We have now implemented stochastic modeling into our tool, and to be transparent and honest, we are letting advisers know how it works to better speak to their clients and use the tool to its fullest.
We are using a Geometric Brownian Motion (GBM) model for the Monte Carlo method.
First, we need to calculate the Brownian Motion Increment, which creates a normal distribution of random numbers centred on 0 we will call this Wt.
Using the formula for GBM
New Fund Value=Old Fund Value ^( ( μ – 1/2 * σ2 )*t + σWt )
So to explain this is basically the old fund value to the power of two terms one is the “drift” this is the stochastic nature or roughly the average growth, the other term is for the volatility and this is the random fluctuations around this drift scaled by the volatility.
The Brownian Motion Increment is calculated by generating a Gaussian distribution and multiplying by the square root of the time interval, as we calculate everything monthly this is calculated monthly too.
This is then fed into the tool for 1,000 iterations and we then order by largest to smallest and then cull the data to remove the bottom 10th percentile and also remove the top 10th percentile to make the data more relevant to the adviser.
This is then charted on top of the Deterministic tool so you can see the effect.
You select the Defaqto risk rating from 2-10 and this will use their Portfolio Standard Deviations for this calculation, you still enter your average return. The options for the standard deviations can be edited and saved in your profile in case you use different risk tools or ratings agencies.