A Basic Probability Question

Hi, I’m an italian student. Here’s my problem:

I created, using a for loop, a portfolio that has an expected future value from here to 30 years (T = 30). This portfolio is based on different combinations of expected future returns, so it follows 1000 paths (N = 1000). Now, once I created this matrix (1000x30), i would like to find, for example, the probability that the portfolio value will not fall below a predetermined threshold in each year. To be more clear, I mean:

- Pr (PortT > Port0), that is the probability that the portfolio value at time T is bigger than the initial value (with 30 <T<0).

or another example:

- The probability that the portfolio at time T+1 will not fall below 10% or 20% compared to previous year (with 30 <T<0).

In Matlab there isn’t a function called “probability” or “prb”, so I don’t know how to do that.

I know this may be a silly question but can you help me?

Thank you

Answer 1

[Matt J]

There's no "prb" function but there is a mean() function and every probability can be expressed as the mean of some binary random variable. This should give you the general idea,

 probBiggerThanInitial = mean(bsxfun(@ge,yourmatrix,yourmatrix(:,1)),1)