Diversification Archives

At what point does diversification becomes “Diworsification”?

December 1, 2025November 30, 2025 by Yann TANGUY

In this article, Yann TANGUY (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2023-2027) explains the concept of “diworsification” and shows how to avoid falling into its trap.

The Concept of Diworsification

The word “diworsification” was coined by famous portfolio manager Peter Lynch to denote the habit of supplementing a portfolio with investments which, instead of improving risk-adjusted return, add complexity. It demonstrates a common misconception of one of the fundamental pillars of the Modern Portfolio Theory (MPT): diversification.

Whereas the adage “don’t put all your eggs in one basket” exemplifies the foundation of prudent portfolio building, diworsification occurs when an investor adds too many baskets and thus loses sight of the quality and purpose of each one.

This mistake comes from a fundamental misunderstanding of what diversification actually is. Diversification is not a function of the quantity of assets owned by an investor but of the interconnections of assets. If an investor introduces assets highly correlated with assets owned to a portfolio, the diversification effect of risk is greatly reduced, and a portfolio’s possible return can be diluted.

Practical Example

Let’s assume there are two investors.

An investor who is interested in the tech industry may hold shares in 20 different software and hardware companies. This portfolio appears diversified on the surface. However, since all the companies are in the same industry, they are all subject to the same market forces and risks. In a decline of the tech industry, it is likely many of the stocks will decline at the same time due to their high correlation.

A second investor maintains a portfolio of three low-cost index funds: one dedicated to the total US stock market, another for the total international stock market, and a third focusing on the total bond market. Despite the simplicity of holding just these three positions, this investor enjoys a far more effective level of diversification in their portfolio. The assets, US stocks, international stocks, and bonds, have a low correlation with one another. Consequently, poor performance in one asset class is likely to be counterbalanced by stable or positive returns in another, resulting in a smoother return profile and a reduction in overall portfolio risk.

The portfolio of the first investor is a perfect case of diworsification. Increasing the number of technology stocks did not do any sort of risk diversification, but it introduced complexity and diluted the effect of performing stocks.

The point at which diversification began to operate to its own harm can be identified with several factors. Diversification’s initial goal is to improve the risk-adjusted return, a concept often evaluated using the Sharpe ratio. Diworsification begins when adding a new asset does not contribute to an improvement in the portfolio’s Sharpe ratio.

You can download the Excel below with a numerical example of the impact of correlation in diversification.

Here is a short summary of what is shown in the Excel spreadsheet.

We used two different portfolios, each with 2 assets and both portfolios having a similar expected return and average volatility of assets. The only difference is that the first portfolio has correlated assets, whereas the second portfolio has non-correlated assets.

Correlated portfolio returns over volatility

Non-Correlated portfolio returns over volatility

As you can see in these graphs, the diversification effect is much more potent for the non-correlated portfolio, leading to higher returns for a given volatility.

Target number of assets for a diversified portfolio

One of the most important considerations when assembling a portfolio is determining the optimal number of assets relative to which greater diversification can be realized prior to the onset of diworsification. Studies of equity markets had indicated that a portfolio of 20 to 30 stocks could diversify away unsystematic risk.

However, this number varies according to different asset classes and the complexity of the assets. In the world of alternative investments, a landmark study, “Hedge fund diversification: how much is enough?,” was published by authors François-Serge Lhabitant and Michelle Learned in 2002, for the Journal of Alternative Investments. The authors aimed to dispel the myth that ‘more is better’ in the complex world of hedge funds. They analyzed the effect of the size of the portfolio on risk and return, determining that although adding to the portfolio reduces risk, the marginal benefits of diversification diminished rapidly.

Importantly they found that adding too many funds could lead to a convergence toward average market returns, effectively eroding the “alpha” (excess return) that investors seek from active management. Furthermore, even when volatility is reduced, other forms of risks, such as skewness and kurtosis, can get worse. The significance of this research is that it offers empirical evidence for the phenomenon of ‘diworsification’—the idea that, after a certain point, adding assets to a portfolio worsens its efficiency.

