In recent weeks, some commentators have suggested that consensus earnings forecasts for the S&P 500 are too high. Currently, bottom-up consensus earnings for the year to the December quarter of 2010 are $74.34.

This is more than 30 per cent higher than bottom-up earnings for the fourth quarter of 2009 of $55.77. The argument runs that this increase is greater than in other business cycles.

There are two ways to approach this objection. The first is to point out that the reason that the rise in earnings is so strong, relative to other business cycles, is that the fall in earnings that preceded it was much larger relative to other business cycles. The second way to approach this problem is to build a model of US earnings.

Earnings are a nominal measure. They go up with prices. Our first assumption then is that we can generate the trend of US earnings by using the US price level. We don’t know what future price levels will be but projections give us a very good guess. So the first thing we do is to produce an exponentially smoothed estimate of the US CPI.

When we try this in our model, we find we have made a good start. The T statistic of the relationship between the US price level and US operating earnings is 12.98. This means that the probability of this being a chance relationship is less than one in ten thousand.

Now we have an estimate of trend. What we need is an estimate of the business cycle.

To represent the business cycle, we use the three-month moving average of the Chicago Fed National Activity Index (CFNAI-3). When we add this to our model, we find that a one standard error change in the CFNAI-3 changes US operating earnings per share by US$15.32 with a lead of two quarters. The T statistic is 10.65.

This means that the probability of this being a chance relationship is also less than one in ten thousand. Our model, using these two variables, explains 78.6 per cent of quarterly variation in US 12 month rolling operating earnings over the 12-year period since the March quarter of 1997.

Considering how simple the model is, this is actually a pretty good job.

The model does a good job of picking out the major cycles in US earnings between 1997 and the end of 2006. Something interesting happens in 2007.

Earnings go up but our model goes sideways. This is because the CFNAI-3 was indicating weakness in the US economy even though some sectors, particularly finance, were showing high profits.

In the first quarter of 2008, earnings crashed down towards our model estimate. Both our model estimate and actual earnings collapsed through 2008 before turning up sharply towards the end of 2009.

What does our model tell us about the future? So far we only have enough data on the CFNAI-3 to be able to forecast our estimate to the first quarter of 2010. Still, this is encouraging. The consensus estimate for the first quarter of 2010 is US$62.02 per share.

Our model estimate is slightly higher at US$67.92 per share.

Most economists believe that the US economy will be back at trend growth rate by the end of this year. Almost all economists believe that the US economy will achieve that next year. Well, if that is true, then the CFNAI-3 will improve from the current level of -0.63 to the level of zero early next year. This is because zero on the CFNAI-3 is equivalent to trend growth rate of the US economy.

So what we then do is we assume in our model that zero is the correct number for the CFNAI-3 in 2010.

This produces a leap in earnings in the middle of 2010. Operating earnings per share rise to US$85.10 by the fourth quarter of 2010. This is almost $US11.00 higher than bottom-up consensus earnings for the same period of $US74.34. This suggests that all the US economy has to do is return to trend growth rate for current consensus estimates for US corporate earnings for 2010 to be surpassed.

**Conclusion**

Some people say that bottom-up earnings estimates for the S&P 500 for 2010 are too optimistic. This is because earnings estimates rise more rapidly than in previous cycles. There are two ways to approach this. The first is to observe that the reason that earnings should rise more rapidly in the cycle is that the previous fall in earnings was much greater than in previous cycles.

The second approach is to build a model. Our simple model explains some 78 per cent of quarterly variation of S&P500 earnings. We apply the common assumption that the US economy will be growing at trend in 2010. When we do so, our model gives us an estimate of $US85.10 by the fourth quarter of 2010.

This is almost $US11.00 higher than the bottom-up consensus earnings for the same period of $US74.34. Very interestingly, we come to the conclusion that consensus estimates for the S&P 500 earnings are not optimistic.

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