**Invesco Dynamic Food & Beverage ETF (**NYSEARCA: PBJ) Analysis: Are food ETFs recession-proof? Food ETFs good investment?

**Summary:**

**1. Statistical testing reveals that the risk of Invesco Dynamic Food & Beverage ETF is statistically similar to that of the S&P 500.**

**2. The returns of Invesco Dynamic Food & Beverage ETF, though lower in terms of long-term growth rate, when compared to S&P 500, are statistically similar to the returns of S&P 500.**

**3. The beta of Invesco Dynamic Food & Beverage ETF stands at 0.7.**

**4. Impact of inflation on this sector is discussed.**

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Presently, with inflated valuations of stocks, many investors are concerned about a price correcting event, or, put simply, a market crash. It does seem a logical conclusion to the present, let's say, exorbitant valuations we see in the markets. Alternatively, it may be argued that asset prices, currently, are fluffed up by 'temporary measures' of monetary and fiscal actions, and these actions cannot continue in perpetuity, of course, and assets revaluation, or a market crash, is only a matter of time.

While this line of reasoning does seem rational, it does not present answers to the questions of strategy alterations; particularly, re-evaluating allocations in the portfolio. Investors with lower risk tolerance may be interested in exploring alternatives that may be safer, to reduce their overall risk exposure.

To that end, companies, primarily in the food industry, seem an attractive proposition. Recession or no recession, peaks of troughs, people would always need to eat. And if demand for the products of these companies is likely to remain constant, even in an economic downturn, theoretically, they should weather a recession, or a price readjustment event rather well, compared to, let's say, companies with ridiculous P/E ratios and, thus, unrealistic valuations – no matter how you readjust your prism of valuation to accommodate prices of these stocks.

### So, are food companies a good recession-proof investment that should perform, comparatively well, in a negative market event?

Most investors are likely to take the ETF approach, of course, and thus, the most prominent player in this space, Invesco Dynamic Food & Beverage ETF (NYSEARCA: PBJ), has been evaluated in this report. It is assessed against the S&P 500 for the examination.

The S&P 500, in the 2020 crash, dropped approximately 25% (From the peak in December 2019 to troughs in March 2020). Comparatively, PBJ during the same time fell by a similar 23% approximately. Does this mean that the risk of the two is approximately the same? Well, to evaluate the risk, scientifically, F test has been conducted in this report.

The Beta of Invesco's PBJ, in relation to the S&P 500, is calculated below. The beta should also provide significant insights into the relation of the ETF in question with the overall market:

The beta of Invesco Dynamic Food & Beverage ETF (NYSEARCA: PBJ) in relation to S&P 500 stands at 0.7, with an R squared value of 0.61, implying a moderate effect size.

Simplistically, this means that if the S&P 500 moves ± 10%, Invesco Dynamic Food & Beverage ETF (PBJ) should move ± 7%. Further, assuming that the sample of the companies included in PBJ reasonably reflects the food sector, we can claim that the beta of the food sector in relation to the market proxy should be about 0.7.

The initial examination of the beta does support the premise that food stocks and ETFs, such as PBJ, shouldn't be hit as severely in a market decline as the overall market. For example, if the market crashes by 30%, the food sector, as per the beta of PBJ, specifically, should fall by 21%. However, for a definitive examination, a F test is conducted below:

Jump to __key takeaway__** **

F test has been conducted to evaluate the difference in variance between Invesco Dynamic Food & Beverage ETF (PBJ) compared to the S&P 500. The hypothesis is constructed as:

H0: σ2XPBJ = σ2SP versus Ha: σ2XPBJ ≠ σ2SP,

, where

σ2PBJ – the variance of the returns of Invesco Dynamic Food & Beverage ETF (PBJ); and

σ2SP – the variance of the returns of S&P 500.

F test for variances, using F distribution (dfnum=353,dfdenom=353) (two-tailed) (validation)

1. H0 hypothesis

Since p-value > α, H0 is accepted.

The sample standard deviation (S) of the S&P 500's population is considered to be equal to the sample standard deviation (S) of ETFPBJ's population.

In other words, the difference between the sample standard deviation (S) of the S&P 500 and ETFPBJ populations is not big enough to be statistically significant.

2. P-value

The p-value equals 0.05091, ( p(x≤F) = 0.9745 ). It means that the chance of type I error, rejecting a correct H0, is too high: 0.05091 (5.09%).

The larger the p-value the more it supports H0.

3. The statistics

The test statistic F equals 1.2314, which is in the 98% region of acceptance: [0.7803 : 1.2816].

S1/S2=1.11, is in the 98% region of acceptance: [0.8833 : 1.1321].

The 98% confidence interval of σ12/σ22 is: [0.9608 , 1.5782].

**The null is not rejected, therefore.**

### What does this mean, simplistically? Is the risk of S&P 500 and Invesco Dynamic Food & Beverage ETF (PBJ) similar?

This means that the variance of weekly S&P500 returns is equal to the variance of Invesco Dynamic Food & Beverage ETF (PBJ); PBJ, for the past 355 weeks has demonstrated a statistically similar risk, compared to S&P 500. This is backed by statistical evidence. In the future, it would be logical to expect PBJ and S&P 500 to have similar risk profiles. One doesn't have a lower risk compared to the other as per the statistical test.

### Another important question is the returns. Are returns of S&P 500 and Invesco Dynamic Food & Beverage ETF (PBJ) similar?

The yearly growth rate (geometric mean) for the S&P 500, for the data set (last 355 weeks), stands at 11.6% p.a.; and

The yearly growth rate (geometric mean) for the Invesco Dynamic Food & Beverage ETF (PBJ), for the data set (last 355 weeks) stands at 6% p.a.