Crossover from Diversification to Diworsification

The crossover from diversification to diworsification is normally marked by three main factors.

The first is diluted returns, as the number of assets increases, the performance of the portfolio starts to resemble that of a market index, albeit with elevated costs. The favorable influence of a handful of significant winners is offset by the poor performance of many other investments.

The second is an increase in costs as each asset, and particularly each asset owned through a managed fund, comes with some costs. These can be transaction costs, management fees, or costs of research. The more assets there are, the costs add up and ultimately impose a drag on final performance.

The third is unnecessary complexity as a portfolio with too many holdings becomes hard to keep tabs on, analyze, and rebalance. Which can confuse an investor about his or her asset allocation and expose the portfolio to unnecessary risk.

Causes of Diworsification

The causes for diworsification differ systematically between individual and institutional investors. For individual investors, this fundamental mistake arises from an incorrect understanding of genuine diversification, far too often leading to an emphasis on numbers rather than quality. Behavioral biases, such as familiarity bias, manifested in a preference for investing in well-known names of firms, or fear of missing out, which drives investors toward recently outperforming “hot” stocks, can generate portfolios concentrated in highly correlated securities.

The causes of diworsification for institutional investors are fundamentally different. The asset management business puts on a lot of strain that can lead to diworsification. Fund managers, measured against a comparator index, may prefer to build oversized funds whose portfolios are similar to the index, a process called “closet indexing.” Even if such a strategy reduces the risk of underperforming the comparator and thus losing clients, it also ensures that the fund will not show meaningful outperformance, all the time collecting fees for what is wrongly qualified as active management. In addition, the sale of complex product types like “funds of funds” adds further levels of fees and can mask the fact that the underlying assets are often far from unique.

How to avoid Diworsification

Diworsification doesn’t refer to an abandonment of diversification. Rather, it demands a more intelligent strategy. The emphasis should move from raw number of holdings to the correct asset allocation of the portfolio. The key is to mix asset classes with low or even adverse correlations to each other, for example, stocks, government securities, real estate, and commodities. This method allows for a more solid shelter from price fluctuations than keeping a long list of homogeneous stocks.

A low-cost and efficient means for many investors to achieve this goal is to utilize broad-market index funds and ETFs. These financial products give exposure to thousands of underlying securities representing full asset classes within a single holding, thus eliminating the difficulties and high costs of creating an equivalent portfolio of single assets.

Conclusion

Modern Portfolio Theory provides an intriguing framework for crafting portfolios for investments, and its essential concept of diversification still forms its basis. However, implementing this concept requires thoughtful consideration. Diworsification represents a misinterpretation of the objective, and not an objective to add assets simply in numbers, but to improve the risk-return of the portfolio as a whole.

A successful diversification strategy is built on a foundation of asset allocation to low-correlation assets. By focusing on the quality of diversification rather than the quantity of positions, investors can create portfolios that are closer to what they want, avoiding unnecessary costs and lower returns of a diworsified outcome.

Why should I be interested in this post?

Diworsification is a trap that should be avoided, and is really easy to avoid when you understand the mechanisms at work behind it.

Useful resources

Lhabitant, F.-S., M. Learned (2002) Hedge fund diversification: how much is enough? Journal of Alternative Investments, 5(3):23-49.

Lynch P., J. Rothchild (2000) One up on Wall Street. New York: Simon & Schuster.

Markowitz, H. (1952). Portfolio Selection. The Journal of Finance, 7(1), 77–91.

About the author

This article was written in November 2025 by Yann TANGUY (ESSEC Business School, Global Bachelor in Business Administration (GBBA), 2023-2027).

