In finance, diversification is the process of allocating capital in a way that reduces the exposure to any one particular asset or risk. A common path towards diversification is to reduce

Keynes, King's, and Endowment Asset Management

in ''How the Financial Crisis and Great Recession Affected Higher Education'' (2015), Jeffrey R. Brown and Caroline M. Hoxby, editors (p. 127 - 150). Conference held September 27-28, 2012.

Macro-Investment Analysis

Prof.

An Introduction to Investment Theory

Prof. William N. Goetzmann, Yale School of Management {{DEFAULTSORT:Diversification (Finance) Financial risk modeling

risk
In simple terms, risk is the possibility of something bad happening. Risk involves uncertainty about the effects/implications of an activity with respect to something that humans value (such as health, well-being, wealth, property or the environm ...

or volatility by investing in a variety of asset
In financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value of ownership that can ...

s. If asset prices do not change in perfect synchrony, a diversified portfolio
Portfolio may refer to:
Objects
* Portfolio (briefcase), a type of briefcase
Collections
* Portfolio (finance), a collection of assets held by an institution or a private individual
* Artist's portfolio, a sample of an artist's work or a ...

will have less variance than the weighted average
The weighted arithmetic mean is similar to an ordinary arithmetic mean (the most common type of average), except that instead of each of the data points contributing equally to the final average, some data points contribute more than others. The ...

variance of its constituent assets, and often less volatility than the least volatile of its constituents.
Diversification is one of two general techniques for reducing investment risk. The other is hedging.
Examples

The simplest example of diversification is provided by the proverb "Don't put all your eggs in one basket". Dropping the basket will break all the eggs. Placing each egg in a different basket is more diversified. There is more risk of losing one egg, but less risk of losing all of them. On the other hand, having a lot of baskets may increase costs. In finance, an example of an undiversified portfolio is to hold only one stock. This is risky; it is not unusual for a single stock to go down 50% in one year. It is less common for a portfolio of 20 stocks to go down that much, especially if they are selected at random. If the stocks are selected from a variety of industries, company sizes and asset types it is even less likely to experience a 50% drop since it will mitigate any trends in that industry, company class, or asset type. Since the mid-1970s, it has also been argued that geographic diversification would generate superior risk-adjusted returns for largeinstitutional investor
An institutional investor is an entity which pools money to purchase securities, real property, and other investment assets or originate loans. Institutional investors include commercial banks, central banks, credit unions, government-linked ...

s by reducing overall portfolio risk while capturing some of the higher rates of return offered by the emerging markets
An emerging market (or an emerging country or an emerging economy) is a market that has some characteristics of a developed market, but does not fully meet its standards. This includes markets that may become developed markets in the future or were ...

of Asia and Latin America.
Return expectations while diversifying

If the prior expectations of the returns on all assets in the portfolio are identical, theexpected return
The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. It is calculated ...

on a diversified portfolio will be identical to that on an undiversified portfolio. Some assets will do better than others; but since one does not know in advance which assets will perform better, this fact cannot be exploited in advance. The return on a diversified portfolio can never exceed that of the top-performing investment, and indeed will always be lower than the highest return (unless all returns are identical). Conversely, the diversified portfolio's return will always be higher than that of the worst-performing investment. So by diversifying, one loses the chance of having invested solely in the single asset that comes out best, but one also avoids having invested solely in the asset that comes out worst. That is the role of diversification: it narrows the range of possible outcomes. Diversification need not either help or hurt expected returns, unless the alternative non-diversified portfolio has a higher expected return.
Amount of diversification

There is no magic number of stocks that is diversified versus not. Sometimes quoted is 30, although it can be as low as 10, provided they are carefully chosen. This is based on a result from John Evans and Stephen Archer. Similarly, a 1985 book reported that most value from diversification comes from the first 15 or 20 different stocks in a portfolio. More stocks give lower price volatility. Given the advantages of diversification, many experts recommend maximum diversification, also known as "buying themarket portfolio
Market portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market, with the necessary assumption that these assets are infinitely divisible.
Richard Roll's cr ...

