Ambiguity Premium Research Articles

A robust financing theory of ICOs under demand uncertainty of products of token platforms

PurposeThe market products produced by Initial Coin Offerings (ICO) platforms are often relatively new and have no previous transaction records and therefore are hard to estimate for its demand. The purpose is to study the impacts of the degree of ambiguity aversion of entrepreneurs to demand uncertainty on the ICO financing ratio, the optimal expected output, the optimal efforts and the token price.Design/methodology/approachIn an optimal ICO design, we introduce demand uncertainty of the product and establish a robust optimization method to solve the ICO optimal design. We compare ICO financing and the general venture capital (VC) financing model. We analyze the impact of demand uncertainty on the optimal ICO financing ratio.FindingsFindings include that the ICO financing ratio is positively related to the degree of ambiguity aversion, the token price is negatively related to the degree of ambiguity aversion and the “ambiguity premium” exists in the ICO market, the optimal effort levels are negatively related with the ICO financing ratio, but positively related with token price, and in the environment of high production cost, VC financing is not as good as ICO financing.Originality/valueWe develop a robust ICO financing model by assuming that the entrepreneur is ambiguity aversive to the demand uncertainty. Analyze the impact of the degree of ambiguity aversion on the ICO financing ratio in theory and find that the entrepreneur can raise funds with the higher ICO token ratio when she has a larger degree of ambiguity aversion to the demand uncertainty. Extend the impact analysis of the degree of ambiguity aversion on the expected token price and find a negative relationship between the expected token price and the degree of ambiguity aversion of the entrepreneur to the demand uncertainty.

Ambiguity, limited market participation, and the cross-sectional stock return

Using expected utility under uncertain probability theory (EUUP, Izhakian, 2017, 2020), we study whether the ambiguity related to individual stocks is priced in the Chinese A-share market and the mechanism behind the ambiguity premium phenomenon. Theoretically, when the asset price is within a specific range, ambiguity-averse investors refrain from participating in trading. As asset ambiguity increases, high ambiguity-averse investors exit the market, with those with lower aversion remaining in the market (limited market participation phenomenon). Investors who remain in the market due to lower ambiguity aversion are willing to accept a low ambiguity premium. Empirically, we measure monthly ambiguity using the volatility of daily stock return distributions within a month and find the following: (1) The equal-weighted average returns of the most ambiguous portfolios (top 20%) are significantly lower than those of the least ambiguous portfolios (bottom 20%). (2) Ambiguity still significantly negatively affects the cross-sectional stock return after controlling for common firm characteristics. (3) The higher the ambiguity, the lower the future trading activity, supporting our theoretical predictions. These findings reveal the mechanism of the negative ambiguity premium in the Chinese A-share market. This study provides new ideas for building a factor-pricing model suitable for the A-share market and a fresh perspective for preventing systemic financial risk.

Cash holdings, ambiguity aversion, and investment puzzles

We consider a real options model with ambiguity to investigate how cash holdings and ambiguity aversion affect a firm’s dynamic investments. First, we prove a unique positive ambiguity coefficient exists when ambiguity exceeds it such that entrepreneurs believe the project is “too valueless to invest in”. Second, the coupons demanded by creditors increase with ambiguity, and cash holdings reduce the ambiguity premium. Our research provides a new explanation as to why companies abandon investment and hold more cash under the influence of the COVID-19 pandemic.

Estimating Household Preferences for Coastal Flood Risk Mitigation Policies Under Ambiguity

AbstractRisk mitigation policies (like dike rising) are essential to address increasing coastal flood risks due to global warming. Furthermore, the optimal level of risk mitigation policy should be determined by public preferences for risk reduction. However, it is difficult to reveal public preferences for coastal flood risk reduction because projections of coastal flood risks inevitably involve uncertainty. This study aims to estimate household preference for coastal flood reduction under ambiguity and multiple projections of coastal flood risks. By coupling storm surge inundation simulations and stated preference experiments with decision models, we estimate the expected loss reduction, risk premium, and ambiguity premium for coastal flood risk mitigation policies. The study shows that ignoring the ambiguity premium causes significant undervaluation of coastal flood risk mitigation.

