Which stock market index/Index based ETF is likely to fall the most in a crash?

**150 years of combined data examined**

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Diversification and overvaluation concerns have moved investors to allocate capital into a wide variety of indices in the US and abroad through ETFs, etc. However, not all indices are equal when it comes to risk exposure. This report analyzes which stock market index from the most prominent indices from around the world is the riskiest investment.

The following indices are evaluated in this report (as ETFs based on these indices are derivative products based on the underlying components of the indices evaluated here, they are also examined here indirectly):

1. S&P 500 (SPX) | SPDR S&P 500 ETF Trust. Symbol: SPY

2. Nasdaq Composite Index (IXIC) | Fidelity Nasdaq Composite Index ETF. Symbol: ONEQ

3. Dow Jones Industrial Average (DJI) | SPDR Dow Jones Industrial Average ETF Trust. Symbol: DIA

4. MSCI EAFE (EFA) | iShares MSCI EAFE ETF. Symbol: EFA

5. Nikkei 225 (N225) | iShares Core Nikkei 225 ETF. Symbol: 1329 (TSE}

6. DAX— Deutscher Aktien Index (GDAXI) | iShares Core DAX® UCITS ETF. Symbol: DAXEXx

7. FTSE 100 (FTSE) | iShares Core FTSE 100 UCITS ETF. Symbol: ISF

8. CAC 40 (FCHI) | Lyxor CAC 40. Symbol: CAC

9. S&P TSX (GSPTSE) | iShares Core S&P/TSX. Symbol: XIC

10. IBEX 35 (IBEX) | Lyxor IBEX 35 (DR) UCITS. Symbol: LYXIB

The value at risk (VaR), mean confidence intervals, mean returns, worst & best monthly returns, sample standard deviations, and variances of the 10 indices are calculated and examined for this analysis.

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

**Data and calculations: **

F-test calculations are included at the end of the report.

## So, what does the data reveal?

Important individual parameters are discussed first, and an amalgamated view is provided in the end:

### Mean returns & monthly growth rate (geometric mean)

Out of the 10 most prominent indices analyzed, IBEX 35 has the lowest monthly mean returns, standing at 0.001% pm; the second-worst monthly returns are of FTSE 100 index, at 0.18% pm, followed by MSCI EAFE at 0.25%.

The best monthly mean returns are of Nasdaq (IXIC), at 1.20% pm, followed by S&P 500 at 0.78%, and Dow Jones (DJI) at 0.70% pm, respectively.

These are the average monthly returns, i.e., the mean of all months observed in the sample per index.

In terms of monthly growth rate (geometric mean), IBEX 35 has the worst monthly growth rate at -0.211%, followed by FTSE 100 at 0.0974%, and MSCI EAFE at 0.122%.

The highest monthly growth rate is of Nasdaq (IXIC), standing at 1.06%, the second-best being that of S&P 500 at 0.673%, and the third-best being that of Dow Jones (DJI), at 0.62%.

This rate is the long-term monthly growth rate, i.e., the compounded rate that would yield the observed capital appreciation.

### Best & worst monthly returns

This parameter identifies the best and worst monthly returns of the 10 indices, as per the monthly data of 15 years per index, and 150 years altogether.

Nikkei 225 has had the worst monthly capital loss of -23.83%, followed by IBEX 35 at 22.21%, and MSCI EAFE at 20.24%.

The indices **with the lowest decline in the worst months** in the data are FTSE 100, at 13.81, Dow Jones (DJI), at 14.1%, & S&P 500 at 16.94%.

The best monthly returns are that of IBEX 25 of 25.18%, CAC 40 at 20.12%, and DAX (GDAXI) at 16.8%.

### Mean Confidence Interval—the range of returns

This parameter measures a range of possible future values likely to be observed, as per a specific confidence level. The confidence level used here is 95%, i.e., statistically, 95% of future observed values should fall in this range, as per the data observed, if future values fluctuate in the historically observed range.

The broadest range is that of IBEX 35 with a 95% confidence interval standing at 0.87% upper limit to -0.87% lower limit, followed by Nikkei 225 with a 1.28% upper limit to -0.36% lower limit, and DAX (GDAXI) with a 1.5% upper limit to -0.10% lower limit.

**The indices with the highest lower limit of the monthly returns** as per the 95% CI analysis are Nasdaq (IXIC) at 0.45%, S&P 500 at 0.13%, & Dow (DJI) at 0.10%; this means that as per the data, the lower limit of the per month returns, 95% of the time, shouldn’t be lower than these values. Nonetheless, there is, of course, a 5% probability of returns being much worse than the values presented here; worse returns than the values given here are also observed in the data.

