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DAX vs. S&P 500, Nasdaq: How much can you lose or gain by investing in DAX compared to U.S. Indices


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This report uses 45 years of data altogether to answer the following questions:


By investing in Deutscher Aktienindex (German stock index) (INDEXDB: DAX),

· How much money can you lose per year and per month? Put simply, an analysis of quantified capital risk.

· How much money can you expect to make by investing in this index? What is a reasonable yield on investment in this index?

· Is the performance of this index better or worse than the top American indices?


Investors are always on the lookout for reasonable opportunities for diversification for, say, lowering their portfolio's risk profile and improving yield on investment/returns. Investors interested in the German stock index can utilize this report to analyze the critical factors for making an allocation decision.


Those considering an allocation in the German stock index through ETFs, such as iShares Core DAX-UCITS-ETF (DE), Xtrackers DAX-UCITS-ETF, & Deka DAX-UCITS ETF, can also utilize the findings of this reports as the aforementioned ETFs follow the index analyzed here.


The following calculations are utilized in this report: mean returns, mean confidence intervals, worst and best monthly returns, variance and sample standard deviation, and correlations:



Key factors


As per the time series analyzed, the mean monthly return of DAX has been approximately identical to the average return of S&P 500, standing at about -10% lower than the returns of S&P. However, the returns have been about -40% lower than the average of monthly returns of Nasdaq. The German index's growth rate is observed to be about 19% lower than S&P & about 50% lower than Nasdaq. Currency fluctuations aren't of importance in this analysis as long-term EURUSD devaluation, 1991- 2021, is negligible (0.1%).


The correlation of returns of DAX with the S&P 500 stands at 0.81 & 0.79 with Nasdaq (IXIC). Thus, the returns are highly correlated.


Further hypothesis testing has been conducted for definitive answers below.

Pooled variance test:


DAX returns comparison S&P 500, DAX returns comparison Nasdaq composite index (IXIC), DAX pooled variance test

What does this mean, simplistically?


The difference between the German index & the U.S. indices' mean returns isn't statistically significant, i.e., one cannot be considered better than the other, as per a pooled variance test.


What about the risk?


The risk profiles are examined through a VaR calculation, which, essentially, provides a measure of the amount at risk as per a specific confidence level (98% CL Used here), sample standard deviation, and variance. Variance and standard deviation of returns are commonly used in practice for examining risk.


The Monthly VaR percentage for DAX stands at 10.4%, with the yearly figure standing at 30.7%; this means that per €1,000 invested in this index/ETF, losses, 98% of the time, should be less than or equal to €104.14 pm and €306.8. There remains a 2% probability, of course, of losses exceeding these figures.


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


As we can see, the VaR figure for the top index from Germany is comparable to the figures of Nasdaq, however, higher than the values for S&P.


Further analysis of the returns, through a F-test, is conducted below for definitive answers:


DAX risk compared to S&P 500, DAX risk analysis, DAX risk analysis compared to Nasdaq composite index (IXIC)

What does this mean simplistically?


While the VaR figures of the three indices are slightly different, the risk profile of DAX, as measured by variance, is comparable to the risk exposure of Nasdaq; however, it is higher than the risk exposure of the S&P 500. 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 the German stock index (yield)?


Mean confidence interval calculations have been utilized to evaluate potential returns with a 95% confidence level, as per the time series analyzed. An investor should expect monthly returns in the range of 1.5%, the upper limit, to -0.1% lower limit. Per €1,000 invested in DAX, an investor should expect returns in the range of €15 to -€1, with a five percent probability of losses or gains exceeding these figures.


The compound growth rate per year for this index stands at approximately 6.7% p.a. The worst monthly returns observed in the time series for this index equal -19.2% & the best monthly returns are observed to be 16.8%. See also: How long does a market bubble last on average?


Putting it all together


The returns and risk profile of DAX somewhat resemble the same of the Nasdaq Composite Index more than that of S&P500. Nonetheless, statistically, we cannot favor the American indices over the German one, as far as returns are concerned.


For long-term inclusion in the portfolio, investors should understand the future prospects of constituents of this index. Other than a few notable names that, have been and are making, considerable gains in emerging markets, where the potential of considerable growth lies, such as Adidas AG (ADS:GR), Daimler AG (DAI:GR), Merck KGaA (MRK:GR), Bayer AG (BAYN:GR), & Siemens AG (SIE:GR), the index doesn't contain names that may excite investors. Investors can also acquire such names individually, rather than buying an ETF based on the whole index, if they can actively make allocations.


The index also lacks tech names that may be considered as 'growth stocks' or names that may develop revolutionary technologies. In recent years, we have seen considerable capital appreciation of growth stocks, such as Amazon (AMZ), Apple (AAPL), Tesla (TSLA); such appreciations, arguably, occurred due to the positive future prospects of these companies (see a discussion on the creative destruction process for a further in-depth understanding of this point).


However, with a lack of growth stocks, and the prevalence of mature stocks, that make volatile moves as per economic and situational scenarios, one must consider that risk and returns ratio more carefully before making a significant allocation in the subject index.


In terms of diversification advantages, due to the high correlation of returns with the American indices examined (particularly with S&P), one cannot logically make a case strong case for an allocation in this index for overall risk reduction.


For diversifying exposure to different business models and segments of economic activity, there are other options available that offer better opportunities, for example, the Swiss market index (see report on Swiss market Index for a further evaluation); alternatively, building a portfolio of individual, attractive international names, arguably, is also a better option.


Investors concerned about stock prices being overvalued in the U.S., similarly, cannot allocate in this index as due to relatively strong correlation of returns with U.S. Indices, a crash or price readjustment event in the U.S. is likely to be similarly negative for DAX as it may be for the top U.S. indices examined in this report. See also: Why do all financial assets correlatively fall in a market crash


The overall condition of the top index of Germany doesn't present fundamentals that may be considered very attractive for long-term growth, therefore.


Investors bullish on the German economy, and the companies included in this index, can make an allocation in this index, nonetheless, in conjunction with allocations in other top indices; however, an allocation of more than 10% of the portfolio cannot be classified as highly warranted.