Minsuk Kwak

A Multi Period Equilibrium Pricing Model

In this paper, we propose an equilibrium pricing model in a dynamic multi-period stochastic framework with uncertain income streams. In an incomplete market, there exist two traded risky assets (e.g. stock/commodity and weather derivative) and a non-traded underlying (e.g. temperature). The risk preferences are of exponential (CARA) type with a stochastic coefficient of risk aversion. Both time consistent and time inconsistent trading strategies are considered. We obtain the equilibriums prices of a contingent claim written on the risky asset and non-traded underlying. By running numerical experiments we examine how the equilibriums prices vary in response to changes in model parameters.

Cumulative Prospect Theory with Generalized Hyperbolic Skewed

We investigate a one-period portfolio optimization problem of a cumulative prospect theory (CPT) investor with multiple risky assets and one risk-free asset. The returns of multiple risky assets follow multivariate generalized hyperbolic (GH) skewed t distribution. We obtain a three-fund separation result of two risky portfolios and risk-free asset. Furthermore, we reduce the high dimensional optimization problem to two 1-dimensional optimization problems and derive the optimal portfolio. We show that the optimal portfolio composition changes as some of investor-specific parameters change. It is observed that the consideration of skewness of stock return distribution has considerable impact on the distribution of CPT investors wealth deviation, and leads to less total risky investment.

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We consider the problem of minimizing capital at risk in the Black-Scholes setting. The portfolio problem is studied given the possibility that a correlation constraint between the portfolio and a financial index is imposed. The optimal portfolio is obtained in closed form. The effects of the correlation constraint are explored; it turns out that this portfolio constraint leads to a more diversified portfolio.

Distribution

We consider the entrepreneur’s problem of having a real investment opportunity with undiversifiable risk in a finite horizon. By explicitly characterizing the consumption and investment problem, we show that the remaining time to undertake the project has a significant impact on the characteristics of a firm’s cash flow or return dynamics. Our theory predicts that a firm with an ample time horizon to invest tends to have a cash flow or the stock return with a higher idiosyncratic volatility. Furthermore, we also extend the baseline model to the cases in which the entrepreneur has several projects that can only be sequentially exercised. In this case, a project with a lower idiosyncratic volatility will be exercised first when the investment horizon is long.

Risk minimization and portfolio diversification

We consider the entrepreneur’s problem of having a real investment opportunity with undiversifiable risk in a finite horizon. By explicitly characterizing the consumption and investment problem, we show that the remaining time to undertake the project has a significant impact on the characteristics of a firm’s cash flow or return dynamics. Our theory predicts that a firm with an ample time horizon to invest tends to have a cash flow or the stock return with a higher idiosyncratic volatility. Furthermore, we also extend the baseline model to the cases in which the entrepreneur has several projects that can only be sequentially exercised. In this case, a project with a lower idiosyncratic volatility will be exercised first when the investment horizon is long.

Decision Horizon and Idiosyncratic Risk

This paper studies the investment timing problem of an entrepreneur with a non-tradable real option with undiversifiable risk. We find that the time preference can have a significant impact on the risk attitude toward the idiosyncratic risk, which results from the wealth effect on the implied option value. If the agent is impatient (patient), an increase in idiosyncratic volatility increases (decreases) the agent’s value and delays (hastens) investment. This finding suggests several important implications and empirical predictions for investment decisions in private firms and public firms with concentrated ownership.

Investment Horizon, Risk-Taking, and Entrepreneurial Project Selection

We consider a capital at risk (CaR) minimization problem in an incomplete market Black-Scholes setting. The optimization problem is studied, given the possibility that a correlation constraint between the wealth process and a financial index is imposed. The optimal portfolio is not unique and it is analytically characterized. In the special case of complete market, the optimal portfolio is unique and is obtained in closed form. The effect of the correlation constraint is also explored; it turns out that this constraint leads to a more diversified portfolio.

Time Preference and Real Investment

We consider the entrepreneur’s problem of having a real investment opportunity with undiversifiable risk in a finite horizon. By explicitly characterizing the consumption and investment problem, we show that the remaining time to undertake the project has a significant impact on the characteristics of a firm’s cash flow or return dynamics. Our theory predicts that a firm with an ample time horizon to invest tends to have a cash flow or the stock return with a higher idiosyncratic volatility. Furthermore, we also extend the baseline model to the cases in which the entrepreneur has several projects that can only be sequentially exercised. In this case, a project with a lower idiosyncratic volatility will be exercised first when the investment horizon is long.