Equilibrium Analysis of Portfolio Insurance

A martingale approach is used to characterize general equilibrium in the presence of portfolio insurance. Insurers sell to noninsurers in bad states, and general equilibrium requires that the risk premium rises to induce noninsurers to increase their holdings. We show that portfolio insurance increases price volatility, causes mean reversion in asset returns, raises the Sharpe ratio and volatility in bad states, and causes volatility to be correlated with volume. We also explain why out-of-the-money S&P 500 put options trade at a higher volatility than do in-the-money puts.     

A computational study on general equilibrium pricing of derivative securities

This paper analyses the accuracy of replicating portfolio methods in predicting asset prices. In a two-period, general equilibrium model with incomplete financial markets and heterogeneous agents, a computational study is conducted under various distributional assumptions. The focus is on the price of a call option on an underlying risky asset. There is evidence that the value of the (approximate) replicating portfolio is a good approximation for the general equilibrium price for CRRA preferences, but not for CARA preferences. Furthermore, there is strong evidence that the introduction of the call option reduces market incompleteness, but that the price of the underlying asset is unchanged. There is, however, inconclusive evidence on the welfare effects of the option. The author thanks Dolf Talman, Andrew Somerville, an anonymous referee, and an Associate Editor for helpful comments. Research funding from the Irish Research Council for the Humanities and Social Sciences is gratefully acknowledged.     

Risk-neutral investors do not acquire information

Give a risk-neutral investor the choice to acquire a costly signal prior to asset market equilibrium. She refuses to pay for the signal under general conditions. The reason is that a risk-neutral investor is indifferent between a risky asset or a safe bond in optimum and expects the same return to her portfolio ex ante, whether or not she acquires information. Risk neutrality thus implies the absence of costly information from asset price in competitive asset markets.     

Cash demand,liquidation costs and capital market equilibrium under uncertainty

In this paper, the portfolio and the liquidity planning problems are unified and analyzed in one model. Stochastic cash demands have a significant impact on both the composition of an individual's optimal portfolio and the pricing of capital assets in market equilibrium. The derived capital asset pricing model with cash demands and liquidation costs shows that both the market price of risk and the systematic risk of an asset are affected by the aggregate cash demands and liquidity risk. The modified model does not require that all investors hold an identical risky portfolio as implied by the Sharpe-Lintner-Mossin model. Furthermore, it provides a possible explanation for the noted discrepancies between the empirical evidence and the prediction of the traditional capital asset pricing model.     

Alternate approach to unify CAPM and APT

We utilize the joint elliptical distribution to model a multi-factor return generating process and derive an equilibrium multi-beta capital asset pricing model (CAPM) in which the market portfolio and a set of nonelliptical factors are sufficient to price all financial assets. Most important, it is shown that the market portfolio, while generally nonelliptical, can proxy all elliptical factors and hence: including elliptical factors in addition to the market portfolio in the pricing equation contribute nothing to asset pricing. While the representative investor prices the exposure of aggregate wealth to various nonelliptical systematic risk factors, individual securities are priced in accordance to their contributions to different aspects of the risk of aggregate wealth. The present model collapses to the Sharpe-Lintner CAPM when either the market investor is neutral to nonelliptical risk factors or when all risk factors follow a joint spherical distribution. When residuals cancel out of the market portfolio, the present model collapses to Conner (1984) pricing model.     

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].     

Ambiguous Information,Portfolio Inertia,and Excess Volatility

I study the effects of risk and ambiguity (Knightian uncertainty) on optimal portfolios and equilibrium asset prices when investors receive information that is difficult to link to fundamentals. I show that the desire of investors to hedge ambiguity leads to portfolio inertia and excess volatility. Specifically, when news is surprising, investors may not react to price changes even if there are no transaction costs or other market frictions. Moreover, I show that small shocks to cash flow news, asset betas, or market risk premia may lead to drastic changes in the stock price and hence to excess volatility.     

