### ISF vs. CSSMI, INDEXFTSE: UKX vs. INDEXSWX: SMI

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Which index is more profitable and a better European investment? Is it the premier British index or the premier Swiss index? To answer these questions, this report analyzes whether the Swiss market Index is a better investment compared to the FTSE 100 Composite Index, United Kingdom's biggest stock index.

Proponents of both present qualitative factors as to why one is better than the other; however, data-derived insights are, of course, more valuable than anecdotes. Thus, this report utilizes 60+ years of data altogether (3+ decades per index) to determine whether one has evidently better returns or lower risk compared to the other.

Hypothesis testing has been conducted in this report for the analysis: A pooled variance test has been conducted for returns, and an F test has been conducted to assess risk.

## So, what does the data reveal?

First, we must consider the long-term growth rate (geometric mean) for the last 3 decades (1988-2021):

**1. The long-term growth rate (geometric mean) of the Swiss Market Index is 6.5% p.a. CHF (8.15%, factoring in USD long-term depreciation against CHF of 1.6% p.a.)**
**(8.46% p.a. in GBP, factoring in GBP long-term decline against CHF of 2.06% p.a.) **

**2. The long-term growth rate (geometric mean) of the ****FTSE 100 index ****is 4.3% p.a. (3.55% in USD, factoring in USD long-term appreciation against GBP)**
** (2.24% in USD, factoring in USD long-term appreciation against GBP)**

**Key Takeaways**

The analysis reveals that the monthly returns of the SMI are statistically identical to the returns of the FTSE100; the risk, as measured by variance, of the returns of the two is also similar, statistically. The data analysis reveals that, statistically, one cannot be considered better than the other, considering the performance of the last 3.4 decades.

Nonetheless, practically, the geometric mean of the SMI is superior. Furthermore, factoring in the exchange rate, CHF/USD or GBP/CHF, SMI's long-term growth rate is revealed as considerably higher than that of ^FTSE, when measured in USD, CHF, or GBP due to the yearly appreciation of CHF against the USD, and GBP, and the poor long-term performance of GBP.

In conclusion, data analysis reveals that the long capital growth rate of SMI, as measured by geometric mean, has been superior to FTSE100's growth rate for the last 34 years. Adjusted for currency fluctuations, the SMI has a far superior returns due to GBP's depreciation against CHF and USD.

On the other hand, the monthly variance of returns, the risk, of the two is comparable and statistically equivalent.

**Further Critical factors**

"The SMI does provide good international exposure through stable names such as Nestlé, Lonza group, Novartis, Roche holdings, etc., its international exposure, thus, is impressive. Nonetheless, FTSE100 also includes renowned names with substantial international exposure; for example, Unilever, Royal Dutch Shell, GlaxoSmithKline, AstraZeneca, Vodafone, Standard Chartered, Rolls-Royce, Coca-Cola, etc.

^FTSE is heavy in the consumer staples sector, financial companies, health care, industrials, and energy. Other than health care, most of these sectors don't seem likely to see exponential growth that some other sectors, such as tech, etc., may see in the next decade.

Consumer staples-related brands, it is argued, may see a significant increase in revenues if apprehensions related to inflation, etc., are realized. Nonetheless, we must understand that inflation is also going to impact the costs of raw materials and supplies, as well as labor costs; all in all, consumer staple brands aren't likely to significantly improve their profits in an inflationary environment due to supply and labor price increases.

For the energy and finance sector, many investors and analysts see limited long-term capital growth or firm-specific growth in the energy sector, for obvious reasons, as the world frantically moves towards renewables.

On the other hand, the finance sector is usually considered a high beta sector exposing investors to higher levels of upside or downside risk as the markets fluctuate. These two sectors combined have a weight of 28.6% in the top British index (finance and energy); in a post-pandemic world of low credit demand, and fervent and dynamic shift towards renewables, investors don't see these sectors as attractive investments presently.

A further point of importance here is the post-Brexit economic uncertainty. There is a potential of upside risk, and downside risk exposure as well. Most economic models are assumptions based, and the actual long-term performance of the British economy is still in question. This uncertainty does create a risk vector for British stocks and indices.

While some firms in ^FTSE are securely diversified in international markets and emerging markets, many are still dependent primarily on the British economy; economic turbulence of any sort may negatively impact the top British Index, therefore. This risk, of course, does not create significant uncertainty for Swiss firms.

Naturally, British investors, as an alternative, may be more drawn towards S&P 500. However, it must be understood that with a possibility of political turmoil or tensions internally, and with international adversaries like China, North Korea, or Iran impacting the major North American Indices, S&P 500 or Nasdaq composite Index may be more exposed and sensitive to geopolitical and internal risks compared to a Swiss index, and this factor must be taken into consideration for long-term allocations.

