# What is the expected return of residential property?

/Since the 1950s, investors have had access to a simple formula to help them calculate the price of an investment. Created by Myron Gordon and Eli Shapiro, and based heavily on the ‘Theory of Investment Value’ by John Burr Williams, the formula describes the price of an asset in terms of only three variables - yield, required return and an expected growth rate.

They established, with a few simplifying assumptions[1], that an asset’s price today (P) should equal its expected dividends next year (D1) divided by the required return (r) minus the expected growth rate (g).

The model is called the Gordon Growth Model, and the full equation is as follows:

Now how on earth can this help us understand the expected return of residential property?

In the real world, we don’t observe the required return (r), but we can observe the price (P), the expected dividends (D1) - which in this case is the expected rent - and we can also use long term historical data to get an estimate for the growth rate (g).

Using this information, we can rearrange the above equation so that, instead of solving for price, we can solve for the required or expected rate of return (r).

The rearranged equation looks like this:

This makes a lot more sense. The expected return for a residential property investment now equals the rental yield (ie, the expected rent divided by the current property value) plus its expected growth rate.

To help reduce subjectivity even further, www.interest.co.nz has a residential investment property yield indicator https://www.interest.co.nz/saving/rental-yield-indicator

Looking at central Auckland as at June 2017, the rental yield was 3.5%[2]. This is probably a high estimate. It assumes you bought a house at the lower quartile price (ie, a low price) but were able to rent it out at the median price. Further, this yield doesn’t account for all costs. As any property owner knows, you don’t get to pocket the gross rent. Amongst other things, you need to pay for property maintenance, insurance, management costs, vacancies, rates and accountancy fees. Not to mention that the value of the time you put in is presumably worth more than $0.

Nevertheless, if we assume that next year’s rental yield is likely to be best approximated by this year’s rental yield, then let’s take that 3.5% as our best estimate of D1/P. Now, to determine our expected return, we need only add expected growth.

Expected growth of what?

Expected growth of property prices (ie, capital gain).

Year on year, this is almost impossible to guess. As we know, property can experience periods of rapid price increases and, at other times, extended periods of flat or subdued growth. However, long run estimates of growth rates can be observed from historical data.

For instance, the Shiller Home Price Index[3] provides long term US house price data back to 1927. We can see that, since the 1920s, US home prices have increased by 3.9% p.a. on average. That compares to US inflation, which increased at 3.0% p.a. over the same period.

Although there have been a few small deviations over the full 90 year period, the long term relationship between house prices and inflation has been remarkably stable. That includes the decade of the 1970s, when US inflation was high and house prices increased at an accelerated rate.

The strength of this relationship is intuitive because, over the very long term, we expect the price of a residential property (particularly a residential investment property) should primarily be driven by the long term growth in rents, which in turn is related to increases in wealth and income, and thus, inflation. In fact, a key observation from the Gordon Growth Model is that, in the long run, the growth in asset prices (capital gains) must be equal to the growth in yield (rental income). Therefore, rather than looking at growth in property prices, you could equally look at the growth in rental income.

Coming back to our central Auckland example, Trade Me Property publishes an index showing the annual change in rental prices http://www.trademe.co.nz/property/price-index/for-rent/.

As at June 2017, a chart of the recent changes in the Auckland residential property price index is as follows:

While in the month of June rental prices were up 3.9% on a year earlier, the average annualised increase over the last 12 months is closer to 3%. In fact, that’s close to what we should currently expect.

While this is above the current New Zealand inflation rate of 1.7%, it’s not significantly different. That also makes sense. In the long term, if rents consistently increased by much more than inflation, rents would consume an ever increasing proportion of a tenant’s income. That wouldn’t be sustainable. In fact, the reason that rents have increased over the rate of inflation at all more likely reflects massive new investment in property, providing better, roomier, warmer and safer rentals. Ultimately, this new investment comes at a cost to the investor.

So, let’s assume the long term growth in rents is 1% above inflation. Since the Reserve Bank of New Zealand has a policy target of maintaining inflation in the range of 1% - 3% on average, we can reasonably expect long term inflation in New Zealand of approximately 2% p.a. Therefore, let’s assume that rents in New Zealand increase on average by 3% p.a.

If rents can be expected to grow at 3% p.a. then it should also be expected that house prices must grow at a similar rate.

If house prices were to go up much faster than rents, this could only lead to an eventual bubble in the property market. If rents were to go up much faster than house prices, then new investors would eventually be attracted into the property market (and push prices up) by seeking to take advantage of the relatively attractive rental yields.

So, if the US data history suggests house prices since 1927 have gone up by almost 1% p.a. above inflation, and price rises are linked to rent increases which are also running at around 1.0% above inflation (in our central Auckland example), then we have a reasonable basis for our long term expected growth rate (g in the equation).

We can now add this growth rate to our rental yield to get our total expected return.

3.5% rental yield + 3% expected long term capital gain = 6.5% p.a.

In other words, the expected return of a central Auckland rental would be 6.5% p.a., assuming an investor could bank all rents without any costs or new investment required, purchase a home at the lower quartile and rent at the median, discount their time to $0, have zero percent vacancy, and increase rents at 1% over the rate of inflation forever.

You may have guessed that we’d suggest the above assumptions may be generous, but that’s for individual investors to reflect on, based on their particular circumstances.

An investor may respond that recently, property values have had double digit price rises per year. That’s true. Unfortunately, rents haven’t been increasing at the same rate. When prices rise faster than rents, it results in a lower yield for new investors. According to www.interest.co.nz, in September 2014 the average gross rental yield in central Auckland was 4.5%.

So, back in 2014, with the same long term inflation assumption, the expected return of central Auckland residential property was 4.5% rental yield + 3% expected long term capital gain = 7.5% p.a. However, the recent rising prices have resulted in an equivalent fall in rental yield for new investors, and a corresponding fall in expected returns, such that the total expected return has fallen to 6.5% p.a.

In other words, an investor on-selling a property to a new investor today is simply selling their property at a lower expected return than they purchased it for.

If you extrapolate that trend out, you realise it can’t go on forever. Eventually, there’s going to be an investor offered such a low expected return that they simply refuse to purchase the property. At that point, the price must fall until the rental yield returns to an attractive level.

The only alternative is that the rental yields themselves would need to increase substantially to justify the higher current property values. Unfortunately, the history of rental price movements is that they are relatively stable. Therefore, it has to be considered extremely unlikely for a market mechanism that historically exhibits considerable stability to suddenly move by a substantial amount in any direction.

So, is property a good investment?

That’s a subject for another article. But having a reasonable approximation of what you expect to earn is at least a starting point to answer that question.

We encourage investors to work with their financial adviser or accountant (so, not someone who may have a conflict of interest in this situation, such as a real estate agent) to determine a reasonable expected return for any property they are considering. This would also involve looking at the nuances of the financing costs, other costs and the time required to put into property maintenance and management.

When investors understand the return they can reasonably expect from an asset, only then are they in a position to consider how else they might earn an equivalent return, to see if that asset is worth investing in.

[1] The model assumes the dividend or yield grows at a constant rate in perpetuity. The model solves for the present value of the infinite series of future dividends.

[2] The indicative yield figures in this table are gross, and are calculated from the REINZ's lower quartile selling price for each area during the previous six months, and the median rent for three bedroom houses calculated from new tenancy bonds received by the Ministry of Business, Innovation and Employment for the same areas/period. This gives an indication of the gross rental yield that would have been achieved in each area if a property was purchased at the lower quartile price and rented at the median rent for that area.

[3] Developed by Nobel Prize winner, Robert Shiller