Statistical testing on the weekly returns has also been conducted below:

The test conducted in this report is the paired t-test, as all companies, in the S&P 500 and the Invesco Dynamic Food & Beverage ETF (PBJ) are reliant on the same underlying economy, primarily. The test has been constructed as stated below.

*H0: μd -* μ0* = 0 versus Ha: μd -* μ0* ≠ 0.*

*, where*

*μd – the mean difference between the monthly returns of S&P500 and *Invesco Dynamic Food & Beverage ETF (PBJ)*.*

*μ0 – 0*

__Paired sample T-test, using T distribution (df=353) (two-tailed) (validation)__

** 1. H0 hypothesis**
Since p-value > α, H0 cannot be rejected.
The average of

**S&P 500-ETFPBJ's**population is assumed to be

**equal to**the μ0. In other words, the difference between the average of

**S&P 500-ETFPBJ**and the μ0 is not big enough to be statistically significant.

**The p-value equals**

__2. P-value__**0.2005**, ( p(x≤T) = 0.8997 ). It means that the chance of type I error, rejecting a correct H0, is too high: 0.2005 (20.05%). The larger the p-value the more it supports H0.

**The test statistic T equals**

__3. The statistics__**1.2825**, which is in the 98% region of acceptance: [-2.337 : 2.337]. x=0.001, is in the 98% region of acceptance: [-0.00186 : 0.00186]. The standard deviation of the difference, S' equals 0.000796, is used to calculate the statistic.

**The observed effect size d is**

__4. Effect size__**small**,

**0.068**. This indicates that the magnitude of the difference between the average and μ0 is small.

### What does this mean, simplistically? S&P 500 and Invesco Dynamic Food & Beverage ETF (PBJ) have statistically similar returns?

This means the returns of the two, S&P 500 and Invesco Dynamic Food & Beverage ETF (PBJ), are statistically the same. Statistically, one does not have a higher return than the other; however, small, incremental movements in S&P 500's favor have resulted in a higher long-term growth rate for the S&P 500.

### Key takeaway and tactical information

PBJ doesn't present a very tempting case in all assessments conducted. The variance, as tested by the F test is the same as that of the S&P 500, and that means, the two have similar risk, statistically. Furthermore, the weekly returns of the two are statistically the same; however, the S&P 500 has a superior yearly growth rate, at about 5% higher than that of PBJ, for the time period observed.

On the other hand, the beta of Invesco Dynamic Food & Beverage ETF (PBJ), stand at 0.7, which does represent a lower covariance compared to some other essential sectors, even pharmaceuticals (beta of pharmaceuticals stands at 0.91 Link), Hospitals/Healthcare Facilities (beta of Hospitals/Healthcare Facilities stands at 1.28 Link), and Trucking (beta of Trucking stands at 1.11 Link). The results, however, aren't, let's say, 'extraordinary,' compared to other options out there that may ensure better capital protection in a market crash or severe recession. For example, ownership and financial operation of farmland at scale comes to mind (see: Is Farmland a Good Investment?). Nonetheless, complex investment strategies and options that require scale operations may not be an option for everyone

In a crash, we should expect Invesco Dynamic Food & Beverage ETF (PBJ) to fall 30% less than the overall market of S&P 500. Nevertheless, this cannot be classified as 'recession proof' as investors are still likely to suffer considerable losses if the overall market crashes. For a 35% crash, which is very realistic, PBJ is expected to crash about 25%. This does provide some protection, yet it isn't significant.

Broadly thus, taking into consideration the overall risk, returns, and qualitative factors, a strong case cannot be made for PBJ, presently.

Active investors can formulate better strategies for protecting their portfolios, or even profiting from a decline when the market does crash. On the other hand, for a passive portfolio, the difference or level of protection that Invesco's PBJ provides, while considerable, isn't 'extraordinary.'

In terms of long-term strategic outlook, food as a sector isn't very exciting either. While it may be argued that it is supposed to be a conservative, low-risk sector, there are, however, other conservative, low-risk sectors, that we can expect a higher growth from, for example, the energy sector, pharmaceutical, and telecom.

For a passive portfolio, if an investor is creating a low variance or low-risk, sub-portfolio, then certainly, PBJ may be included in the sub-portfolio for achieving higher diversification. This approach would be sensical.

However, allocating a large portion of the primary portfolio to PBJ, even for risk mitigation, does not make much economic sense or strategic sense. The F test reveals a risk profile for PBJ that is statistically similar to that of the S&P 500, and the paired variance test reveals that the returns are statistically similar to the S&P 500.

It does have a low beta, and therefore, it may be added to a low-risk sub-portfolio for diversification; however, in terms of allocations for the main portfolio, it doesn't stand out as an attractive opportunity and, therefore, presently, we cannot recommend it as an investment that should be given a higher allocation.

Conservative investors should note that with a beta of 0.7, Invesco Dynamic Food & Beverage ETF (PBJ) is not recession or market crash proof; if that is the primary objective, then it is best to look at alternative hedging strategies for capital protection. The best application for PBJ is to be part of a low-risk sub-portfolio.

Finally, due to recent expansionary monetary policy, with an unprecedented increase in the money supply, concerns of long-term secular inflation are becoming very real. Price increases of essential items also seem likely, therefore. As an essential item in the consumer basket, inflation may not impact consumer demand for this sector, but it is very likely to impact non-essential sectors.

Logically, that means that more of the disposable income of people may go towards essentials, and the sector in question thus may see an elevated level of revenues, which may aid in long-term stock price appreciation at a higher rate compared to non-essential sectors

### Data:

**Holdings (4/30/21) (excel file. Source: Invesco) **

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