financing efﬁciency of securities-based crowdfunding · securities-based crowdfunding this paper...

LeedsB U S I N E S S

Financing Efficiency ofSecurities-Based Crowdfunding

David C. Brown - University of Arizona

Shaun William Davies - University of Colorado, Boulder

Digital Finance, Market Disruption, and Financial Stability

2018 Conference

Banque de France & Toulouse School of Economics

Paris 2018

Securities-Based Crowdfunding This Paper

Motivational Quote


And for start-ups and small businesses, this bill [JOBS Act] is

a potential game changer. Right now, you can only turn to a

limited group of investors – including banks and wealthy

individuals – to get funding. Laws that are nearly eight

decades old make it impossible for others to invest. But a lot

has changed in 80 years, and it’s time our laws did as well.

Because of this bill, start-ups and small business will now

have access to a big, new pool of potential investors –

namely, the American people. For the first time, ordinary

Americans will be able to go online and invest in

entrepreneurs that they believe in.

—President Barack Obama, April 5, 2012

Signing the JOBS Act

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Private Value versus Common Value Goods


Securities-based crowdfunding is a new form of venture financing

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Appeal founded on the success of rewards-based crowdfunding

which has harnessed the wisdom of the crowd

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All-or-nothing financing thresholds imply only the popular,

and likely profitable, products receive sufficient financing

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Participation signals consumer demand and gives valuable

information to the entrepreneur (see Chemla and Tinn, 2018)

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Reward-based crowdfunding relies on private value goods

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Value can be different for each individual

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Securities-based crowdfunding relies on common value goods

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Value is the same for everyone

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Value is the same for everyone

RESEARCH QUESTION: Can securities-based

crowdfunding be as successful as rewards-based

crowdfunding?

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Main Findings


We consider an entrepreneur’s optimal crowdfunding offering

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Main Findings



The problem is characterized by the key features of the

crowdfunding environment

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Main Findings





(i) Dispersed, privately-informed investors are required to

finance a new venture,

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Main Findings







(ii) Investors communicate by contributing or by abstaining,

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Main Findings








(iii) The entrepreneur uses the the information conveyed by

aggregate contributions to either pursue the risky venture or

to cancel it.

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Main Findings










to cancel it.

Our main finding is that the entrepreneur’s optimal offering cannot

aggregate the wisdom of the crowd

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Main Findings










to cancel it.

Our main finding is that the entrepreneur’s optimal offering cannot

aggregate the wisdom of the crowd

Ex post decision-making by the entrepreneur gives rise to a

loser’s blessing which erodes investors’ incentives to

contribute based on their private informationin a truthful manner

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Securities-Based Crowdfunding Loser’s Blessing

The Loser’s Blessing


To understand the loser’s blessing, consider this simple example

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Suppose there is a continuum of investors (i.e., representative of

lots and lots of investors)

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Investors’ total collective capital is $1MM

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A project is raising $500K (all-or-nothing threshold)

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Investors receive noisy binary signals about the project’s quality

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Project can be good (gross return ∆ > 1) or bad (gross

return of 0)

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return of 0)

Signals are accurate with 75% probability

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return of 0)


By the (strong) law of large numbers, 75% of investors receive agood signal if the project is good,

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return of 0)


By the (strong) law of large numbers, 75% of investors receive agood signal if the project is good,

or, 25% of investors receive a good signal

if the project is bad

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Investment Breakdown


Consider a candidate equilibrium in which investors contribute

according to their signals

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Good project raises $750K ⇒ project is financed

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Contributing investors earn gross return of ∆ > 1

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Bad project raises $250K ⇒ project is canceled

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Contributing receive capital back (gross return of 1)

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This cannot be an equilibrium!

