It is a great pleasure to revisit the previous version of the pricing model of Legg Mason (LM). During the last two years it has been stable and is based on the index related to food (food at home, FH) and the index of appliances (APL) from the housing index. Due to the uncertainty in the defining indices and closing prices as the parameter characterizing given shares, the lead of the FH has slightly changed from 4 months in the previous model to 5 months in the current model. The appliance index still leads by 13 months.
Overall, the predicted time series is very close to the observed one in Figure 1, with standard deviation of $7.33 between July 2003 and December 2010. The largest input to the standard deviation comes from a short period in 2006. Otherwise, both curves are very close even during the dramatic fall from $80 per share in the end of 2007 to $10 per share in February 2009 and during the fast recovery in 2009. The best-fit 2-C model [1] for LM(t) is as follows:
LM(t)= -3.61*FH(t-5) – 9.30*APL(t-13) + 16.62(t-2000) + 1317.6
The predicted curve actually leads the observed price by 5 months, as red line in Figure 1 illustrates. Therefore, one can foresee all major changes in the price. Without loss of generality, the LM price is completely defined by the behaviour of the two defining CPI components.
Currently, the model predicts a quick growth in the share price. Therefore, it would be instructive to revisit the prediction at a monthly rate. In January and February 2011, the price is expected at $45 and $56, respectively. Today, the price is at $36.
Figure 1. Observed and predicted LM share prices.
References
1. Kitov, I. (2010). Deterministic mechanics of pricing. Saarbrucken, Germany, LAP Lambert Academic Publishing.
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