Economic uncertainty: Mispricing and ambiguity premium

AbstractWe uncover two channels of effect in the financial market when investors face macroeconomic uncertainty. Conditional on a common mispricing index, we find that economic uncertainty exposure (EUE) induces disagreement, which amplifies mispricing. The highest EUE quintile produces an annualised mispricing alpha of 9.96%, more than double the unconditional mispricing effect. An ambiguity premium of 3.84% alpha is documented in the “non‐mispricing” quintile. The EUE‐induced mispricing effect is different from the existing limits of arbitrage explanations. The ambiguity premium is predictably observed during the unfolding of shocks of COVID‐19 to the market.

Ambiguity of scientific probability predictions and willingness-to-pay for climate change mitigation policies

We estimate a smooth ambiguity preference function, wherein an individual faces multiple probability predictions of policy outcomes, and then empirically measure their willingness-to-pay for the policy, ambiguity attitude, and ambiguity premium. Climate change mitigation policy is used as the example. The estimation results reveal that most people have ambiguity-seeking attitudes, but that these attitudes are heterogeneous across individuals. People who are older, are university graduates, have higher income, or trust more in science show stronger ambiguity-seeking attitudes. Their willingness-to-pay can be underestimated if ambiguity is not considered. Moreover, individuals with stronger ambiguity-seeking attitudes support aggressive mitigation policies more strongly. Our estimation strategy is generally applicable to policy evaluations wherein policy outcomes are ambiguous.

Ambiguous Text

Investors infer ambiguity from text in news and social media. A proxy for information ambiguity is developed from text processing and used in regression tests against the S&P 500 returns. A risk-neutral agent model with uniform prior beliefs is developed to explain the ambiguity premium or discount under unfavorable or favorable market conditions agnostic of the ambiguity preferences. The model postulates that the ambiguity premium is often elusive in efficient markets due to returns unpredictability, and the information ambiguity as an omitted variable bias in the fundamental relationship between risks and returns. Empirically, the author finds that news media drives equity prices more than social media except from June 2009 to November 2016.

Ambiguity, asset illiquidity, and price variability

I develop a sequential trading model with ambiguity-averse market makers and provide a theoretical explanation to the historical coincidence of ambiguous events, asset illiquidity, and price variability. My model implies that the bid-ask spread of an asset contains an additive component of ambiguity premium. As a result, higher ambiguity generally leads to lower asset liquidity. More interestingly, asset prices are variable under particular conditions: specifically, only mixed-strategy equilibria exist, such that market makers probabilistically set multiple prices. Further analysis confirms that, compared with risk, ambiguity plays a unique role in explaining price variability.

Ambiguity premium and transaction costs

We generalize the optimal investment model of an ambiguity averse investor with transaction costs. Along the lines of Maenhout (2004), we first show that ambiguity (or model uncertainty) leads to an increase in effective risk aversion by ambiguity aversion even with transaction costs. We compute the utility cost associated with suboptimal investment decisions, which is the so-called ambiguity premium. We then find that ignoring ambiguity aversion with and without transaction costs generates large ambiguity premia when ambiguity aversion is moderate, and the cost of ignoring it becomes larger with higher ambiguity aversion. This would, thus, still support the importance of ambiguity aversion channel for portfolio choice, even concerning the friction markets.

Risk, ambiguity, and equity premium: International evidence

We empirically examine the relation between risk, ambiguity, and market equity premium in 21 international stock markets. After estimating each country's degree of ambiguity from intraday data of iShares country ETFs (exchange-traded funds), we find a positive risk-return tradeoff. Investors' attitudes toward ambiguity is conditional on their expectations of probability of gains, but its relationship is nonlinear. This nonlinearity in ambiguity premium is more prominent in emerging markets. Additionally, we conduct a cross-country analysis, which shows that cross-country variations in cultural and institutional factors affect investors' behavior. Our international evidence supports that ambiguity alongside risk are the key determinants of investors' decision-making.

