A Utility-Based Model of Common Stock Price Movements

This paper develops and tests a nonlinear utility-based econometric model of the temporal behavior of aggregate stock price movements based on a constant relative risk aversion utility function and an observable information set consisting of aggregate consumption, aggregate dividends, and past stock prices. The stochastic process derived from time-series analyses of consumption and dividends measured over annual intervals is used to derive and empirically test a closed-form solution for stock-price movements. The endogenization of discount rate changes in the utility-based model is shown to be more consistent with aggregate stock price movements over a twenty-year holdout period than constant discount rate models. The model is also used to estimate the representative investor's relative risk aversion. The estimate of 4.22 is consistent with that used by Grossman and Shiller in their perfect foresight model and is significantly higher than the relative risk aversion of 1.0 implied by logarithmic utility.     

Market pricing of executive stock options and implied risk preferences

When managers get to trade in options received as compensation, their trading prices reveal several aspects of subjective option pricing and risk preferences. Two subjective pricing models are fitted to show that executive stock option prices incorporate a subjective discount. It depends positively on implied volatility and negatively on option moneyness. Further, risk preferences are estimated using the semiparametric model of Aït-Sahalia and Lo (2000). The results suggest that relative risk aversion is just above 1 for a certain stock price range. This level of risk aversion is low but reasonable, and it may be explained by the typical manager being wealthy and having low marginal utility. Related to risk aversion, it is found that marginal rate of substitution increases considerably in states with low stock prices.     

A Model of International Asset Pricing with a Constraint on the Foreign Equity Ownership

This paper derives a closed-form valuation model in a two-country world in which the domestic investors are constrained to own at most a fraction, δ, of the number of shares outstanding of the foreign firms. When the “δ constraint” is binding, two different prices rule in the foreign securities market, reflecting the premium offered by the domestic investors over the price under no constraints and the discount demanded by the foreign investors. The premium is shown to be a multiple of the discount, the multiple being the ratio of the aggregate risk aversion of the domestic and foreign investors. Given the aggregate risk-aversion parameters, the equilibrium premium and discount are determined by the severity of the δ constraint and the “pure” foreign market risk.     

Asset pricing under quantile utility maximization

“Focus on the downside, and the upside will take care of itself” is a famous quote among professional investors. By considering an agent who follows this advice, we reproduce the first and second moments of stock returns, risk-free rate and consumption growth. The agent's behavior toward risk is analogous to a relative risk aversion of about 3 under expected utility, the elasticity of intertemporal substitution is about 0.5 and the time discount factor is below 1. In particular, the proposed model separates time and risk preferences in an innovative way.     

The Illiquidity Discount of Life Insurance Investments

We incorporate an illiquid life insurance investment in the multi-period investment strategy of an investor with constant relative risk aversion and independent and identically distributed returns. In our setup, the liquid and the illiquid assets are risky and correlated and the illiquid investment cannot be rebalanced. We calculate the illiquidity discount as the difference in certainty equivalent rates of return between the optimal strategy with all assets being rebalanced in each period and the strategy with the illiquid investment. Calibrating our model to data of the German market we find a negative relationship between the level of risk aversion and the illiquidity discount when the investor does not rebalance at all. However, when the investor rebalances his liquid assets in each period to hedge against the illiquid investment the illiquidity discount becomes economically negligible.     

Non-addictive Habit Formation and the Equity Premium Puzzle

I analyse a model in a simple representative-agent economy with one risky and one riskless asset, populated by habit forming consumer-investors. These consumer-investors exhibit non-addictive habit formation in the sense that the current consumption rate of the consumer-investors can fall below their past habit-forming consumption rate. I endogenise the real riskless rate of return in this representative-agent economy and find that the equity premium puzzle is resolved for plausible values of the coefficient of relative risk aversion, the discount rate, and the intensity of non-addictive habit formation. These values have been validated in previous empirical or survey-based studies. Non-addictive habit-formation studied here complements and extends current research on habit-forming preferences. Given a constant investment opportunity set, the real riskless rate in the economy increases with relative risk aversion of the consumer and decreases as the habit-formation intensity increases. Extensions with time-varying investment opportunity sets could explain the low risk-free rate and the relatively large variability of the market return over the variability of the risk-free rate through time.     

