## What is Portfolio Optimization?

Portfolio optimization is nothing but a process where an investor receives the right guidance with respect to selection of assets from the range of other options and in this theory projects/programs are not valued on an individual basis rather the same is valued as a part of a particular portfolio.

### Explanation

An optimal portfolio is said to be the one that has the highest Sharpe ratioSharpe RatioSharpe Ratio, also known as Sharpe Measure, is a financial metric used to describe the investors’ excess return for the additional volatility experienced to hold a risky asset. You can calculate it by, Sharpe Ratio = {(Average Investment Rate of Return – Risk-Free Rate)/Standard Deviation of Investment Return} read more, which measures the excess return generated for every unit of risk taken.

Portfolio optimization is based on Modern Portfolio Theory (MPTMPTAn investment model like modern portfolio theory or MPT allows investors to choose from a variety of investment options comprising of a single portfolio for earning maximum benefits and that too at a market risk which is way lower than the various underlying investments or assets.read more). 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, i.e.; they should have a low correlationCorrelationCorrelation is a statistical measure between two variables that is defined as a change in one variable corresponding to a change in the other. It is calculated as (x(i)-mean(x))*(y(i)-mean(y)) / ((x(i)-mean(x))2 * (y(i)-mean(y))2.read more. Any optimal portfolio based on the MPT is well-diversified in order to avoid a crash when a particular asset or asset class underperforms.

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### Process of Optimal Portfolio

Asset AllocationAsset AllocationAsset Allocation is the process of investing your money in various asset classes such as debt, equity, mutual funds, and real estate, depending on your return expectations and risk tolerance. This makes it easier to achieve your long-term financial goals.read more for an optimal portfolio is essentially a two-part process:

**Selecting Asset Classes**– Portfolio managersPortfolio ManagersA Portfolio Manager is an executive responsible for making investment decisions & handle investment portfolios for fulfilling the client’s investment-related objectives. Also, he/she works towards maximizing the benefits & minimizing the potential risks for clients. read more 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.

#### 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 the 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 this is that at that point, the Sharpe ratio (which measures the increase in expected returnExpected ReturnThe Expected Return formula is determined by applying all the Investments portfolio weights with their respective returns and doing the total of results. Expected return = (p1 * r1) + (p2 * r2) + ………… + (pn * rn), where, pi = Probability of each return and ri = Rate of return with probability. read more 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 Of The PortfolioThe portfolio return formula calculates the return of the total portfolio consisting of the different individual assets. The formula is computed by calculating the return on investment on individual asset multiplied with respective weight class in the total portfolio and adding all the resultants together. Rp = ∑ni=1 wi riread more. 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 frontierEfficient FrontierThe efficient frontier, also known as the portfolio frontier, is a collection of ideal or optimal portfolios that are expected to provide the highest return for the minimum level of risk. This frontier is formed by plotting the expected return on the y-axis and the standard deviation on the x-axis.read more 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 riskThe Unsystematic RiskUnsystematic risk refers to risk that is generated in a specific company or industry and may not be applicable to other industries or the economy as a whole. There are two types of unsystematic risk: business risk and financial risk.read more 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, i.e., there are no transaction 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, kurtosisKurtosisKurtosis in statistics is used to describe the distribution of the data set and depicts to what extent the data set points of a particular distribution differ from the data of a normal distribution. It determines whether the data is heavy-tailed or light-tailed.read more, etc. when using the return data as inputs. It is often found that the returns are not normally distributedNormally DistributedNormal Distribution is a bell-shaped frequency distribution curve which helps describe all the possible values a random variable can take within a given range with most of the distribution area is in the middle and few are in the tails, at the extremes. This distribution has two key parameters: the mean (µ) and the standard deviation (σ) which plays a key role in assets return calculation and in risk management strategy.read more. 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 coefficientCorrelation CoefficientCorrelation Coefficient, sometimes known as cross-correlation coefficient, is a statistical measure used to evaluate the strength of a relationship between 2 variables. Its values range from -1.0 (negative correlation) to +1.0 (positive correlation). read more, 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. The 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

This has been a guide to Portfolio Optimization and its definition. Here we discuss the process of an optimal portfolio, limitations, advantages, and examples of portfolio optimization. You can learn more about portfolio management from the following articles –

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