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Whether you are looking at an ideal/suitable property in Phoenix, Tucson, or Scottsdale, there are certain fundamental factors related to the Arizona market that you should know before you take that big decision.

This work examines all critical issues related to making a buy/sell decision that first-time home buyers, investors, realtors, and all those interested in the market should know. 4+ decades of house price transactions have been examined in this analysis.

Few tips before we get into the analysis:

Buying a property is a major decision with long-term ramifications; thus, a calculated, measured approach is likely to the difference between long-term financial security or difficulty. So, the first rule is to make a decision divorced of emotionality. Modern marketing is designed to elicit an emotional response—so keep your guard up for that.

Put simply, when you are considering a property, instead of only picturing yourself and your loved ones in that space, also think about the long-term financial and economic realities—such realities are discussed in detail in this work, to provide you the mental filters you need to navigate through all the biases and spurious marketing you are likely to be exposed to.

## Is it a good time to buy a house in Arizona (Phoenix, Scottsdale, Tucson)?

In recent periods (Q1 2020—Q1 2022), house prices in AZ have risen at an average rate of 4.41% per quarter; however, the long-term average quarterly appreciation—excluding periods of high volatility—stands at 1.4%. This means that prices in recent periods have risen at a rate that is 215% times higher than the long-term average quarterly price appreciation.

Prices, we must understand, cannot continue to rise at an unsustainable rate. If an asset has a long-term average appreciation of, say, 10%, but it rises 50% for two periods, can we assume it'll continue to rise at such an unsustainable rate?

No, there is a principle of reversion to mean that comes into play; if an asset has price changes that are drastically different from its long-term performance, yet its fundamentals haven't changed drastically, then we can expect that in future periods, the price change per period will normalize, so it's more in line with the long-term average per period change. This anticipation is a logical expectation of reversion to mean, i.e., price appreciation that is out of the zone of acceptability of long-term trend will relapse to be in line with the long-term trend.

This concept has been empirically observed and adheres to principles of validity. If prices of a specific asset rise exponentially without significant changes in the fundamentals, we can expect prices to fall, to be in line with long-term average performance.

Brief examples: (1) equity prices in the late '90s rose at an unsustainable level, however, a significant correction occurred in the early 2000s; (2) due to a diminishing of lending requirements (subprime mortgages) in the late 2000s, the property market started rising at an unsustainable level—of course, a significant correction followed.

We must also understand that buying 'at the peak' of the market—if done purely as an investment—is unwise; most of the time, such decisions are driven by greed, not rational strategizing—most of the time, those that buy at the peak are usually left 'holding the bag' as per the greater fool theory (people buy overvalued assets believing they'll be able to sell them at an even higher value at a later date [to a higher fool]).

See also:

Some may ask: So, what is a reasonable quarterly appreciation in the AZ market, that can be considered 'compatible' with the long-term trend?

As per a 99% confidence interval, quarterly price appreciation in the range of 1.9%—0.94% is within the trend range, as per the data. If prices rise above or below this range, we can confidently say that the prices are violating the long-term trend and are likely to revert to mean in future periods.

Prices, since Q1 2020—Q1 2022 have risen at an average rate of 4.41%, which is obviously above the acceptable trend rate, logically, prices should experience an adverse period to return to long-term trend; this means that quarterly price change rate may fall below the trend line discussed above (0.94% per quarter) to compensate for the abnormal price appreciation in recent periods.

A quick rule of thumb for trend assessment: Whenever the percentage change line in the above-presented graph exceed the 2.5% percentage change on the upside or falls below 0%, market participants should identify prices moving outside the range of long term trend, expectations regarding a reversal in subsequent periods would be logical, i.e., prices cannot continue to increase beyond the 2.5% mark per quarter, nor can they continue to fall below 0% for a sustained period—the principle of reversion to mean will come into play, and a reversal should occur.

There is a further nuance that we must understand. If the fundamentals of an asset change, we can expect the long-term trend rate of appreciation to change. For the AZ property market, this would mean that if demand for houses rises by, say, 500% & sustains at that level, yet new developments aren't meeting the demand, then we are likely to see prices rise and a new trend rate emerge due to a sustained increase in demand; a change in fundamentals, thus, is likely to change the long-term trend rate.

Nonetheless, in recent periods, we haven't seen a 200% increase in the population of, say, Tucson or Scottsdale, nor has inflation risen by 200%--thus, we can reasonably say that quarterly price change in the future, as observed during the 2008 crisis period, may fluctuate to revert to the long-term trend rate (and we may see quarters of price decline as well). However, when the market sentiment changes, new buying opportunities emerge, which can aid homeowners if they don't make an ill-timed decision!