Equilibrium relations in a capital asset market: A mean absolute deviation approach

We consider the equilibrium in a capital asset market where the risk is measured by the absolute deviation, instead of the standard deviation of the rate of return of the portfolio. It is shown that the equilibrium relations proved by Mossin for the mean variance (MV) model can also be proved for the mean absolute deviation (MAD) model under similar assumptions on the capital market. In particular, a sufficient condition is derived for the existence of a unique nonnegative equilibrium price vector and derive its explicit formula in terms of exogeneously determined variables. Also, we prove relations between the expected rate of return of individual assets and the market portfolio.     

General equilibrium pricing of options on the market portfolio with discontinuous returns

When the price process for a long-lived asset is of a mixedjump-diffusion type, pricing of options on that asset by arbitrageis not possible if trading is allowed only in the underlyingasset and a risk-less bond. Using a general equilibrium framework,we derive and analyse option prices when the underlying assetis the market portfolio with discontinuous returns. The premiumfor the risk of jumps and the diffusions risk forms a significantpart of the prices of the options. In this economy, an attemptedreplication of call and put options by the Black-Scholes typeof trading strategies may require substantial infusion of fundswhen jumps occur. We study the cost and risk implications ofsuch dynamic hedging plans.     

Underestimation of portfolio insurance and the crash of October 1987

We examine market crashes in the multiperiod framework of Glostenand Milgrom (1985). Our analysis shows that if the market'sprior beliefs underestimate the extent of dynamic hedging strategiessuch as portfolio insurance, then the price will be greaterthan that which would be implied by fundamentals if the extentof portfolio insurance were known with certainty. Over time,the market learns of the amount of portfolio insurance, andconsequently reevaluates the previous inferences drawn frompurchases that were erroneously regarded as based on favorableinformation. The result is that the price falls when the amountof portfolio insurance is revealed.     

Forecasting market turbulence using regime-switching models

We propose an early warning system to timely forecast turbulence in the US stock market. In a first step, a Markov-switching model with two regimes (a calm market and a turbulent market) is developed. Based on the time series of the monthly returns of the S&P 500 price index, the corresponding filtered probabilities are successively estimated. In a second step, the turbulent phase of the model is further specified to distinguish between bullish and bearish trends. For comparison only, a Markov-switching model with three states (a calm market, a turbulent bullish market, and a turbulent bearish market) is examined as well. In a third step, logistic regression models are employed to forecast the filtered probabilities provided by the Markov-switching models. A major advantage of the presented modeling framework is the timely identification of the factors driving the different phases of the capital market. In a fourth step, the early warning system is applied to an asset management case study. The results show that explicit consideration of the models’ signals yields better portfolio performance and lower portfolio risk compared to standard buy-and-hold and constant proportion portfolio insurance strategies.     

Optimal portfolio choice of gold assets in the differential market and differential game structures

Portfolio choices of gold-related assets for market investors and dealers may not only depend on price differences and the inflation rate, but may also react to the market participants’ strategic behavior and risk attitude. This study develops a two-agent stochastic differential game model to solve the portfolio choice problem of the asset allocations of gold spot, futures, and cash for market participators who are exposed to inflation risks. The equilibrium prices of spot and futures driven by the volatility rate and co-variances that reflect various risk sources are also determined. Specifically, regarding the choice of hedging tools, market participators may prefer gold spot to futures for the purpose of hedging inflation risk. By capturing the stylistic facts of differential market and multiple agent structures, the article can develop a more reasonable and practical model to usefully explain the gold portfolio choices and pricing in the gold markets.     

Equilibrium with investors using a diversity of deviation measures

It has been argued that investors who optimize their portfolios with attention paid only to mean and standard deviation will all end up choosing some multiple of a certain master fund portfolio. Justification for the capital asset pricing model of classical portfolio theory, which relates individual assets to such a master fund, has come from this direction in particular. Attempts have been made to provide solid mathematical support by showing that the imputed behavior of investors is a consequence of price equilibrium in a market in which assets are traded subject to budget constraints, and optimization is carried out with respect to utility functions that depend only on mean and standard deviation.     