". Unfortunately, identifying that portfolio is not straightforward.
The earliest definition comes from the capital asset pricing model which argues the maximum diversification comes from buying a ''pro rata'' share of all available asset
In financial accounting, an asset is any resource owned or controlled by a business or an economic entity. It is anything (tangible or intangible) that can be used to produce positive economic value. Assets represent value of ownership that can ...

s. This is the idea underlying index funds.
Diversification has no maximum so long as more assets are available. Every equally weighted, uncorrelated asset added to a portfolio can add to that portfolio's measured diversification. When assets are not uniformly uncorrelated, a weighting approach that puts assets in proportion to their relative correlation can maximize the available diversification.
"Risk parity" is an alternative idea. This weights assets in inverse proportion to risk, so the portfolio has equal risk in all asset classes. This is justified both on theoretical grounds, and with the pragmatic argument that future risk is much easier to forecast than either future market price or future economic footprint. "Correlation parity" is an extension of risk parity, and is the solution whereby each asset in a portfolio has an equal correlation with the portfolio, and is therefore the "most diversified portfolio". Risk parity is the special case of correlation parity when all pair-wise correlations are equal.
Effect of diversification on variance

One simple measure offinancial risk
Financial risk is any of various types of risk associated with financing, including financial transactions that include company loans in risk of default. Often it is understood to include only downside risk, meaning the potential for financial ...

is variance
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its population mean or sample mean. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbe ...

of the return on the portfolio. Diversification can lower the variance of a portfolio's return below what it would be if the entire portfolio were invested in the asset with the lowest variance of return, even if the assets' returns are uncorrelated. For example, let asset X have stochastic return $x$ and asset Y have stochastic return $y$, with respective return variances $\backslash sigma^\_x$ and $\backslash sigma^\_y$. If the fraction $q$ of a one-unit (e.g. one-million-dollar) portfolio is placed in asset X and the fraction $1-q$ is placed in Y, the stochastic portfolio return is $qx+(1-q)y$. If $x$ and $y$ are uncorrelated, the variance of portfolio return is $\backslash text(qx+(1-q)y)=q^\backslash sigma^\_x+(1-q)^\backslash sigma^\_y$. The variance-minimizing value of $q$ is $q=\backslash sigma^\_y/;\; href="/html/ALL/l/sigma^\_x+\backslash sigma^\_y.html"\; ;"title="sigma^\_x+\backslash sigma^\_y">sigma^\_x+\backslash sigma^\_y$Diversification with correlated returns via an equally weighted portfolio

The expected return on a portfolio is a weighted average of the expected returns on each individual asset: :$\backslash mathbb;\; href="/html/ALL/l/\_P.html"\; ;"title="\_P">\_P$ where $x\_i$ is the proportion of the investor's total invested wealth in asset $i$. The variance of the portfolio return is given by: :$\backslash underbrace\_\; =\; \backslash mathbb;\; href="/html/ALL/l/\_P\_-\_\backslash mathbb[R\_P.html"\; ;"title="\_P\; -\; \backslash mathbb[R\_P">\_P\; -\; \backslash mathbb[R\_P$ Inserting in the expression for $\backslash mathbb;\; href="/html/ALL/l/\_P.html"\; ;"title="\_P">\_P$: :$\backslash sigma^\_\; =\; \backslash mathbb\backslash left[\backslash sum^\_x\_i\; R\_i\; -\; \backslash sum^\_x\_i\backslash mathbb[R\_i]\backslash right]^2\; .$ Rearranging: :$\backslash sigma^\_\; =\; \backslash mathbb\backslash left[\backslash sum^\_x\_i(R\_i\; -\; \backslash mathbb[R\_i])\backslash right]^2$ :$\backslash sigma^\_\; =\; \backslash mathbb\backslash left[\backslash sum^\_\; \backslash sum^\_\; x\_i\; x\_j(R\_i\; -\; \backslash mathbb[R\_i])(R\_j\; -\; \backslash mathbb;\; href="/html/ALL/l/\_j.html"\; ;"title="\_j">\_j$ :$\backslash sigma\_^=\backslash mathbb\backslash left;\; href="/html/ALL/l/sum\_^x\_^(R\_-\backslash mathbb;\; \_;"title="sum\_^x\_^(R\_-\backslash mathbb[R\_">sum\_^x\_^(R\_-\backslash mathbb[R\_$ :$\backslash sigma\_^=\backslash sum\_^x\_^\backslash underbrace\_+\backslash sum\_^\backslash sum\_^x\_x\_\backslash underbrace\_$ :$\backslash sigma^\_\; =\; \backslash sum^\_\; x^\_\; \backslash sigma^\_\; +\; \backslash sum^\_\; \backslash sum^\_\; x\_i\; x\_j\; \backslash sigma\_$ where $\backslash sigma^\_$ is the variance on asset $i$ and $\backslash sigma\_$ is the covariance between assets $i$ and $j$. In an equally weighted portfolio, $x\_i\; =\; x\_j\; =\; \backslash frac\; ,\; \backslash forall\; i,\; j$. The portfolio variance then becomes: :$\backslash sigma^2\_P\; =\; \backslash frac\; \backslash \; \backslash bar^\_\; +\; n(n-1)\; \backslash frac\; \backslash frac\; \backslash bar\_$ where $\backslash bar\_$ is the average of the covariances $\backslash sigma\_$ for $i\backslash neq\; j$ and $\backslash bar^2\_i$ is the average of the variances. Simplifying, we obtain :$\backslash sigma^\_\; =\; \backslash frac\; \backslash bar^\_\; +\; \backslash frac\; \backslash bar\_\; .$ As the number of assets grows we get the asymptotic formula: :$\backslash lim\_\; \backslash sigma^2\_P\; =\; \backslash bar\_.$ Thus, in an equally weighted portfolio, the portfolio variance tends to the average of covariances between securities as the number of securities becomes arbitrarily large.Diversifiable and non-diversifiable risk

