In the last post, we looked at the changing dynamics of modelling county-wide averages for Napa cab prices by year. My suggested method for dealing with the uncertain and changing nature of predicting cab prices was to use a combination of scenario and sensitivity analysis. I went ahead and did this myself and the exercise has yielded new insight into Napa cab price modeling that I would like to share here. Before we delve into that, though, I would like my readers to understand some important context.
Long-term forecasting is much more difficult than single-year forecasting. The single-year forecast posted in this blog for Napa cab is as statistically air-tight as they come – as long as one uses the output properly, these types of predictions will greatly improve revenue projections. VFA’s long-term models tend to also be very sound statistically. The biggest challenge, which yields the best results, is predicting when the grape market cycle will crest and trough. It is virtually impossible to do this perfectly for 30 years stretching into the future. Furthermore, once the projection misses one crest or trough, the rest of the projection is then skewed off the true market cycle.
Instead, VFA creates the projection, which will serve well for big picture issues, such as determining the ability of a vineyard to service a loan or estimating long-term returns on investment. Over those 30 years, however, yearly projections and updates must be done to modify the projection and keep it true to reality. A great deal of the mathematics of these updates and of the long-term projections is focused on predicting the pivotal years in the grape market cycle. These elements of the model are key to accuracy. They explain a great deal of price variation, and account for much of the correlation between VFA’s models and actual prices.
Napa Cabernet Sauvignon Prices Are No Longer Cyclical (Mostly)
Napa cabernet, to an extent that is truly unique, no longer conforms to the typical cyclical nature of winegrape prices. Take a look at the chart below:
Figure 1: Napa County Cabernet Prices and Trendline, 1991-2013
We clearly see a cyclical effect in actual prices (blue line). This cyclical effect, however, is hard to identify without the trendline – see earlier blog post – because the trendline, representing the increase in Napa cab prices over time, explains most of the year-to-year price variation. For instance, during the “trough” of 2005-2007, prices were still right at the long-term trendline. Furthermore, as time goes on, it seems to become less important.
I attempted to use a variety of hybrid linear-cyclical models to predict prices, but the variables related to the grape cycle could not reach even the barest minimum of statistical significance. This means two things: (a) predictive models for Napa cab are best done using simple, linear modeling with sensitivity analysis; and (b) our predictive abilities are greatly diminished because of this. That is, we cannot find a model that can differentiate between the cyclical effect and the noise. Note that this is true only for the 30 year models; VFA’s one-year Napa cab models still use variables that measure and predict cyclical shifts at very high levels of statistical significance (p-values <.01).
So, How Do the Linear Models Fare?
VFA's research has yielded a final, working model that I then back-fit to the period in the chart above (1991-2013). I performed both a formal statistical analysis and an easier to digest analysis of how actual prices compare to the estimates. If you just want to look at the results, go ahead and skip these next two sections, but I think they provide important context and quantification of how useful the projection is. Linear models, if you’re not familiar with the term, are based on linear formulae such as (y = ax + b) or (y = 1/a^t). The main point of differentiation from other models applicable to the winegrape price predictions is that they do not attempt to measure cyclical variables or use rolling averages.
The multiple R (simple correlation) for the model is .9670 indicating that all but 3.3% of Napa cab’s price is explained by the model. This is significantly lower than all of VFA's other models' correlations, which are typically above .99 and are all above .98. Anyways, I think we are on solid ground if we extrapolate from the difference between this model and the one-year model, which also measures the effect of the market cycle, that the cyclical nature of supply and demand can account for no more than 3% of Napa cab’s price (and probably less, especially in the future, as we shall see.) The long-term short market for Napa cab drives most of cab’s pricing dynamics. Surprised? Yeah, I didn't think so. The standard deviation is $349.83. The p-values for all of the variables used are essentially 0, with the highest one being less than one-thousandth of a percent. If you’re new to this blog and statistics, smaller p-values are better. Rigorous researchers typically want p-values of one-percent or less. So, we have a reliable model, with considerably less accuracy than our other models. Still, we can't be spoiled here. The model is still very useful, as our statistical analysis shows.
The following table shows how the model would have fared in the real world for the period studied:
The left-most column contains the actual prices for that year; the next column contains the price predicted by the model; the red column is the number below which the predicted price should fall 2.5% of the time, whereas the green column contains the number it should fall above 2.5%; it should fall below the Min80 10% of the time and the Max80 10% of the time each. The two right-most columns show the difference between actual and projected prices in both nominal and percentage terms. The three columns on the left are color-coded to allow a reader to quickly see when they fall outside of the Min and Max ranges. For instance, in 2003 the estimated price was $3,542.16, but the actual price ended up being $4,010.85. The model predicted a 10% chance of the price exceeding $3930.83, which it did, and a 2.5% chance of it exceeding $4153.02, which it did not. Prices came in at $468.69 more than predicted, a difference of 13%. Note that the Min and Max ranges are meant for projections into the future, but are back-fit here to illustrate how pricing dynamics going ahead are different from those of the past.
Once you understand how this table works, you can quickly see that the model back-fits quite poorly. As time goes on, however, and the market cycle’s effect weakens, the model starts to fit much better. The harvests of 2010 and 2011 saw the weakest predictions in the past decade. In these years, the effects of the Great Recession caught up to grapes that had been insulated for a couple of years by the period of their contracts. This is an example of one weakness in long-term projections: VFA is unable to predict what the general economic conditions will be and, therefore, cannot include these effects in long-term models. Note that VFA’s single-year predictions use already-available macroeconomic data and a model could be easily tweaked to accommodate macroeconomic predictions from anyone bold (or foolish) enough to make them. If VFA could predict economic conditions, by the way, I would likely be on a beach somewhere drinking something sparkling, instead of doing multivariate analysis of winegrape prices.
One last note: this model also indicates that macroeconomic conditions - inflation excluded - actually have only a minor effect on winegrape prices. Even the Great Recession threw numbers off by at most 8% or 9% and probably less, as it is unlikely that all of that variation is rooted in a single cause. Many people will be surprised by this and many will not believe me, but time and again, all the analysis I do shows this to be the case. The wine cycle is typically the most important factor in determining winegrape prices for any given region-variety combination, followed by inflaton, with the general economy being a distant third. For Napa cab, neither the cycle nor the economy are very important.
Conclusion and Forward Projection:
Right now, producing a model for Napa cab prices that will work well in the future and back-tests well, is pretty much impossible, since, over the past two decades the pricing dynamic has changed considerably. It is my opinion, however, supported by the data, that linear modeling will serve the industry well in the future, as the market cycle becomes less and less important. Due to the lower correlations, however, sensitivity analysis is vital to long-term financial planning for vineyard owners and financial plans should be made with particular attention paid to the lower probability bounds, or with a downward adjustment of the numbers of three or four percent to take into account the chance that the model is off and "be on the safe side." With no further ado, here is VFA’s 30 year projection for Napa cab prices, including the historical time period studied, and the 80% and 95% probability ranges:
Figure 2: Historical and Projected Napa County Cabernet Sauvignon Prices, with Sensitivity Analysis