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on 11-06-2022

1. What is Diversification?

The first rule of finance is that investing involves risk. Returns are never guaranteed, and investors should pay specific attention when choosing stocks and other securities.

The major types of risks that an investor is exposed to are inflation rate risk, business risk, political risk, liquidity risk, interest rate risk, foreign investment risk, and default risk.

  1. Inflation rate risk refers to risks that unexpected inflation could significantly impact the purchasing power of a currency.
  2. Business risk is the risk that a company would not operate as efficiently as expected because of internal problems or external threats like an introduction of a better product by a competitor.
  3. Political risk refers to the risk of an unfavourable political situation for investment in a particular country.
  4. Liquidity risk is the risk that an investor will not be able to quickly sell their securities in the market at the fair market price.
  5. Interest rate risk is the risk that a change in interest rates could impose on a particular investment. For instance, an increase in interest rates leads to a decrease in bond prices, so a bondholder’s return would be compromised in such an event.
  6. Foreign investment has many risks involved, one of which could be a change in the exchange rate, which could decrease an investor’s returns in their currency.
  7. Default risk is the risk that a company will not be able to pay its obligations to the investors.

These risks could be classified into two broad categories – risks associated with a particular company’s performance (known as unsystematic risk) and risks associated with the economy as a whole (systematic risk). Thus, if an investor has positions in many different companies, they are effectively reducing the company-specific risk, but they cannot reduce the systematic risk because this risk affects all companies. This practice of reducing the unsystematic risk is called diversification. Investors should diversify their portfolios by holding a variety of stocks, bonds, and other securities to make sure that a drop in the price of any individual holding will not impact their returns significantly.

There are multiple ways of calculating risk. The most commonly used is the standard deviation of a security’s returns. Standard deviation is a statistical term that measures how dispersed the values in a particular set of numbers are from the mean. The higher the standard deviation of the returns, the more volatile they are, and thus the higher the risk that an investor assumes by holding the given security. Industry professionals also use another way of measuring risk called “beta”. Beta (which comes from the Greek letter β) relates the volatility of a stock or a portfolio to the volatility of the overall market. A beta of one means that the stock moves in perfect relation to the market, while a beta of more than one means that the stock’s returns are more volatile than the overall market. That is, if a stock’s beta is 1.2 and the overall market increases by 1%, the stock should theoretically have a return of 1.2*1%=1.2%. A beta of less than one signifies more stable security that is less impacted by general swings in the market, and a stock with a beta of less than zero means that the stock moves opposite to the market. In reality, because of the systematic risk that affects all companies, there are rarely stocks that move opposite to the market and have a negative beta. A notable exception to this rule is gold which historically has been considered a zero-beta asset.


2. Risk by Asset Class

Risk is closely associated with return. In general, the riskier the asset, the higher the return. This logic stems from the fact that investors should be compensated with a higher return for bearing higher risks.

Different asset classes carry different risks. The least risky assets are the Treasury Bills (short term bonds issued by the Canadian government). They are usually considered to be “risk-free”, and their return is used as a benchmark for the short-term inflation rate. In general, bonds issued or guaranteed by the federal, provincial, and municipal governments tend to be least risky, and bonds with shorter duration tend to be less risky than similar bonds with longer duration because economic conditions could change more in the long-term. Corporate bonds tend to be a bit riskier than government bonds because they include default risk (the government is essentially free of default risk). Thus, bonds issued by more stable companies (well-established with sufficient cash inflows and income) will be less risky that smaller growth companies for which the probability of default is considerably higher. The level of bond risk is most commonly reflected by the bond ratings performed by analytics companies like Moody’s and Standard and Poor’s. Bonds rated Aaa (or AAA) have the highest rating and the lowest risk. Bonds with ratings of Baa (or BBB) and higher are referred to as investment grade and carry low to moderate risks. Ratings below that are considered junk (or speculative) since they involve a lot of risk. A short guide to the bond ratings can be found in Table 1 below.

Moody’s and Standard and Poor’s Bond Ratings

Table 1. Moody’s and Standard and Poor’s Bond Ratings

Equities are the riskiest asset class, and their expected return is also the highest. Bonds are usually guaranteed by a pledge on assets of the company, and bondholders are paid first in case of bankruptcy, while shareholders are entitled only to residual claims on whatever is left after bondholders are compensated. Stocks also do not pay regular interest like bonds, and the dividends they may wish to pay are up to the discretion of management; thus, they are uncertain.


