1. Selling Unsaleable Assets:
The Case of Banks NPLs
Roberto Violi (+)
(+) Banca d’Italia, Financial Markets and Payment Systems Department Senior Director;
“Sovereign Risk and the Euro: Lessons from the Crisis”, University of Bologna, October 2017

2. Italian-Style TALF: Players and Structure
Term Asset-Backed Securities Loan Facility
SPV financing PE Funds and Issuing Bonds
PE Funds buying NPLs from Banks
Equity Investors in PE Funds
Bond Investors buying Bonds issued by SPV
Banks selling NPLs
Servicer managing NPLs Cash Flows Repayment, Foreclosures and Asset Sales

3. Chart 1: Italian-Style TALF

4. Modelling Assets Sale: Benchmark

5. Modelling Assets Sale: NPLs vs. Benchmark

6. Modelling Assets Sale: implied option value

7. Modelling Assets Sale: PE Fund PayOff

8. Modelling Assets Sale: SPV and Servicer Pay-Offs

9. Modelling Assets Sale: PE Fund Shareholder Optimal Choice

10. Modelling Assets Sale: PE Fund Shareholder Optimal Choice

11. Modelling Assets Sale: Model Simulation: Parameters and Results
Parameters Setting:
Riskless rate: r = 0
NPLs value (normalised): M = 1
Lending Maturity (years): T = 5
Loan-to-Value: λ = 90%
Servicer performance-fee strike value: 𝑴 𝑮 = 1.15
Servicer annual fixed fee (% of NPLs value): 𝒈 = 1%
Vega parameter entering the incentive performance payment : 𝒉 𝝈 = 20%

12. Modelling Assets Sale: Model Simulation: Parameters and Results
Parameters Setting:
SPV performance fee share: 𝑮 𝑺𝑯 = 80%
Bank share of NPLs underperformance: 𝜸 𝑩 = 40%
NPLs underperformance charged to PE Fund: 𝜸 𝑭 = 10%
𝑮 𝑺𝑯 percentage also applies to the fixed fee, while 𝟏−𝑮 𝑺𝑯 , is the share paid by the Fund (e.g. 20%)

13. Simulation Results: Values and Spread
Modelling Assets Sale:
Model Simulation: Parameters and Results
Simulation Results: Values and Spread
Lending Spread: R= [4.00 ; 5.00] percent;
NPLs Return Standard Deviation: σM =[16.60 ; ] percent
• Risk-Neutral Probability of PE Fund ATM non-recourse option [66.87; 70.68] percent
• Risk-Neutral Probability for ATM performance-fee option:
[29.16; ] percent
• Bank exposure to the non-recourse option held by the PE Fund is within a range of [8.86 ; 11.36] percent of NPLs value

14. Parameters Setting: Expected Return
Modelling Assets Sale:
Model Simulation: Parameters and Results
Parameters Setting: Expected Return
Liquidity premium (Jensen-Alpha w.r.t benchmark) on the NPLs portfolio: α = 3%
Correlation parameter between stock market return (e.g. benchmark) and NPLs portfolio return: ρ = 0.75
Stock Market (e.g. Benchmark) Volatility: σE = 25%
Stock Market Implied Leverage (Equity-to-Asset Ratio): E/S = 1/3
Stock Market Expected Return (Equity-Premium): μE - r = 2.5%

15. Simulation Results: Expected Returns
Modelling Assets Sale:
Model Simulation: Parameters and Results
Simulation Results: Expected Returns
PE Fund Shareholder Expected Return: ; ] percent;
SPV-issued Bond Expected Return: [2.584 ; 3.357] percent;
Servicing expected return [4.665 ; 6.739] percent;
NPLs portfolio expected return: [4.798 ; 5.065] percent;
NPLs portfolio Sharpe-Ratio: [ ; ],
Vis-a-vis 0.10 for the stock market(benchmark);
NPL portfolio «beta», computed on the implied asset return for the benchmark portfolio:[ ; ];

16. Simulation Results: Expected Returns
Modelling Assets Sale:
Model Simulation: Parameters and Results
Simulation Results: Expected Returns
• Physical Probability ATM non recourse option
[6.58 ; 7.81] percent
• Physical Probability of Bondholder Loss:
[10.17; 13.47] percent;
Physical Probability ATM Performance-Fee:
[89.13; 86.62] percent;