How to code the 3 sigma method

Hi guys, I need to code the 3 sigma method in Matlab and I don't know how to do it. Basically the idea is to create a range from mean + 3 sigma(standard deviation) to mean - 3 sigma. Then I need to construct a dummy variable (not sure about that) to see how many times the SP500 returns are outside this range basically and then compute the probability of having this values in the whole set of observations. The aim is to compute the empirical probability of having booms and busts (extrema) and comparing this probability with the one coming from a Normal distribution (theoretical probability).

Your help would be very appreciated. Thanks.

Guys I tried this code but I got an error in the dummy variable ... r_logActual are the log returns of 6 assets ( matrix).

for x=1:6

upperbound(x,:) = mean(r_logActual(:,x))+3*std(r_logActual(:,x));

lowerbound(x,:) = mean(r_logActual(:,x))-3*std(r_logActual(:,x));

end

for n = 1:6

    if r_logActual(:,n) <= upperbound(n:1) & r_logActual(:,n) >= lowerbound(n:1)

emp_prob(x)=1;

    else

        emp_prob(x)=0;

    end

end

Answer 1

[Sindhu Priya]

Hi Enrico,

There is a small mistake in the logic where you compare the upperbound and lowerbound with the actual values.

upperbound(n:1) & lowerbound(n:1) will return a 0X1 column vector, it might be the line which is causing the error.

The corrected code is as follows,

for x=1:6

upperbound(x,:) = mean(r_logActual(:,x))+3*std(r_logActual(:,x));

lowerbound(x,:) = mean(r_logActual(:,x))-3*std(r_logActual(:,x));

end

for n = 1:6

      if r_logActual(:,n) <= upperbound(n,1) & r_logActual(:,n) >= lowerbound(n,1)
          emp_prob(x)=1;

      else
          emp_prob(x)=0;
      end
 end

Hope it will resolve the issue.