Another critical point: chances of the FED increasing rates are still high; the implementation of contractionary monetary policy (rate hikes) increases the risk of recessions, and with a market as sensitive as the Arizona market, the price may fluctuate considerably in coming periods, and those making the decision should also be vigilant of monetary policy risk.

Now, let's tackle the fundamentals:

## Is buying/holding real estate in Arizona a good option?

Returns

Posing this question to a realtor is analogous to asking a barber whether you need a haircut—secondly, discussing with those that aren't thoroughly proficient in financial analysis isn't ideal.

Let's get into the fundamentals now.

House prices in Arizona—long term—grew at a rate of 1.24% quarterly (geometric mean); this, approximately, equates to a 5% annual growth rate of price in nominal terms, and about 2% inflation-adjusted real growth p.a. The national quarterly growth rate (long term geometric mean) of property prices stands at 1.19%; this means that prices in AZ's market rose at a rate 4.2% higher than national figures. While this figure may seem inconsequential, it, in fact, is consequential when considerable property values are involved, i.e., homes valued over $800,000.

Nonetheless, statistical testing (paired t-test) confirms that the difference between national & AZ market returns isn't statistically significant (results of all statistical tests available below).

All in all, as per the data, we can say with confidence that house prices in Arizona rise at a marginally higher growth rate when compared to the national average—however, the difference isn't statistically significant.

This means that while we can't say that the AZ property market—as far as returns are concerned—has a potential of returns superior to the national average, we can say that it isn't a market that has performed poorly compared to the national average. So, our first simple parameter signals neutrality.

This graph presents a comparison of the historical performance of the two markets.

The risk

Another—perhaps most critical concern—is risk. Are house prices in AZ riskier, i.e., more susceptible to sudden fluctuations in value, when compared to the overall U.S. market?

To answer this question, volatility (standard deviation) of home sale transactions is compared. For scientific thoroughness, a statistical test (F test) has also been conducted.

The data reveals that the volatility of the AZ market (2.90%) is about 16% higher compared to the national market; statistical testing confirms that the difference is statistically significant.

Another critical risk parameter used in financial analysis is 'value at risk (VaR)':

The quarterly VaR of AZ prices in -4.7%/the yearly Var stands at 9.4%; put simply, this means that in worst-case scenarios (such as a recession or external economic shock), home prices 98% of times, shouldn't fall below -4.7% per quarter, and -9.4% in a year. This VaR/risk figure, when compared to the national figure, is about 200% higher.

Simplifying further: Per every $100,000 of property value in AZ, in the worst-case, the price shouldn't fall below $953,000 98% of times; if you buy a property for $1 million, if a recession hits the economy, the price of the property, as per the data—most likely—will not fall below $953,000 in a quarter & $906,000 p.a.; the probability of prices falling below the figure presented is 2%.

The worst quarterly decline in the Arizonian housing market stands at -7.32%; nonetheless, it is also important to note that residential property values declined about -19% from Q1 2007 to Q2 2012. Thus, in an adverse period, similar to the 2008 distress period, prices can decline about 20% in a few years, which is a very concerning figure. Suffice to say that the data supports the VaR value calculated above.

Risk-adjusted returns

While returns and risk are the most widely examined parameters, risk-adjusted returns are of paramount importance; risk-adjusted returns are returns net of the risk-free rate (i.e., the rate earned on government bonds), per unit of risk. The ratio used to calculate this parameter is the Sharpe ratio:

Sharpe ratio of residential properties (long-term price appreciation as per transactions observed) in AZ stands at 9.4%; the same figure for the national market stands at 8.7%. This figure translates to 9.4 percent returns in the AZ market per 1 unit of risk taken. For comparison, the Sharpe ratio of the S&P 500 stands at 7.7%; this means that the AZ market has been a viable market for long-term investment.

Nonetheless, the figures presented above don't necessarily translate to the housing market being a better investment than the S&P 500; that's because there are maintenance and related costs associated with real estate investing, which aren't associated with purely financial investments.

On the other hand, housing also provides a utility, i.e., you can live in the house or rent it out—the value of such utility cannot be measured very accurately, as rents or cost of occupancy can be variable, dependent on a number of factors beyond the scope of this analysis.

Suffice to say that the residential property market in Arizona—overall—can be classified as a very competent long-term investment, which has performed marginally better than the national market and has the potential of delivering risk-adjusted returns that are better than purely financial assets (stocks/bonds/derivatives, etc.)