“Don’t look for the needle in the haystack. Just buy the haystack.“ – John Bogle

December 1, 2025November 6, 2025 by Hadrien PUCHE

Over the past decade, investing has become more accessible than ever. Anyone with a smartphone can now buy or sell shares, cryptocurrencies, or ETFs within seconds. While this democratization of finance has clear benefits, it has also led many to lose money by chasing “the next big stock.” Retail investors often believe they can find the next Tesla or Nvidia: the famous “needle in the haystack.” Yet, as history repeatedly shows, only a small fraction succeed.

That is precisely what John C. Bogle, the founder of Vanguard and the father of index investing, warned against. His advice was simple yet profound: stop trying to find the needle, just buy the entire haystack.

In this article, Hadrien PUCHE (ESSEC Business School, Grande École Program, Master in Management, 2023-2027) comments on Bogle’s timeless quote, exploring how it captures one of the most important principles in modern investing: diversification.

About John C. Bogle

John Clifton Bogle (1929 – 2019) was an American investor and philanthropist best known as the founder of The Vanguard Group, one of the world’s largest asset management firms. In 1976, Bogle created the first index fund available to individual investors, the Vanguard 500 Index Fund, designed to replicate the performance of the S&P 500 index rather than beat it.

At the time, his idea was revolutionary. The prevailing belief was that skilled managers could consistently outperform the market through superior stock selection and market timing. Bogle argued the opposite: after accounting for management fees, transaction costs, and human error, most active managers fail to beat the market over the long term. His philosophy emphasized simplicity, discipline, and cost-efficiency, principles that now underpin the $12 trillion global index fund industry.

John C. Bogle
John Bogle

Analysis of the quote

Bogle’s quote encapsulates a powerful truth: successful investing does not require finding hidden gems, but rather owning the market as a whole. The “needle in the haystack” represents the elusive high-performing stock every investor dreams of. Yet statistically, most attempts to find it fail. By buying the entire “haystack” (that is, the full market) investors automatically own all the winners and minimize the risk of missing them.

Empirical research overwhelmingly supports this idea. Over time, a small number of stocks account for the majority of total market gains. A study by Hendrik Bessembinder (2018) found that, since 1926, just 4% of U.S. stocks generated the entire net wealth created by the stock market. Most others either underperformed or disappeared entirely. Thus, identifying the few long-term winners ex ante is nearly impossible. The rational solution is to own the entire market, a strategy that index funds make accessible and affordable.

Bogle’s insight also reflects humility: acknowledging that even professionals struggle to outperform broad market indexes. By accepting this, investors shift their focus from beating the market to participating in its long-term growth.

Financial concepts related to the quote

I present below three fiancial concepts: diversification, index funds, and the efficient portfolio frontier.

Diversification

Diversification is the cornerstone of modern portfolio theory. It refers to spreading investments across different assets or sectors to reduce risk. By owning a broad range of companies, an investor limits the impact of any single firm’s poor performance.

Bogle’s philosophy embodies this principle. Buying the entire market, through an index fund tracking, for example, the S&P 500 or the CAC 40, ensures exposure to hundreds of firms across multiple sectors. The failure of one or two is offset by the success of others.

In practice, diversification improves a portfolio’s risk-adjusted return. It does not eliminate risk entirely but reduces idiosyncratic risk (the risk specific to individual companies). What remains is systematic risk, which affects the entire market and cannot be diversified away. This relationship is evident when observing how portfolio risk declines as the number of securities increases.

Risk of a portfolio as a function of the number of assets

Index funds

Index funds are collective investment vehicles that aim to replicate the performance of a specific market index, such as the S&P 500 (U.S.), the MSCI World (Global), or the CAC 40 (France). They hold the same securities as the index, in the same proportions, ensuring the fund’s return closely matches that of the benchmark. Because they are passively managed, index funds have very low management fees (often 10 to 20 times cheaper than traditional mutual funds). They also provide instant diversification: by buying one share of an S&P 500 ETF, you effectively invest in 500 companies.