商业银行票据贴现利率的市场化转型——以Shibor为基准的定价模型研究

中国人民银行规定商业银行实行基于再贴现率加点生成贴现利率的票据定价模式。在中国票据市场快速发展过程中,由于货币政策调整和利率市场化进程等因素,使得票据贴现利率波动频繁并逐步显现出基于再贴现利率基准定价模式的缺陷,主要包括贴现利率存在跌破再贴现利率的背离现象、贴现利率定价模式未体现票据市场化程度、再贴现利率的货币传导功能逐步弱化等。本文提出票据贴现利率采取基于Shibor加点差的定价模式具有资金成本依据和契合票据业务特点等方面的优势,并具有推进利率市场化、沟通不同金融市场联系和促进货币政策传导等作用。     

Bank Funding Risks,Risk Aversion,and the Choice of Futures Hedging Instrument

Currently, theories of financial futures hedging are based on either a portfolio-choice approach or a duration approach. This article presents an alternative: a firm-theoretic model of bank behavior with financial futures. Assuming the bank is uncertain about cash CD interest rates and the quantity of CDs it needs in the future, expressions for the optimal futures hedge are derived under constant absolute risk aversion and constant relative risk aversion. The performance of these two strategies is estimated from 1981–1983 using either the recently developed CD futures contract or the T-Bill futures contract. These results are also compared with the performance of a portfolio-choice strategy and a routine hedging strategy. The analysis indicates that the CD futures market can serve a hedging purpose that is not served by the previously established T-Bill futures market.     

The consequences of discount rate selection for defined benefit liabilities

This paper provides evidence on the use of discount rates for calculating defined benefit liabilities (DBL), and their impact on value relevance and audit fees for Australian listed companies between 2011 and 2016. We document that the average discount rate is 3.96% but the yearly range across companies is 4.03% (2.76% excluding multinationals with multiple plans), despite the fact that AASB 119 provides guidance to use the yield of high quality corporate bonds or, if there is not a deep market, government bonds. We then find that the DBL or unfunded component (DBL less the fair value of the plan’s assets) is value relevant, but is less so when a higher discount rate is used. Furthermore, we document that audit fees are higher when the DBL is larger, or the discount rate is higher, consistent with greater audit effort and risk. Overall, this paper contributes to the accounting literature by documenting both the discretion available in discount rate selection and its consequences.     

Asymmetric Effects of Interest Rate Changes on Stock Prices

This study examines the stock price adjustment process around announcements of changes in the federal funds rate target in the 1990s using an asymmetric autoregressive exponential GARCH model (ASAR‐EGARCH). We find that target change announcements convey new information to the stock market. Risk aversion increases before the announcement of a rate change, and especially before the announcement of a joint target and discount rate change. The volatility estimates suggest that such joint rate changes send a clearer signal to the stock market about monetary policy objectives relative to unilateral target changes. Our findings are consistent with overreaction in the wake of bad news (rate hikes), and point to a shift in volatility from before to after the rate change announcement since the adoption of the immediate disclosure policy of the Federal Open Market Committee in February 1994.     

Portfolio Choice and Life Insurance: The CRRA Case

We solve a portfolio choice problem that includes life insurance and labor income under constant relative risk aversion (CRRA) preferences. We focus on the correlation between the dynamics of human capital and financial capital and model the utility of the family as opposed to separating consumption and bequest. We simplify the underlying Hamilton–Jacobi–Bellman equation using a similarity reduction technique that leads to an efficient numerical solution. Households for whom shocks to human capital are negatively correlated with shocks to financial capital should own more life insurance with greater equity/stock exposure. Life insurance hedges human capital and is insensitive to the family's risk aversion, consistent with practitioner guidance.     

Discount rates for long-term projects: the cost of capital and social discount rate compared

Research on the cost of capital and on the social discount rate (SDR) has developed largely along separate paths. This paper offers an overview and comparison of both concepts. The consumption-based theory of discount rates is common to both, but there are striking differences in how the cost of capital and SDR are estimated. A project's cost of capital is inferred in practice from market data, by a well-established package of techniques, and project risk makes a large difference. In contrast, the SDR is estimated by applying judgement about the welfare of future generations, in the setting of consumption-based theory. Project risk has tended to be ignored under the SDR approach.     

Information asymmetry,contract design and process of negotiation: The stock options awarding case

Stock option plans are used to increase managerial incentives, and business practices usually set the exercise price equal to the stock market price. The purpose of this paper is to underline the importance of a process of negotiation leading to a possible equilibrium contract satisfying both managers and shareholders. The two key variables of the model are the percentage of equity capital offered by the shareholders to the managers and the exercise price of the options that may be at a discount. We explicitly introduce risk aversion and information asymmetries in the form of (i) an economic uncertainty in the gain of cash flow, (ii) possibly biased information between the two parties and (iii) a noise in the valuation price of the stock in the market. The existence of a process of negotiation between shareholders and managers leading to a possible disclosure of private information is highlighted. As a conclusion, we show that “efficient” stock option plans should be granted in a context of trade-off between the percentage of capital awarded to managers and the discount in stock price.     

