It's been a week since the Reserve Bank of New Zealand made its first hike in the cash rate in nearly three years, up 25 basis points to 2.75 per cent, but not a single bank has announced a hike in its lending rate, including the variable mortgage rate.An increase is inevitable and the delay is a bit surprising, especially when compared to Australia, where the big banks usually follow the central bank's rate move within one day.With more customers having moved to variable rates in the past couple of years as floating rates became cheaper than fixed rates, one would have expected the banks to jump at the opportunity of announcing a hike that it can easily justify because of the rise in the cash rate.  The need to lift rates is moderated by the fact that variable rate loans are a minority of all home loans in New Zealand, given the popularity of fixed rate, though often short-term, loans.New Zealand banks took many months to reduce their variable home loan rates following the last change in the RBNZ's official cash rate, a cut of 50 bps in April 2009 to 2.50 per cent. For the first few months variable rates were effectively frozen, and reflecting the rising cost of deposits and wholesale funding.In fact on average variable home loan rates in New Zealand never fully reduced to reflect the 50 bps cut in the OCR in 2009. The variable today stands at around 6.10 per cent on RBNZ data.