A general equilibrium model of portfolio insurance

This article examines the effects of portfolio insurance onmarket and asset price dynamics in a general equilibrium continuous-timemodel. Portfolio insurers are modeled as expected utility maximizingagents. Martingale methods are employed in solving the individualagents' dynamic consumption-portfolio problems. Comparisonsare made between the optimal consumption processes, optimallyinvested wealth and portfolio strategies of the portfolio insurersand 'normal agents'. At a general equilibrium level, comparisonsacross economies reveal that the market volatility and riskpremium are decreased, and the asset and market price levelsincreased, by the presence of portfolio insurance.     

The Impact of Large Portfolio Insurers on Asset Prices

We develop a simple model in which the presence of portfolio insurers in a market of risk-averse traders leads to multiple equilibria for the pricing of financial assets and can cause an increase in volatility, including insurance-induced price drops. We demonstrate, however, that centralized portfolio insurance firms may actually reduce, not increase, volatility, even if the existence of these firms increases the total amount of funds under insurance.     

The Impact of Catastrophes on Insurer Stock Volatility

This article investigates the impact of natural catastrophes and the 9‐11 attacks on (1) the volatility of insurance stocks and (2) the correlation of insurance stocks with the market. We find that natural catastrophes increase the volatility of insurance stocks. They also have a tendency to reduce the correlation of insurance stocks and the market. Investors can, consequently, diversify natural catastrophe risk by additionally holdings of a market portfolio. However, this does not hold for 9‐11. The events of 9‐11 led to increases in volatility and, simultaneously, to an increase in correlation. We also find evidence that 9‐11 increased the beta of insurance stocks.     

Transparency in the Mortgage Market

This paper studies the impact of transparency in the mortgage market on the underlying real estate market. We show that geographic transparency in the secondary mortgage market, which implies geographic risk based pricing in the primary market, can limit risk-sharing and make house prices more volatile. Ex ante, regions prefer opaque markets to enable insurance opportunities. We discuss the implications for risk based pricing and house price volatility more generally. In addition, we investigate the specific conditions under which competitive lenders would optimally choose to provide opaque lending, thus reducing volatility in the real estate market. We show that in general the opaque competitive equilibrium is not stable, and lenders have incentive to switch to transparent lending if one of the geographic regions has experienced a negative income shock. We propose market and regulatory mechanisms that make the opaque competitive equilibrium stable and insurance opportunities possible.     

Long-term negative fund alpha: Is it caused by bad skill or bad luck?

This paper examines the sources of long-term negative fund alpha. We compare the actual loser funds with a control group of bootstrapped loser funds. We find that the returns of the two fund groups are co-integrated, and that they are similar in market risk exposure, alpha consistency, portfolio holdings, and GARCH volatility. The test results show that long-term negative fund alpha occurs due to bad luck rather than to bad skill.     

Stock market overreactions to bad news in good times: a rational expectations equilibrium model

This article presents a dynamic, rational expectations equilibriummodel of asset prices where the drift of fundamentals (dividends)shifts between two unobservable states at random times. I showthat in equilibrium, investors' willingness to hedge againstchanges in their own 'uncertainty' on the true state makes stockprices overreact to bad news in good times and underreact togood news in bad times. I then show that this model is betterable than conventional models with no regime shifts to explainfeatures of stock returns, including volatility clustering,'leverage effects,' excess volatility, and time-varying expectedreturns.     

On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity

In this paper, we consider a novel approach for the fair valuation of a participating life insurance policy when the dynamics of the reference portfolio underlying the policy are governed by an Asymmetric Power GARCH (APGARCH) model with innovations having a general parametric distribution. The APGARCH model provides a flexible way to incorporate the effect of conditional heteroscedasticity or time-varying conditional volatility and nests a number of important symmetric or asymmetric ARCH-type models in the literature. It also provides a flexible way to capture both the memory effect of the conditional volatility and the asymmetric effects of past positive and negative returns on the current conditional volatility, called the leverage effect. The key valuation tool here is the conditional Esscher transform of Bühlmann et al. (1996, 1998). The conditional Esscher transform provides a convenient and flexible way for the fair valuation under different specifications of the conditional heteroscedastic models. We illustrate the practical implementation of the model using the S&P 500 index as a proxy for the reference portfolio. We also conduct sensitivity analysis of the fair value of the policy with respect to the parameters in the APGARCH model to document the impacts of different conditional volatility models nested in the APGARCH model and the leverage effect on the fair value. The results of the analysis reveal that the memory effect of the conditional volatility has more significant impact on the fair value of the policy than the leverage effect.     

