The S&P 500 has been plummeting this month, following a strong rally since the start of this year, while the safe-haven asset ‘gold’ has been rising higher. Regardless of a dovish Fed, the Treasury market is still exhibiting worrisome economic signals, as the yield curve remains relatively flat, while certain sections have already inverted, such as the 10yr yield falling below the 6-month yield. The most widely watched section of the yield curve is the 2yr/10yr section. An inversion at this section is considered a recession-harbinger, which encourages certain investors to turn more bearish on equities and instead increase exposure to safe-haven assets, including gold. Gold is a common asset class used as a hedging vehicle within investment portfolios.This article assesses the 12-month performances of both the S&P 500 and gold, following the previous six 2yr/10yr inversions, to help determine how investors should position themselves this time round in the event that the 2yr/10yr section of the yield curve inverts again. While such an inversion would signal a recession ahead, the S&P 500 could still offer more attractive returns than gold even amid rising economic concerns.
Performance trends in both asset classes
The table below exhibits the 12-month performances of the S&P 500 and gold following the previous six inversions at the 2yr/10yr yield curve section. The average, standard deviation, and range have also been calculated for the historical returns.
Note: Returns collated using data from Yahoo Finance and World Gold Council.
Contrary to the beliefs of risk-averse/bearish investors, the S&P 500 offers better return potential than safe-haven asset ‘gold’ following 2yr/10yr inversions. The S&P 500 not only has a higher average return at 9.71%, but its distribution of returns also offers a lower standard deviation and a narrower range of returns. The returns of gold are much more widely spread out, ranging from 50.98% to -32.67%, making it harder for investors to gauge its potential future performance based on historical trends.
Nevertheless, the returns of the S&P 500 still hold quite a high standard deviation and range, and we must further evaluate to determine how effective this average return is at reflecting genuine future performance potential.
Assessing how well our returns data fit a normal distribution allows us to uncover insightful characteristics about our dataset and evaluate how useful our data is to base investment decisions upon.
Note that one of the appealing features of a normally distributed dataset is that the average (mean) return holds the highest probability of occurring, with the standard deviation determining how confidently/accurately we can gauge the range of potential future returns based on the average return and historical data overall. Furthermore, if the returns data were to approximately follow a normal distribution, then the mean return and standard deviation could be used to determine the probability densities for obtaining specific returns for both our asset classes, and thus would allow us to incorporate these statistical characteristics into prediction analysis.
Results from normality tests
Normality tests for the distribution of returns data, for both our asset classes (S&P 500 and gold), have been carried out using XLSTAT.
Various hypothesis tests are commonly conducted to determine whether our dataset follows a normal distribution or not. The Shapiro-Wilk test in particular is useful for assessing the normality of datasets with small sample sizes, like ours. The null-hypothesis for our test is that our dataset follows a normal distribution. The results from the Shapiro-Wilk Test can be found summarized below:
Metric | S&P 500 | Gold |
Test Statistic (W) | 0.86 | 0.99 |
Critical Threshold | 0.79 | 0.79 |
p-value (Two-tailed) | 0.18 | 0.99 |
Alpha | 0.05 | 0.05 |
The Test Statistics (W) are above the critical thresholds, and the p-values are above our significance level of 5% (0.05). This allows us to accept the null hypothesis for both our asset classes, that our datasets indeed follow a normal distribution. However, it is not sufficient to simply rely on such a hypothesis test to determine the normality of our dataset, we must also review the Quantile-Quantile plots (Q-Q plots) and Probability-Probability plots (P-P plots). The Q-Q plots and P-P plots for both our asset classes can be found below (generated using XLSTAT).
Ideally, for both the Q-Q plots and P-P plots, we would want to see the points fall on the y=x line. However, this is not the case for neither asset classes, suggesting that there are notable deviations between the normal distribution and the distribution of our sample observations.
In fact, the normal distribution histograms for both our asset classes below clearly reveal that our datasets do not follow a normal distribution.
Therefore, while the S&P 500 does indeed have a higher average return with a lower standard deviation (compared to gold), the lack of normality in the distribution of returns for both asset classes undermines the extent to which investors can expect the S&P 500 and gold to deliver returns close to their average historical returns.
