VENTURE STRUCTURE
CAPITAL: AND INCENTIVES
YORAM LANDSKRONER
and JACOB PAROUSH
ABSTRACT Venture capital is a major source of tinancing for firms in their early stages of development. Such businesses, especially in the high technology industries, are characterized by a high degree of uncertainty and asymmetry of information. In this paper we analyze the relationship between a venture capital organization (“capitalist”) and the initial owner of an entrepreneurial entity in which it invests (“entrepreneur”). We focus on the agency problems and derive a compensation
system. In our model the capitalist provides
a combination of equity and debt financing while the owner provides equity financing which serves as a signal affecting the beliefs (“optimism”) of the capitalist. The interesting result is that since the capitalist is assumed to be more risk averse than the entrepreneur, preneur at the optimum.
I.
he is made to be more optimistic than the entre
INTRODUCTION
Venture capital represents a relatively new form of financing which has emerged in the last two decades. These funds have been a major source of financing for young businesses at the early stages of their development.’ Such businesses, especially in the high technology industries, are characterized by high degree of uncertainty and asymmetry of information. These characteristics have led to the development of the specialized form of venture capital financing.2 Direct all correspondence to: Yoram Landskroner, School of Business Administration, The Hebrew University of Jerusalem, Mt. Scopus, Jerusalem 91905, Israel; Jacob Paroush, School of Business, BarIlan University, Jersalem, Israel. International Review of Economics and Finance, 4(4): 317332 Copyright 0 1995 by JAI Press Inc. ISSN: 10590560 All rights of reproduction in any form reserved.
317
318
YORAM LANDSKRONER
and JACOB PAROUSH
New business entities raise funds from different sources. Initial financing is provided by the founder, usually a specialist who contributes entrepreneurship (and other talents) as well as capital. Eventually a successful firm will meet the increasing financing needs by raising funds from a public offering of its stock or by merging into another corporation. Venture capital funds are invested in the interim stage: after the funds of the founder are exhausted but before the firm ‘goes public.’ In general, venture capital is provided in the form of equity financing but may also appear in the form of debt or a combination of the two (including preferred stock and convertible securities).3 Venture capital organizations enter into two types of contracts: an internal contract between the investors that provide the funds to the venture capital organization and an external one with the firm (entrepreneur) in which it invests. Sahlman (1990) describes and analyzes the structure of venture capital organizations and the relationship between the parties involved. In this paper we analyze the relationship between the venture capital organization (the ‘capitalist’), the entrepreneurial venture in which it invests and the initial owner (‘entrepreneur’). We address the agency problem under asymmetric information which exists between the capitalist and the entrepreneur. We focus on the compensation system derived under conditions of uncertainty regarding the outcome of the venture.” We consider a firm (project) in the early stage of its development where no prior knowledge (observations) about it exists, and thus it is without access to public capital markets. A single transaction between two parties, entrepreneur and capitalist is examinedthis first round of financing may be followed in the future by additional rounds of financing. The entrepreneur (owner) provides his own capital and raises outside capital to be used by the firm. The capitalist receives compensation in the form of a fixed fee (debt), and a share of the firm’s income in return for his (equity) investment while the entrepreneur receives a share of the firm’s income. In the absence of competitive capital markets, it is assumed that the entrepreneur and the capitalist face increasing financing costs in raising capital. An agency model of “capital structure” is analyzed, the purpose of which is to determine the optimal amount of external financing raised by the firm, and the optimal capital structure of the firm (debt vs equity). The inclusion of both debt and equity financing is one of the interesting features of this paper. Additionally, the optimal distribution of the enterprises’s income in the “incentive scheme” is determined.5 The owner and the capitalist have different expectations, before entering into their relationship, as to the income their joint venture will generate. It is presumed here that the owner has relatively superior information about the distribution of returns (“inside information”) but not perfect information since this is a new venture without prior observations. Over time and repeated play, the entrepreneur will gain information and correct his biases. As Casson (1982) argued, unequal information among marketplace participants sets the stage for the entry of the entrepreneur. That is, when information is heterogenous and unequally distributed, individuals can exploit superior knowledge. The crucial point of the paper is that the owner can influence the beliefs of the capitalist (make him or her more/less “optimistic”) through his observed actions (such as his/her investment). That is, the owner’s capital serves a dual purpose: as an input of the firm in generating its income and also as a signalling device to attract external capital. In modeling the signalling aspect of the problem, the entrepreneur is assumed to be a Stackelberg leader in choosing his capital input. Thus, the signalling approach is incorporated into this analy
