Why does my code return the wrong Expected Default Frequency?

I am attempting to calculate the one year EDF of a firm using the iterative method of Bharath and Shumway (2008). When I calculate an answer I get an EDF of 0.98 (I know that the firm in question has an EDF of ~ 0.30. What am I doing wrong?

Here's the code I have written:

%loads test datafile with equity and debt values in it 
load test_dd.mat

%The risk free rate
  Rf = 0.03;
  T = 1;

%volatility of equity from time series of market cap data(Value_equity)
Log_returns_equity = zeros(length(Value_equity),1);
for i=1:length(Value_equity)-1 
    Log_returns_equity(i+1,1) = log(Value_equity(i+1)/Value_equity(i));
end
standard_dev_equity = std(Log_returns_equity(end-364:end,1));
volatility_equity = standard_dev_equity*sqrt(365); 

%Initial estimate of volatility_v using the last data observations.
Volatility_v = volatility_equity*((Face_value_debt(end,1)/(Value_equity(end,1)+Face_value_debt(end,1)))); 

% loop will solve for v_firm each day. Then caclulate the volatility_v. Iteration occurs until the starting volatitliy_v equals the volatility calculated from the returns of v_firm
V_firm_years = zeros(365,1);
End_Volatility_v = 0; 
counter = 0;

%loops until convergence
while abs(Volatility_v-End_Volatility_v)>0.001 
    counter = counter+1;

      %leaves volatlity_v unchanged for initial loop
      if counter>1
          Volatility_v = End_Volatility_v; 
      end
      row_counter = 0;

      %For last 365 days of data, solve for value of vfirm using fzero
      for i=(length(Value_equity)-364):(length(Value_equity))

          % Initial guess at V_firm
          guess = 5000000; 

          %solve for Vfirm at each day over last year, usingfunction solveMerton(see second section of code)
          f=@(z)solveMerton(Volatility_v,Face_value_debt(i,1),Value_equity(i,1),Rf,T,z); 
          V_firm= fzero(f,guess); 

     %write v_firm estimate to matrix
    row_counter = row_counter+1;
          V_firm_years(row_counter,1) = V_firm;
      end

      %calculate returns over the last year based on the values of V_firm
     Log_V_returns =zeros(365,1);
      for i=1:365-1 %Calculates the log returns
         Log_V_returns(i+1,1) = log(V_firm_years(i+1)/V_firm_years(i)); 
      end

      %calculate volatility of v based on this series of returns
      standard_dev =std(Log_V_returns);
      End_Volatility_v = standard_dev*sqrt(365); 
  end

%Once convergence occurs, Volatility_V set equal to volatiltiy from last iteration
Volatility_v = End_Volatility_v;

%Calculates Mu
mu = mean(Log_V_returns(end-364:end,1));

%calculates the distance to default  
dd = (log(V_firm_years(end)/Face_value_debt(end))+(mu-0.5*Volatility_v^2)*T)/Volatility_v;

%calculates the EDF
EDF = normcdf(-dd)

The function which is called to actually solve the Black-Scholes-Merton for v_firm in each iteration is below:

function Y= solveMerton(Volatility_v,Face_value_debt,Value_equity,Rf,T,z)

V_firm = z;

%Black-Scholes-Merton model
d1 =(log(V_firm/Face_value_debt) + (Rf + 0.5*Volatility_v^2)*T)/(Volatility_v*sqrt(T));
d2 = d1 - (Volatility_v*sqrt(T));
N_d1 =normcdf(d1);
N_d2 =normcdf(d2);

%set equal to zero in order to solve
Y =(V_firm*N_d1)-(exp(-Rf*T)*Face_value_debt*N_d2)-Value_equity;

end

The test datafile that I have used is available from: https://www.dropbox.com/s/pz1shbryt4c1wrl/test_data.mat

Source of method: Bharath, Sreedhar T., and Tyler Shumway. 2008. “Forecasting Default with the Merton Distance to Default Model.” Review of Financial Studies 21 (3): 1339–69.

[Javier]

Annual Volatility is: dailyVol*sqrt(250)

Answer 1

[Alberto]

I am trying through the use of the Merton model to recover some default probability of some US firms to investigate about the moral hazard of the CRAs. I have built my personal merton model but it do not work. I have seen that you upload your merton model but I do not understand when you write standard_dev_equity = std(Log_returns_equity(end-364:end,1));.IN PARTICULAR THE PART end-364:end,1. My datas are a matrix of equity with dimensions 263 (trading days)*120(firms) and a vector of debt with dimensions (1*120). I will really appreciate if you can explain this part of your model