### Portfolio Optimization Definition:

In order to understand what the purpose of portfolio optimization is, let’s take a brief glimpse as to what is portfolio? In the financial world, it is common for an individual, hedge fund, an investment company or any financial institution to hold the investments, the collection of investment held by them is known as portfolio. Portfolio optimization is the process of selecting the precise extent of several assets to be held in a portfolio to enhance its worth. The process is in accordance to some criterion which further coalesces either directly or indirectly with respect to the expected value of the portfolio’s rate of return as well as of the return’s dispersion and possibly other measures of financial risk.

### Portfolio Optimization Theory:

In 1950, Harry Markowitz fathered the famous Modern Portfolio Optimization Theory. The theory is based on the assumption that an investor at any given time will be willing to maximize a portfolio’s expected return reliant on any a particular amount of risk which is measured by the standard deviation of the portfolio’s rate of return. All the portfolios those fit this criterion are termed as efficient portfolios, often investors are faced with a trade-off between excepted return and risk involved for they want expect higher returns on investment and in order to achieve a higher expected return, they’ll have to take more risks.

**Efficient Frontier: **Efficient frontier is a curve on the graph that represents the risk-expected return relationship of efficient portfolios. Each point on the efficient frontier represents efficient portfolios, and they are well-diversified.

### Different Ways to Portfolio Optimization:

Different ways to portfolio optimization quantifies risk in different ways. The traditional measure, standard deviation, or the square (variance) are not really considered as reliable risk measures, amongst them a few of these measures include the Sortino ratio and the CVaR (Conditional Value at Risk).

### Portfolio Optimization Methods:

One thing you should know is that not only do the bonds and equities differ in their financial characteristics fundamentally but also have different systematic risks involved and hence one can treat as separate asset classes.

Portfolio optimization methods as we know of it occurs in two stages. The first stage entails optimizing weights of asset classes to hold. The second phase or the stage is about optimizing weights of assets within the same asset class.

Choosing the proportions placed in equities versus bonds can be cited as an example for the former one. While choosing the proportions of the stock sub-portfolio placed in stocks A, B, and C comes under the second stage.

If investors hold a couple of the portfolio in each class offers them some diversification to them, and if they account different specific assets within each class enables them to afford further diversification. Following this two-step procedure will allow you as an investor to eliminate non-systematic risks both on the individual asset and the asset class level.

One of the most prominent approaches to portfolio optimization is to identify a von Neumann-Morgenstern utility function. This function is defined upon the final portfolio wealth and the prior purpose is to maximize the expected value of utility. This particular objective function is increasing in wealth in order to reflect a preference for higher rather than lower returns. It’s concave for when it reflects the risk aversion.

### Portfolio Optimization Strategies:

Investment is no child’s play and it requires a ridiculous amount of experience as it is a forward looking activity. There are various portfolio optimization strategies followed by different investors. The co variances of returns and level of risk involved must be anticipated rather than observed to act well in time. Stock prices often show momentous differences between their historical or forecast values and what is experienced. In addition to this investors are prone to several risks, and it is taken under consideration by the portfolio optimization. Financial crises are characterized by a prominent increase in correlation of stock price movements which may critically debase the perks of diversification.

Precise estimation of the Variance Covariance matrix is paramount in mean-variance optimization framework. Quantitative techniques are effective, and are known to use Monte-Carlo simulation with the Gaussian copula and well-specified marginal distributions.

Other optimization strategies that focus on minimizing tail-risk are Value-at-Risk, Conditional Value-at-Risk in investment portfolios. These measures are very well favored amongst investors who are risk averse. In order to reduce exposure to tail risk, predictions of asset returns using Monte-Carlo imitation with vine copulas to allow for lower (left) tail dependence (e.g., Clayton, Rotated Gumbel) across large portfolios of assets are advisable.

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