Venture Capital: Structure and incentives
319
sis as it relates to the financing decision of the firm. Leland and Pyle (1977) in common with the model presented here, consider the owner’s signal to outsiders to be his equity investment in the fitm6 In the present model the firm does not have access to competitive capital markets and there is a presumption of an increasing financing cost to the investors. Our paper is related to the analytical literature on venture capital. Cooper and Carleton (1979) study how the payoff should be partitioned between the entrepreneur and the capitalist to insure value maximizing investment policy. Chan (1983) is concerned with how financial intermediaries improve allocation of investment capital. Chan, Siegel, and Thakor (1990) deal with uncertainty about the skill of one party and the possibility of transfer of control. None of these papers however focus on the issues in this paper. In Section II we present the model and in Section III, the characteristics of the optimal solutions. The case of multiple venture capitalists (outside investors) is presented and analyzed in Section IV Conclusions are presented in Section V.
II.
THE
MODEL
This section presents a model of a single transaction between two parties: an entrepreneur (the founder and initial owner) and a venture capitalist, who finance a joint venture and share its income. The entrepreneur supplies equity capital, y, and an “entrepreneurship” input (not modeled explicitly). The capitalist supplies capital, x, in two forms, equity and debt, denoted x1 and x2, respectively. The enterprise generates an uncertain income r (J + x) where r is one plus a random rate of return. Total income is distributed between the capitalist (Z,) and the entrepreneur (Z,). Zp = yrx, + px2 Z,
(1)
= r(y +x)  yrxl  px2 (2)
= ry+(ly)rxl+(r/3)x2.
The parameters $5, r) are contractually specified in advance. In fact, (p, $ are determined by the entrepreneur to raise outside capital for the venture and thus serve as an incentive (compensation) scheme for the capitalist. Given the incentives or parameters of the contract, the capitalist responds by determining both his total contribution to the venture, X, and its decomposition into x1 and x2. Thus, (p, r) are parameters in the capitalist’s revenue function and are controllable factors in the entrepreneur’s cost function. Typically, p >l because it has a dimension of one plus an interest rate while 0 c y < 1 because the entrepreneur, who contributes his “entrepreneurship” in addition to capital, is compensated by receiving more than his share of equity (and the capitalist less), i.e., the proportions of the entrepreneur and the capitalist in the return of equity are: Y+(lY)xl Y+xl
y
>and<. Y+xl
yxyx, Y+xl
Xl
Y+xl
YORAM LANDSKRONER
320
and JACOB PAROUSH
The capitalist’s income, Z, consists of two parts: interest income pxz, and uncertain income Z,, consists of three income on his equity investment, ‘yml .7 The entrepreneur’s components: income from his equity investment ry, the entrepreneurship return which is paid from the capitalist’s equity return, (1  y) rxl and the uncertain return on financial leverage (r  p)xz. The unique feature here is the “entrepreneurship fee” (1  $ rxl added to his income, which is paid out of the capitalist equity income. In the absence of competitive capital markets, it is also assumed that each of the parties faces an increasing economic opportunity cost in raising his capital. The entrepreneur’s financial opportunity co st is denoted by c(y) and the capitalist’s by d(x). It is further assumed that marginal costs are strictly positive and increasing, that is, c’ > 0, d'> 0,c"> 0,d">0. Thus, the total net income from the joint venture is rO) + x)  pxl px2  c(y) for the entrepreneur and yrx, + @x2  d(xl+ x2)for the capitalist. It is assumed that the cost of financing (risk premia) increases with the amount raised, but is not affected by the uses of those funds: venture capital debt or equity financing. The two parties differ in two respects: their preferences and beliefs. More precisely, they are assumed to have different attitudes toward risk and different perceptions or evaluations of the risk and returns involved in the venture. The utility functions of the entrepreneur and the capitalist defined over the net return, are denoted by U and V, respectively (where U’ > 0, CT”5 0,V'> 0,V" I 0).The subjective density (probability) functions of the rate of return are denoted byf(r) and g(r) for the entrepreneur and capitalist, respectively. Assuming that both are VonNeumann Morgenstern expected utility maximizers, the capitalist’s problem is to maximize:
.fV(w, +Px24x)
MrW
(3)
with respect to xl and x2 for every given contract (0,~). Given the capitalist functions xt (p, r) and x2 (p, r), the entrepreneur’s problem is to maximize:
IU(r(y+x1
+
x2) yx1

Px2 c(y)lf(rW.