3. How to Achieve Good Diversification?

The general way of diversifying risk is by investing in multiple different companies and asset classes. The marginal benefit of adding a new security to a portfolio tends to decrease as the number of securities in higher. This is because all securities have systematic risk which cannot be diversified away, and at some point, when a portfolio is well-diversified, the investor cannot achieve additional diversification as the only risk involved in their portfolio is the general market risk. A well-diversified portfolio will consist of at least 30 different securities as shown in Figure 1 below. The graph depicts how the risk (measured by the standard deviation of the portfolio on the y-axis) decreases as the number of securities in the portfolio increases. One could clearly see that the highest reductions of standard deviation occur when the portfolio consists of very few positions, and how there is virtually no additional benefit of diversification once a portfolio reaches 30 positions as the standard deviation at that point is approximately equal to the standard deviation of a portfolio with 500 positions. (For more information about how the graph was constructed you can read Appendix 1.)

The Relationship Between Risk (Standard Deviation) and the Number of Stocks in a Portfolio

Figure 1. The Relationship Between Risk (Standard Deviation on the y-axis) and the Number of Stocks in a Portfolio (on the x-axis).


            Apart from the number of stocks in a portfolio, an investor should also consider the correlation between the individual holdings. Correlation is a statistical measure of the dependence of two sets of data. It measures how much two stocks tend to move in the same direction. The highest correlation is 1 and it signifies that as one stock moves up, the other stock will proportionally move up with the first one. The lowest correlation is -1 and is shows that as one stock moves us, the other stock will decrease by a proportional amount. A correlation of 0 indicates that the two shares are not related and move independently of one another. Few stocks will have negative correlation because of the systematic risk that causes all stocks in the economy to move in the same direction to a certain extent. When choosing shares, investors should aim to select stocks with lower correlation as this will provide a higher diversification benefit. Stocks that move together will not bring much diversification because they tend to be impacted by the same factors, and if one stock goes down, the other will also likely go down, and the investor will lose a material part of their investment.

            One good way of achieving low correlation is selecting stocks from different industries. Companies in the same industries will have similar threats. For example, a sharp unexpected increase in gas prices will negatively impact the whole transportation sector, and most transportation companies’ stocks will likely decrease, while this price change will have a negligible impact on the technology sector. Buying stocks of companies that engage in different industries reduces risk and creates diversification.

            Another way for achieving low correlation is by investing in different asset classes. Having a portfolio that includes stocks, bonds, real estate, commodities, etc. will provide for more diversification because most asset classes have very low and even negative correlation as there are few factors that could affect all investments negatively at the same time. For instance, stock and bond prices generally tend to move in opposite directions. In favourable economic conditions investors will prefer to invest in stocks as they will provide for a bigger benefit of capital gain, which will push stock prices up. However, during recessions individuals switch to bonds which have more secure and less risky return, which pushes the bond prices up and stock prices down.

            In an economy there are some general factors that will impact all investments, such as interest rates and inflation. That is why investing abroad could also prove to be an effective diversification strategy. Yet, these investments are still not risk-free as most major economic swings tend to spread globally because of the interconnectedness of modern society. For instance, the 2007-2009 recession started in the U.S., yet it caused a world-wide economic downturn.


4. How does Diversification Work?

When an individual invests in a portfolio, their return will be a weighted average of the returns of each asset in the portfolio. For example, if a portfolio consists of $1,000 invested in AAPL (Apple) and $2,000 in MSFT (Microsoft) and for a given period AAPL’s return is 9% and MSFT’s is 6%, the portfolio’s return will be 1000/(1000 + 2000) * 9% + 2000/(1000 + 2000) * 6% = 7%. The standard deviation of the returns, however, do not only depend on the relative weights of the assets in the portfolio, but also on the correlation between the stocks. The exact statistical equation could be found in Appendix 2. An important takeaway from that equation is that the portfolio standard deviation will always be lower than the average of the standard deviations of the individual assets as long as they are not perfectly correlated (in reality there are no two stocks with perfect correlation of 1). Thus, by adding more securities in a portfolio, an investor decreases the standard deviation of returns of the portfolio, while the overall return will increase if the new stock’s return is higher than the current portfolio return (A note of caution: adding extra stocks does not always reduce the standard deviation; you can find further explanation in point 6. Note of Caution).


5. How much Diversification is Too Much?

While the benefits of diversification for risk reduction are undeniable, extreme diversification is not particularly advisable either because it may compromise returns, diversification benefits are negligible on portfolios of more than about 30 stocks, and it might generate higher fees.

