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This report utilizes data from the last decade and a half per index & 45 years in total to answer the following questions:

If you invest in the French stock index, CAC 40 (FCHI),

· How much can you lose per month & per year, i.e., what are the capital risks?

· How much can you expect to gain, i.e., what is a reasonable expected yield on investment?

· Is the performance of this index particularly better or worse than the S&P 500 and Nasdaq composite index?

Diversification and lowering the exposure to a particular index are crucial factors for reducing the overall risk exposure of a portfolio. Investors from North America thus have an interest in identifying other suitable indices for diversification, and international investors, similarly, evaluate whether they are getting a good deal with the index(es) that they hold in their portfolio.

The performances evaluated here is, of course, also applicable for the ETFs based on these indices, such as Lyxor CAC40 (CAC), Amundi-CAC40 ETF (C40), EasyETF-CAC40 (E40), DBXT CAC40 ETF (X40), HSBC-CAC40 ETF (EPA: K40), SPDR S&P-500 ETF Trust (SPY), & Fidelity Nasdaq Composite Index ETF (ONEQ).

The factors evaluated in this report are: value at risk (VaR), mean returns, mean confidence intervals, correlations, sample standard deviations, variances, & worst & best monthly returns.

Below, the results of the calculations are provided first, followed by an amalgamated discussion.

Results of calculations:

### Key takeaways

The mean monthly returns (average) of CAC, as per the time series analyzed, have been 64% **lower** than that of S&P 500 and 77% lower than that of Nasdaq. The French index's growth rate (geometric mean) has been 78% lower than that of S&P and 85% **lower **than that of Nasdaq. We can disregard currency fluctuation in this analysis as long-term EURUSD fluctuations, 1991- 2021, are negligible (0.1%). The correlation of CAC 40's returns is 0.81 with the S&P 500 & 0.77 with Nasdaq (IXIC).

### Risk

The sample standard deviation and variance of returns, which measure the dispersion of observed values from the mean, and used in practice for assessing risk, have been calculated/examined here to evaluate risk.

As per the data, the monthly & yearly percentage value at risk, i.e., the maximum amount you can lose as per the 98% confidence interval by investing in the French index is 10.7% pm & 34.5% p.a. This means that per €1000 invested in CAC 40, an investor may lose an amount less than or equal to €100.7 in a month & €349 per year, with a 98% probability attached. There remains a 2% probability of losses exceeding more than the aforementioned figures.

The VaR percentage for S&P 500 stands at 8.22% or $82.2 per $1000 pm & 28.5% p.a., or $284.6 per $1000. For Nasdaq (IXIC) the monthly figure is 9.17% or $91.7 pm and 31.8% p.a., or $317.5 yearly per $1000 invested.

As we can see, as per the VaR calculations, the French index exposes investors to higher risk than the two American indices; however, further statistical testing has been conducted below for definitive answers:

**F-tests, have been conducted to examine the risk further:**

### What does this mean, simplistically?

Even though we observed a difference in the risk value of the three through a VaR calculation, the French Index's risk is statistically identical to the risk profile of the two American indices compared, and statistically, CAC cannot be considered as having a lower or a higher risk profile than the risk profile of the American indices compared.

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

### How much can you gain by investing in CAC 40 (investment yield)?

As per the 95% mean confidence interval calculations, monthly returns 95% of the time, should fluctuate in a range of 1.02% to -0.46%. Per €1000 invested, an investor can expect to see returns in the range of €10.02 to €-4.6 per month; yearly, as per the long-term geometric mean, the growth rate (the expected appreciation rate) stands at 1.77%. This low rate is observed due to highly pronounced fluctuations in price movement.

For S&P, the expected monthly returns have a range of 1.42% to 0.13%; yearly expected returns stand at 8.4%. For Nasdaq, the monthly return range is observed to be 1.94% to 0.45%; the yearly figure stands at 13.5%.

Hypothesis testing has also been conducted for confirmation:

**Pooled variance tests:**

### What does this mean, simplistically?

Hypothesis testing confirms that the returns of the French index (FCHI) are statistically identical to the returns of the American indices compared. Statistically, therefore, we cannot favor the U.S. indices over the French one. However, practically, the American indices have demonstrated superior performance. See also: How long does a market bubble last on average?

### Putting it altogether

While statistically, we cannot favor one index in this analysis over others, practically, we must accept that the performance of the leading French index has been inferior to that of the U.S. indices. With many alternative options available for diversification, a strong case, strictly as per the data, cannot be made in favor of the French index examined.

The statistically insignificant differences observed can also compound over time, resulting in a lower yield. Thus, the French index in subject, cannot be recommended for an investor seeking an option to make a significant allocation for diversification.

In terms of constituents, there are some promising, stable names in the index that, long-term, are likely to perform strongly. Notably, companies such as L'Oréal, Carrefour, Orange, Michelin are making inroads in developing markets, with strong growth achieved in certain jurisdictions by these names. Nonetheless, an investor can acquire these names separately if she wishes to gain exposure to such names. Acquiring these names by acquiring a CAC40-ETF would expose the investor to names that might not be desirable and increase the overall risk exposure.

A further deficiency evident is a lack of stocks that may be classified as 'growth stocks.' Such stocks are usually in the tech sector; however, the CAC 40 lacks exciting names in the tech space that might be considered as working on—or capable of producing/introducing— revolutionary technologies.

This, of course, is not the case for the S&P 500 or Nasdaq composite index, as these indices are growth stock heavy. On the flip side, an investor may be concerned that growth stocks are overvalued, and thus, she may be looking for opportunities for diversification. It would be more suitable for such an investor to acquire individual attractive French stocks in conjunction with other attractive international names, as discusses above rather than an ETF; however, if this isn't possible, then perhaps, the ETF approach would be the only route left. Caution must be exercised, nonetheless, and the factors discuss in this report thoroughly reexamined

Presently, therefore, an allocation higher than 5% in the portfolio, at the maximum in this index, cannot be highly justified if the investor does not have a specific strategy that demands enhanced exposure to French stocks.

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