response
(4)
It is presumed that the capitalist is more risk averse than the entrepreneur, and with some loss of generality the analysis is simplified by assuming that the entrepreneur is risk neutral while the capitalist is riskaverse, that is, U" = 0 and v” c 0.’ Thus, the entrepreneur’s objective function is now simplified to: ;y + (1 +x1 where The to the about
+ (FD)X,c(y)
(5)
; is the subjective expected rate of return of the venture. second facet of this analysis concerns the heterogeneous beliefs of the two parties venture. The capitalist assumes that the entrepreneur enjoys superior information the firm. We assume that he/she has superior, but not perfect, information. That is,
his/her subjective
expected return,;,
is positively
correlated
with the true rate of return,
but is not necessarily equal to it.9 In this analysis it is presumed that the capitalist becomes more optimistic about the venture’s prospects as the entrepreneur’s contribu
Venture
Capital:
Structure
and Incentives
tions increase. More specifically, G(r) = 1 g(s)& oo
321
G(r 1yt)~G(r
is the capitalist’s
subjective
1~2) for every value of r if yt > ~2, where cumulative
distribution
function.
In other
words, for every r, the capitalist assigns higher probabilities to more favorable states of the world (s 2 r) under yI than under ~2. The capitalist’s expected utility, then, is conditioned on y; his optimal solutions, x1 and x2 , are functions
of y as well as (0, r).
Define the first two moments of the capitalists’s subjective density fynction of r:;(y) = jrg(rly)dr as the expected rate of return, and 6(y) = j[rg(y)] g(rly)dr as the variance of the rate of return. The random variable r(y) is now decomposed as follows:
(6)
r(y) = P(Y) + $y)&(y)
where E(Y) is a standardized random variable with E&(y) = 0 and B2(y) = 1 for every y. With these assumptions and the concomitant decomposition, the entrepreneur’s optimization problem can now be written as: Max{;y+(ly)rx,+(;p)x~c(y)} Y, P* Y
s.t.,~1,
x2
lhv=
_fV{y$y)xl
+ Px2 4~) + r~(y)&(u)xl~g(rly)~r.
In this problem the entrepreneur is a Stackelberg and the contract parameters $4 r).
III.
CHARACTERISTICS A.
The
leader in choosing
his capital input y,
OF THE SOLUTION
Capitalist
For every given value of y, p, ‘y, the first order condition tion problem w.r.t. x2 is given by
of the capitalist’s
optimiza
[P  d’(x)] EV= 0 (8)
where
EV’
= jV’g(rly)dr
is the positive
expected
(8) marginal
utility.
It follows
from
equation (8) that p = d’(x). That is, in equilibrium the marginal borrowing rate of the capitalist equals his lending rate, the important implication of equation (8) is that the total investment of the capitalist, x = xl + x2, is determined by p and d’(x) and is independent
of his attitudes
toward
risk, the parameter
of the density
sharing rule y and the action of the entrepreneur y (Figure 1)” novel result is that since xt is riskless with a positive marginal
function
of r, the
The explanation of this revenue, it is a residual
322
YORAM LANDSKRONER
and JACOB PAROUSH
Figure 1.