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An abstaining investor should deviate and contribute (despite

receiving the bad signal)

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If his signal is correct ⇒ No risk

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If his signal is incorrect ⇒ Owns a share in a good project

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If his signal is incorrect ⇒ Owns a share in a good project

No incentive-compatible, truth-telling equilibria exist

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Securities-Based Crowdfunding The Model

Base Model Setup


Entrepreneur has a risky project with investment capacity K > 0

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Base Model Setup



Chooses offering quantity (investment size κ)

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Base Model Setup




Allow entrepreneur to also choose price as an extension

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Base Model Setup





Project is either type G or type B (equal probability)

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Base Model Setup






Chooses how to deploy raised investor capital (K ) (r or s)

V (K ,F |r) =

{

∆1GK − K K ≤ K

∆1GK − K K > K ,

V (K ,F |s) = 0 ∀K

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Base Model Setup







V (K ,F |r) =

{

∆1GK − K K ≤ K

∆1GK − K K > K ,

V (K ,F |s) = 0 ∀K

N ≥ 2 ex ante identical investors

Each investor receives free signal F ∈ {G, B}

Pr(F = G|G) = Pr(F = B|B) = α > 12

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Base Model Setup







V (K ,F |r) =

{

∆1GK − K K ≤ K

∆1GK − K K > K ,

V (K ,F |s) = 0 ∀K

N ≥ 2 ex ante identical investors

Each investor receives free signal F ∈ {G, B}

Pr(F = G|G) = Pr(F = B|B) = α > 12

Investors contribute κ based on equilibrium

strategies g ∈ [0,1] (for G) and b ∈ [0,1] (for B)

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Entrepreneur’s Learning


Contributed investor capital tells entrepreneur how many investors

contributed (n = K/κ)

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Entrepreneur updates beliefs based on number of contributions

and forms posterior ρ(n, ~π) in which ~π are investors’ equilibrium

contribution strategies

ρ(n, ~π) = Pr(n∩G)Pr(n∩G)+Pr(n∩B)

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Entrepreneur chooses risky deployment (r ) if, and only if,

ρ(n, ~π)∆− 1 ≥ 0

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ρ(n, ~π)∆− 1 ≥ 0

There exists a threshold return ∆(n) such that the entrepreneur

invests iff ∆ ≥ ∆(n)

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ρ(n, ~π)∆− 1 ≥ 0

There exists a threshold return ∆(n) such that the entrepreneur

invests iff ∆ ≥ ∆(n)

∆(n) maps to threshold number of contributing investors n

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Entrepreneur’s Problem


maxκ∈R+

E [V (K ,F |d)]

s.t. gi ∈ arg maxg∈[0,1]

Π(G, {g, b}|~π−i , κ,n),

bi ∈ arg maxb∈[0,1]

Π(B, {g, b}|~π−i , κ,n),

Π(G, ~πi |~π−i , κ,n) ≥ 0 and Π(B, ~πi |~π−i , κ,n) ≥ 0,

d =

{

r if n ≥ n

s otherwise,

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Entrepreneur’s Problem


maxκ∈R+

E [V (K ,F |d)]

s.t. gi ∈ arg maxg∈[0,1]

Π(G, {g, b}|~π−i , κ,n),

bi ∈ arg maxb∈[0,1]

Π(B, {g, b}|~π−i , κ,n),

Π(G, ~πi |~π−i , κ,n) ≥ 0 and Π(B, ~πi |~π−i , κ,n) ≥ 0,

d =

{

r if n ≥ n

s otherwise,

Definition: First-best financing efficiency is characterized by,

(i) K ≥ K if n ≥ n,

(ii) and truthful reporting by each investor,

g = 1 and b = 0.

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Risky Deployment Regions


Minimum Number of Investors Neededfor Risky Deployment

∆

1 Investor 2 Investor 3 Investor 4 Investor

D(1)

D(2)

D(3)D(4)

Figure : Risky deployment regions with N = 4.