The capital asset pricing model introduced the concepts of diversifiable and non-diversifiable risk. Synonyms for diversifiable risk are idiosyncratic risk, unsystematic risk, and security-specific risk. Synonyms for non-diversifiable risk aresystematic risk
In finance and economics, systematic risk (in economics often called aggregate risk or undiversifiable risk) is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggr ...

, beta
Beta (, ; uppercase , lowercase , or cursive ; grc, βῆτα, bē̂ta or ell, βήτα, víta) is the second letter of the Greek alphabet. In the system of Greek numerals, it has a value of 2. In Modern Greek, it represents the voiced labi ...

risk and market risk
Market risk is the risk of losses in positions arising from movements in market variables like prices and volatility.
There is no unique classification as each classification may refer to different aspects of market risk. Nevertheless, the mos ...

.
If one buys all the stocks in the S&P 500
The Standard and Poor's 500, or simply the S&P 500, is a stock market index tracking the stock performance of 500 large companies listed on stock exchanges in the United States. It is one of the most commonly followed equity indices. As of ...

one is obviously exposed only to movements in that index
Index (or its plural form indices) may refer to:
Arts, entertainment, and media Fictional entities
* Index (''A Certain Magical Index''), a character in the light novel series ''A Certain Magical Index''
* The Index, an item on a Halo megastru ...

. If one buys a single stock in the S&P 500, one is exposed both to index movements and movements in the stock based on its underlying company. The first risk is called "non-diversifiable", because it exists however many S&P 500 stocks are bought. The second risk is called "diversifiable", because it can be reduced by diversifying among stocks.
In the presence of per-asset investment fees, there is also the possibility of overdiversifying to the point that the portfolio's performance will suffer because the fees outweigh the gains from diversification.
The capital asset pricing model argues that investors should only be compensated for non-diversifiable risk. Other financial models allow for multiple sources of non-diversifiable risk, but also insist that diversifiable risk should not carry any extra expected return. Still other models do not accept this contention.
An empirical example relating diversification to risk reduction

In 1977 Edwin Elton and Martin Gruber worked out an empirical example of the gains from diversification. Their approach was to consider a population of 3,290 securities available for possible inclusion in a portfolio, and to consider the average risk over all possible randomly chosen ''n''-asset portfolios with equal amounts held in each included asset, for various values of ''n''. Their results are summarized in the following table. The result for ''n''=30 is close to ''n''=1,000, and even four stocks provide most of the reduction in risk compared with one stock.Corporate diversification strategies

In corporate portfolio models, diversification is thought of as being vertical or horizontal. Horizontal diversification is thought of as expanding a product line or acquiring related companies. Vertical diversification is synonymous with integrating the supply chain or amalgamating distributions channels. Non-incremental diversification is a strategy followed by conglomerates, where the individual business lines have little to do with one another, yet the company is attaining diversification from exogenous risk factors to stabilize and provide opportunity for active management of diverse resources.Fallacy of time diversification

The argument is often made that time reduces variance in a portfolio: a "time diversification". A common belief is younger investors should avoid bonds and emphasize stocks, due to the belief investors will have time to recover from any downturns. Yet this belief has flaws, as John Norstad explains: A paper by Vanguard Investment Counseling & Research explores the collected research on this topic further, in general supporting Norstad's conclusion, but allowing for the counteracted effects of inflation risk and human capital:History

Diversification is mentioned in theBible
The Bible (from Koine Greek , , 'the books') is a collection of religious texts or scriptures that are held to be sacred in Christianity, Judaism, Samaritanism, and many other religions. The Bible is an anthologya compilation of texts of ...