which will be increased up to a point where marginal cost equals marginal revenue. Thus, the total investment is independent of risk considerations and parameters of the contract while the amount of equity is not. The first order condition w.r.t. xl, the capitalist’s equity investment, is [y;  d’(x)]EV’
+ yBE( V’E) = 0
where E( V’E) = I[ V’&(y)]g(rly)d r is the expected value of the product of the marginal utility and the random element of the rate of return. Because E(E) = 0 the product is equal to the covariance of V’ and E. This covariance is negative: E(V&) = cov (V’E) < 0 since the capitalist is assumed to be risk averse, v” < 0. The assumptions d” > 0 and V” < 0 guarantee that the second order condition holds globally. Substituting 0 for d’(x) in equation (9) and rewriting yields:
SP = A(x,) or
Yb y;f3
(10) = y6A(xl)
where A(xl) = E(V’&)/EV’>O is a factor representing the capitalist’s attitudes toward risk. This factor is related to the PrattArrow measure of absolute risk aversion.” Equation (10) is compatible with a well known result in the finance literature. It states at the outset that the price (per unit) of risk (yi  p/r&, ) is determined in equilibrium by the investor’s risk aversion. The product of this risk aversion factor and the risk of the investment y& determine the risk premium y; p in equilibrium. The equations (8) and (9) or (10) describe a two stage decision by the capitalist: in the first stage he or she determines the total investment in the venture, according to the lending rate and the financing cost. In the second stage he or she determines the allocation
Venture Capital:
Structure
and Incentives
323
Figure 2.
between the riskless debt and risky equity. This allocation is determined by characteristics of the investor A(xl) and the investment i (y) and 6 (y), and thus by the action of the entrepreneur, and the incentives y and p (Figure 2). The effect of the entrepreneur’s action y on the capitalist may now be defined. An increase in y will render the capitalist “more optimistic” in his beliefs about the distribution of t. This will be taken to mean either an increase in the subjective expected return, i(y) and/or a decrease in risk 6 (y), that is,l* WY)
WY)
a,‘Oandav
SO
(13)
where at least one of the strong inequalities prevails. It is important to recall that, in equation (8), y does not affect the total capital contributed by the capitalist. Thus, y affects the “capital structure” alone, or equity vs. debt contributed by the capitalist. Following equation (lo), it can be determined that, given an increasing absolute risk aversion function (dAl&, > 0), either an increase of i(y) or a decline in B(y), as specified in equation (13), will increase the price of risk and thereby increase equity capital xl. Thus, as the capitalist becomes more optimistic, he will contribute more of his capital in the form of risky equity and less in the form of debt. Investigation of the effects of the actions of the entrepreneur may now be completed. These effects include signal y and the incentives y and 0 on the actions of the capitalist and total capital contributed x and its structure, that is, equity x1, vs debt x2. Total differentiation of equation (8) w.r.t. p, y, and y yields,
(14)
YORAM LANDSKRONER
324 Total differentiation
and JACOB PAROUSH
of equation (10) w.r.t. p,r, and y yields
(15)
Combining
equations
(14) and (15) yields
(16)
The main findings are: 1. 2.
3.
The capitalist’s total investment in the firm, x is determined by p and is independent of y, y, and A; The equity investment of the capitalist, x1, is affected positively by both the return on equity, y, and the investment of the entrepreneur, y. An increase in y increases his optimism (given his risk aversion) and, thus, his risky investment in the firm. An increase in p will increase his lending at the expense of his equity investment; An increase of the risk aversion factor, A, will not affect total investment of the capitalist, but will reduce his equity (risky) investment.
B.
The Entrepreneur
The entrepreneur’s optimal decisions regarding his financing y, and the incentives may now be determined. His objective function, as specified in equation (4) is: Max NY, Pt YJ YTP> Y*
(17)
where D = ;(I Y)x~(Y$,Y)
+ (;
P>x2(y$,r)
y, 13
+ ;Y C(Y).
Venture Capital:
Structure
The first order conditions
and Incentives
325
are:
D,
axI = i+(Py;)=p’(y)
D,
=
=
0
(~y;)$ixi =0 ax1
DP = ;(l~)~+(;p)
ax2
x2
(19)
= 0.
