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Portfolio Optimization

Diversification & Efficient Frontier

What is diversification?

Spreading investments over different securities and asset classes in order to reduce the overall portfolio risk by means of preventing downfall of a single security, is termed as diversification.

Benefits of diversification

  1. Helps earn higher returns with a lower level of risk

  2. Improves knowledge among different investment instruments

  3. Prevents portfolio and monetary losses during times of extreme volatility

  4. Combines the benefits of different investment instruments

  5. Adds the advantage of compounded returns

  6. Benefit of geographical diversification by investing in foreign securities

  7. Cross-sector investments result in reducing volatility existing in a certain sector

  8. Offers a certain peace of mind

Understanding Correlations

Diversification tends to perform best when the assets are uncorrelated or have little or negative correlation.

Correlation exists between +1 and -1

  • A correlation of +1 implies a direct and equal movement between assets

  • A correlation of -1 implies an exactly opposite movement between assets

  • A correlation of 0 means that the assets are independent and movement of one doesn’t affect the other















This graphical distribution of investments is an excellent way to understand the standing of a diversified portfolio.

Portfolios A, B and C show varied returns and risks, however, a rational investor would want a decent return with a considerable level of risk. Portfolio P, the diversified portfolio, containing equal amounts of securities A, B and C, offers just this advantage. Efficient Frontier















To best understand the efficient frontier, we should refer to the graph above.

As we can see, portfolios P and Q give the same level of return, however, at different risk levels. Q offers the same return at a lower risk. As a return, any investor would prefer Q over P.

The curved line that runs through here is called the efficient frontier. Any portfolio located on the efficient frontier provides a maximum possible return given a certain risk level. Any portfolio located under this frontier is not deemed as efficient because the same return can be generated with lower risk.

The point R represent the Global Minimum Variance Portfolio implying the lowest level of risk offered after diversification.

Risk-free Asset

Risk-free asset is termed as any security offering a given level of return with negligible probability of default.
















A risk-free asset is located on the y-axis as there is a guaranteed return on it without risk. This way we can extend the efficient frontier with the risk-free frontier being tangent to it.

Modern Portfolio Theory

The concept of efficient frontier is broadly covered under the umbrella of Modern Portfolio Theory (MPT).

It is often wondered whether one should invest across industries or countries. When studying a particular industry or country, the most important thing to understand is the level of variation in stocks of that class. Some countries tend to have booming economies and stock markets, and it makes better sense to invest in such countries. However, if an industry is showing excellent performance, companies within that industry should be targeted.

Limitations of MPT

1. In a multi-period horizon, even risk-free assets tend to show variation in returns and portfolio modelling is not optimal

2.As certain investor face issues from purchasing securities on a margin basis, optimal portfolios may not be achieved

3.There is an assumption of normal distribution on asset returns which is very wrong for individual equities as correlations vary 4.Investor rationality and behavior vary and every investment is subject to sentiments

5.Historical performance doesn’t truly indicate the future performance of assets

6.Securities of any sizes and amounts cannot always be bought as there are certain guidelines with respect to the minimum lots in the case of certain assets.


Despite the criticism and appreciation that MPT receives, investors all around the world use MPT in some way or other as diversification with even the smallest number of securities is done by investors. This way, the concept of portfolio optimization is favored with the usage of MPT and as an early investor, an extensive knowledge of MPT and diversification is crucial to delve deeper into investments and stock markets. The best way to understand fundamentals of diversification is via graphs and visuals as true returns are always measured visually.

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