On equilibrium asset price processes

In this article we derive necessary and sufficient conditionsthat must be satisfied by equilibrium asset price processesin a pure exchange economy. We examine a world in which assetprices follow a diffusion process, asset markets are dynamicallycomplete, all investors maximize their (state-independent) expectedutility of consumption at some future date, and investors havenonrandom exogenous income. We show that it is necessary andsufficient that the coefficients of an equilibrium diffusionprice process satisfy a partial differential equation and aboundary condition. We also examine how the dynamics of assetprices are related to the shape of the representative investor'sutility function through the boundary condition. For example,in a constant-volatility economy, the expected instantaneousreturn of the market portfolio is mean reverting if and onlyif the relative risk aversion of the representative investoris decreasing in terminal wealth.     

Options Trading and the CAPM

This article studies equilibrium asset pricing when agents facenonnegative wealth constraints. In the presence of these constraintsit is shown that options on the market portfolio are nonredundantsecurities and the economy's pricing kernel is a function ofboth the market portfolio and the nonredundant options. Thisimplies that the options should be useful for explaining riskyasset returns. To test the theory, a model is derived in whichthe expected excess return on any risky asset is linearly related(via a collection of betas) to the expected excess return onthe market portfolio and to the expected excess returns on thenonredundant options. The empirical results indicate that thereturns on traded index options are relevant for explainingthe returns on risky asset portfolios.     

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.     

The performance of model based option trading strategies

This paper analyzes returns to trading strategies in options markets that exploit information given by a theoretical asset pricing model. We examine trading strategies in which a positive portfolio weight is assigned to assets which market prices exceed the price of a theoretical asset pricing model. We investigate portfolio rules which mimic standard mean-variance analysis is used to construct optimal model based portfolio weights. In essence, these portfolio rules allow estimation risk, as well as price risk to be approximately hedged. An empirical exercise shows that the portfolio rules give out-of-sample Sharpe ratios exceeding unity for S&P 500 options. Portfolio returns have no discernible correlation with systematic risk factors, which is troubling for traditional risk based asset pricing explanations.     

The Effect of Sequential Information Arrival on Asset Prices: An Experimental Study

A complete understanding of security markets requires a simultaneous explanation of price behavior, trading volume, portfolio composition (ie., asset allocation), and bid-ask spreads. In this paper, these variables are observed in a controlled setting—a computerized double auction market, similar to NASDAQ. Our laboratory allows experimental control of information arrival—whether simultaneously or sequentially received, and whether homogeneous or heterogeneous. We compare the price, volume, and share allocations of three market equilibrium models: telepathic rational expectations, which assumes that traders can read each others minds (strong-form market efficiency); ordinary rational expectations, which assumes traders can use (some) market price information, (a type of semi-strong form efficiency); and private information, where traders use no market information. We conclude 1) that stronger-form market models predict equilibrium prices better than weaker-form models, 2) that there were fewer misallocation forecasts in simultaneous information arrival (SIM) environments, 3) that trading volume was significantly higher in SIM environments, 4) and that bid-ask spreads widen significantly when traders are exposed to price uncertainty resulting from information heterogeneity.     

Arbitrage and Viability in Insurance Markets

Insurance markets are subject to transaction costs and constraints on portfolio holdings. Therefore, unlike the frictionless asset markets case, viability is not equivalent to absence of arbitrage possibilities. We use the concept of unbounded arbitrage to characterize viable prices on a complete and an incomplete insurance market. In the complete market, there is an insurance contract for every possible event. In the incomplete market, risk can be insured through proportional and excess of loss like insurance contracts. We show how the the structure of viable prices is affected by the portfolio constraints, the transaction costs, and the structure of marketed contracts.     

Bank portfolio choice with private information about loan quality: Theory and implications for regulation

This paper models bank asset choice when shareholders know more about loan quality than do outsiders. Because of this informational asymmetry, the price of loans in the secondary market is the price for poor quality loans. Banks desire to hold marketable securities in order to avoid liquidating good quality loans at the ‘lemons’ price, but also have a countervailing desire to hold risky loans in order to maximize the value of deposit insurance. In this context, portfolio composition and bank safety is examined as a function of the market distribution of loan quality, and the distribution of deposits. The model suggests that off-balance sheet commitments have little effect on bankruptcy risk, and induce banks to hold more securities. We also show that an increase in the bank equity requirement will unambiguously increase bank safety in the long run. In the short run, banks are unambiguously riskier on-balance sheet, although the effect on bank safety is ambiguous.