(20)
Each of these equations, in fact, describes a relationship between marginal revenue (the left hand side) and marginal cost (the right hand side). A diagrammatic illustration of these equations is presented in Figures 35. The entrepreneur’s own capital optimal value, y*, is reached at the point where his marginal cost c’(y) equals the marginal revenue, ; + (p  y&)xtlay , as in equation (18). Marginal revenue consists of direct marginal revenue, and indirect marginal revenue (p  y;)ax, /ay . Indirect marginal revenue emerges as a result of additional external capital, which is motivated by y, axtlay . The term 0  yr = ;( 1  y)  (;  p) is the net expected gain per dollar from the raising of external equity capital. This point is illustrated in Figure 3 in which the positive difference y*  yo serves as a motivation for the additional external equity capittl. The2second order conditions required for the stability of the solution are C” > 0 and a xtlay c 0. Equation (19) establishes the equilibrium condition for y. Here, the marginal cost is ixt , the payment to external equity; marginal revenue is the gain from the additional external capital (p yi)axllay. Since ; > /3, equation (19) implies that y< rll (1 + q) C1where n is the elasticity of x1 with respect to y, A; in Fi ure 4, the second order condition necessary for the marginal revenue 9 < 0 . This condition must be prevalent at the optimum for the stability to decline is a xllay of the solution. Finally, the optimal incentive p is determined by equation (20) and presented in Figure 5. Marginal cost is x2  i( 1  y)ax,Iafi w h ere the first term, x2, is a direct marginal cost . an indirect marginal cost due to the inverse 1s effect of p on xl. Marginal revenue is (;  p)ax,/ap. Th e second order conditions necesand the second term, ;( 1  y)axtlap sary
for the solution are a2x2/ap2
c 0 anda2x,/ap2
c 0.
An interesting result concerning the subjective beliefs of the entrepreneur compared with those of the capitalist is obtained by combining first order conditions of the two parties. From equation (19), the first order condition of the entrepreneur, we obtain p > y r, similarly the first order condition of the capitalist, equation (lo), yields, y j(y) > p. Thus at the optimum we obtain: P(y) > i.
(21)
In other words, to be a regular internal solution, y must be large enough so that i(y) will exceed 7. The rationale of this result is clear. Since the capitalist is assumed to be more risk averse than the entrepreneur, the latter must encourage the capitalist to be more optimistic, if he has to induce him to supply external equity capital.t3 This may be a serious obstacle
326
YORAM LANDSKRONER
and JACOB PAROUSH
;+(p
P
Figure 3.
_
ax,
Y
r” Figure 4.
X,;(
3x1
(ip); P Figure 5.
3x1
Yha;;
Venture Capital:
Structure
and Incentives
327
in raising external capital for a new venture. It should be noted that we are dealing with the first round of financing with no prior observations about the project and therefore with no indication about the true rate of return. At this state, it is unclear which of the two rates of return is closer to the true rate re The result of equation (21) is a necessary condition that holds until the return is realized for the first time. Of course in the long run when the game (project) is repeated and observations about the true rate of return are obtained, the gap between the two subjective beliefs converges and the difference between the two perceived rates ;  ; disappears. Additional rounds of financing will take place and the behavior of the firm may be described by a model such as Leland and Pyle, where the equilibrium condition would be i(y) = ;.
Iv.
MULTIPLE
AGENTS
Thus far, only a single source of external financing (the capitalist) has been considered. In this section, two specialized sources of external financing are introduced: one providing only equity capital and the second only debt financing. It is implied that these are two independent sources, with independent financing cost functions. That is, di is a function of xi only, while previously d was a function of both x1, x2. Denote by XI the equity capital contributed by Capitalist 1, and by x2 the debt financing provided by Capitalist 2, and dl(xl) and d2(x2) are the financing opportunity cost of the two capitalists, respectively. The objective function is: MaxjV[yrxl Xl
 dl(xl Mrly)ldr
(22)
for the first capitalist, and
Md3x2 
d2(x2)1
X2
(23)
for the second. The second capitalist makes, by assumptions, a riskless investment (through lending) and maximizes his profit. Since only the first capitalist faces uncertainty, only his beliefs will be affected by the signal of the entrepreneur, y. Solutions for the Capitalists The first order condition of the capitalist yields
yid’, = A orfd’,
= y&A.