This simplicity explains their rapid growth. According to Morningstar, index funds and ETFs now represent more than 50% of all U.S. equity fund assets. Their accessibility and transparency have fundamentally reshaped global investing.

However, one subtle limitation is that most major indexes are market-cap weighted, meaning the largest companies exert the greatest influence. As of 2025, the “Magnificent 7” (Tesla, Nvidia, Apple, Microsoft, Alphabet, Meta, and Amazon) represent nearly 35% of the index’s total value. The chart below illustrates their growing share of total market capitalization over time, highlighting how even “diversified” investors are increasingly concentrated in a handful of mega-cap technology firms.

Market capitalization of the Magnificent 7 as a share of index total

The efficient portfolio frontier

Introduced by Harry Markowitz in 1952, the efficient frontier illustrates the optimal trade-off between risk and (expected) return for a diversified portfolio. Each point on the curve represents the best possible expected return for a given level of risk.

Efficient frontier graph

Index investing often lies near this efficient frontier. Because broad indexes like the S&P 500 already aggregate thousands of investors’ information and preferences, they effectively represent a “market portfolio” close to the optimal mix. Passive investors benefit from this efficiency without needing to forecast which assets will outperform.

Understanding the efficient frontier also reveals why chasing high returns through concentrated bets is dangerous. While such strategies may yield spectacular results occasionally, they almost always involve disproportionate risk.

My opinion about this quote

I believe this quote perfectly captures the essence of modern investing: simplicity often outperforms sophistication. Many individuals (and professionals) spend enormous time and money trying to beat the market, often with limited success. The SPIVA (S&P Indices Versus Active) report consistently shows that the majority of actively managed funds underperform their benchmark indexes over the long term. As of 2024, for instance, more than 85% of U.S. equity funds lagged the S&P 500 over a 10-year period.

The chart below illustrates this trend across different investment horizons, showing that the longer the time frame, the harder it becomes for active managers to outperform their benchmarks.

Most US equities fund managers fail at outperforming the S&P500 index

The reasons are clear: high management fees, excessive trading, and the psychological pressure to deliver short-term results. Fund managers often prioritize annual bonuses over long-term compounding, leading to decisions driven by incentives rather than rational analysis.

At the same time, Bogle’s approach is not entirely without nuance. Index funds may appear perfectly diversified, but as noted earlier, their concentration risk has increased with the rise of mega-cap tech firms. Buying “the market” today means owning a portfolio dominated by a handful of giants. That, too, is an investment choice, one that has worked well recently but may not always hold true.

Therefore, the essence of Bogle’s wisdom is not that index investing is flawless, but that it is rational. It reflects humility, an understanding that long-term success comes not from prediction, but from participation, discipline, and patience.

Why should you be interested in this post?

For students and young professionals, this quote offers two critical lessons.

First, from a personal investing perspective, it highlights the power of simplicity. Investing through low-cost index funds allows anyone, regardless of expertise, to participate in long-term market growth without the stress of constant stock-picking. It is a proven strategy for building wealth steadily over time.

Second, from a professional standpoint, understanding how and why index funds dominate modern markets is essential. Whether you aim to work in asset management, corporate finance, or risk consulting, you must grasp how passive investing shapes market dynamics, liquidity, and valuation.

Ultimately, Bogle’s message goes beyond finance. It teaches intellectual humility: the recognition that long-term discipline often triumphs over short-term brilliance.

Useful resources

Vanguard official website

Bessembinder, H. (2018). Do Stocks Outperform Treasury Bills? Journal of Financial Economics.

SPIVA U.S. Scorecard (2024)

Markowitz, H. (1952). Portfolio Selection. Journal of Finance.

Bogle, J. C. (2017). The Little Book of Common Sense Investing.

About the Author

The article was written in November 2025 by Hadrien PUCHE (ESSEC Business School, Grande École Program, Master in Management, 2023-2027).

