It is an interesting exercise to quantitatively assess the future of Berkshire Hathaway (BRK.B). The Oracle of Omaha is considered one of the greatest investors ever. Here we would like to introduce a deterministic model for a Berkshire share price. The company is a publicly owned investment manager that has a highly diversified structure with interests ranging from GEICO to Dairy Queen.
The model is deterministic since it has been obtained by decomposition of a share price into a weighted sum of two consumer price indices. One may follow our simple assumption that the growth in the CPIs related to Berkshire -- e.g., transportation services (TS) and dairy products (DAIRY) -- might be seen in the change of the pricing power for the studied company. These two CPIs are revealed as the drivers of the price of Berkshire shares. However, they were actually selected using the LSQ method from a set of 92 different (not seasonally adjusted) CPIs. The best model predicting the monthly closing prices adjusted for dividends and splits has the smallest RMS error from July 2003 to March 2012.
We have borrowed the time series of monthly closing prices of Berkshire from Yahoo Finance (the closing price for March 2012 is included) and the CPI estimates through February 2012 are published by the BLS. The best-fit model for BRK.B(t) is as follows:
BRK.B(t) = -0.802DAIRY(t-11) - 2.24TS(t-7) + 21.13(t-2000) + 584.66, March 2012
where BRK.B(t) is the Berkshire share price in U.S. dollars and t is calendar time. Figure 1 displays the evolution of the defining CPIs since 2002. Instructively, both indices are relevant to the BRK.B structure and have negative slopes. The DAIRY index likely has a larger impact on the growth of the price because of higher amplitude oscillations. The TS index is rather a linear line since 2002, with only a small positive fluctuation (negative impact on the price) at the end of 2008.
Figure 2 depicts the high and low monthly prices for a Berkshire share, together with the predicted and measured monthly closing prices. The predicted prices are well within the limits of the share price uncertainty. The model residual error is shown in Figure 3, with the standard deviation between July 2003 and March 2012 of $4.73.
The accelerated growth in the DAIRY index since April 2011 induced a mid-term decline in the share price. This rise in dairy price had not come to an end yet, and we cannot exclude that the actual share price will return to the predicted level of $73 by the third quarter of 2012. The TS price index does not show any sign of deceleration, and food prices together with dairy products will likely be rising until 2014. If the model is right, we may observe in 2013 some further decline in Berkshire share prices.
Click to enlarge all images.
Figure 1. The evolution of defining indices.
Figure 2. Observed and predicted monthly closing prices for a Berkshire share.
Figure 3. The model residual error: sterr=$4.73.