Thus, as an alternative, allocation in SMI, through iShares SMI ETF, does not seem illogical. Circumspection is very important, primarily proactively. If more than 35% of an investor's portfolio is allocated to British and North American indices, prudence would command lowering it to no more than 25%, and the SMI can play an important role there. Doing so would reduce exposure to geopolitical risks and other North America-specific idiosyncratic risks, and long-term economic risks that the UK is exposed to, presently.

For example, an investor with 35% or more of her portfolio allocated to British and North American Indices, should consider diversifying due to a build-up of a cluster of external and internal possibilities that can negatively impact the British and North American Indices.

While it is true that British economic deficiencies or turmoil in, or associated with North America, should substantially impact the SMI as well, as the SMI declined 53.42%, peak to troughs, in the 2008 financial crisis, and 21.6% in the 2020 market crash, compared to Nasdaq's similar decline of 52.1 for the 2008 financial crisis, and about 20% for the 2020 market crash, it is important to note that groups such as Nestle, Swatch, Lonza, Novartis, Roche, etcetera, are growing in multiple emerging economies.

Their growth and future prospects of growth in emerging economies are very much comparable to top names in, say, the S&P 500 and FTSE100 as well.

Nonetheless, both the SMI and FTSE100 lack clusters of impressive tech names that may hold the potential of exponential growth. Both indices lack a concentration of names that may be classified as 'capable of significant growth in the future,' as usually, it is the innovative, tech-related names that hold the potential of exponential growth, high p/e ratios, etc., that result in impressive capital growth for long-term investors.

Presently, it is worth noting that the US is the biggest export market of Switzerland.

Long-term, while the sensitivity of SMI to international financial fluctuations should remain present, the reliance of its constituents on North America should continue to decline. Thus, it does make sense to have some exposure to SMI.

However, exposure should be limited to below 15% in the overall portfolio, ideally around 10%, with the broader assumption being that SMI is a slightly 'mellower' version of a top global index, such as the S&P 500, with its constituents demonstrating healthy growth in emerging markets. The most prominent growth opportunity in FTSE100 is the health care and financial sector, arguably; however, we cannot expect exponential growth in these sectors long-term.

While SMI does include financial heavyweights, the financial sector makes up less than 15% of the index. Another point worth understanding is that while the two indices in question have statistically similar monthly returns and risk, the Swiss franc has appreciated at a long-term rate of about 2.6% p.a. (geometric mean), against GBP. Thus, the returns of the investor in the Swiss Index, when converted back (yearly) into GBP (or USD), would have gained through currency appreciation as well (with the investment denominated in CHF).

Without conversion back into GBP or USD, the currency difference, combined with the monthly returns, would compound, further increasing the returns of the British investor compared to the FTSE100.

All in all, the Swiss Market Index does present a good diversification opportunity for British investors and other international investors; its risk is comparable to the premier British Index, and it has names that are further penetrating emerging markets and have a healthy foothold in developed markets as well.

Allocation of 10% of the portfolio in the Swiss Market index, at the very maximum, would benefit an investor by providing a higher degree of international diversification, that too through solid names, reducing concentration of British and North American names in the portfolio" (see also:__ ____S&P500vsSMI__).

### Data and calculations

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.

### Pooled variance test

__Two sample t-test (pooled variance), using T distribution (DF=799.0000) (two-tailed) (validation)__

__1. H0 hypothesis__

Since p-value > α, H0 is accepted.

The average of **SMI's** population is considered to be **equal to **the average. of the **FTSE100's** population.

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

__2. P-value__

p-value equals **0.465766**, ( p(x≤T) = 0.767117 ). This means that if we would reject H0, the chance of type I error (rejecting a correct H0) would be too high: 0.4658 (46.58%).

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

__3. The statistics__

The test statistic T equals **0.729735**, is in the 98% critical value accepted range: [-2.3310 : 2.3310].

x1-x2=0.0022, is in the 98% accepted range: [-0.007000 : 0.001666].

The statistic S' equals 0.00301

__4. Effect size__

The observed standardized effect size is **small** (0.052). That indicates that the magnitude of the difference between the average and average is small.

### F test

__F test for variances, using F distribution (dfnum=400,dfdenom=399) (two-tailed) (validation)__

__1. H0 hypothesis__

Since p-value > α, H0 is accepted.

The sample standard deviation (S) of **SMI's** population is considered to be **equal to **the sample standard deviation (S) of **FTSE100'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.

__2. P-value__

The p-value equals **0.1131**, ( p(x≤F) = 0.9434 ). It means that the chance of type I error, rejecting a correct H0, is too high: 0.1131 (11.31%).

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

__3. The statistics__

The test statistic F equals **1.172**, which is in the 98% region of acceptance: [0.792 : 1.2626].

S1/S2=1.08, is in the 98% region of acceptance: [0.89 : 1.1237].

The 98% confidence interval of σ12/σ22 is: [0.9282 , 1.4798].

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