Hedge fund diversification

January 13, 2023 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) discusses the notion of hedge fund diversification by analyzing the paper “Hedge fund diversification: how much is enough?” by Lhabitant and Learned (2002).

This article is organized as follows: we describe the primary characteristics of the research paper. Then, we highlight the research paper’s most important points. This essay concludes with a discussion of the principal findings.

Introduction

The paper discusses the advantages of investing in a set of hedge funds or a multi-strategy hedge fund. It is a relevant subject in the field of alternative investments since it has attracted the interest of institutional investors seeking to uncover the alternative investment universe and increase their portfolio return. The paper’s primary objective is to determine the appropriate number of hedge funds that an portfolio manager should combine in its portfolio to maximise its (expected) returns. The purpose of the paper is to examine the impact of adding hedge funds to a traditional portfolio and its effect on the various statistics (average return, volatility, skewness, and kurtosis). The authors consider basic portfolios (randomly chosen and equally-weighted portfolios). The purpose is to evaluate the diversification advantage and the dynamics of the diversification effect of hedge funds.

Key elements of the paper

The pioneering work of Henry Markowitz (1952) depicted the effect of diversification by analyzing the portfolio asset allocation in terms of risk and (expected) return. Since unsystematic risk (specific risk) can be neutralized, investors will not receive an additional return. Systematic risk (market risk) is the component that the market rewards. Diversification is then at the heart of asset allocation as emphasized by Modern Portfolio Theory (MPT). The academic literature has since then delved deeper on the analysis of the optimal number of assets to hold in a well-diversified portfolio. We list below some notable contributions worth mentioning:

Elton and Gruber (1977), Evans and Archer (1968), Tole (1982) and Statman (1987) among others delved deeper into the optimal number of assets to hold to generate the best risk and return portfolio. There is no consensus on the optimal number of assets to select.
Evans and Archer (1968) depicted that the best results are achieved with 8-10 assets, while raising doubts about portfolios with number of assets above the threshold. Statman (1987) concluded that at least thirty to forty stocks should be included in a portfolio to achieve the portfolio diversification.

Lhabitant and Learned (2002) also mention the concept of naive diversification (also known as “1/N heuristics”) is an allocation strategy where the investor split the overall fund available is distributed into same. Naive diversification seeks to spread asset risk evenly in the portfolio to reduce overall risk. However, the authors mention important considerations for naïve/Markowitz optimization:

Drawback of naive diversification: since it doesn’t account for correlation between assets, the allocation will yield a sub-optimal result and the diversification won’t be fully achieved. In practice, naive diversification can result in portfolio allocations that lie on the efficient frontier. On the other hand, mean-variance optimisation, the framework revolving he Modern Portfolio Theory is subject to input sensitivity of the parameters used in the optimization process. On a side note, it is worth mentioning that naive diversification is a good starting point, better than gut feeling. It simplifies allocation process while also benefiting by some degree of risk diversification.
Non-normality of distribution of returns: hedge funds exhibit non-normal returns (fat tails and skewness). Those higher statistical moments are important for investors allocation but are disregarded in a mean-variance framework.
Econometric difficulties arising from hedge fund data in an optimizer framework. Mean-variance optimisers tend to consider historical return and risk, covariances as an acceptable point to assess future portfolio performance. Applied in a construction of a hedge fund portfolio, it becomes even more difficult to derive the expected return, correlation, and standard deviation for each fund since data is scarcer and more difficult to obtain. Add to that the instability of the hedge funds returns and the non-linearity of some strategies which complicates the evaluation of a hedge fund portfolio.
Operational risk arising from fund selection and implementation of the constraints in an optimiser software. Since some parameters are qualitative (i.e., lock up period, minimum investment period), these optimisers tool find it hard to incorporate these types of constraints in the model.