Summary of risk & returns analysis:

## Critical factors for buying decision/future property values

One critical factor that governs residential property values is demand. Demand is fundamentally driven by the number of people looking to acquire homes for a personal residence or as an investment; both types of property acquisitions are, in turn, dependent on the number of people living or moving in an area. Thus, logically, the population growth rate is a critical parameter when it comes to assessing demand.

Arizona's population grew at a rate of 1.13% per year (geometric mean); the U.S. national population, on the other hand, grew at 0.635% p.a. (geometric). Moreover, the total population in AZ grew by about 12% in the last decade (2010-2020)—while the national population grew by about 6.53%.

This means that the annual growth rate of AZ's population is greater, by a very significant 78%, compared to the national population growth rate; its population grew 84.6% more than the national population in the last decade. It is also important to note that AZ is presently among the most popular states for internal relocation (i.e., people moving from other states).

Therefore, as far as population growth—and subsequently demand is concerned—analysis reveals that AZ is in a favorable position compared to national figures, and demand is likely to remain healthy if current trends persist.

It is also important to note that favorable headlines and developments can significantly increase investor interest and positively impact property prices; this means that if a major company, or influential figures, announce a move to, say, Phoenix, property prices are likely to see a positive boost (as observed in Austin, TX).

All in all, demand from investors & those buying a house for self-occupancy is likely to remain healthy and higher than the national figures; nonetheless, it is also important to note that demand is more likely to rise disproportionately, meaning more desirable/gentrified/posh areas are likely to attract more interest than the overall market in AZ.

Still, it is important to keep in mind that buyers' perceptions (and demand) can change in a very short amount of time, impacting prices considerably. The Arizona housing market has a very high sensitivity of 1.76 (beta) to national house prices—this means that, as per the regression model, if house prices nationally fall by, say, 10%, house prices in Arizona, as per the data, can fall by about 17.6%.

As per our analysis regarding the impact of recessions on house prices in the U.S., can fall by about 5.3% (nominal) in a recessionary period.

Hence, as per the regression model, in the next recessionary period, prices of homes in Arizona—in the absolute worst case—can decline by about 9.33%, which, of course, is a significant figure. Prices in a long-term adverse period, as witnessed around the 2008 crisis period, can decline by about 20%.

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### Results of statistical tests

Paired sample T-test, using T(df:187) distribution (two-tailed)[Validation]

##### 1. H0 hypothesis

Since the p-value > α, H0 can not be rejected. The difference between the averages of the two populations is not big enough to be statistically significant. A non-significance result can not prove that H0 is correct, only that the null assumption can not be rejected.

##### 2. P-value

The p-value equals 0.5906, ( P(x≤-0.5389) = 0.2953 ). It means that the chance of type I error, rejecting a correct H0, is too high: 0.5906 (59.06%). The larger the p-value the more it supports H0.

##### 3. Test statistic

The test statistic T equals -0.5389, which is in the 95% region of acceptance: [-1.9727, 1.9727]. The 95% confidence interval of Difference AZ-National returns is: [-0.00361, 0.002061].

##### 4. Effect size

The observed effect size d is very small, 0.039. This indicates that the magnitude of the difference between the average of the differences and the expected average of the differences is very small.

F test for variances, using F distribution (dfnum=187,dfdenom=187) (two-tailed) (validation)

1. H0 hypothesis
Since p-value < α, H0 is rejected.
The sample standard deviation (S) of Marlet:AZ's population is considered to be not equal to the sample standard deviation (S) of Market:National 's population.
In other words, the difference between the sample standard deviation (S) of the two populations is big enough to be statistically significant.

2. P-value The p-value equals 0, ( p(x≤F) = 1 ). It means that the chance of type I error (rejecting a correct H0) is small: 0 (0%). The smaller the p-value the more it supports H1. 3. The statistics The test statistic F equals 4.6837, which is not in the 98% region of acceptance: [0.7107 : 1.4071]. S1/S2=2.16, is not in the 98% region of acceptance: [0.843 : 1.1862]. The 98% confidence interval of σ12/σ22 is: [3.3286 , 6.5903].

### Primary References

Barlevy, G. (2015). Bubbles and fools. Economic Perspectives, 39(2), 54-77.

U.S. Federal Housing Finance Agency, All-Transactions House Price Index for Arizona [AZSTHPI], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/AZSTHPI

U.S. Federal Housing Finance Agency, All-Transactions House Price Index for the United States [USSTHPI], retrieved from FRED, Federal Reserve Bank of St. Louis; https://fred.stlouisfed.org/series/USSTHPI