However, even though the distribution of returns for both asset classes does not follow a normal distribution, the very statistics reflecting the lack of normality offer us useful insights into which asset class investors are better-off investing in following yield curve inversions.
Skewness and Kurtosis are two important statistics to consider when assessing the shape of the distribution for our data. Let’s consider skewness first.
While the skewness (relative to the normal distribution) for both asset classes is quite low, the S&P 500 holds a higher skewness than gold. This implies that following 2yr/10yr inversions, the returns for the S&P 500 are more positively skewed (relative to the mean return) than the returns for gold, which further undermines the case for allocating towards gold over the S&P 500 in such scenarios.
Both asset class returns hold negative kurtosises (relative to the normal distribution). Negative kurtosis is considered a reflection of extremely thin tails, implying that the extreme values of the distribution have a lower chance of occurring. The S&P 500 holds a lower kurtosis than gold, which implies that the extreme returns for the S&P 500 (both positive and negative) have a lower probability of occurring compared to the extreme returns of gold. When assessing kurtosis, it is useful to also incorporate the skewness for the data to determine whether our kurtosis values are favorable or not. We found that the returns of the S&P 500 are more positively skewed than the returns of gold. In fact, the histograms earlier reveal that for the gold returns distribution, all the values on the left of the mean return are negative returns, whereas for the S&P 500 returns distribution, there are negative as well as positive returns to the left of the mean return. Therefore, the fact that gold returns have a higher kurtosis than the S&P 500 returns (albeit negative) implies that the extreme negative returns of gold have a higher probability of occurring than the negative returns of the S&P 500. This offers another reason to undermine the strategy of holding gold over the S&P 500 following an inversion at the 2yr/10yr yield curve section. Note that the higher kurtosis of gold returns also implies a higher probability of extreme positive returns as well; however, the fact is that gold returns are notably less positively skewed (almost no skewness) than the S&P 500 returns and the less desirable returns profile to the left of the mean return (compared to the S&P 500) suggests that the higher kurtosis poses a greater risk of extreme downside returns than offering greater chances of extreme upside returns, in comparison to the distribution of S&P 500 returns. Thus, if the 2yr/10yr were to invert again going forward, these statistical revelations undermine the strategy of minimizing S&P 500 exposure and increasing gold exposure.
Bottom Line
Gold is a popular safe-haven asset to which investors tend to hold exposure to in varying proportions as part of their portfolios, commonly as a hedging vehicle. While certain risk-averse investors prefer to allocate more capital to gold as opposed to the S&P 500 following 2yr/10yr inversions amid fears of worsening economic conditions, there is statistical evidence supporting the case to hold more exposure to equities over gold. The precious metal does not necessarily offer more attractive returns than stocks following yield curve inversions; in fact, the asset class does not even guarantee positive returns during the 12-month period following such events. From our assessment we found that during such periods, S&P 500 returns offer a higher average return (9.71% vs. 8.71%), lower standard deviation (13.78% vs. 29.38%), and more positively skewed returns (0.23 vs. 0.05) compared to gold.
Nevertheless, there are still chances of gold potentially outperforming the S&P 500. As always, investors should incorporate these statistical findings with other factors (specific to the relevant time period) that influence the performance of both asset classes. For the S&P 500, investors should take into consideration fundamentals such as equity valuations, earnings growth rates and earnings forecasts to determine whether to continue holding exposure to the index once the 2yr/10yr section has inverted. For gold, one should evaluate factors such as the supply/demand dynamics and the value of the US Dollar (as it is a dollar-denominated commodity) following an inversion.
The current spread between the 2yr and 10yr yield stands at about 16 basis points (at time of writing), and there is certainly a chance of inversion at this section going forward. Based on the statistical findings from this research, investors should not naively shift towards the safe-haven gold following such an inversion, as the S&P 500 could certainly still outperform the precious metal. If and when this inversion takes place, investors should evaluate the fundamentals of both asset classes (as explained above) to ensure they don’t miss out on potential higher returns in the S&P 500 over gold.
Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.