Conclusion

Due to entry restrictions, data scarcity, and a lack of meaningful benchmarks, hedge fund investing is difficult. The paper analyses in greater depth the optimal number of hedge funds to include in a diversified portfolio. According to the authors, adding funds naively to a portfolio tends to lower overall standard deviation and downside risk. In this context, diversification should be improved if the marginal benefit of adding a new asset to a portfolio exceeds its marginal cost.

The authors reiterate that investors should not invest “naively” in hedge funds due to their inherent risk. The impact of naive diversification on the portfolio’s skewness, kurtosis, and overall correlation structure can be significant. Hedge fund portfolios should account for this complexity and examine the effect of adding a hedge fund to a well-balanced portfolio, taking into account higher statistical moments to capture the allocation’s impact on portfolio construction. Naive diversification is subject to the selection bias. In the 1990s, the most appealing hedge fund strategy was global macro, although the long/short equity strategy acquired popularity in the late 1990s. This would imply that allocations will be tilted towards these two strategies overall.

The answer to the title of the research paper? Hedge funds portfolios should hold between 15 and 40 underlying funds, while most diversification benefits are reached when accounting with 5 to 10 hedge funds in the portfolio.

Why should I be interested in this post?

The purpose of portfolio management is to maximise returns on the entire portfolio, not just on one or two stocks. By monitoring and maintaining your investment portfolio, you can accumulate a substantial amount of wealth for a range of financial goals, such as retirement planning. This article facilitates comprehension of the fundamentals underlying portfolio construction and investing. Understanding the risk/return profiles, trading strategy, and how to incorporate hedge fund strategies into a diversified portfolio can be of great interest to investors.

Useful resources

Academic research

Elton, E., and M. Gruber (1977). “Risk Reduction and Portfolio Size: An Analytical Solution.” Journal of Business, 50. pp. 415-437.

Evans, J.L., and S.H. Archer (1968). “Diversification and the Reduction of Dispersion: An Empirical Analysis”. Journal of Finance, 23. pp. 761-767.

Lhabitant, François S., Learned Mitchelle (2002). “Hedge fund diversification: how much is enough?” Journal of Alternative Investments. pp. 23-49.

Markowitz, H.M (1952). “Portfolio Selection.” The Journal of Finance, 7, pp. 77-91.

Statman, M. (1987). “How many stocks make a diversified portfolio?”, Journal of Financial and Quantitative Analysis , pp. 353-363.

Tole T. (1982). “You can’t diversify without diversifying”, Journal of Portfolio Management, 8, pp. 5-11.

About the author

The article was written in January 2023 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

Systematic risk and specific risk

November 30, 2021 by Youssef LOURAOUI

In this article, Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022) presents the systematic risk and specific risk of financial assets, two fundamental concepts in asset pricing models and investment management theories more generally.

This article is structured as follows: we introduce the concept of systematic and specific risk. We then explain the mathematical foundation of this concept. We finish with an insight that sheds light on the relationship between diversification and risk reduction.

Portfolio Theory and Risk

Markowitz (1952) and Sharpe (1964) developed a framework on risk based on their significant work in portfolio theory and capital market theory. All rational profit-maximizing investors seek to possess a diversified portfolio of risky assets, and they borrow or lend to get to a risk level that is compatible with their risk preferences under a set of assumptions. They demonstrated that the key risk measure for an individual asset is its covariance with the market portfolio under these circumstances (the beta).

The fraction of an individual asset’s total variance attributable to the variability of the total market portfolio is referred to as systematic risk, which is assessed by the asset’s covariance with the market portfolio. In the article systematic risk, we develop the economic sources of systematic risk: interest rate risk, inflation risk, exchange rate risk, geopolitical risk, and natural risk.

Additionally, due to the asset’s unique characteristics, an individual asset exhibits variance that is unrelated to the market portfolio (the asset’s non-market variance). Specific risk is the term for non-market variance, and it is often seen as minor because it can be eliminated in a large diversified portfolio. In the article specific risk, we develop the economic sources of specific risk: business risk and financial risk.

