## Is ISEQ better than S&P 500 or Nasdaq Composite Index? 80 Years of Data Examined

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Allocation of capital, a critical concern in portfolio management, demands in-depth analysis. This report examines whether the Ireland Stock Market (ISEQ) is better than Nasdaq or S&P 500.

Proponents present a number of reasons why the ISEQ is better than the top US-based indices; however, only a rational analysis can extract inferences from data. Regardless of the proposed advantages or disadvantages of the three, this report relies solely on data to draw conclusions. 80 years of data has been analyzed in this report, for an in-depth and up to date analysis.

### So, what does the data reveal? Which is better, Ireland Stock Market, S&P 500, or Nasdaq?

First, we must consider the long-term growth rate (geometric mean) of the three for the last 3 decades (1991-2021):

**1. The long-term growth rate (geometric mean) of Ireland Stock Market (ISEQ) stands at 6.2% p.a. (EUR) (long-term currency fluctuation (EURUSD) from time-series 1991-2021 are negligible (0.1%), thus omitted) **** **

**2. The long-term growth rate (geometric mean) of Nasdaq composite index is 11% p.a. (USD)**

**3. The long-term growth rate (geometric mean) of S&P 500 is 10.2% p.a. (USD)**

It is evident that long-term growth rates are not similar; however, this parameter is very simplistic and does not take into account the long-term monthly movements that can help us ascertain any differences between the three, with significant nuance.

Jump to __Key Takeaways__

Hypothesis testing is employed in this report to gauge the returns and the risk, for equivalence. The pooled variance test and the F test is used for this analysis:

Pooled variance test is conducted as:

H0: µ1 -µ2 = 0, vs H1: µ1 -µ2 ≠ 0

The mean returns of Index 1 minus Index 2 (comparison) are analyzed for equivalence.

F test has been conducted as:

H0: σ1 = σ2, vs H1: σ1 ≠ σ2

The variance of the returns of Index 1 is compared to the variance of the returns of Index 2 (comparison) to assess equivalence.

### Analysis (difference of returns) (80 years of data analyzed in total)

ISEQ vs. S&P 500 (374 months of data analyzed for S&P 500, and 210 months for ISEQ)

Pooled variance test:

__Two sample t-test (pooled variance), using T distribution (DF=582.0000) (two-tailed) (validation)__

** 1. H0 hypothesis**
Since p-value > α, H0 is accepted.
The average of

**ISEQ'**population is considered to be

**equal to**the average. of the

**S&P 500's**population. In other words, the difference between the average of the two populations is not big enough to be statistically significant.

**p-value equals**

__2. P-value__**0.453394**, ( p(x≤T) = 0.226697 ). This means that if we would reject H0, the chance of type I error (rejecting a correct H0) would be too high: 0.4534 (45.34%). The larger the p-value the more it supports H0.

**The test statistic T equals**

__3. The statistics__**-0.750273**, is in the 98% critical value accepted range: [-2.3328 : 2.3328]. x1-x2=-0.0031, is in the 98% accepted range: [-0.009600 : 0.002290]. The statistic S' equals 0.00410

**The observed standardized effect size is**

__4. Effect size__**small**(0.065). That indicates that the magnitude of the difference between the average and average is small.

### What does this mean, simplistically? Is S&P 500 better than ISEQ?

There is no evidence with any statistical significance backing the assumption that the ISEQ's monthly returns are statistically different from S&P 500's monthly returns. The returns are statistically similar, and there is evidence supporting this conclusion.

### What about the risk? Is the risk of Ireland Stock Market and S&P 500 the same?

F test has been conducted for definitive answers:

__F test for variances, using F distribution (dfnum=209,dfdenom=373) (two-tailed) (validation)__

** 1. H0 hypothesis**
Since p-value < α, H0 is rejected.
The sample standard deviation (S) of ISEQ

**'S**population is considered to be

**not equal to**the sample standard deviation (S) of

**S&P 500's**population. In other words, the difference between the sample standard deviation (S) of the two populations is big enough to be statistically significant.

**The p-value equals**

__2. P-value__**0.000002984**, ( p(x≤F) = 1 ). It means that the chance of type I error (rejecting a correct H0) is small: 0.000002984 (0.0003%). The smaller the p-value the more it supports H1.

**The test statistic F equals**

__3. The statistics__**1.7482**, which is not in the 98% region of acceptance: [0.7481 : 1.3229]. S1/S2=1.32, is not in the 98% region of acceptance: [0.8649 : 1.1502]. The 98% confidence interval of σ12/σ22 is: [1.3215 , 2.3369].

### What does this mean, simplistically? Is Ireland Stock Market riskier than the S&P 500?

There is evidence with statistical significance backing the assumption that ISEQ's risk is different from the risk of the S&P 500, as measured by variance. It is riskier than the S&P 500, and the risk profiles are not similar; there is statistical evidence backing this conclusion.

ISEQ vs. Nasdaq (374 months of data analyzed for Nasdaq, and 210 months for ISEQ)

Pooled variance test:

__Two sample t-test (pooled variance), using T distribution (DF=582.0000) (two-tailed) (validation)__

** 1. H0 hypothesis**
Since p-value > α, H0 is accepted.
The average of

**ISEQ'S**population is considered to be

**equal to**the average. of the

**Nasdaq's**population. In other words, the difference between the average of the two populations is not big enough to be statistically significant.

**p-value equals**

__2. P-value__**0.196357**, ( p(x≤T) = 0.0981784 ). This means that if we would reject H0, the chance of type I error (rejecting a correct H0) would be too high: 0.1964 (19.64%). The larger the p-value the more it supports H0.

