NEW YORK (Real Money) -- The market is moving quickly and I'm writing this 10 minutes after the release of the jobs report, but I'll try to keep my comments to what I see as the near-term consequences for traders.

Headline number very strong

As I wrote on Tuesday, I thought a 50,000 additional jobs beat could be a game changer. We got a 54,000 beat, and I'd argue that this indeed should change the whole conversation about how Fed policy might evolve. Not only did we get a strong beat, but the prior figures were revised up by 32,000. The Household Survey, which is used to calculate the unemployment rate, also came in strong at 272,000.

Wage growth

Perhaps even more important than the headline job figure, Average Hourly Earnings, which is probably the most popular measure for wages, grew 0.3% month over month, and 2.3% year over year. Both were 0.1% better than expected. The year-over-year gain of 2.3% ties the highest figure since the Great Recession ended. Worth noting that year-to-date wages have grown by an annualized 3.37%.

Unemployment rate rises

Despite the very strong job gains, unemployment rose by 0.1% due to a large increase in the labor force (397,000 more people). I'm skeptical that this will stick. The Labor Participation Rate has been stuck between 62.7% and 62.9% for the last 14 months, and yet we've had five separate months when the size of the labor force moved by at least 300,000 in a single month. In other words, I think the trend is actually flat, but we're likely to bounce around within that.

Consequences for the Fed

The wage growth is the most encouraging sign for the Fed. It indicates that we are indeed close to full employment, which in turn suggests that continued stimulus will not have any positive effect. The fact that unemployment rose by a tenth isn't meaningful. I don't think this will cause the Fed to move in June, but this should increase the odds of a September hike substantially.

Market reaction

Bonds are "bear steepening," which means that rates are generally rising, but shorter-term bonds are rising by more than longer-term bonds. This suggests the market is increasing its view of where the Fed is going. The five-year is 12bps higher and the 30-year is just 5bps higher.

Worth noting that inflation-protected bonds are only outperforming slightly today, suggesting that the market expects the Fed to raise rates before the higher wages can actually turn into materially higher inflation. Also worth noting that credit is performing poorly.

The gap between the five-year and the 30-year has room to run further. Right now, the yield gap between the two is 133bps, but in past rate hiking cycles, this measure has typically dropped to between 0bps to 50bps. This trade has not worked well so far this year, but I continue to advocate it.

Editor's Note: This article was originally published on Real Money at 9:21 a.m. EST on June 5.

This article is commentary by an independent contributor. At the time of publication, the author held no position in the stocks mentioned.