Mathematical foundations

Following the Capital Asset Pricing Model (CAPM), the return on asset i, denoted by R_i can be decomposed as

img_SimTrade_return_decomposition

Where:

R_i the return of asset i
E(R_i) the expected return of asset i
β_i the measure of the risk of asset i
R_M the return of the market
E(R_M) the expected return of the market
R_M – E(R_M) the market factor
ε_i the specific part of the return of asset i

The three components of the decomposition are the expected return, the market factor and an idiosyncratic component related to asset only. As the expected return is known over the period, there are only two sources of risk: systematic risk (related to the market factor) and specific risk (related to the idiosyncratic component).

The beta of the asset with the market is computed as:

Beta

Where:

σ_i,m : the covariance of the asset return with the market return
σ_m² : the variance of market return

Total risk can be deconstructed into two main blocks:

Total risk formula

The total risk of the asset measured by the variance of asset returns can be computed as:

Decomposition of total risk

Where:

β_i² * σ_m² = systematic risk
σ_εi² = specific risk

In this decomposition of the total variance, the first component corresponds to the systematic risk and the second component to the specific risk.

Effect of diversification on portfolio risk

Diversification’s objective is to reduce the portfolio’s standard deviation. This assumes an imperfect correlation between securities. Ideally, as investors add securities, the portfolio’s average covariance decreases. How many securities must be included to create a portfolio that is completely diversified? To determine the answer, investors must observe what happens as the portfolio’s sample size increases by adding securities with some positive correlation. Figure 1 illustrates the effect of diversification on portfolio risk, more precisely on total risk and its two components (systematic risk and specific risk).

Figure 1. Effect of diversification on portfolio risk

Source: Computations from the author.

The critical point is that by adding stocks that are not perfectly correlated with those already held, investors can reduce the portfolio’s overall standard deviation, which will eventually equal that of the market portfolio. At that point, investors eliminated all specific risk but retained market or systematic risk. There is no way to completely eliminate the volatility and uncertainty associated with macroeconomic factors that affect all risky assets. Additionally, investors can reduce systematic risk by diversifying globally rather than just within the United States, as some systematic risk factors in the United States market (for example, US monetary policy) are not perfectly correlated with systematic risk variables in other countries such as Germany and Japan. As a result, global diversification eventually reduces risk to a global systematic risk level.

You can download below two Excel files which illustrate the effect of diversification on portfolio risk.

The first Excel file deals with the case of independent assets with the same profile (risk and expected return).

Figure 2 depicts the risk reduction of total risk in as we increase the number of assets in the portfolio. We manage to reduce half of the overall portfolio volatility by adding five assets to the portfolio. However, the decrease becomes more and more marginal as we add more assets.

Figure 2. Risk reduction of the portfolio. img_SimTrade_systematic_specific_risk_1 Source: Computations from the author.

Figure 3 depicts the overall risk reduction of a portfolio. The benefit of diversification are more evident when we add the first 5 assets in the portfolio. As depicted in Figure 2, the diversification starts to fade at a certain point as we keep adding more assets in the portfolio. It can be seen in this figure how the specific risk is considerably reduced as we add more assets because of the effect of diversification. Systematic risk (market risk) is more constant and doesn’t change drastically as we diversify the portfolio. Overall, we can clearly see that diversification helps decrease the total risk of a portfolio considerably.

Figure 3. Risk decomposition of the portfolio. img_SimTrade_systematic_specific_risk_2 Source: Computations from the author.

The second Excel file deals with the case of dependent assets with the different characteristics (expected return, volatility, and market beta).

Academic research

A series of studies examined the average standard deviation for a variety of portfolios of randomly chosen stocks with varying sample sizes. Evans and Archer (1968) and Tole (1982) calculated the standard deviation for portfolios up to a maximum of twenty stocks. The results indicated that the majority of the benefits of diversification were obtained relatively quickly, with approximately 90% of the maximum benefit of diversification being obtained from portfolios of 12 to 18 stocks. Figure 1 illustrates this effect graphically.

