<p>With probability <span class="math-container">$1-\alpha$</span> the project is distressed and you have to invest another <span class="math-container">$1$</span> at time 1, so your expected total investment is <span class="math-container">$1+(1-\alpha)$</span>.</p>

CC BY-SA 4.0
2022-11-28T10:51:48.540Z
thank you for your answer!  I still have question."    If the  project  is distressed,  the project  yields  no payoff  at date 1, except  for the safe cash  flow πi." so when there is distress, the investor can still get  safe cash flow π.  Then why did the investor have to invest another 1 dollar at date 1? he can just using the π to pay the invest.
peter
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2022-11-28T13:37:13.207Z
@peter, only if $\pi\ge 1$, but for total payoff it doesn't matter anyway where this money comes from.
VARulle
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2022-11-28T14:42:44.257Z
if π≥1, then the investor doesn't need another 1 to reinvest, so his total investment is just 1. if π<1, the investor just needs additional 1- π to reinvest, then his total investment is 1 + (1-π). So his expected total investment is α 1+(1-α)[1 + (1-π)], which is not 1+(1−α).
peter
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2022-11-29T09:02:52.803Z
@peter, well, if the project is distressed, then you have to reinvest, otherwise you will not earn the $\rho_1$. This holds independently of how big the $\pi$ is, because it's simply an assumption of the model.
VARulle
CC BY-SA 4.0
2022-11-28T09:23:07.053Z
2022-11-28T09:23:07.053Z
VARulle
<p>FARHI E, TIROLE J, 2012. Collective Moral Hazard, Maturity Mismatch, and Systemic Bailouts[J/OL]. American Economic Review, 102(1): 60-93. DOI:10.1257/aer.102.1.60.</p>
<p>in this paper on page 67, the assumption 1 says
<code> rho_1 &gt; 1- Pi + 1 - alpha</code></p>
<p>the footnote 18 explain the intuition of this condition: the return of invest 1 dollar on date 0 and 1 respectively are rho_1 + Pi, the costs are 1 +(1-Alpha).</p>
<p>how does the (1- Alpha) term comes out?</p>

<finance>
a question about assumption 1 of tirole 2012 AER paper
peter
# a question about assumption 1 of tirole 2012 AER paper

(Asked by: username_0 on 2022-11-28)

FARHI E, TIROLE J, 2012. Collective Moral Hazard, Maturity Mismatch, and Systemic Bailouts[J/OL]. American Economic Review, 102(1): 60-93. DOI:10.1257/aer.102.1.60.

in this paper on page 67, the assumption 1 says
 `rho_1 > 1- Pi + 1 - alpha`

the footnote 18 explain the intuition of this condition: the return of invest 1 dollar on date 0 and 1 respectively are rho\_1 + Pi, the costs are 1 +(1-Alpha).

how does the (1- Alpha) term comes out?

**Tags:** finance

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## 1 answers

### Answer by username_1 on 2022-11-28. Score: 3

With probability $1-\alpha$ the project is distressed and you have to invest another $1$ at time 1, so your expected total investment is $1+(1-\alpha)$.

> **Comments:**
> **username_0**: thank you for your answer!  I still have question."    If the  project  is distressed,  the project  yields  no payoff  at date 1, except  for the safe cash  flow πi." so when there is distress, the investor can still get  safe cash flow π.  Then why did the investor have to invest another 1 dollar at date 1? he can just using the π to pay the invest.  
> **username_1**: @peter, only if $\pi\ge 1$, but for total payoff it doesn't matter anyway where this money comes from.  
> **username_0**: if π≥1, then the investor doesn't need another 1 to reinvest, so his total investment is just 1. if π<1, the investor just needs additional 1- π to reinvest, then his total investment is 1 + (1-π). So his expected total investment is α 1+(1-α)[1 + (1-π)], which is not 1+(1−α).  
> **username_1**: @peter, well, if the project is distressed, then you have to reinvest, otherwise you will not earn the $\rho_1$. This holds independently of how big the $\pi$ is, because it's simply an assumption of the model.  

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