(24)
Ye
This is a generalization of equation (10). A result similar to that of equation (10) occurs if St = 0, with the caveat that in equation (lo), d’ is a constant equal to p, but now 61 is a function of XI The first order condition for the second capitalist yields:
P = d’2W.
(25)
YORAM LANDSKRONER
328 Total differentiation
of equations
(24) and (25) w.r.t. p, y and y yields
Y($ $A)
ax,
s= 2
and JACOB PAROUSH
d”,(xl)
AdA” + wdxl
(27)
= dff2;x2)>’
ax2 ax2
*=s=O. Note that equation (15) is a special case of equation (26), in which d’,(x,) = 0. Thus, the existence of two separate financing sources generates several results. Each incentive has only a direct effect on a single source of financing, y on x 1 and p on x2, such that an increase in either incentive will increase the total external investment. In the previous case, with its single source of financing, each incentive has a direct, positive effect on its own form of financing and a negative effect on the substitute form. As a result, only p had an effect on total investment while both p and y affected the composition of external capital. The signal provided by the entrepreneur, y, affects only the equity capitalist, but has no effect on the lender (second capitalist), thus, an increase in y increases the external investment. In the previous case, an increase in y had two offsetting effects on the two financing forms, so that the entrepreneur’s action had no effect on the total external funds raised, but influenced capital structure only. Solution for the Entrepreneur The entrepreneur’s objective function
where
is assumed to be:
F = (1  y) ‘x1 ti, y> + (F  b) x2 (p) + Fy  c(v).
The first order conditions
are: Fy = (ly),+;
ax,
= c’(y)
ax, Fr = (1 y)r
= ‘;r, ax2
FB
=
(is,;rrr
=
x2
(2% (30)
(31)
Venture Capital:
Structure
and Incentives
329
That is, marginal revenue in equilibrium equals marginal cost with respect to each of the parameters. The net [email protected] gain per dollar of external equity is (1  y) i? Interestingly, unlike the previous case y = . I+rl
V.
CONCLUSION
This paper has analyzed the behavior of an entrepreneur and the response of a capitalist in a venture capital context. In our problem we consider first round financing for a new firm where no prior observations about its return exist. The entrepreneur is assumed to have superior but not perfect information concerning the outcome of the venture. In a feedback system the entrepreneur, who is a Stackelberg type leader, uses two types of controls: an incentive scheme, and signalling to affect the action of the capitalist. The signal is the equity investment of the owner in the venture and is used to change the capitalist’s beliefs, rendering him more optimistic. Thus, the owner’s capital serves a dual purpose: as an input generating income and as a signal. The interesting result is that since the capitalist is assumed to be more riskaverse, at the optimum he is made to be more optimistic than the entrepreneur. In our analysis we considered two models. In Model I, a single capitalist supplies equity and debt financing. The entrepreneur supplies “entrepreneurship,” for which he or she is compensated by a fee paid from the capitalist’s equity income. The entrepreneur also supplies capital which affects the equity investment of the capitalist (his total investment in the firm, determined by the interest rate, is unaffected). In Model II specializing capitalists are considered, thus equity and debt capital is assumed to be independent. Here the signal affects both total external financing and its composition. The debt incentive (p) in both models determines total external investment, and has a direct positive effect on debt financing (x2) and negative or zero effect on equity financing (xl). The equity incentive, ‘y, affects total investment only in Model II; it has a direct positive effect on x1 and negative or zero effect on x2. Note that, in Model I, the positive effect of debt incentive p, on x2, is greater than its negative effect on x1, while the positive effect of the equity incentive y, on x1 is exactly offset by its negative effect on x2.
Summary Table.