Liquidity and Risk Management with Ambiguity

We formulate a robust theory of liquidity and risk management based on two fundamental frictions: 1) the entrepreneur cannot alienate his human capital, and 2) the entrepreneur worries about model uncertainty and seek robust decisions. In line with max-min expected utility, a robust entrepreneur makes decisions under some endogenous worst case, which generates significant distortions for risk-sharing, corporate investment, and consumption. With regard to concern for ambiguity aversion, the entrepreneur optimally responds by lowering the maximal debt capacity, under-investing and under-consuming. However, the impacts of ambiguity on risk hedging is ambiguous due to the interactions between robustness and limited commitment constraints. These distortions are greater the more financially constrained the firm is. Furthermore, we show that the optimal consumption rule is no longer deterministic but stochastic when taking the preference for robustness into account. Implications for implied ambiguity premium and persistent productivity shocks are also studied.

Information Inertia

ABSTRACTWe show that aversion to risk and ambiguity leads to information inertia when investors process public news about assets. Optimal portfolios do not always depend on news that is worse than expected; hence, the equilibrium stock price does not reflect this bad news. This informational inefficiency is more severe when there is more risk and ambiguity but disappears when investors are risk‐neutral or the news is about idiosyncratic risk. Information inertia leads to news momentum (e.g., after earnings announcements) and is consistent with low household trading activity. An ambiguity premium helps explain the macro and earnings announcement premium.

모호성(Ambiguity) 프리미엄과 기대수익률

본 연구에서는 주식수익률 분포의 모호성에 대한 대리변수로 최근 주식수익률의 확률 분포와 과거 수익률의 확률분포 간의 차이를 비모수적 방법으로 측정하는 Kolmogorov-Smirnov(KS) 통계량과 Kuiper(K) 통계량을 제시한다. 주식수익률의 모호성이 커질수록 이를 싫어하는 투자자들은 이러한 주식에 대해 프리미엄을 요구할 것이고, 따라서 모호성 프리미엄에 따라 기대수익률은 높아질 것이다. 본 연구에서는 국내 주식시장 내에 이러한 모호성 프리미엄이 존재하는지를 밝히고자 한다. 본 논문의 분석결과를 살펴보면, 수익률 분포의 모호성이 큰 주식이 평균적으로 더 높은 수익률을 갖는 것으로 나타났다. 또한, 분포의 불확실성이 가장 큰 포트폴리오(B)를 매수하고 가장 작은 포트폴리오(S)를 매도하는 전략을 구사하여 유의한 양의 위험조정수익률을 얻을 수 있음을 발견하였다. 본 논문의 분석결과는 기존의 이론 연구에서는 주장하고 있으나 실증적으로 밝혀내지 못한 모호성 프리미엄이 한국 주식시장에 존재하는 것으로 해석될 수 있다.

An Option Pricing Model with Probability Measure Ambiguity

This paper develops an option pricing model that admits probability measure ambiguity. It formulates a piecewise risk-ambiguity-neutral probability density function and derives analytical pricing formula. Options and their underlying assets are exposed to different scopes of ambiguity that cannot be hedged, implying that options are generically non-redundant assets and have different Sharpe ratios than the underlying assets. Introduction of probability measure ambiguity reduces the in-sample and 1-day (5-day) out-of-sample pricing errors of the Black-Scholes-Merton model by 80% and 66% (61%) in pricing S&P 500 index options, and remarkably alleviates volatility smile. Option-implied market ambiguity premium is counter-cyclical and contains distinct information compared to VIX.

Economic Uncertainty Exposure and Cross-Sectional Return: Mispricing and Risk Premium

We study the effect of economic uncertainty exposure (EUE) on cross-sectional return differentiating the mispricing from ambiguity-premium effects. Conditional on a common mispricing index, we find that EUE induces disagreement which amplifies mispricing. The highest EUE quintile produces an annualized mispricing alpha of 9%, more than double the unconditional mispricing effect. An ambiguity premium of 4.2% alpha is documented in the “non-mispricing” quintile. The EUE induced mispricing effect is different from existing limits of arbitrage explanations, such as idiosyncratic risk. The ambiguity premium is a new source of the risk premium that is robust to the latest risk models.

