One shouldn't put all their eggs in one basket, but in which baskets to keep the eggs is a question that still remains in investment management.

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Investors are in a constant quest for alpha, i.e., returns above the performance of the benchmark index in their jurisdiction; this objective, coupled with the need for increasing overall portfolio resilience against adverse events, & lowering portfolio volatility in relation to returns, create a constant requirement for evaluating different options and achieving higher diversification.

Diversification is a fundamental requirement for reducing concentration risk and for ensuring that the investor(s) isn't overexposed to specific sectors, markets, or regions where a particular adverse event may severely impact the portfolio. Moreover, adequate diversification also helps in the lowering of the risk-return relationship of the portfolio if done appropriately.

While there are many more benefits of diversification proposed by academics & analysts, this work isn't about the benefits of diversification; the objectives of this work are very specific. This work analyzes which stock market index and ETFs based on them provide the best returns, bearing in mind the risk. Furthermore, which international index/ETF (from the top 15 indices) provides the best risk-adjusted diversification opportunity is also examined.

This work utilizes the Sharpe ratio, correlation analysis, and value at risk analysis for this examination.

In our report regarding the riskiest stock market indices & ETFs, we thoroughly examined the 'riskiness' of the top indices/ETFs, i.e., which are the riskiest and least risky constituents from the analyzed sample (see full report).

This work, however, does the opposite and evaluates the best opportunities available amongst the top, widely renowned options.
** Jump to **__findings__

### Methodology

The Sharpe ratio (calculated as [Average return of the subject – the risk-free return in the primary jurisdiction of the subject]/volatility (sample standard deviation), is used to evaluate which ETF/Index provides the highest returns per 1 unit of risk.
**A further clarification:
**If an asset provides 10% returns per period and has a volatility of 5% (i.e., typically, the asset provides returns between the range of 5% to 15%), the Sharpe ratio for such subject would be 2, i.e., for every 1 unit of risk, the asset provides 2 units of return, on average; thus, it can be classified as an attractive option.

On the other hand, if an asset provides an average return of, say, 10%, but the volatility of the asset during such period is 20%, the Sharpe ratio of the asset would be 0.5, i.e., on average, the asset provides 0.5 units of return per 1 unit of risk, and thus we can see the first asset, as per the volatility & returns, would be favored by analysts.

This method is used to evaluate the best ETF/Index, considering the long-term returns, risk (volatility), and the risk-free rate in the primary jurisdiction of the subject. For the risk-free rate, the 30-year treasury constant maturity rate is used per the subject's domicile (other than Brazil's Bovespa, for which a 10Y rate is used); for example, the US rate is used for the S&P 500, the Canadian 30-year treasury constant maturity rate is used for the Canadian index, and so on. ** **

Secondly, the correlation of each subject in the analysis is calculated in relation to the S&P 500, which, due to its prominence, is used as a quasi-benchmark. The Sharpe ratio (SR) figure is divided by the correlation of returns of the subject with the benchmark for the calculation of a ratio (described as RCD ratio).

This ratio, put simply, is an analysis of the risk-adjusted returns divided by the correlation of the subject with the S&P 500, i.e., the higher the SR of the assets per level of correlation with the benchmark, the higher the RCD ratio.

**A further clarification:
**

The higher SR figure is essentially a risk-adjusted return figure; dividing this figure by the correlation value gives us a correlation-adjusted return value that also integrates the risk of the asset. The higher this ratio is, the better the asset is for diversification; this is because an asset with a lower correlation with SP500 (the denominator in the equation [used as a benchmark in this work]), and a higher Sharpe ratio (numerator) would have a higher value than a compared asset that has a lower value numerator (SR) and a higher value denominator (correlation with the benchmark).

The third calculation used is a further finalizing risk adjustment where the previous ratio is adjusted for the VaR of the subject, i.e., the RCD ratio is divided by the value at risk figure (maximum expected losses as per a confidence level [95% used in this work]). This ratio further presents an adjusted value and enables the selection of the index with the highest SR, lowest correlation with the SP500, and lowest VaR. The third ratio is henceforth described at RCD-VAR ratio.

**A further clarification:
**

A subject with a high RCD ratio (numerator) and a low VaR value (denominator), would have a higher RCD-VAR value than an alternative with a low RCD ratio (numerator) divided by a high value at risk value (denominator).

Mathematically, the calculation, most simply, can be expressed as follows:

The results of the above-stated calculations identify the ETF/Index that yields the highest risk-adjusted returns & the best option for portfolio diversification.

Don't worry, the results are explained in simple terms, so a non-technical audience should not find it difficult to understand the findings of this work!