Stock volatility predictability in bull and bear markets

The recent literature on stock return predictability suggests that it varies substantially across economic states, being strongest during bad economic times. In line with this evidence, we document that stock volatility predictability is also state dependent. In particular, in this paper, we use a large data set of high-frequency data on individual stocks and a few popular time-series volatility models to comprehensively examine how volatility forecastability varies across bull and bear states of the stock market. We find that the volatility forecast horizon is substantially longer when the market is in a bear state than when it is in a bull state. In addition, over all but the shortest horizons, the volatility forecast accuracy is higher when the market is in a bear state. This difference increases as the forecast horizon lengthens. Our study concludes that stock volatility predictability is strongest during bad economic times, proxied by bear market states.     

Equilibrium Portfolio Strategies in the Presence of Sentiment Risk and Excess Volatility

Our objective is to identify the trading strategy that would allow an investor to take advantage of "excessive" stock price volatility and "sentiment" fluctuations. We construct a general equilibrium "difference-of-opinion" model of sentiment in which there are two classes of agents, one of which is overconfident about a public signal, while still optimizing intertemporally. Overconfident investors overreact to the signal and introduce an additional risk factor causing stock prices to be excessively volatile. Consequently, rational investors choose a conservative portfolio; moreover, this portfolio depends not just on the current price divergence but also on their prediction about future sentiment and the speed of price convergence.     

Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility

Given an investor maximizing utility from terminal wealth with respect to a power utility function, we present a verification result for portfolio problems with stochastic volatility. Applying this result, we solve the portfolio problem for Heston's stochastic volatility model. We find that only under a specific condition on the model parameters does the problem possess a unique solution leading to a partial equilibrium. Finally, it is demonstrated that the results critically hinge upon the specification of the market price of risk. We conclude that, in applications, one has to be very careful when exogenously specifying the form of the market price of risk.     

Equilibrium analysis of volatility clustering

Volatility clustering is a pervasive feature of equity markets. This article studies volatility clustering in an equilibrium setting by generalizing the CRRA and CARA representative agent models of finance. In equilibrium, the market portfolio follows a volatility regime-switching process in which the volatility level is determined by the agent's local risk aversion. Using monthly data, the empirical tests reveal that at least four volatility regimes are necessary to fit the data. While one of the models explains the GARCH effects in the data, an analysis of the Euler equation pricing errors suggests that both models are likely misspecified. Since the models can be used to closely approximate any state-independent utility function, it is doubtful that there exists any representative agent equilibrium (with state-independent utility) that is consistent with the data. An equivalent interpretation is that the market portfolio price process is not a diffusion process of the type studied by Bick [Bick, A., On viable diffusion price processes of the market portfolio, J. Finance 45 (1990) 673–689] and He and Leland [He, H., Leland, H., On equilibrium asset price processes, Rev. Financ. Stud. 6 (1993) 593–617].     

On stock-based loans

We investigate the equilibrium interest rate charges on non-recourse and recourse loans secured by stock. In such loans, the client retains the option to prepay and recover the collateral stock. We adopt a structural model of the firm where debt levels, with endogenous bankruptcy, affect equity dynamics. Complicating matters, the link between total equity and the price of a share of stock that forms the collateral depends on the extent of dilutions and buybacks that occur. For levered firms, due to dilution in bad states of nature, stock prices typically fall faster than equity values; and for firms that engage in buybacks in good states of nature, stock prices will rise faster than equity values. Banks that ignore these features underestimate the equilibrium interest rate charge on stock-based loans. We provide an analysis of individual stock-based loans and their portfolio characteristics, the latter of which can be used by banks to ascertain capital requirements.     

Trading with Asymmetric Volatility Spillovers

Abstract:  We study the profitability of trading strategies based on volatility spillovers between large and small firms. By using the Volatility Impulse-Response Function of Lin (1997) and its extensions, we detect that any volatility shock coming from small companies is important to large companies, but the reverse is only true for negative shocks coming from large firms. To exploit these asymmetric patterns in volatility, different trading rules are designed based on the inverse relationship existing between expected return and volatility. We find that most strategies generate excess after-transaction cost profits, especially after very bad news and very good news coming from large or small firm markets. These results are of special interest because of their implications for risk and portfolio management.     

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.     

