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I want to get a "score" which measures the efficiency of truck planners at a site which despatches boxes of identical size to multiple destinations. This is measured by how full each truck is, on average, when despatched - a figure which is called "loadfill". A team of planners decide how to allocate boxes to trucks, in theory to maximise this.

I have successfully calculated a daily weighted score which reflects the loadfill of the average truck in percentage terms, subject to certain weighting factors*. Unsurprisingly, this figure is strongly correlated with the total number of boxes produced and despatched each day - because the more you send out, the fuller the average individual container is likely to be.

What I want to do is, in non-statistical terms, to take out the effect of the total volume of boxes, and get a measure of how much of the score was accounted for by the transport planners' skill. (I have assumed that these are the only two significant variables, which does not seem an unreasonable assumption given my personal knowledge of our business.)

I am familiar with the CAPM model in finance, which (as I understand it) involves regressing the performance of a stock over time on the performance of the general market, and then taking the intercept as a measure of the individual performance of that stock once the market movement effect has been removed - called "alpha" in the model. I am wondering if it would be valid for me to take the same approach as a crude measure of planning efficiency - regressing the loadfill score over time on the quantity despatched, and using the intercept as the measure of planning efficiency - or at least, the proportion of variation which is not explained by simple changes in volumes. By doing this for a series of months, I could theoretically use the intercept scores as a measure of monthly performance of the team.

Is this valid? My immediate sense is that this sounds very questionable. But I can't think of any immediate intuitive difference between the two scenarios. I know that the proper interpretation of the intercept of OLS is complicated, but depends partly on whether it would be meaningful for x to have a zero value. I do know that generally, the intercept is meaningless, but then that makes me wonder why, then, the intercept is meaningful in CAPM, and under what circumstances the model can be applied in non-financial contexts.

If it is valid, how would I interpret this intercept "alpha" figure, except in the general sense that "higher is better"?

Note that in the above, I have assumed that CAPM does indeed have validity - I do know that there's a debate about it among financial econometricians but haven't read much of the literature.

*The weighting factors are unlikely to be statistically significant in terms of inter-day variation and I suspect the effect they have will be either randomly or uniformly distributed across days.

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The CAPM, $E(r_i)-r_F = \beta (E(r_M)-r_F)$ is in debate, the market return is not the only factor that explains asset returns.

The alfa as a performance measure is another story. It is better to understand as the real individual "gross" performance minus what is expected for that situation:

$\alpha_i = \bar{R_i} - E(R_i) $

Then if you assume the CAPM as a model for expected result you get

$\alpha_i = \bar{R_i} - r_F - \beta (\bar{r_M}-r_F)$

Of course, this could be estimated in one step by a regression equation in the sample

$R_i - r_F= \alpha + \beta (r_M - r_F) + \epsilon$

If you change your model for expected results you will get a different performance measure, but with the same "spirit". In that case, the performance is adjusted for known factors (thus, the $\alpha$ measures the supposed individual power/skill/luck ...). For example, the $\alpha$ with the factorial models in the mutual fund performance.

What happens if you take a simple model for expected results? You end with a questionable performance measure if that model does not fully explains how the gross performance is obtained. For example, we could assume the market model:

$E(r_i) = \beta E(r_M)$

Then we estimate $\alpha$ with the following regression

$R_i = \alpha + \beta r_M + \epsilon$

In your case, the $\alpha$ will have more informative power with a good model for expected results.

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