Sunday, September 11, 2005

Long-Short pair and Residual Reversion: Tata Motors and Maruti

Many hedge funds run long-short equity portfolio, i.e. they go long one stock and short another to make money on the valuation spread. There are two key questions in analyzing a long-short pair: (a) Is there a valuation difference between two stocks which would converge over a period of time? (b) What is the return from the long-short pair on a risk-adjusted basis?

How should risk be thought of in the long-short world? We can measure the beta of the long-short portfolio to get a handle of the risk. Remember that beta is the square root of covariance of the two-stock portfolio, which in this case would be {Variance-1 + Variance-2 + 2sqrt(variance-1*variance-2)}. The lower the beta, the better it is.

If the two stocks have the same beta, then the beta of the long-short portfolio is 0. This is intuitive - if one stock goes up by x% and the second falls by the same, then the total return from the portfolio is 0, assuming equal weight of both stocks in the portfolio.

However, if between the two stocks that had historically had the same beta, one stock has fallen (or risen) more than the other recently, then the other stock would fall (or rise) more than the first over the coming time period - provided nothing changed fundamentally between the two stocks, and there is reason to believe that the historical relationship would hold in the future. This is what some analysts define as Residual Reversion.

Over the past year, I have become convinced that residual reversion exists between the stocks of Tata Motors and Maruti. Again and again, there share prices have diverged, and again and again they have converged. The stocks have similar betas, they operate in the same industry - Maruti holds 50% share in the Indian passenger market segment, while Tata Motors enjoys a 17% share.

One should however remember that Maruti shareholders might not enjoy the full benefit of Maruti's growth in the future as the Indian middle class expands - the new car plant proposed by Maruti is a 50-50 JV between Maruti and Suzuki, Japan. As such, Maruti's shareholders will get only half the growth from new car sales. So, TAMO might be a better buy in the long run.

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