In this analysis, a railcar leasing client needed outside expertise in choosing the best mix of railcars in their future portfolio to maximize the revenue potential, while minimizing the fleet ownership risks and costs. This post outlines how the problem was formulated, what data was collected and analyzed and the techniques employed within the framework to arrive at the optimal portfolio mix scenario. The work began by identifying the operating constraints and investment criteria governing the client’s growth strategy, keeping in mind the objective of selecting the optimal portfolio mix given the constraints.

The Question in a Nutshell: The client aspired to grow their portfolio over four-fold taking advantage of the depressed secondary market for the used railcars. The challenge was to analyze the historical data, forecast the demand for various railcar types given the future outlook, and select the portfolio that maximizes revenue potential while minimizing the risks and the costs.

Kavi’s Approach Strategy

Based on Kavi’s domain expertise in railcar forecasting and knowledge of the factors that drive railcar demand, the solution approach recommended was to run a multivariate analysis against numerous envisioned possibilities.

The first step was to forecast the demand for various railcar types based on demand drivers and macroeconomic factors for the next five years. The forecast was then used as input to the model that optimizes the revenue for different fleet mix scenarios with minimizing risks and operating costs.

Input Data Available to us: A 10 year history of various economic as well as railcar demand drivers such as car loadings, hopper vs. reefer vs. gondola traffic patterns, the entire North America car loadings and empty movements. To this, a 5-year look-ahead window (monthly for near future, quarterly for further out) of revenues and costs was applied to derive recommendations.

Cost Parameters

• Price of new railcars by car type
• Fair market value – the price of used fleet cars
• Lease rates by railcar type
(Monthly and quarterly, by gondola, hoppers, flats, boxcars, tanks etc.)

Which are the leading indicators? And what do they tell us?

Autocorrelation functions: : In these types of prediction and problems, there are certain factors that tend to be leading indicators (early signals) and some that are lagging indicators (their effect shows up in the target variables only after a few quarters). An ACF (auto-correlation functions across time periods t, t+1, t+2 etc.) analysis was used to systematically identify the factors as leading or lagging, and backtested against historical data to assess their actual impact (magnitude) on the rail car demand, profitability and cost.

Railcar demand Macro-economic factors

On top of the regression to 10 years of history of explanatory variables, car loads, bookings, industry trends, a factorial analysis of a range of economic factors (optimistic to conservative) for the next 5 years (20 quarters) was also run.

Scenario Analysis A low risk (conservative estimates for all macro-economic factors in the forecast) and higher risk cases were considered. Similarly, forecasts of revenue/costs that were high or low were also considered.

Stochastic analysis of railcars

Stochastic Simulation

We performed replications of the simulation (stochastic factorial experiments) on a battery of cases with varying levels of risk and revenue assumptions. From the results, the forecast of the anticipated railcar demand and revenue ranges for the next 5 years was built with a desired confidence interval.

Putting It All Together

With all these in place, the risk-to-potential revenue of the client’s current fleet mix, as well as for all the other options in their proposed portfolio was estimated.

In addition to the mix options proposed by the client, Kavi extended the analysis by combining the best elements of other fleet mix options into new and better combinations. This allowed certain fleet-mixes to be immediately ruled out because they had both higher risks with lower expected revenues than other scenarios. The final analysis demonstrated that the dollar value difference among the different options amounted to several hundred millions.