# What is the relationship between Intrest Rates and the Median House Price in NZ in the past 20 years? : PersonalFinanceNZ

Hello Redditors. 🙂

I was a bit bored so I decided to do my own little investigation into the relationship between interest rates and the median house price in NZ in the past 20 years. We are often told that this is a significant factor in the rise of house prices so I was interested in what there was to find. There is not a very interesting conclusion but a surprise along the way. I hope you enjoy my little analysis. It is not intended for people with knowledge of how the housing market and interest rates work as much of my analysis will be overexplained. Instead, it is a simplified and broken down analysis for people who are learning about this sort of thing and would prefer a slower and more of a breakdown of the different factors at play. It’s also not very precise and relies on some assumptions that are probably not so true so that this as a broader example instead of the numbers themself.

Please also note that I am new to this sort of thing so I would love to have feedback and to be corrected.

I start with a simple question: **how much has a mortgage repayment on the median value house in NZ changed?** I have assumed that the mortgage is at the average 2 year fixed rate of interest. You may note that the interest rates in the dataset are too high, this is because the interest rate data is provided by the reserve bank who take an aggregate view and not the best rate available.

Firstly, here is the median house price in NZ as of Q1 of each year:

Source: globlalpropertyguide.com

As I’m sure you can see there is an overall growth that is relatively consistent apart from a small dip after the subprime mortgage crisis. Next here are the average interest rates in the past 20 years:

Source: https://www.rbnz.govt.nz/statistics/key-graphs/key-graph-mortgage-rates

As we can see there is a clear downwards trend. What we are most interested in, however, is how these two interact to find the cost of mortgage repayment on the median house at the average rate of interest. Using the very helpful PMT excel formula I was able to find that this is what the repayment is:

Calculated using the PMT function on Excel

**I have assumed a 20% downpayment.**

As we can see there is a clear upwards trend in the data. I will refer to this data is the median mortgage as it is the median house price at the average rate.

Of course, this information is only relevant in context. It is necessary to compare this to the median income over the same time period. This poses a second question: **how much has the median mortgage changed in comparison to median income?**

When calculating this using data from Stats NZ we get this comparison:

Income Source: Stats NZ

As we can see there is actually a very interesting trend that the median income is rising faster than the cost to service a mortgage. To really see what is going on, we want to calculate the proportion of the median income that is required to service the median mortgage. Calculating this renders this interesting graph:

**Please note that I have calculated the after-tax rate and accounted for the changes in tax brackets over the past 20 years using IRD tools (was very challenging).**

If you were to view the percentage of income paid on your mortgage is the measure of housing affordability (this is definitely not the whole picture), then we come to the startling conclusion that although housing is considerably more expensive on face value, the actual cost of servicing the mortgage of the house is not less affordable than over the past 20 years and is actually considerably lower than over much of the past 12 years. In this conclusion, there are of course many many many important notes to be made. Firstly, this is the national median income as is not reflective of the higher growth seen in main centres. Secondly, this conclusion does not take into account the difficulty of having to save for an ever-expanding deposit. Thirdly, it does not account for bank stress testing to actually qualify for a home loan. Fourthly, It assumed that people are always on the 2-year rate. You get the point, it is a flawed analysis. But, it does show us an important pattern to understand our broader question.

An interesting note is that by this logic there is more room for house price growth when using this measurement. Thanks to u/social-prof for putting it in the comments. I did the quick maths and at 85% proportion of income, I calculate the median value to be $858,000.

**Please do note that I am not saying housing is more affordable because it isn’t. Instead, I am using this approximation to show the role that interest rates pay in the mortgage repayment amount. **

Going back to our original question, however: **What is the relationship between interest rates and the median house price in NZ in the past 20 years?**

So far we have seen that the mortgage repayment on the median house has increased alongside incomes to mean that the median mortgage repayment makes up a lower proportion of the median income than over much of the last 12 years.

To answer the final and most important question there needs to be a bit of theory about how buyers and investors decide how much to pay. The theory goes that as interest rates decrease, the cost of mortgage repayment goes down, and thus people are able to borrow to pay to more at auction.

Consider a first home buyer who is able to afford to pay $1380 per fortnight. They have come to this number by making a personal budget. If interest rates are 6% they decided that they are able to get a loan of $500,000 and they are very happy. So they go to an auction and buy a house for $625,000 (don’t forget about their deposit). In an alternative world, interest rates are 2%. They calculate that they are able to get a loan for $811,000 instead and can thus pay $1,013,000 even though they earn the exact same amount. When this happens en mass, we can see how lots of cashed-up buyers are able to bid-up the price during a pandemic and recession.

Consider an investor whos calculations depend even more on this mortgage payment. They will calculate the return on investment (how much money they make back on their initial investment) by considering the rent they can earn, maintenance etc. If you said that an investor had to get 6% RoI, that 6% threshold is a calculated off the mortgage payment, rental income, and maintenance. It would appear that as long as the mortgage repayment is under a certain level we can see that investors have little regard for the actual value of the house. They then compete with other investors, FHB and other buyers who all drive the bidding up and then house prices go up.

The overall message from these examples is that people change their total offer to meet what they are willing to pay per month depending on the interest rate.

**note that the investor example is significantly oversimplified as it doesn’t include other nuanced factors that influence investment. I have used it as it does display the role of the interest rates in the house prices quite effectively.

Conclusion: Intrest rates have a large effect on the median price of an NZ home.

Have a good one :))