## Why Diversification Reduces or Eliminates Firm Specific Risk

Why do we distinguish between the different types of risk? Risk that affect one of a few firms, i.e., firm specific risk, can be reduced or even eliminated by investors as they hold more diverse portfolios due to two reasons.

• The first is that each investment in a diversified portfolio is a much smaller percentage of that portfolio. Thus, any risk that increases or reduces the value of only that investment or a small group of investments will have only a small impact on the overall portfolio.

• The second is that the effects of firm-specific actions on the prices of individual assets in a portfolio can be either positive or negative for each asset for any period. Thus, in large portfolios, it can be reasonably argued that this risk will average out to be zero and thus not impact the overall value of the portfolio.

In contrast, risk that affects most of all assets in the market will continue to persist even in large and diversified portfolios. For instance, other things being equal, an increase in interest rates will lower the values of most assets in a portfolio. Figure 3.5 summarizes the different components of risk and the actions that can be taken by the firm and its investors to reduce or eliminate this risk.

Diversification: This is the process of holding many investments in a portfolio, either across the same asset class (eg. stocks) or across asset classes (real estate, bonds etc.

Figure 3.5: A Break Down of Risk

Figure 3.5: A Break Down of Risk

Actions/Risk that ^ ^Actions/Risk that affect only one Affects few Affects many affect all investments firm firms firms

Actions/Risk that ^ ^Actions/Risk that affect only one Affects few Affects many affect all investments firm firms firms

Firm can Investing in lots Acquiring Diversifying Diversifying Cannot affect reduce by of projects competitors across sectors across countries

Investors Diversifying across domestic stocks Diversifying globally Diversifying across can asset classes mitigate by

While the intuition for diversification reducing risk is simple, the benefits of diversification can also be shown statistically. In the last section, we introduced standard deviation as the measure of risk in an investment and calculated the standard deviation for an individual stock (Disney). When you combine two investments that do not move together in a portfolio, the standard deviation of that portfolio can be lower than the standard deviation of the individual stocks in the portfolio. To see how the magic of diversification works, consider a portfolio of two assets. Asset A has an expected return of ^a and a variance in returns of o2a, while asset B has an expected return of ^b and a variance in returns of o2b. The correlation in returns between the two assets, which measures how the assets move together, is pab.5 The expected returns and variance of a two-asset portfolio can be written as a function of these inputs and the proportion of the portfolio going to each asset.

02portfolio = wa2 o2a + (1 - wa)2 o2b + 2 wa wb PAB OA Ob

5 The correlation is a number between -1 and +1. If the correlation is -1, the two stocks move in lock step but in opposite directions. If the correlation is +1, the two stocks move together in synch.

where wa = Proportion of the portfolio in asset A The last term in the variance formulation is sometimes written in terms of the covariance in returns between the two assets, which is OAB = PAB ^A Ob

The savings that accrue from diversification are a function of the correlation coefficient. Other things remaining equal, the higher the correlation in returns between the two assets, the smaller are the potential benefits from diversification. The following example illustrates the savings from diversification.

Illustration 3.2: Variance of a portfolio: Disney and Aracruz

In illustration 3.1, we computed the average return and standard deviation of returns on Disney between January 1999 and December 2003. While Aracruz is a Brazilian stock, it has been listed and traded in the U.S. market over the same period. 6 Using the same 60 months of data on Aracruz, we computed the average return and standard deviation on its returns over the same period:

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