# Diversifying Investment Essay

Diversifying investment  is a risk management  technique that is used to minimize the risk of individual securities  by investing  in  a portfolio  of securities. That is, if investors reduce their reliance on particular assets, they can more easily bear a downturn  on an individual security. Diversification is the cornerstone of modern portfolio theory that has seen wide applications in financial decision making. Both firms and individuals diversify investments.  The former  diversify by investing in individual activities, while the latter diversify by investing in portfolios rather  than in individual assets.

In portfolio  theory,  investors  are assumed  to  be risk averse, that  is, they prefer lower to higher risk for a given return  and will accept a higher risk only if they are compensated  with a higher  return.  This creates  indifference curves, lines on which risk and return  combinations  are offered to investors  and as long as investors are on this line, they are indifferent on where to invest. Namely, as risk increases, return increases as well, so that investors are compensated for  the  increased  risk  they  take  on.  The expected return  of an investment  in a single asset is the sum of the returns  on that investment  conditional  on the probability  of every return  occurring.  For example, if there is 60 percent  probability that an investment earns a 5 percent  return  and 40 percent  probability that  it will earn 15 percent,  the expected  return  on this investment  is 9 percent,  which is the weighted average of the  probability  of each event  occurring. Furthermore, the expected return  on an investment portfolio, i.e., on a combination  of investments, is the sum of the weighted average of the returns of the individual holdings of the portfolio.

On the other hand, variance measures the variability of returns  and is used as a benchmark  for the risk of individual assets. In a single asset, the variance is the square root of the difference between the realized and the expected  return  on the asset. However, the variance of a portfolio of assets is proportional to the weights that  are invested on each asset, to the variance of individual assets, and also to the  degree of correlation between the individual assets.

## Correlation

Correlation is a measure of interrelationship between assets and measures the extent to which the returns from two investments  move together.  If the correlation coefficient is +1 this means that  the returns  of the  two investments  always change proportionately in the same direction (perfect positive correlation). A correlation  coefficient of –1 means that  the returns always move proportionately in the  opposite  directions (perfect negative correlation). When the correlation coefficient is zero, this means that the returns have no correlation  whatsoever and their returns  are independent from one another.

The essence of diversification lies on the correlation coefficient of securities. Since the variance of a portfolio has two components,  the individual securities’ variance component and the correlation  coefficient component,  when two assets are negatively correlated, i.e., when the second component is negative, the portfolio variance is greater  than  portfolio variance. In other  words, by investing in securities with negative correlation,  the overall risk of the portfolio is reduced. If the correlation  is zero, the second term of the portfolio variance is zero, so the variance of the portfolio is simply the sum of the individual variances of each stock included in the portfolio. The benefit of diversification is eliminated when the correlation coefficient is +1. Thus, other things equal, the smaller the correlation  between two assets, the smaller the variance (risk) of the portfolio of the two assets. One can create the same risk level and higher expected returns by diversifying one’s investments across a wide range of stocks. The only assumption  is that as long as the individual  stocks  are  not  perfectly  correlated,  the risk-return combination  of the portfolio will be better than the risk-return combinations of all individual stocks. The benefit of diversification increases as the degree of correlation  decreases. This creates the efficient frontier,  which represents  the set of portfolios that  give the highest return  at each level of risk, or alternatively, the lowest risk at each level of return.

The above is also extended  to portfolios of assets of more than two individual securities. Even though the computation of the correlation  of more than two securities  becomes  very complex,  the  principle  of diversification applies to complex portfolios providing that none of the securities are perfectly positively correlated. Also, as the number  of securities that are included  in a portfolio  increases, the benefit that  is derived from diversification of adding one more asset to the portfolio decreases. In other words, the benefit that is derived from the reduction in risk by increasing the number  of holdings in a portfolio is outweighed by the additional  costs (transaction  and monitoring costs) that are associated with increasing the number of securities. For that reason, it has been studied that individual investors do not need to hold more than 1– 15 assets in order to capture 90 percent of the benefits from diversification, while for individual investors the number of shares should not exceed 50.