This finding has been modified in two subsequent studies. Statman (1987) examined the trade-off between diversification benefits and the additional transaction costs associated with portfolio expansion. He concluded that a portfolio that is sufficiently diversified should contain at least 30–40 stocks. Campbell, Lettau, Malkiel, and Xu (2001) demonstrated that as the idiosyncratic component of an individual stock’s total risk (specific risk) has increased in recent years, it now requires a portfolio to contain more stocks to achieve the same level of diversification. For example, they demonstrated that the level of diversification possible in the 1960s with only 20 stocks would require approximately 50 stocks by the late 1990s (Reilly and Brown, 2012).

Figure 4. Effect of diversification on portfolio risk Source: Computation from the author.

You can download below the Excel file which illustrates the effect of diversification on portfolio risk with real assets (Apple, Microsoft, Amazon, etc.). The effect of diversification on the total risk of the portfolio is already significant with the addition of few stocks.

We can appreciate the decomposition of total risk in the below figure with real asset. We can appreciate how asset with low beta had the lowest systematic out of the sample analyzed (i.e. Pfizer). For the whole sample, specific risk is a major concern which makes the major component of risk of each stock. This can be mitigated by holding a well-diversified portfolio that can mitigate this component of risk. Figure 5 depicts the decomposition of total risk for assets (Apple, Microsoft, Amazon, Goldman Sachs and Pfizer).

Figure 5. Decomposition of total risk Source: Computation from the author.

You can download below the Excel file which deconstructs the risk of assets (Apple, Microsoft, Amazon, Goldman Sachs, and Pfizer).

Why should I be interested in this post?

If you’re an investor, understanding the source of risk is essential in order to build balanced portfolios that can withstand market corrections and downturns.

If you are a business school or university undergraduate or graduate student, this content will help you in broadening your knowledge of finance.

Useful resources

Academic research

Campbell, J.Y., Lettau, M., Malkiel, B.G. and Xu, Y. 2001. Have Individual Stocks Become More Volatile? An Empirical Exploration of Idiosyncratic Risk. The Journal of Finance, 56: 1-43.

Evans, J.L., Archer, S.H. 1968. Diversification and the Reduction of Dispersion: An Empirical Analysis. The Journal of Finance, 23(5): 761–767.

Markowitz, H. 1952. Portfolio Selection. The Journal of Finance, 7(1): 77-91.

Mossin, J. 1966. Equilibrium in a Capital Asset Market. Econometrica, 34(4): 768-783.

Reilly, R.K., Brown C.K. 2012. Investment Analysis & Portfolio Management, Tenth Edition. 239-245.

Sharpe, W.F. 1963. A Simplified Model for Portfolio Analysis. Management Science, 9(2): 277-293.

Sharpe, W.F. 1964. Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19(3): 425-442.

Statman, M. 1987. How Many Stocks Make a Diversified Portfolio?. The Journal of Financial and Quantitative Analysis, 22(3), 353–363.

Tole T.M. 1982. You can’t diversify without diversifying. The Journal of Portfolio Management. Jan 1982, 8 (2) 5-11.

About the author

The article was written in November 2021 by Youssef LOURAOUI (Bayes Business School, MSc. Energy, Trade & Finance, 2021-2022).

The Concept of Diworsification

Practical Example

Target number of assets for a diversified portfolio

Crossover from Diversification to Diworsification

Causes of Diworsification

How to avoid Diworsification

Conclusion

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About John C. Bogle

Analysis of the quote

Financial concepts related to the quote

Diversification

Index funds

The efficient portfolio frontier

My opinion about this quote

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About the Author

Introduction

Key elements of the paper

Conclusion

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Portfolio Theory and Risk

Mathematical foundations

Effect of diversification on portfolio risk

Academic research

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Academic research

About the author