### Sample standard deviation (SSD) & variance of returns

Sample standard deviation and variance of returns essentially measure the variance of returns from the mean, with a low value indicating that the returns observed in the past (in the data set) tend to be close to the mean, and a high value indicating that the dispersion of the observed value from the mean is high. Variance and sample standard deviation are commonly used in practice to measure the risk of a particular security or portfolio(s).

As per the data analyzed, IBEX 35 has the highest Standard Deviation of returns, at 5.93%, followed by Nikkei 225 at 5.5% and DAX (GDAXI) at 5.4%; F-test (a statistical variance test used to assess risk) conducted on the three, aforementioned, confirms that the risk profile of the three indices with the highest SSD is statistically equivalent, i.e., their risk profile is statistically similar.

The indices with the lowest sample standard deviation are S&P/TSX at 3.92%, FTSE 100 at 4%, and Dow (DJI) at 4.2%; F-test conducted on these three also confirms that their risk exposure is statistically similar, i.e., they have statistically similar risk exposure; lowest amongst the indices observed.

### Value at Risk—VaR

One of the most important parameters for investors is the value at risk, or how much money they can lose by investing in a particular security. If an investor is deciding which index they should invest in, say, through an ETF, one of the most important questions on their mind should be: how much money can I lose? Investors prefer a quantification of losses with a data-derived probability attached with the risk value.

VaR, fundamentally, is the assessment/evaluation of possible losses based on historical data, at a given confidence interval (CI) & for a specific period. For example, a VaR calculated at 98% CL would indicate a value that possible future loss should be lower than or equal to, for a given confidence level; i.e., if a portfolio has a VaR of $10 per month with a 98% CL, then losses 98% of the time, as per the data, should be lower than or equivalent to $10.

This parameter does not provide an absolute guarantee, however. For example, with a 98% confidence level for a VaR figure of $10 in the above-stated example, there would still be a 2% probability of losses exceeding $10; thus, an intelligent investor should possess the commonsense & understanding that in that scenario, in the absolute worst imaginable case, they can lose 100% of their investment. The 2% probability of losses exceeding $10 should be used as an analytical risk probability of worst-case, i.e., losses of over $10 in our example, with a maximum upward limit, of course, of 100% loss.

Coming back to data assessment: the VaR analysis confirms that as per the data, IBEX 35 exposes investors to the risk of highest possible losses per investment of 12.8% per month and 42.3% per year; this means that an investor that invests €1,000 in this index, as per the assessment, can lose €121.8 pm, and €423 per year. This also means that investors in this index, 95% of the time, as per the data, can experience losses lower than, or equal to, 12.8% pm & €423 per year; with a 2% probability of losses being higher than these figures.

The second highest VaR figure is for Nikkei 225, with a monthly VaR percentage standing at 11% and a yearly figure standing at 37.82%; i.e., per ¥1,000 invested in this index, an investor can lose an amount equal to, or lower than, ¥110 pm and ¥378.2 per year, and there is a 98% probability that losses shouldn’t exceed these figures for the given periods.

The third highest figure is for DAX (GDAXI), with a monthly VaR percentage of 10.41% and a yearly VaR percentage of 36.1%. i.e., per €1,000 invested in this index, losses should be equal to or lower than €104.1 pm & €361 per year, as per 98% VaR.

On the other hand, the indices with the lowest monthly & yearly VaR are S&P/TSX, with a monthly VaR percentage of 7.67% & annual figure of 26.6%, followed by Dow (DJI), monthly VaR percentage of 7.99 & yearly figure of 27.7%, and FTSE with a monthly value for the same of 8.4% & annual value of 27.84%.

### The amalgamation of all factors analyzed

**The assessment of all factors confirms that the IBEX 35 is the riskiest stock index to invest in as per the data and comparison of the top 10 most prominent indices; the second riskiest index is Nikkei 225, and the third riskiest is DAX (GDAXI)—this is an assessment based on a number of factors such as sample standard deviation, the variance of returns, value at risk, range of returns, and impact on portfolio returns. **

**These three indices are also likely to fall the most in value, i.e., crash in a crisis period.**

Essentially, those wanting to diversify their portfolio or those building a diversified portfolio and considering the addition of international stock indices through ETFs, etc., should ideally avoid the riskiest indices/ETFs based on these indices unless they have a specific strategy that utilizes the highly amplified movements of these indices compared to others.

Those wanting to lower the correlations of returns of different allocation in their portfolio can achieve that objective through other indices/ETFs as these three names discussed do not seem ideal for, say, retail investors, retirees, or individuals willing to build a long-term portfolio.

Unnecessarily high-risk exposure can become a vector of high losses in distressed financial conditions; continual compounding of severe adverse events (losses) can destroy wealth rather than preserve or grow it.

### F-test Calculations

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