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Investor Incentive Compatibility


Invest based on signal G (i.e., g = 1):∑N−1

n=n−1

(

αPr(n|G, ~π,N − 1) (∆−1)nn+1 − (1 − α)Pr(n|B, ~π,N − 1) n

n+1

)

≥ 0,

Abstain based on signal B (i.e., b = 0):∑N−1

n=n−1

(

(1 − α)Pr(n|G, ~π,N − 1) (∆−1)nn+1 − αPr(n|B, ~π,N − 1) n

n+1

)

< 0.

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n=n−1

(


n+1

)

≥ 0,


n=n−1

(


n+1

)

< 0.

g = 1 incentive compatible if ∆ ≥ ∆n,G

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n=n−1

(


n+1

)

≥ 0,


n=n−1

(


n+1

)

< 0.


b = 0 incentive compatible if ∆ < ∆n,B

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n=n−1

(


n+1

)

≥ 0,


n=n−1

(


n+1

)

< 0.


b = 0 incentive compatible if ∆ < ∆n,B

∆ ∈(

∆n,B

,∆n,G

]

⇒ Incentive compatibility region

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Incentive Compatibility Regions



∆

1 Investor 2 Investors 3 Investor 4 Investors

∆1,G

∆2,G∆3,G ∆4,G

∆1,B

∆2,B

∆3,B

∆4,B

Figure : Incentive Compatibility regions.

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Overlap



∆

1 Investor 2 Investors 3 Investor 4 Investors

D(1)

D(2)

D(3)D(4)

∆1,B

∆2,B

∆3,B

∆4,B

Figure : First-best regions.

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Discussion


There are many regions in which entrepreneur’s first-best

deployment decision is not congruent with investors’ incentivecompatibility constraints

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Discussion




All first-best breakdowns are due to incentive compatibility

constraint for investors observing B not holding, i.e., ∆ ≥ ∆n,B

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Discussion






This is due to the loser’s blessing

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Discussion







Ex post decision-making by entrepreneur implicitly hedges

investors against bad projects

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Discussion









Investors internalize hedge and invest in projects despite bad

signals

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Discussion










signals

Financing Inefficiencies worsen as N increases

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Discussion










signals

Financing Inefficiencies worsen as N increases

Less likely that any individual investor is pivotal

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Discussion


10 20 30 40

0.0%

50.0%

100.0%%

of∆

with

First-

Best

N

α = 35

α = 23

α = 34

Figure : Percentage of ∆ that support first-best equilibria as a function of N

for α ∈{

35, 2

3, 3

4

}

.

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Extension with Price Setting


First-best breaks down because expected returns are too high

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First-best efficiency may be restored by punishing investors with

lower expected returns

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In contrast, many models of initial public offerings show that

incentive compatible truth telling is achieved by rewarding

investors with higher expected returns

See Rock (1986) and Benveniste and Spindt (1989)

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We show that first-best may be implemented by increasing the

price of the offering (lowering expected returns)

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First-best is always possible if signals are free

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With costly information acquisition, entrepreneur faces a trade off

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Higher offering price ⇒ better incentive compatibility

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Higher offering price ⇒ better incentive compatibility

Higher offering price ⇒ fewer

informed investors

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Concluding Remarks


We identify a novel economic tension coined the loser’s blessing

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Concluding Remarks



Unlike the winner’s curse which discourages participation

despite good information, the loser’s blessing encourages

participation despite bad information

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Concluding Remarks






We shows that the loser’s blessing erodes financing efficiency

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Concluding Remarks







Rewards-based crowdfunding is efficient because investors

buy benefits according to their private values

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Concluding Remarks









Securities-based crowdfunding is inefficient because

investors buy securities with common values

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Concluding Remarks











Incorporating consumer-like investors may enhance efficiency

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Concluding Remarks












A bundled good consisting of a financial security (common

value) and a perk (private value)

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Concluding Remarks












A bundled good consisting of a financial security (common

value) and a perk (private value)

Example, purchasing equity in a local

micro brewery

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