But Alexander sasy in the BNZ Weekly Overview that he would only do that if he had a reasonable belief that fixed rates are about to rise.
"My analysis of the margins suggests we are close to a round of rate rises.
"So I find myself prepared to sacrifice the nice low 6.09% and lock in two years at 6.65% with an expectation that I will average an interest rate cost over the next two years near 0.75% lower than if I float."
He says he does not find the three year rate attractive as taking it will save only 0.4% compared with floating for the entire three years.
More than that, Alexander says if BNZ's forecasts prove correct, two years at a 6.65% fixed rate then one year floating will yield a total three year average cost of 7.1% compared with the current three year fixed rate of 7.15%.
"It looks better to fix two years then float than fix three years, so I would fix two years."
He says expectations that the Reserve Bank will restart its tightening cycle in March next year firmed up last week following the release of stronger than expected jobs data.
He says in particular borrowers should note this point: "If we can have a period as we have passed through recently where data surprise on the weak side and wholesale interest rates rally, we can also have a period when data will be surprisingly strong and rates will jump quite sharply".
The proportion of mortgages sitting at a floating rate hit 40.3% at the end of September from 23% a year ago and a low of just 12.7% in December 2007. This is the highest proportion floating in eight years.
Alexander says discussions with home owners show most seem to be quite happy sitting floating and are prepared to ride the cycle with few feeling that the economy will get so strong and inflationary pressures so immense that these rates will jump massively.
However he says if he had a desire to fix and had been happy floating in recent months he would now be thinking seriously about moving into a two or three year rate given that the chances of these rates falling further are minor. But says the chances of these rates rising in the near future are increasing.
However Westpac Weekly Commentary says the Reserve Bank's more cautious stance in its Financial Stability Report suggests that floating rates will remain on hold for several more months.
It says fixed-term rates could rise in that time, but only if there is substantial turnaround in sentiment on the global economy and as a result there is no urgency to fix right now.
ANZ Market Focus says after the Reserve Bank Financial Stability Report was released, not only did Governor Bollard take the opportunity to remind the market that his view of the economy had not fundamentally changed since September, he took the unusual step of saying that there had been "some misinterpretation" of the data.
ANZ says it was the comment that "we'd look for the market to correct that and we'll be talking further about that when we put out the Monetary Policy Statement" that was really telling, and suggests that he has no urgency to adjust policy.
"Interestingly, Bollard also made pointed references to the interaction between interest rates and the exchange rate, noting that the high NZD "does reduce pressure on monetary policy and the markets will presumably reach the conclusion".
ANZ says all in all it thinks these were significant comments, and while the market has reacted, short end rates are still higher than they were in the weeks leading up to the October OCR Review.
"As such, we see scope for rates to move lower yet as we approach the December MPS."