Performance Evaluation under Adverse Selection and Correlation Ambiguity

We develop a model wherein a risk-neutral but ambiguity-averse principal contracts with a risk-averse agent who has a risky project. Both the agent and the principal can observe the project output and a public signal. The correlation between the output and the public signal is private information to the agent but is an ambiguous random variable to the principal. Then, apart from moral hazard, the optimal contract takes into consideration both adverse selection and ambiguity aversion simultaneously. Due to the classic trade-off between rent and efficiency, the principal lowers contract power for the agent with a low correlation project (the l-type agent) and compensates her for luck. However, aversion to correlation ambiguity counteracts with this rent reducing effect by making the principal weight the l-type agent more. Consequently, although ambiguity lessens the principal's value, it could improve social welfare by increasing efficiency of the l-type agent. We further extend the model by incorporating an aggregate signal whose variance depends on the ambiguous distribution of all the projects and allowing the agents to be ambiguity-averse. In this case, the principal has to respect the agent's model choice and compensates her for ambiguity premium, which again decreases contract power. With ambiguity-sharing, the pair of optimal separating contracts is metamorphosed compared to those in the baseline model.

Knight Meets Sharpe: Capital Asset Pricing under Ambiguity

This paper extends the classical mean-variance preferences to mean-variance-ambiguity preferences by relaxing the assumption that probabilities are known, and instead assuming that probabilities are uncertain. In general equilibrium, the two-fund separation theorem is preserved and the market portfolio is identified as efficient. Thereby, introducing ambiguity into the capital asset pricing model indicates that the \emph{ambiguity premium} corresponds to systematic ambiguity, which is distinguished from systematic risk. Using the measurable closed-form beta ambiguity, well-known performance measures are generalized to account for ambiguity alongside risk. The introduced capital asset pricing model is empirically implementable and provides insight into empirical asset pricing anomalies. The model can be extended to other applications, including investment decisions and valuations.

An additive model of decision making under risk and ambiguity

We extend the mean–variance (risk–value) tradeoff model to decision making under both risk and ambiguity. This model explicitly captures the tradeoff between the magnitude of risk and the magnitude of ambiguity. A measure that ranks lotteries in terms of the magnitude of ambiguity can also be obtained using this separation. By applying our model to asset pricing under ambiguity, we show that the equity premium can be decomposed into two parts: the risk premium and the ambiguity premium. Further, combining this model with the standard risk–value model, we build on the risk–ambiguity tradeoff to provide the value–risk–ambiguity preference model that does not rely on an approximation argument as the mean–variance model.

Dispersion of beliefs, ambiguity, and the cross-section of stock returns

Abstract We examine whether ambiguity is priced in the cross-section of expected stock returns. Using the cross-sectional dispersion in real-time forecasts of real GDP growth as a measure for ambiguity, we find that high ambiguity beta stocks earn lower future returns relative to low ambiguity beta stocks. This negative predictive relation between the ambiguity beta and future returns is consistent with theory, which predicts the marginal utility of consumption to rise when ambiguity is high. We further show that the ambiguity premium remains significant after controlling for exposures to expected real GDP growth, VIX, and financial market dislocations index.

Earnings volatility, ambiguity, and crisis‐period stock returns

AbstractFinancial crises are marked by substantial increases in ambiguity where prices appear to decouple from fundamentals. Consistent with ambiguity‐based asset pricing theories, we find that ambiguity concerns are more severe for firms with higher earnings volatility, causing investors to demand a higher ambiguity premium for such firms. While there is no relation between earnings volatility and stock returns under normal conditions, there is a significant negative relation between crisis‐period stock returns and prior earnings volatility. The effect is stronger in firms with low institutional ownership and low analyst following, consistent with ambiguity concerns being greatest amongst firms with unsophisticated investors.