I have two separate models of a metals resources company.
Each model produces a series of accounting and cashflows forecast for different assets, and consolidates these to a overall group view.
1. The first model is life of asset
, it models the forecast entire life of the portfolio (asset by asset) in annual periods.
2. The second model is a funding
model, it focuses on balance sheet liquidity. It forecasts a two year period broken into quarters.
While the models have a different design, they use the same data sources and they are aligned deterministically.
For forecast and decision making, probabilistic analysis is used to take into account the relative correlations and historical volatilities between different commodity prices, foreign exchange rates and key cost drives.
Both models use geometric brownian motion with a mean reversion modification for commodity prices - as commodity prices (outside gold and perhaps silver) are widely accepted to mean revert over the longer term when hypothetically supply and demand reach equilbrium.
For the same underlying assumptions, and consistent probabilistic parameters, the funding
model produces a significantly smaller range of outcomes over the first two years than the life of asset
On face value the reason for this is logical:
The life of asset model produces a single price that is used over the entire period.
The funding model produces four different prices series over the first year, the price of the last quarter matches the price outcomes from the life of asset model.
So expressing this as an option model, the commodity price at expiry of the first annual period is the same for both models (regardless of how many steps the time period is broken into).
In terms of profit forecasting, when looking at an extreme downside price outcome, the funding model has a significantly higher average price over the first year than the life of asset model, as prices in the funding model don't reach the same level as the life of asset model until the last quarter.
This at once appears deceptively simple but complex.
Intuitively before I looked at this, I expected both models to produce the same "average" price over a period, regardless of how many intervals that time period is divided into. But if this occurred, then there would be different prices in both models at the end of the first period. Which would be incorrect.
Have I missed something simple?