Objective and Responses
I
Model Entrepreneur Objective Function
Ty + (1 + y) TX, + (F  p, q  c (_v)
Capitalist Objective Function
E(V h ‘xl+
Response Capitalist y signal
;
j3 debt incentive y equity incentive
+ 0
!3x2  d&t+ x1 + +
II
x2)1 1
EW
h TX1 dl(Xl)l
x2 
X
+
Xl +
+ 
+ +
0 +
1
pY2

44X2)
x2 0 + 0 (continued)
YORAM LANDSKRONER
330 Summary Table. Model Decisions (FOC) Entrepreneur
Objective
Y
and Responses (continued)
I
[(ly)r(ip)la;r+’
and JACOB PAROUSH
II
ax,
= c’(y)
a.\,
[Cl
r,+jy,+r = c’(y)
ax, [(I YPl
l(tY)‘(‘P)I~+;x,
ax,+ ix,
ACKNOWLEDGMENTS We acknowledge the comments made by an anonymous referee. Yoram Landskroner would like to thank the Krueger Center for Finance for financial support.
NOTES 1. Venture capitalists also provide funds for firms at other stages such as financing of leveraged buyouts and acquisitions. In this paper however we focus on the early stage financing. 2. Private investors have set up different organizational structures to provide venture capital. The three types of firms are: limited partnerships, corporate subsidiaries and small business investment corporations. The largest and fastest growing organizations are the limited partnerships. Under this arrangement private investors, including institutional investors, purchase limited partnership interests in a venture capital fund which is managed by a venture capitalist (the general partner). 3. The risks inherent in the early stages, and the lack of collateral made these businesses in many cases unacceptable customers for the traditional commercial lending institutions who provide exclusively debt financing. 4. We abstract from other features such as the management role that the capitalist may play. 5. Stiglitz (1974) derived a model of risk sharing and incentives in a study of sharecropping. This model extended the understanding of the operations of the closely held firm. 6. The first application of signaling to finance theory has been done by Ross (1977). Downes and Heinkel (1982) empirically examined the relationship of firm value and two types of signals: the fraction of ownership retained by an entrepreneur and the divided policy of a firm. 7. In this framework we have assumed that the borrowing x2 is done by the entrepreneur against his personal account. Thus we assume no default risk on the debt of the firm. This simplifies the analysis without affecting the optimization process.
331
Venture Capital: Structure and Incentives
8. This is a simplifying assumption; the nature of our results will not change in the general case, in which the entrepreneur is risk averse, if he remains less risk averse than the capitalist. 9. The relationship between the true, but unknown rate of return on the venture, r. and the entrepreneur’s evaluation of this rate of return r, may be assumed to be of a linear regression type: r=a+bro+u ?=a
and
+ br,
where u, the error term, reflects the intrinsic uncertainty of the venture. The parameters reflect the entrepreneur’s subjective biases. Over time or with experience, as the game is repeated, the entrepreneur will correct his biases in a kind of recurring process of the form:
rtaf it+1 = 
6r
where t is a time or experience index. 10. This result is similar to the solution of a general portfolio selection problem, in which the investor faces a riskfree and risky asset and increasing costs. His total investment will be determined only by the riskfree return, and by the cost. His attitude toward risk and the riskiness of the assets will determine the composition of his portfolio: proportions of the risky and the riskfree assets. 11. The relationship between risk aversion factor A, and the PrattArrow measure of absolute risk aversion
V“ R = v is obtained by a Taylor expansion
around the mean:
A  y&x,R(w) where w = (@ 
(11)
p)xl + px  d(x) is the wealth at the mean and x = xl + x2 is a constant $
= y&R(w) + y&x$
g
= y&R(w) + y6q [r; 
I
(12)
PI $0,
that is, the expression is positive either under constant or increasing absolute risk aversion or under increasing relative risk aversion where the measure of relative risk aversion: = xlR(w).
yp y2e2 12.
In general, “more optimistic”
with the case ‘2 variance optimism.”
< 0 and ‘9
aG(rlY)< 0;
means 
which can also be consistent
&
> 0. We however, have limited ourselves
to “mean
332
YORAM LANDSKRONER
and JACOB PAROUSH
The crucial role played by “optimism” in investmentfinancing decisions was emphasized by Keynes, “... a large proportion of our positive activities depend on spontaneous optimism rather than on a mathematical expectation.” “... our decisions can only be taken as a result of animal spiritas a spontaneous urge to action rather than inaction” (1961, pp. 161). 13. This result is consistent with that obtained by Paroush and Rubinstein (1982).
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