Effort, Idiosyncratic Risk and Investment Under Uncertainty

<p>This thesis is based upon four very simple premises: 1. managers, not shareholders make the investment decisions for the firm; 2. managers do more than just say "yes" or "no" to investments, they can also exert effort that affects the payoff from investment; 3. executive compensation schemes can cause managers to hold more stock than is optimal for diversification purposes; and 4. many investments can be delayed and involve irreversible capital costs as well as uncertain payoffs. Combining these four premises gives the two central questions this thesis attempts to answer: 1. How does the level of managerial stock-ownership affect the investment decisions managers make for the firm? and 2. given the answer to (1), how does this affect the shareholder's decision to hire a manager? In this thesis I use a continuous time "Real Options" framework to answer these questions. The form of the utility function assumed for the manager has a huge impact on the tractability of the modelling. The assumption of Constant Relative Risk Aversion (CRRA) utility as opposed to Constant Absolute Risk Aversion (CARA) causes the manager's valuation of the cash flow (the very first step of the modelling) to become wealth dependent. This in itself is an interesting issue, but it also poses interesting numerical issues and makes the later steps of the analysis intractable. Because of this we split the substantive analysis of this thesis into two parts. In the first we assume CARA utility in order to remove wealth dependence from the valuation and obtain a "clean path" to the end goal of a dynamic model of hiring, effort and irreversible investment. In the second we focus on CRRA utility thus allowing the manager's valuation to depend on his financial wealth. We then explain the resultant numerical issues, and the appropriate approach to their solution.</p>

Effort, Idiosyncratic Risk and Investment Under Uncertainty

<p>This thesis is based upon four very simple premises: 1. managers, not shareholders make the investment decisions for the firm; 2. managers do more than just say "yes" or "no" to investments, they can also exert effort that affects the payoff from investment; 3. executive compensation schemes can cause managers to hold more stock than is optimal for diversification purposes; and 4. many investments can be delayed and involve irreversible capital costs as well as uncertain payoffs. Combining these four premises gives the two central questions this thesis attempts to answer: 1. How does the level of managerial stock-ownership affect the investment decisions managers make for the firm? and 2. given the answer to (1), how does this affect the shareholder's decision to hire a manager? In this thesis I use a continuous time "Real Options" framework to answer these questions. The form of the utility function assumed for the manager has a huge impact on the tractability of the modelling. The assumption of Constant Relative Risk Aversion (CRRA) utility as opposed to Constant Absolute Risk Aversion (CARA) causes the manager's valuation of the cash flow (the very first step of the modelling) to become wealth dependent. This in itself is an interesting issue, but it also poses interesting numerical issues and makes the later steps of the analysis intractable. Because of this we split the substantive analysis of this thesis into two parts. In the first we assume CARA utility in order to remove wealth dependence from the valuation and obtain a "clean path" to the end goal of a dynamic model of hiring, effort and irreversible investment. In the second we focus on CRRA utility thus allowing the manager's valuation to depend on his financial wealth. We then explain the resultant numerical issues, and the appropriate approach to their solution.</p>

Moving beyond the cost–loss ratio: economic assessment of streamflow forecasts for a risk-averse decision maker

A large effort has been made over the past 10 years to promote the operational use of probabilistic or ensemble streamflow forecasts. Numerous studies have shown that ensemble forecasts are of higher quality than deterministic ones. Many studies also conclude that decisions based on ensemble rather than deterministic forecasts lead to better decisions in the context of flood mitigation. Hence, it is believed that ensemble forecasts possess a greater economic and social value for both decision makers and the general population. However, the vast majority of, if not all, existing hydro-economic studies rely on a cost–loss ratio framework that assumes a risk-neutral decision maker. To overcome this important flaw, this study borrows from economics and evaluates the economic value of early warning flood systems using the well-known Constant Absolute Risk Aversion (CARA) utility function, which explicitly accounts for the level of risk aversion of the decision maker. This new framework allows for the full exploitation of the information related to a forecasts' uncertainty, making it especially suited for the economic assessment of ensemble or probabilistic forecasts. Rather than comparing deterministic and ensemble forecasts, this study focuses on comparing different types of ensemble forecasts. There are multiple ways of assessing and representing forecast uncertainty. Consequently, there exist many different means of building an ensemble forecasting system for future streamflow. One such possibility is to dress deterministic forecasts using the statistics of past error forecasts. Such dressing methods are popular among operational agencies because of their simplicity and intuitiveness. Another approach is the use of ensemble meteorological forecasts for precipitation and temperature, which are then provided as inputs to one or many hydrological model(s). In this study, three concurrent ensemble streamflow forecasting systems are compared: simple statistically dressed deterministic forecasts, forecasts based on meteorological ensembles, and a variant of the latter that also includes an estimation of state variable uncertainty. This comparison takes place for the Montmorency River, a small flood-prone watershed in southern central Quebec, Canada. The assessment of forecasts is performed for lead times of 1 to 5 days, both in terms of forecasts' quality (relative to the corresponding record of observations) and in terms of economic value, using the new proposed framework based on the CARA utility function. It is found that the economic value of a forecast for a risk-averse decision maker is closely linked to the forecast reliability in predicting the upper tail of the streamflow distribution. Hence, post-processing forecasts to avoid over-forecasting could help improve both the quality and the value of forecasts.

