A number of important theorems in finance rely on the ability of investors to trade any amount of a security without affecting the price. However, there exist several frictions, such as trading costs, short sale restrictions, circuit breakers, etc. that impact price formation. The influence of market imperfections on security pricing has long been recognized. Liquidity, in particular, has attracted a lot of attention from traders, regulators, exchange officials as well as academics.
Liquidity, a fundamental concept in finance, can be defined as the ability to buy or sell large quantities of an asset quickly and at low cost. The vast majority of equilibrium asset pricing models do not consider trading and thus ignore the time and cost of transforming cash into financial assets or vice versa. Recent financial crises, however, suggest that, at times, market conditions can be severe and liquidity can decline or even disappear. Such liquidity shocks are a potential channel through which asset prices are influenced by liquidity. Amihud and Mendelson (1986) and Jacoby, Fowler, and Gottesman (2000) provide theoretical arguments to show how liquidity impacts financial market prices. Jones (2001) and Amihud (2002) show that liquidity predicts expected returns in the time-series. Pastor and Stambaugh (2003) find that expected stock returns are cross sectionally related to liquidity risk.
Whilst non-linear models are often used for a variety of purposes, one of their prime uses is for forecasting, and it is in terms of their forecasting performance that they are most often judged. However, a casual review of the literature suggests that often the forecasting performance of such models is not particularly good. Some studies find in favour, but equally there are studies in which their added complexity relative to rival linear models does not result in the expected gains in terms of forecast accuracy. Just over a decade ago, in their review of non-linear time series models, De Gooijer and Kumar (1992) concluded that there was no clear evidence in favour of non-linear over linear models in terms of forecast performance, and we suspect that the situation has not changed very much since then. It seems that we have not come very far in the area of non-linear forecast model construction.
We argue that the relatively poor forecasting performance of non-linear models calls for substantive further research in this area, given that one might feel uncomfortable asserting that non-linearities are unimportant in describing economic and financial phenomena. The problem may simply be that our non-linear models are not mimicing reality any better than simpler linear approximations, and in the next section we discuss this and related reasons why a good forecast performance ‘across the board’ may constitute something of a ‘holy grail’ for non-linear models.
This paper develops a model to study how entrepreneurs and venture capital investors deal with effort provision, moral hazard, asymmetric information and hold-up problems when contracts are incomplete and investment proceeds in stages. How much value is lost in the entrepreneur-venture capital relationship relative to the first-best? How does the value lost depend on risk and the time-pattern of required investment? What determines whether a positive-NPV project can in fact be financed? What are the advantages and disadvantages of staged financing? Are there significant efficiency gains from syndication of later-stage financing?
We combine effort provision, moral hazard, and hold up problems of the entrepreneur-venture capital relationship into one model. We argue that these and related questions should not be analyzed one by one, but jointly in a common setting. Some features of venture-capital contracting may not solve a particular problem, but instead trade off one problem against another. For example, a study that focused just on the option-like advantages of staged investment could easily miss the costs of staging, particularly the negative feedback to effort if venture-capital investors can dictate financing terms in later stages and can hold up the entrepreneur. We will show that these costs can be so significant that staged investment may actually reduces NPV relative to 100 percent upfront financing even after accounting for the costs of the inefficient project continuation decisions of the latter.
