Selling Unsaleable Assets: The Case of Banks NPLs Roberto Violi (+) (+) Banca d’Italia, Financial Markets and Payment Systems Department Senior Director; Roberto.Violi@bancaditalia.it “Sovereign Risk and the Euro: Lessons from the Crisis”, University of Bologna, 26-27 October 2017

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

Chart 1: Italian-Style TALF

Modelling Assets Sale: Benchmark  

Modelling Assets Sale: NPLs vs. Benchmark  

Modelling Assets Sale: implied option value    

Modelling Assets Sale: PE Fund PayOff  

Modelling Assets Sale: SPV and Servicer Pay-Offs  

Modelling Assets Sale: PE Fund Shareholder Optimal Choice  

Modelling Assets Sale: PE Fund Shareholder Optimal Choice  

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%

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%)

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 ; 19.33] 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; 29.68] 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

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%

Simulation Results: Expected Returns Modelling Assets Sale: Model Simulation: Parameters and Results Simulation Results: Expected Returns PE Fund Shareholder Expected Return: 15.950 ; 12.780] 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: [0.2552 ; 0.2366], Vis-a-vis 0.10 for the stock market(benchmark); NPL portfolio «beta», computed on the implied asset return for the benchmark portfolio:[0.7192 ; 0.8261];

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;