Dynamic Portfolio Choice with Stochastic Wage and Life Insurance

We study optimal insurance, consumption, and portfolio choice in a framework where a family purchases life insurance to protect the loss of the wage earner's human capital. Explicit solutions are obtained by employing constant absolute risk aversion utility functions. We show that the optimal life insurance purchase is not a monotonic function of the correlation between the wage and the financial market. Meanwhile, the life insurance decision is explicitly affected by the family's risk preferences in general. The model also predicts that a family uses life insurance and investment portfolio choice to hedge stochastic wage risk.     

Why Is Long‐Horizon Equity Less Risky? A Duration‐Based Explanation of the Value Premium

We propose a dynamic risk‐based model that captures the value premium. Firms are modeled as long‐lived assets distinguished by the timing of cash flows. The stochastic discount factor is specified so that shocks to aggregate dividends are priced, but shocks to the discount rate are not. The model implies that growth firms covary more with the discount rate than do value firms, which covary more with cash flows. When calibrated to explain aggregate stock market behavior, the model accounts for the observed value premium, the high Sharpe ratios on value firms, and the poor performance of the CAPM.     

The Pricing of Risk and Sentiment: A Study of Executive Stock Options

Option pricing models accounting for illiquidity generally imply the options are valued at a discount to the Black‐Scholes value. Our model considers the role of sentiment, which offsets illiquidity. Using executive stock options and compensation data from 1992 to 2004 for S&P 1500 firms, we find that executives value employee stock options (ESOs) at a 48% premium to the Black‐Scholes value. These premia are explained by a sentiment level of 12% in risk‐adjusted, annualized return, suggesting a high level of executive overconfidence. Subjective value relates negatively to illiquidity and idiosyncratic risk, and positively to sentiment in all specifications, consistent with the offsetting roles of sentiment and risk aversion.     

Accounting for Risk and Return in Equity Valuation

Standard valuation models forecast cash flows or earnings, add a growth rate, and discount the cash flows to their present value with a discount rate that typically reflects the cost of capital. But as the author argues, projecting the long‐term growth rate is essentially speculative; and along with uncertainty about the growth rate, analysts generally do not have a good grasp of the discount rate either. Thus, instead of reducing uncertainty, these two features effectively compound uncertainty in valuations in the sense that slight changes in the growth rate or discount rate can change the valuation considerably. In this article, the author proposes an alternative approach that views the investor's problem as one of challenging the speculations that are built into the current market price, particularly the speculation about growth. Rather than building in a speculative growth rate (and thereby treating it as if it were a certainty), the author's approach turns the problem on its head by using an accounting analysis of the firm's current earnings and cash flows that provides a basis for recognizing the speculative component of the current stock price. More specifically, the author's analysis identifies the future earnings growth path that is implied by the market price, which can then be evaluated with the question: Do I want to pay for this growth? Because growth expectations are risky, additional analysis can be used to provide an understanding of the risk and return to buying growth, and of the upside and downside if risk growth expectations are not realized. By taking such an approach, investors incorporate their understanding of risk not by increasing the discount rate, but by recognizing that the primary risk in investing is the risk of overpaying for growth.     

TIME VARIABILITY IN MARKET RISK AVERSION

We adopt realized covariances to estimate the coefficient of risk aversion across portfolios and through time. Our approach yields second moments that are free from measurement error and not influenced by a specified model for expected returns. Supporting the permanent income hypothesis, we find risk aversion responds to consumption-smoothing behavior. As income increases, or as the consumption-to-income ratio falls, relative risk aversion decreases. We also document variation in risk aversion across portfolios: risk aversion is highest for small and value portfolios.     

Modeling and monitoring risk acceptability in markets: The case of the credit default swap market

Minimal discounted distorted expectations across a range of stress levels are employed to model risk acceptability in markets. Interactions between discounting and stress levels used in measure changes are accommodated by lowering discount rates for the higher stress levels. Acceptability parameters represent a maximal and minimal discount rate, a maximal stress level and the speed of rate reduction in response to stress. An explicit model relating credit default swap (CDS) prices to default probabilities is formulated with a view to making the default risk market acceptable. Data on CDS prices and default probabilities for the six major US banks obtained from the Risk Management Institute of the National University of Singapore is employed to estimate parameters defining acceptability and the movements in market implied recovery rates. We observe that the financial crisis saw an increase in the maximal discount rate and its spread over the minimal rate along with an increase in the maximal stress level being demanded for acceptability and a stable pattern for the speed of rate adjustment through the period. The maximal rate, rate spread and stress levels have come down but with periods in the interim where they have peaked as they did in the crisis. Recovery rates have oscillated and they did fall substantially but have recovered towards 40 percent near the end of the period.