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1/11/11

Goldman Sachs pricing model

We have been trying to build a preliminary pricing model for Goldman Sachs (GS) since 2008. This company was included in our study of bankruptcy cases in the USA [1]. All in all, the model was not stable over time and the prediction for 2009 was wrong. Originally, the stock price was defined by the index of housing operations (HO) and that of food away from home (SEFV).

In this post we present a new model as based on the CPIs available till November 2010 and the December closing price of GS. Now, the defining CPIs are the index of other food at home (OFH) and the housing index (H). Thus, the difference between the preliminary and current models might be not large because the original indices are very close to the new ones. Our quantitative approach is described in [1,2].

Figure 1 depicts the overall evolution of both involved consumer price indices. These two defining components provide the best fit model between March 2010 and December 2010 and the best-fit 2-C model for GS(t) is as follows:

GS(t) = -11.06*OFH(t) +11.06H(t-12) - 1.82(t-2000) – 99.4

The predicted curve in Figure 2 does not lead the observed price. The residual error is of $14.45 for the period between March 2003 and December 2010. The price of a GS share is relatively well defined by the behaviour of the two defining CPI components but the model does not foresee the price. During the last quarter of 2010, the predicted price is well below the observed one and the residual error is large. We expect the residual to return to the zero line in the first or second quarter of 2011. A drop in the actual price is likely but the predicted price might rise as well.


Figure 1. Evolution of the price of OFH and H.


Figure 2. Observed and predicted GS share prices.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $14.45.

References
1. Kitov, I. (2010), Modelling share prices of banks and bankrupts, Theoretical and Practical Research in Economic Fields, ASERS, vol. I(1(1)_Summer), pp. 59-85

2. Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.



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