The famous investor and CEO of Berkshire Hathaway Warren Buffett has said that “Diversification is a protection against ignorance. It makes little sense if you know what you are doing.”[1] The idea behind this quote is that an investor could generate higher returns by concentrating their investments in one or few companies in a limited number of industries. This stems from the idea that even if diversification reduces the risk, it might compromise the returns. This is because if one holds a diversified portfolio, the gains from some of the securities could be offset to a great extent by the loses of other assets. Instead, Warren Buffett suggests that if an investor has a good understanding of specific companies and industries, they could generate higher returns by predicting the market movements in advance. For instance, an expert in the technology sector can sense and correctly interpret news about the industry and quickly react by either buying or short selling the securities which will generate returns in both upswings and downswings of the market. A real-life example will be Warren Buffett himself. The Berkshire Hathaway’s investment portfolio (Buffett’s company) is rather lightly diversified with 41% of the portfolio invested in only one company, Apple (AAPL), and 72.2% invested in their top five holdings (Apple, Bank of America, American Express, Chevron, and Coca-Cola) as of the first quarter of 2022.[2] However, a certain strategy could be sustained only if one has a good understanding of the companies and industries they are investing in and can quickly identify and trade upon different market trends and news. This strategy also requires a lot of active trading on the investor’s side as opposed to a conservative buy and hold strategy.

For most investor, however, it is unrealistic to assume that they can continually track the market and execute a lot of buy and sell orders for a short period of time. Still, even for a more passive buy and hold strategy excessive diversification could not be ideal. As argued before, diversification benefits are virtually exhausted once a portfolio has about 30 different positions. At this point the majority of the risk is systematic risk and it cannot be diversified away by adding new securities. Instead, the addition of new securities could undermine the returns of overall portfolio following the logic from the previous paragraph. The returns of the portfolio are just a weighted average of the returns of the individual securities, so investors would be compromising their overall returns since material upturns of a specific stock would be dampened in a portfolio consisting of too many securities.

Apart from potentially decreasing returns, an extremely diversified portfolio could potentially generate higher fees for the investor since they will need to trade many securities. The amount of fees, however, depend on a great extent to the specific securities and brokerage fees.

Investors seeking a relatively passive strategy with stable returns should diversify their portfolio of assets to decrease the portfolio risk, yet they should be careful not to diversify too much because this could damage the returns and trigger higher fees.


6. Note of Caution

An important note to make is that diversification does not guarantee that the standard deviation (and thus the risk) will be reduced. As explained previously, the standard deviation of two assets put in a portfolio will be lower than the average standard deviation of the assets. However, this does not imply that the portfolio’s standard deviation will be lower than both assets’ standard deviations, it will just be lower than their average standard deviation. Thus, adding a very volatile asset to a portfolio might as well increase the portfolio’s total volatility. For instance, if an investor has an asset A with a standard deviation of 1.4% and adds another asset B with a standard deviation of 3%, the new portfolio’s standard deviation could be 1.6%, which is lower than the two assets’ standard deviations (average standard deviation = (1.4% + 3%)/2 = 2.2%), yet it is higher than the standard deviation of just holding asset A.

Investors should also keep in mind that the risk of an asset (as measured by its standard deviation) is calculated solely using historical returns. Historical returns, however, are not a perfect reflection of the future; instead, they are just a benchmark that professionals use to estimate the risk. The asset might underperform and turn out to be riskier than expected.

Diversification is very useful for decreasing (and ultimately eliminating) the systematic risk, however there is still some systematic risk that cannot be diversified away. Thus, no diversification strategy will result in a completely risk-free investment.


7. Appendix 1 – Graph

The point representing the portfolio of 30 stocks is the SPDR Dow Jones Industrial Average ETF Trust, which measures the performance of the Dow Jones Industrial Average index. The point representing the portfolio of 500 stocks is the Vanguard 500 Index Fund, which measures the performance of the S&P 500 index. The other points represent portfolios constructed using the first eleven stocks of the Dow Jones Industrial Average index in alphabetical order. For a detailed breakdown of the composition of the portfolios, please refer to Table 2. The returns and their associated standard deviations are calculated using the daily stock adjusted close for a period of 5 years between June 05, 2017, and June 2, 2022, downloaded from Yahoo finance.

Portfolio Composition

Table 2. Portfolio Stock Composition


8. Appendix 2 – Formula

The exact statistical equation is that the portfolio standard deviation is equal to the square root of the sum of each stock’s variance times the corresponding weight squared plus two times the covariance of the stocks times their weights:

Portfolio Standard Deviation

, where σ is the portfolio’s standard deviation, wi refers to the weight associated with stock i, V is the symbol for variance, Ri is the return of stock i, and Cov(Ri, Rj) is the covariance of the returns of stocks i and j. (For the purpose of this text the proof of the aforementioned formula is omitted since it involves a good understanding of statistics.)


Author: Alexander Natchev


[1] Yahoo Finance. “Warren Buffett: 3 to 6 Stocks Is Enough.”, 2021

[2] Investopedia. “Top 5 Positions in Warren Buffett’s Portfolio.”, 2022

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