**The test statistic T equals**

__3. The statistics__**-1.293484**, is in the 98% critical value accepted range: [-2.3328 : 2.3328]. x1-x2=-0.0067, is in the 98% accepted range: [-0.01200 : 0.002290]. The statistic S' equals 0.00519

**The observed standardized effect size is**

__4. Effect size__**small**(0.11). That indicates that the magnitude of the difference between the average and average is small.

### What does this mean, simplistically? Is Nasdaq better than the Ireland Stock Market?

There is no evidence with any statistical significance backing the assumption that Ireland Stock Market's monthly returns are statistically different from Nasdaq's monthly returns. The returns are statistically similar, and there is evidence supporting this conclusion.

### What about the risk? Is the risk of Ireland Stock Market and Nasdaq the same?

F test has been conducted for definitive answers:

__F test for variances, using F distribution (dfnum=209,dfdenom=373) (two-tailed) (validation)__

** 1. H0 hypothesis**
Since p-value > α, H0 is accepted.
The sample standard deviation (S) of

**ISEQ'S**population is considered to be

**equal to**the sample standard deviation (S) of

**Nasdaq's**population. In other words, the difference between the sample standard deviation (S) of the two populations is not big enough to be statistically significant.

**The p-value equals**

__2. P-value__**0.06899**, ( p(x≤F) = 0.0345 ). It means that the chance of type I error, rejecting a correct H0, is too high: 0.06899 (6.9%). The larger the p-value the more it supports H0.

**The test statistic F equals**

__3. The statistics__**0.7974**, which is in the 98% region of acceptance: [0.7481 : 1.3229]. S1/S2=0.89, is in the 98% region of acceptance: [0.8649 : 1.1502]. The 98% confidence interval of σ12/σ22 is: [0.6028 , 1.0659].

### What does this mean, simplistically? Is Nasdaq riskier than the Ireland Stock Market?

There is no evidence with any statistical significance backing the assumption that the variance of the Nasdaq is different from the variance of Ireland Stock Market. The two have similar variance, and there is no statistical evidence to support that monthly returns of one have a different level of risk compared to the other.

For risk-adjusted returns of indices analyzed in this report, i.e., returns offered per unit risk & other diversification concerns, see our report: Which stock indices/index-based ETFs provide the best risk-adjusted returns

### Key Takeaways

Analysis of over 80 years of combined data reveals that the monthly returns of the three indices in question are statistically identical. Statistically, one cannot be crowned as 'better than others,' as far as monthly returns are concerned.

The risk, however, as measured by variance, is a slightly different story; ISEQ has a higher variance compared to S&P 500, but statistically similar monthly returns compared to S&P 500 & Nasdaq. The risk profile of ISEQ is similar to that of Nasdaq.

The long-term yearly growth rate comparison, in the first part of this report, does present a discrepancy; ISEQ has a long-term growth rate of 6.2%, which, of course, is lower than that of S&P 500 and Nasdaq.

Considering the risk profile of ISEQ being higher than that of S&P 500, but equivalent to that of Nasdaq, the risk parity theory would prescribe: 1. ISEQ's returns should increase over time, so the long-term growth rate (geometric mean), equals that of Nasdaq, or 2. The risk, as measured by variance, of ISEQ should decline, for the risk returns relation to have equivalence with that of Nasdaq, for example.

Alternatively, it is also possible that the difference in long-term growth rates is because of a temporary boom in asset prices in the US, caused by the dovish approach by FED, combined with the expansionary fiscal policy. Asset prices could, 'readjust,' put mildly, in the US. In the Long-term, this may result in the returns of the Nasdaq, for example, to be on par with ISEQ's returns.

Furthermore, presently, it should also be noted that the long-term GDP growth observed in the Irish economy may seem enticing. An investor may assume that the impressive GDP growth long-term in the Irish economy may result in impressive growth in the country's stock index; however, this is not likely.

Ireland is used by a number of international organizations (primarily North American organizations) as a sub-operational jurisdiction to reduce their tax liabilities (tax haven, simplistically). Long-term analysis of the growth of corporate profits and corporate tax collected, reveals a growth rate that is lower than the GDP growth rate in Ireland. This condition is established by observing the difference between Irelands GDP and GNP, which in 2019 was about 19%.

The difference in the GNP and GDP means that foreign domiciled agents in Ireland contribute to what is registered as 'Irish productivity,' thus, this productivity is included in the Irish GDP; however, it is productivity attributed to foreign agents and, therefore, not included in Irelands GNP, but in the GNP of the foreign agents' home countries.

While the GNP to GDP ratio of Ireland has been improving, Ireland's GDP growth rate, as an indicator, still is not one to rely on to forecast the long-term appreciation of the Irish stock index in question.

Presently, therefore, recommending the ISEQ is not a possibility. ISEQ has demonstrated a higher level of variance (risk), compared to the S&P 500, but a slightly depressed long-term growth rate compared to both Nasdaq and S&P 500.

There is a possibility of downward asset-price readjustment in the US indices, so the long-term growth rate readjusts on par with that of ISEQ. Nonetheless, the US indices, frankly, have names that can still be considered exciting, with a possibility of 'leapfrogging' innovation coming from these names, especially in tech. This is not the case with the ISEQ.

In conclusion, while the risk of a significant price readjustment for the US indices seems to be closing, it still does not warrant choosing ISEQ, presently. Internationally, other opportunities do present exciting prospects, with reasonable valuations; for example, emerging Asian tech companies, etcetera.

Therefore, in conclusion, the ISEQ does not present an opportunity that can be classified as exciting, and logical reasoning cannot be devised to allocate, more than 5% of a portfolio, to ISEQ. Other international opportunities present better opportunities, if international exposure is the fundamental objective.

### Excel Data:

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