## Findings

Table 1. Results of calculations

### So which index or ETF provides the highest risk-adjusted returns?

The results indicate that, out of the 15 most widely recognized indices and ETFs based on them, the **Nasdaq Composite index (IXIC, ETF:ONEQ) provided the best risk-adjusted returns in the analyzed time-series of 15 years, with an SR value of 0.188, i.e., for every 1 unit of risk, this index provided 18% returns**.

**The second place goes to S&P 500 (ETF:SPY) with an SR of 0.121, and the third to Dow Jones (ETF:DIA) SR 0.111.**

**Outside the US, the DAX— Deutscher Aktien Index (ETF:DAXEXx), with SR value of .1051, stands out as providing the best risk-adjusted returns, as per the data analyzed (for an in-depth analysis of DAX, see our ****thorough report****. **

**The second place here goes to Korea Composite Stock Price Index KOSPI (ETF:EWY), SR of 0.0805, the third-place goes to Nikkei 225 (ETF:TSE 1329) with SR of 0.073 & the fourth to the Toronto Stock Exchange S&P/TSX (ETF:XIC), SR of 0.45) See our thorough ****report on S&P/TSX****).**

As we can see, other than the DAX, the performance of the international constituents of the analysis has been weaker than the American ones. Even the DAX has a considerably lower SR than that of Nasdaq (IXIC); Nasdaq's SR is 80% higher than DAX's, thus, a very substantial difference.

### Which is the best Index/ETF for diversification (amongst the topmost widely available fund), considering the risk and returns

In this section, the results of the RCD and the RCD-VAR ratios are discussed for the identification of best diversification opportunities amongst the most notable names analyzed in this work

As per the RCD-VAR ratio, again, Nasdaq (IXIC) emerges as the best opportunity with a value of 2.04; this means that the risk-adjusted returns of this ETF/index, further adjusted for correlation with the S&P 500 and the value at risk figure (95% confidence level), are the highest compared to others in the analysis.

The second place as per the RCD goes to Dow jones (DJII); note that the SP500, used as the benchmark here in the second part of the analysis, is excluded.

Nonetheless these numerical winners shouldn't be considered optimal for our analysis because (1) these are American indices & some stocks included in one US index may be included in others as well, thus doubling exposure unnecessarily. Furthermore, investors, for lowering exposure to the USA, may require international exposure & (2) the RCD-VAR ratio of the aforementioned is high due to high average returns, the correlation of the two, however, is still high.

**The best diversification-opportunities outside of the US:
**

The constituent with the RCD-VAR ratio (ratio value included in brackets next to the name of the constituent) outside the US are (1) DAX (1.24), (2) the Swiss Market Index SMI (ETF:CSSMI) (1.23), which is only fractionally behind DAX, (3) Korean KOSPI (1.19), (4) Nikkei 225 (0.94).

(for further in-depth reports of Swiss Market Index, see our section on SMI)

What this means, simplistically, is that taking into consideration the returns, volatility, correlation with SP500, and the value at risk of investing in the 15 constituents analyzed in this report, the 4 mentioned above stand out as optimal opportunities for allocation/adding to a long-term portfolio, as per the data analysis.

Allocations based on data are likely to produce better results than a simple qualitative analysis; furthermore, a data-analysis-supported model that includes qualitative analysis is likely to deliver the best results.

For example, the data-derived rankings for the best indices/ETFs are provided in this work, and a further integration of qualitative aspects with the insights provided here would be the best approach for planning & selecting diversification opportunities.

Qualitatively, we must consider whether the performance of the companies in the indices analyzed here are likely to perform, as they have in the past, or, due to impacts of emerging trends and business forces in the industries they operate in, their future performance is likely to deteriorate or improve, etcetera.

### Important considerations

One further issue that investors should understand is that while it is imperative to achieve adequate diversification, as explained in the first part of this work, there are, nonetheless, limitations of diversification.

For example, while diversification is likely to reduce the exposure to microeconomic risks (related to specific sectors, industries, or companies), idiosyncratic & regional risks, in a broader economic meltdown/crash, however, the correlation of almost all financial assets is observed to increase with each other, i.e., in an adverse economic environment/crash, all financial assets usually go down in value sharply.

Thus, while there are tremendous benefits of a diversified portfolio, diversification does not provide protection against a broader international financial crisis/meltdown, as observed during the 2020 period & the 2008 crisis, to name a few.

Another important point worth understanding is that ratios discussed in this work have limitations as well. If an asset has a negative average return, the Sharpe ratio and other methods discussed here don't provide any meaningful results; in that case, the analyst must increase or decrease the time-series analyzed for identifying a period that does present positive returns. Still, such a method wouldn't be ideal.

Furthermore, if the risk-free rate used in the analysis of a particular asset is higher than its average returns, the ratios applied in this work, as explained, would not yield meaningful results.

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