Prediction of Legg Mason share price

According to [1], the model for Legg Mason (LM) is defined by the index of food (F-CUUS0000SAF ) and that of appliances (APL-CUUR0000SEHK). The former CPI component leads the share price by 4 months and the latter one leads by 13 months. From our past experience, the larger is the lag the more unreliable is the model. However, both defining components provide the best fit model between August 2009 and June 2010. Both coefficients in the LM model are positive. This means that increasing food price forces the share price up. The fall in the index of appliances has been compensating *see Figure 1) both the increase in F and positive linear time trend in the share price, as defined by the slope of +33.024. So, the best-fit 2-C model for LM(t) is as follows:

LM(t) = 5.88F(t-4) + 8.29APL(t-13) + 33.024(t-2000) + 1425.45

The predicted curve in Figure 2 leads the observed price by 4 months with the residual error of $6.89 for the period between July 2003 and June 2010. In other words, the price of a LM share is completely defined by the behaviour of the two CPI components.

The model does predict the share price in the past and foresees no significant increase in the next quarter, in July through September 2010. Considering the overall fall in the S&P 500 in 2010, one should not expect any growth in stock prices at all.

Figure 1. Evolution of the price index of food (F) and appliances (APL).The latter has been falling since July 2009.

Figure 2. Observed and predicted LM share prices.

Figure 3. Residual error of the model. Mean residual error is 0 with standard deviation of $6.89. the largest errors were observed in 2005 and 2006.

References

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