I see an offer for a 15 year fixed jumbo at 4.5% with a 4.622% APR while on the some advertisement it shows a 5/1 ARM jumbo at 3.875% with a 3.283% APR.
Why is one APR higher and the other lower?
You can't use APR to compare loans with different periods.
The rate on the 5/1 Jumbo ARM has a lower APR because the government does not allow the lender to use the initial/teaser rate to calculate the APR for the entire loan. (This is to address misleading terms where the first payment is at 0.1%, then pops up to a higher rate.)
So, the lender calculates the APR based on the current rate of the underlying index, which is lower than the initial rate offered by the lender. They do this because they don't have a crystal ball to project the LIBOR (or some other) rate index 5 years in the future.
Unless your crystal ball is telling you that you are absolutely going to be moving in 5-7 years, AND you have a big downpayment, it's probably crazy to sign up for an ARM in 2011.
I believe that because it is an ARM and is based on some index, the APR calculation is based on what the index (and thus the rate) will be when it starts adjusting.
I think when the mortgage provider makes the calculation, they assume the rate will be the same when the adjusting period starts as it is today. So if the index stays the same as it was when this mortgage started, the rate will actually adjust downward.
Edit: the APR being higher in the fixed rate is likely due to the fees associated with the loan, which are blended into the rate to calculate APR.