## What is Portfolio Optimization?

Portfolio Optimization is the process of selecting the best process by allocating resources to a combination of assets that provide the highest expected return for every unit of risk taken. An optimal portfolio is said to be the one that has the highest Sharpe ratio, which measures the excess return generated for every unit of risk taken.

Portfolio optimization is based on Modern Portfolio Theory (MPT). The MPT is based on the principle that investors want the highest return for the lowest risk. To achieve this, assets in a portfolio should be selected after considering how they perform relative to each other, ie, they should have a low correlation. Any optimal portfolio based on the MPT is well-diversified in order to avoid a crash when a particular asset or asset class underperforms.

### Process of Optimal Portfolio

Asset Allocation for an optimal portfolio is essentially a two-part process:

**Selecting Asset Classes**– Portfolio managers first choose the asset classes that they want to allocate funds to, and then they decide the weight of every asset class be included. Common asset classes include Equities, Bonds, Gold, Real Estate.**Selecting Assets within Class**– After deciding the asset classes, the manager decides how much of a particular stock or a bond does she want to include in the portfolio. The Efficient Frontier represents on a graph the risk-return relationship of an efficient portfolio. Each point on this curve represents an efficient portfolio.

### Examples of Portfolio Optimization

Let’s see some practical examples of portfolio optimization to understand it better.

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#### Example #1

If we take an example of Apple and Microsoft based on their monthly returns for the year 2018, the following graph shows the Efficient Frontier for a portfolio consisting only of these two stocks:

The X-axis is the standard deviation and y-axis is the portfolio return for the level of risk. If we combine this portfolio with a risk-free asset, the point on this graph where the Sharpe ratio is maximized represents the optimal portfolio. It is the point at which the capital allocation line is tangential to the efficient frontier. The reason behind is that at that point, the Sharpe ratio (which measures the increase in expected return for every additional unit of risk taken) is the highest.

#### Example #2

Suppose we want to combine a risky portfolio having only BestBuy and AT&T stocks and a risk-free asset with a return of 1%. We will plot the Efficient Frontier based on the return data for these stocks and then take a line which starts at 1.5 on the Y-axis and is tangential to this Efficient Frontier.

The X-axis represents the Standard Deviation and Y-axis represents the Return of the portfolio. An investor who wishes to take on less risk can move toward the left of this point and high risk-taking investors to move to the right of this point. An investor who does not wish to take any risk at all would just invest all the money in the risk-free asset but at the same time limit his/her portfolio return to 1%. An extra return will be earned by taking the risk.

### Advantages of Portfolio Optimization

Below mentioned are some of the major advantages of portfolio optimization:

**Maximizing Return –**The first and foremost objective of portfolio optimization is maximizing return for a given level of risk. The risk-return trade-off is maximized at the point on the efficient frontier that represents the optimal portfolio. So managers pursuing the process of portfolio optimization are often able to achieve high returns per unit of risk for their investors. This helps with client satisfaction.**Diversification –**Optimal Portfolios are well diversified in order to do away with the unsystematic risk or the non-priced risk. Diversification helps in protecting investors against downside in case a particular asset underperforms. The other assets in the portfolio will protect the investor’s portfolio from crashing and the investor stays in a comfortable zone.**Identifying Market Opportunities –**When managers indulge in such active management of the portfolio, they track a lot of market data and keep themselves updated with the markets. This practice can help them identify opportunities in the market ahead of the others and take advantage of those opportunities for the benefit of their investors.

### Limitations of Portfolio Optimization

Below mentioned are some of the major limitations of the portfolio optimization:

**Frictionless Markets –**The Modern Portfolio Theory, on which the concept of portfolio optimization is based, makes certain assumptions in order to hold true. One of the assumptions is that the markets are frictionless, ie, there are no transactions costs, constraints, etc that prevail in the market. In reality, this is often found to not be true. There are frictions in the market and this fact makes the application of modern portfolio theory complicated.**Normal Distribution –**Another assumption under the modern portfolio theory is that the returns are normally distributed. It ignores the concepts of skewness, kurtosis, etc when using the return data as inputs. It is often found that the returns are not normally distributed. This violation of assumption under the modern portfolio theory again makes it challenging to use.**Dynamic Coefficients –**The coefficients used in the data for portfolio optimization such as the correlation coefficient can change as the market situations change. The assumption that these coefficients stay the same might not be true in all cases.

### Conclusion

Portfolio Optimization is good for those investors who want to maximize the risk-return trade-off since this process is targeted at maximizing the return for every additional unit of risk taken in the portfolio. The managers combine a combination of risky assets with a risk-free asset to manage this trade-off. The ratio of risky assets to the risk-free asset depends on how much risk the investor wants to take. Optimal Portfolio does not give a portfolio that would generate the highest possible return from the combination, it just maximizes the return per unit of risk taken. The Sharpe ratio of this portfolio is the highest.

### Recommended Articles

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