## Limits

However, there are limits to diversification. These limits are set by the two types of risk that are embedded in asset prices. The first type of risk is called unique or unsystematic risk that refers to the effect that random events may have on individual firms. These events are unique and can be diversified away. The second type of risk is called systematic or market risk and it refers to the risk that is embedded in all securities of a single market, a single industry, or even a single country. For example, the interest  rate risk is a type of systematic risk that  affects all securities  of one country.  Thus, as long as portfolios  are constructed of assets that include securities from one country, the interest rate risk is no diversifiable and will only be embedded in the total variability of the constructed portfolios.

The way to minimize the systematic risk is to create portfolios of securities that share very few common elements. For example, one can eliminate the country-specific risk by investing in assets in a wide range of countries.  Also, the stock-specific risk is diversified away by maintaining  a portfolio of assets that is a combination  between different types of securities, i.e., bonds, deposits, works of art, real estate. As a rule of thumb, a well-diversified portfolio should not contain more than  40 percent  of its value in individual stocks and the remainder  should be invested in other forms according  to the investor’s liquidity and risk return preferences.

In  practice   the  portfolio  theory  of  diversification  has found  computational difficulties, since, for example, for a portfolio of 300 securities more than 45,000 need to be calculated. In addition,  diversifying investment  theory is difficult to apply in physical investment  decisions  as, in  contrast  with  financial assets, the  calculation  of correlation  coefficients in physical investments  is not always accurate. Further, some difficulties become apparent when applying the diversification theory  to a multiperiod  model. Also, should firms that  diversify their individual activities be rewarded for their actions? In other words, should firms evaluate  the  correlation  of each  project  with its portfolio of existing projects? If so, then the value of a firm’s portfolio of individual projects should be greater than the value of the sum of the parts, thus the present value principle is no longer applicable.

Fortunately, diversification is very difficult to apply in firms in such a manner.  This stems from the fact that  individual  investors  are  able to  diversify their investments  more easily. So, investors can invest in a firm this week and pull out next week, whereas a firm would find it extremely difficult to do the same with an investment project.

## Applications

The theory  of investment  diversification  has found wide applications in the construction of indexes that are designed to track the performance  of individual securities. Such specific indices are the index funds that contain all stocks that are traded in an index and can be sold as a ready-made  investment  portfolio to individual investors. The fund’s objectives are to offer simple, diversified solutions at a low cost, yet the main disadvantages  of such  funds  are the  tracking  error that results from failing to replicate the index accurately and the fact that index funds can only produce the return of the index and not outperform it.

Bibliography:

1. Altman, Handbook of Financial Markets and Institutions (John Wiley & Sons, 1987);
2. Brealey and A. Myers, Principles of Corporate Finance (McGraw-Hill, 2003);
3. John A. Doukas  and  Ozgur  Kan, “Investment Decisions  and  Internal  Capital  Markets: Evidence from Acquisitions,” Journal of Banking and Finance (v.32/8, August 2008);
4. Edwin J. Elton, Martin Gruber,  Stephen J. Brown and  William  N. Goetzmann,  Modern  Portfolio Theory and Investment Analysis (Wiley, 2007);
5. Pike and B. Neal, Corporate Finance and Investment: Decisions and Strategies (Prentice Hall, 2006);
6. Pilbeam, Finance and Financial Markets  (Palgrave, 2005);
7. Rutterford and M. Davison, An  Introduction  to Stock Exchange Investment (Palgrave,  2007);
8. Laura Sether,  Online  Trading  (W&A, 2007);
9. Peter J. Tanous, Build a Winning Portfolio: Investment Strategies for Meeting Your Financial Goals (Kaplan, 2008);
10. Valdez, An Introduction to Global Financial Markets (Palgrave, 2007).

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