The January effect across volatility regimes

Using a Markov regime switching model, this article presents evidence of the well-known January effect on stock returns. The specification allows a distinction to be drawn between two regimes: one with high volatility and another with low volatility. We obtain a time-varying January effect that is, in general, positive and significant in both volatility regimes. However, this effect is larger in the high-volatility regime. In sharp contrast with most of the previous literature, we find two major results: (1) the January effect exists for all sizes of portfolio; (2) the negative correlation between the magnitude of the January effect and portfolio size fails across volatility regimes. Moreover, our evidence supports a slight decline in the January effect for all sizes of portfolio except the smallest, for which it is even larger.     

(S,s)-adjustment Strategies and Hedging under Markovian Dynamics

We study the destabilizing effect of hedging strategies under Markovian dynamics with transaction costs. Once transaction costs are taken into account, continuous portfolio rehedging is no longer an optimal strategy. Using a non-optimizing (local in time) strategy for portfolio rebalancing, explicit dynamics for the price of the underlying asset are derived, focusing in particular on excess volatility and feedback effects of these portfolio insurance strategies. Moreover, it is shown how these latter depend on the heterogeneity of the insured payoffs. Finally, conditions are derived under which it may be still reasonable, from a practical viewpoint, to implement Black–Scholes strategies.     

Multifrequency news and stock returns

Equity prices are driven by shocks with persistence levels ranging from intraday horizons to several decades. To accommodate this diversity, we introduce a parsimonious equilibrium model with regime shifts of heterogeneous durations in fundamentals, and estimate specifications with up to 256 states on daily aggregate returns. The multifrequency equilibrium has higher likelihood than the Campbell and Hentschel [1992. No news is good news: an asymmetric model of changing volatility in stock returns. Journal of Financial Economics 31, 281–318] specification, while producing volatility feedback 10 to 40 times larger. Furthermore, Bayesian learning about volatility generates a novel trade-off between skewness and kurtosis as information quality varies, complementing the uncertainty channel [e.g., Veronesi, 1999. Stock market overreaction to bad news in good times: a rational expectations equilibrium model. Review of Financial Studies 12, 975–1007]. Economies with intermediate information best match daily returns.     

Portfolio Insurance Strategies when Hedging Affects Share Prices

Option-based portfolio insurance can result in coordinated buying and selling, which destabilizes markets such that hedgers fail to achieve their objective. Gennotte and Leland (1990) show portfolio insurance strategies can have an impact on price movements. Ramanlal and Mann (1996) show how price movements, in turn, can alter hedging strategies. In this paper, we combine these separate effects and develop an equilibrium, executable hedging strategy. This hedging strategy requires less rebalancing than traditional portfolio insurance; more important, it achieves downside protection with a less destabilizing impact on security prices.     

Household Life Cycle Protection: Life Insurance Holdings, Financial Vulnerability, and Portfolio Implications

Using the Survey of Consumer Finances, we examine the life cycle demand for different types of life insurance. Specifically, we test for the consumer's aversion to income volatility resulting from the death of a household's wage‐earner through the purchase of life insurance. We first develop a financial vulnerability index to control for the risk to the household. We then examine the life cycle demand for life insurance using several definitions of life insurance. We find, in contrast to previous research, that there is a relationship between financial vulnerability and the amount of term life or total life insurance purchased. In addition, we find older consumers use less life insurance to protect a certain level of financial vulnerability than younger consumers. Secondly, our study provides evidence that life insurance demand is jointly determined as part of a household's portfolio. Finally, we consider the impact of family members' nonmonetary contribution on the household's life cycle protection decision. Our results provide some evidence that households take into account the value of nonmonetary contribution in their insurance purchase.     

Bank exposure to market fear

We find that increases in implied market volatility (a proxy for market fear) have a significant impact on returns of bank stocks, above and beyond systematic risk proxied by the expected excess market return during a bad economic regime. Large bank returns are favorably affected by increases in implied market volatility during the crisis, while small banks are adversely affected by increases in implied market volatility. We attribute the different effects among the size-categorized bank portfolios to the perception that large banks are protected by too-big-to-fail policies. Within the sample of small banks, the adverse share price response to increased implied market volatility is more pronounced for banks that rely more heavily on non-traditional sources of funds, use a high proportion of loans in their assets, have a higher level of non-performing assets, and have a relatively low provision for loan losses. The adverse effect of negative innovations in implied market volatility on small bank returns during the crisis is primarily driven by exposure of their loan portfolio to weak economic conditions.