure of futures prices) into expected risk premiums and expected changes in spot prices helps us shed some light on the different results across the futures and spot markets. Most interestingly, we find that momentum in futures prices cannot be explained by a sustained trend in spot prices.

Momentum and mean-reversion in commodity spot and futures markets

We study momentum and mean-reversion strategies in commodity futures prices and their relationship to momentum and mean-reversion in commodity spot prices. We find that momentum performs well in futures markets, but not in spot markets, and that mean-reversion performs well in spot markets, but not in futures markets. A decomposition of the basis (the slope of the term-structure of futures prices) into expected risk premiums and expected changes in spot prices helps us shed some light on the different results across the futures and spot markets. Most interestingly, we find that momentum in futures prices cannot be explained by a sustained trend in spot prices.