Executive Summary

Diversification is a way to reduce risk by investing in a variety of assets or business ventures.

Systematic risk is not diversifiable, while idiosyncratic risk can be reduced or even eliminated.

Portfolio diversification depends on riskaversion and time horizon, and the portfolio mix must be rebalanced periodically.

Overdiversification/“diworsification” can occur under certain conditions. Business diversification relies on endogenous opportunities, whose value depends on how flexibilities such as timing and expansion options are managed.
Introduction
To diversify is to do things with variety in order to improve wellbeing. Diversification is thus a common and fundamental concept in both daily life and business. However, the practice is primarily known as a way of reducing risk by investing in a variety of assets or business ventures. Buying one utility stock in the East coast and one in the West will minimize local shocks, while maintaining roughly the same return as buying either of the two alone. A shop at a resort selling both umbrellas and sunglasses clearly will have a less variable income whether a sunny or a rainy day comes up.
To obtain the optimal strategy of diversification, the risk must be defined and the associated investment opportunities modeled. In addition, the utility or investor’s risk tolerance and investment horizon must be specified. In terms of asset allocation and portfolio choice, the risk is usually defined as the standard deviation of the portfolio return. This measures the variability of the return relative to the expected value of the return. Given a fixed level of expected return, the strategy that generates the minimum variance is preferred. To achieve this, the optimal diversification among the assets will usually be required. The risk tolerance of an investor determines the tradeoff between return and risk, as well as the level of risk to take.
Modern Portfolio Theory
Without a formal framework, naive diversification calls for an allocation of an equal amount of money across N assets, and thus it is also known as the 1/N rule. This rule goes back to as early as the fourth century, when Rabbi Issac bar Aha suggested: “One should always divide his wealth into three parts: a third in land, a third in merchandise, and a third ready to hand.” Naive diversification is clearly not optimal in general. For example, when investing in a money market and a stock index, few investors will allocate 50% to the money market.
In 1951 Markowitz published his famous portfolio theory, which provides the optimal portfolio weights on a given N risky assets (stocks) once the expected returns, covariances, and variances of the assets are given, along with the investor’s risk tolerance, in a quadratic utility function. The resulting optimal portfolio is a full diversification with money invested in all of the risky assets. The benefits of diversification depend more on how the assets perform relative to one another than on the number of assets you want to invest. The more the assets do not behave alike—that is, the lower the correlations among them—the more the risk can be minimized by holding the right mix of them.
The optimal portfolio is not riskfree. It is simply the one that has the minimum risk among all possible portfolios of the assets for a given a level of expected return. For any asset, one can decompose its total risk into two components, systematic/marketwide risk and idiosyncratic risk. The optimal portfolio has only market risk, because idiosyncratic risk is diversified away. As a result, there is no point in taking any idiosyncratic risk. But market risk is unavoidable. Intuitively, the return on a suitable portfolio of all stocks in the market has only the market risk, and will not be affected by bad news from some companies, which is likely be offset by good news from others. However, a war, a national disaster, or a global crisis will likely affect the entire portfolio in one direction.
With leverage, the optimal portfolio can theoretically be designed to obtain any desired level of expected return by taking certain necessary risk. The greater the desired expected return on the optimal portfolio, the higher is the risk. Without borrowing and short selling, the diversified portfolio must have an expected return between the highest and the lowest of the asset expected returns. However, the risk is often much smaller than the lowest risk of all the assets.
An efficient portfolio is one that offers either the highest expected return for a given level of risk or the lowest level of risk for a given expected return. The efficient frontier represents that set of portfolios that has the maximum expected return for every given level of risk. No portfolio on the efficient frontier is any better than another. Depending on the investor’s risk tolerance, the investor chooses theoretically one, and only one, efficient portfolio on the frontier.
The investment opportunity set is static in the mean–variance framework underlying the Markowitz portfolio theory. As investment opportunities change over time, many argue for time diversification—that the risk of stocks diminishes with the length of the investment horizon. While this is debatable, the benefit of diversification across assets, and much of the mean–variance theory, carry through into dynamic portfolio choice models with changing investment opportunities. However, due to incomplete information (such as parameter and model uncertainties), trading costs (such as learning and transaction costs), labor income, and solvency conditions, it can be optimal theoretically to underdiversify—to not invest in all assets. Diversification purely for the sake of diversification can cause unnecessary diversification or overdiversification, to end up diworsification i.e. worsening off from bad diversification.
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