### 90 years of data analyzed in total

*Summary: *

*1. Data analysis reveals that monthly returns of Hang Seng, Nasdaq and S&P 500 have been statistically similar.*

*2. Risk profile of Hang Seng is not the same as S&P 500, Hang Seng is riskier.*

*3. Risk profile of Nasdaq and Hang Seng is similar*

*4. Hang Seng, in the long-term, is likely to see a slight improvement in monthly returns, or a reduction in variance (risk)*

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### Allocation of capital, a critical concern in portfolio management, demands an in-depth analysis. The question this report examines is whether Hang Seng is better than Nasdaq or S&P 500.

Proponents present a number of reasons why the Hang Seng (HSI) 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. 90 years of data has been analyzed in this report, 3 decades each per index, for an in-depth and up to date analysis.

### So, what does the data reveal? Which is better, Hang Seng, 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 Hang Seng is 6.95% p.a. (currency fluctuations can be ignored due to a linked exchange system in Hong Kong)

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

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

Right of the bat, we can see some difference in long-term growth rates; 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 of difference (returns and risk), Hang Seng, S&P 500, and Nasdaq **

### Hang Seng vs. Nasdaq (374 months of data analyzed)

Pooled variance test:

__Two sample t-test (pooled variance), using T distribution (DF=746.0000) (two-tailed) (validation)__

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

**HSI'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__**0.614687**, ( p(x≤T) = 0.307344 ). This means that if we would reject H0, the chance of type I error (rejecting a correct H0) would be too high: 0.6147 (61.47%). The larger the p-value the more it supports H0.

**The test statistic T equals**

__3. The statistics__**-0.503605**, is in the 98% critical value accepted range: [-2.3314 : 2.3314]. x1-x2=-0.0024, is in the 98% accepted range: [-0.01100 : 0.001785]. The statistic S' equals 0.00483

**The observed standardized effect size is**

__4. Effect size__**small**(0.037). That indicates that the magnitude of the difference between the average and average is small.

The null is not rejected, therefore.

### What does this mean, simplistically? Is Nasdaq better than Hang Seng?

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

### What about the risk? Is the risk of Hang Seng and Nasdaq the same?

F test has been conducted for definitive answers:

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

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

**HSI'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__**0.04166**, ( p(x≤F) = 0.9792 ). It means that the chance of type I error, rejecting a correct H0, is too high: 0.04166 (4.17%). The larger the p-value the more it supports H0.

**The test statistic F equals**

__3. The statistics__**1.2352**, which is in the 98% region of acceptance: [0.7856 : 1.273]. S1/S2=1.11, is in the 98% region of acceptance: [0.8863 : 1.1283]. The 98% confidence interval of σ12/σ22 is: [0.9704 , 1.5724].

The null is not rejected, therefore.

### What does this mean, simplistically? Hang Seng is riskier than Nasdaq?

There is no evidence with any statistical significance backing the assumption that the variance of Nasdaq is statistically different from the variance of Hang Seng. 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.

### Hang Seng vs. S&P 500 (374 months, or more than three decades of data analyzed)

Pooled variance test:

__Two sample t-test (pooled variance), using T distribution (DF=748.0000) (two-tailed)(validation)__

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

**HSI's**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__**0.774412**, ( p(x≤T) = 0.612794 ). This means that if we would reject H0, the chance of type I error (rejecting a correct H0) would be too high: 0.7744 (77.44%). The larger the p-value the more it supports H0.

**The test statistic T equals**

__3. The statistics__**0.286712**, is in the 95% critical value accepted range: [-1.9631 : 1.9631]. x1-x2=0.0012, is in the 95% accepted range: [-0.008200 : 0.001288]. The statistic S' equals 0.00420

**The observed standardized effect size is**

__4. Effect size__**small**(0.021). That indicates that the magnitude of the difference between the average and average is small.

The null is not rejected, therefore.

### What does this mean, simplistically? Hang Seng does not yield a higher return, compared to S&P 500?

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

### What about the risk? Is the risk of Hang Seng and S&P 500 the same?

F test has been conducted for definitive answers:

__F test for variances, using F distribution (dfnum=374,dfdenom=374) (two-tailed) (validation)__

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

**HSI'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**, ( 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.

**The test statistic F equals**

__3. The statistics__**2.7081**, which is not in the 98% region of acceptance: [0.7858 : 1.2726]. S1/S2=1.65, is not in the 98% region of acceptance: [0.8865 : 1.1281]. The 98% confidence interval of σ12/σ22 is: [2.1281 , 3.4462].

__F test for variances, using F distribution (dfnum=374,dfdenom=374) (right-tailed) (validation)__

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

**HSI's**population is considered to be

**greater than**the sample standard deviation (S) of

**S&P 500's**population.

**The p-value equals**

__2. P-value__**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.

**The test statistic F equals**

__3. The statistics__**2.7081**, which is not in the 98% region of acceptance: [-∞ : 1.2371]. S1/S2=1.65, is not in the 98% region of acceptance: [-∞ : 1.1122]. The 98% confidence interval of σ12/σ22 is: [2.1892 , Infinity].

### What does this mean, simplistically? Is Hang Seng riskier than S&P 500?

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

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 from the analysis

In-depth data analysis reveals that the monthly returns of HSI, S&P 500, and Nasdaq are statistically identical; there is no statistical evidence backing the assumption that one yields a higher monthly return than the other. However, risk is a slightly different story.

The risk associated with monthly Nasdaq returns is statistically similar to the risk associated with the monthly returns of HSI, as measured by the variance of the returns of 60 years of combined data analyzed. But the risk associated with monthly S&P 500 returns is not statistically similar to the risk associated with the monthly returns of HSI; HSI is riskier than the S&P 500, but its risk profile is identical to that of Nasdaq.

In conclusion, the data analysis reveals that long-term, the geometric growth rate of HSI has been slightly depressed, compared to Nasdaq and the S&P 500; yet it is somewhat riskier, as its variance has been higher than that of S&P 500.

Applying the risk parity theory, we can state that in the long run, 1. the returns of HSI should appreciate at a slightly elevated level than historic returns, or 2. The variance of returns, or risk, should reduce.

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 HSI's returns.

Presently, nonetheless, recommending HSI is not an option; there is political turmoil in the Hong Kong region, which can negatively impact the market in the long run. Also, even with a brief period of political normalcy, the possibility of the re-emergence of political turmoil in the region remains high; this condition increases HSI's risk, as gauged qualitatively. Thus, currently, Nasdaq and S&P 500 appear more accessible, manageable, and less risky.

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