Heterogeneous Beliefs

There is a representative investor in a complete single‐period market if all investors have log utility or if all investors have CARA utility, even if investors have different beliefs. This extends to dynamic markets for log utility but not for CARA utility. With CARA and other LRT utility, the concept of a representative investor can be extended to include a random discounting factor that is either a supermartingale or a submartingale. If there are short sales constraints, then assets may be overpriced relative to average beliefs, because pessimistic investors are constrained from trading on their beliefs. The overpricing is an increasing function of the dispersion of beliefs. In a dynamic market with short sales constraints, prices can exceed even the values of optimistic investors (a speculative bubble).

Moving beyond the cost-loss ratio: Economic assessment of streamflow forecasts for a risk-averse decision maker

A large effort has been made over the past 10 years to promote the operational use of probabilistic or ensemble streamflow forecasts. Numerous studies have shown that ensemble forecasts are of higher quality than deterministic ones. Many studies also conclude that decisions based on ensemble rather than deterministic forecasts lead to better decisions in the context of flood mitigation. Hence, it is believed that ensemble forecasts possess a greater economic and social value for both decision makers and the general population. However, the vast majority, if not all, of existing hydro-economic studies rely on a cost-loss ratio framework that assumes a risk-neutral decision maker. To overcome this important flaw, this study borrows from economics and evaluates the economic value of early warning flood systems using the well-known CARA utility function, which explicitly accounts for the level of risk aversion of the decision maker. This new framework allows for the full exploitation of the information related to a forecasts' uncertainty, making it especially suited for the economic assessment of ensemble or probabilistic forecasts. Rather than comparing deterministic and ensemble forecasts, this study focuses rather on comparing different types of ensemble forecasts. There are multiple ways of assessing and representing forecast uncertainty. Consequently, there exists many different means of building an ensemble forecasting system for future streamflow. One such possibility is to dress deterministic forecasts using the statistics of past error forecasts. Such dressing methods are popular among operational agencies because of their simplicity and intuitiveness. Another approach is the use of ensemble meteorological forecasts for precipitation and temperature, which are then provided as inputs to one or many hydrological model(s). In this study, three concurrent ensemble streamflow forecasting systems are compared: simple statistically dressed deterministic forecasts, forecasts based on meteorological ensembles and a variant of the latter that also includes an estimation of variable uncertainty. This comparison takes place for the Montmorency River, a small flood-prone watershed in south central Quebec, Canada. The assessment of forecasts is performed for lead times of one to five days, both in terms of forecasts' quality (relative to the corresponding record of observations) and in terms of economic value, using the new proposed framework based on the CARA utility function. It is found that the economic value of a forecast for a risk-averse decision maker is closely linked to the forecast reliability in predicting the upper tail of the streamflow distribution.

Portfolio Selection with Subsistence Consumption Constraints and CARA Utility

We consider the optimal consumption and portfolio choice problem with constant absolute risk aversion (CARA) utility and a subsistence consumption constraint. A subsistence consumption constraint means there exists a positive constant minimum level for the agent’s optimal consumption. We use the dynamic programming approach to solve the optimization problem and also give the verification theorem. We illustrate the effects of the subsistence consumption constraint on the optimal consumption and portfolio choice rules by the numerical results.

Impact of Risk Aversion on Price and Quality Decisions under Demand Uncertainty via the CARA Utility Function

This paper investigates optimal price and quality decisions of a manufacturer-retailer supply chain under demand uncertainty, in which players are both risk-averse decision makers. The manufacturer determines the wholesale price and quality of the product, and the retailer determines the retail price. By means of game theory, we employ the constant absolute risk aversion (CARA) function to analyze two different supply chain structures, that is, manufacturer Stackelberg model (MS) and retailer Stackelberg model (RS). We then analyze the results to explore the effects of risk aversion of the manufacturer and the retailer upon the equilibrium decisions. Our results imply that both the risk aversion of the manufacturer and the retailer play an important role in the price and quality decisions. We find that, in general, in MS and RS models, the optimal wholesale price and quality decrease with the risk aversion of the manufacturer but increase with the risk aversion of the retailer, while the retail price decreases with the risk aversion of the manufacturer as well as the retailer. We also examine the impact of quality cost coefficient on the optimal decisions. Finally, numerical examples are presented to illustrate the different degree of effects of players’ risk aversion on equilibrium results and to compare results in different models considered.