, in the book of Ecclesiastes which was written in approximately 935 B.C.:
:But divide your investments among many places,
:for you do not know what risks might lie ahead.
Diversification is also mentioned in the Talmud
The Talmud (; he, , Talmūḏ) is the central text of Rabbinic Judaism and the primary source of Jewish religious law (''halakha'') and Jewish theology. Until the advent of modernity, in nearly all Jewish communities, the Talmud was the center ...

. The formula given there is to split one's assets into thirds: one third in business (buying and selling things), one third kept liquid (e.g. gold coins), and one third in land (real estate
Real estate is property consisting of land and the buildings on it, along with its natural resources such as crops, minerals or water; immovable property of this nature; an interest vested in this (also) an item of real property, (more genera ...

). This strategy of splitting wealth equally among available options is now known as "naive diversification", "Talmudic diversification" or "1/n diversification", a concept which has earned renewed attention since the year 2000 due to research showing it may offer advantages in some scenarios.
Diversification is mentioned in Shakespeare's ''Merchant of Venice
''The Merchant of Venice'' is a play by William Shakespeare, believed to have been written between 1596 and 1598. A merchant in Venice named Antonio defaults on a large loan provided by a Jewish moneylender, Shylock.
Although classified as ...

'' (ca. 1599):
:My ventures are not in one bottom trusted,
:Nor to one place; nor is my whole estate
:Upon the fortune of this present year:
:Therefore, my merchandise makes me not sad.
Modern understanding of diversification dates back to the influential work of economist Harry Markowitz
Harry Max Markowitz (born August 24, 1927) is an American economist who received the 1989 John von Neumann Theory Prize and the 1990 Nobel Memorial Prize in Economic Sciences.
Markowitz is a professor of finance at the Rady School of Management ...

in the 1950s, whose work pioneered modern portfolio theory (see Markowitz model).
An earlier precedent for diversification was economist John Maynard Keynes
John Maynard Keynes, 1st Baron Keynes, ( ; 5 June 1883 – 21 April 1946), was an English economist whose ideas fundamentally changed the theory and practice of macroeconomics and the economic policies of governments. Originally trained in ...

, who managed the endowment of King's College, Cambridge
King's College is a constituent college of the University of Cambridge. Formally The King's College of Our Lady and Saint Nicholas in Cambridge, the college lies beside the River Cam and faces out onto King's Parade in the centre of the cit ...

from the 1920s to his 1946 death with a stock-selection strategy similar to what was later called value investing
Value investing is an investment paradigm that involves buying securities that appear underpriced by some form of fundamental analysis. The various forms of value investing derive from the investment philosophy first taught by Benjamin Graham a ...

. While diversification in the modern sense was "not easily available in Keynes's day" and Keynes typically held a small number of assets compared to later investment theories, he nonetheless is recognized as a pioneer of financial diversification. Keynes came to recognize the importance, "if possible", he wrote, of holding assets with "opposed risks ..since they are likely to move in opposite directions when there are general fluctuations" Keynes was a pioneer of "international diversification" due to substantial holdings in non-U.K. stocks, up to 75%, and avoiding home bias at a time when university endowments in the U.S. and U.K. were invested almost entirely in domestic assets.David Chambers, Elroy Dimson, Justin Foo (2015)Keynes, King's, and Endowment Asset Management

in ''How the Financial Crisis and Great Recession Affected Higher Education'' (2015), Jeffrey R. Brown and Caroline M. Hoxby, editors (p. 127 - 150). Conference held September 27-28, 2012.

See also

*Central limit theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themse ...

*Coherent risk measure
In the fields of actuarial science and financial economics there are a number of ways that risk can be defined; to clarify the concept theoreticians have described a number of properties that a risk measure might or might not have. A coherent ris ...

* Dollar cost averaging
* Equity repositioning
* Financial correlation
*List of finance topics
The following outline is provided as an overview of and topical guide to finance:
Finance – addresses the ways in which individuals and organizations raise and allocate monetary resources over time, taking into account the risks entailed ...

* Modern portfolio theory
*Systematic risk
In finance and economics, systematic risk (in economics often called aggregate risk or undiversifiable risk) is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggr ...

References

External links

Macro-Investment Analysis

Prof.

William F. Sharpe
William Forsyth Sharpe (born June 16, 1934) is an American economist. He is the STANCO 25 Professor of Finance, Emeritus at Stanford University's Graduate School of Business, and the winner of the 1990 Nobel Memorial Prize in Economic Sciences. ...

, Stanford University
Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is conside ...

An Introduction to Investment Theory

Prof. William N. Goetzmann, Yale School of Management {{DEFAULTSORT:Diversification (Finance) Financial risk modeling