# Actuarial Science Modern Portfolio Theory

A portfolio is the collection of investments. Ideally these investments are chosen in such a way to help the investors achieve their financial goals. An investor parks his hard earned money in different financial instruments with an expectation to multiply his initial investment manifold times. But as an investor, one is always apprehensive of the fact that whether his decisions would work in his favour and help him in achieving the desired return. What if things work contrarian to one’s belief? A deviation in the market, specifically when the market moves against the way will have an enormous impact on the financial health of that investor.

So is there any formula to maximize the returns and minimize risk or Is there a way to reduce the investor’s investment risk by creating a diversified portfolio so that the portfolio as a whole can produce strong returns in any economic climate?

That’s where the idea of Modern Portfolio Theory also called as Mean-Variance Portfolio Theory comes into the picture. MPT, a hypothesis put forth by Dr. Harry Markowitz in his paper “Portfolio Selection” in the year 1952.

**What is MPT?**

Modern Portfolio Theory specifies a method to an investor to construct a portfolio that gives the maximum return for a specified risk or the minimum risk for a specified return. It specifies how investment decisions affect the entire portfolio. This theory also gives emphasis to the words of Paul Heyman, ”I’ve always been a big believer in diversification for anybody. It’s never good to put off your efforts and all of your time and all of your financial resources into just one project. Diversification is the key for any individual and any business.” Thus, it advocates how diversification can reduce the inherent risk present in a portfolio.

For instance, if you invest in 5 stocks individually without even giving a thought of how these stocks affect your entire portfolio then you are at mercy of the stock market alone. If stocks in the general drop, you could face a serious risk without anything to offset that risk. If instead of putting all the eggs in one basket, one diversifies the portfolio and invests partially in the bond market or any other asset category which does not have any direct relation with the stock market then one stands up a chance to offset that risk. So, in case even if the share price plunges there might occur again in the different asset class which would, in turn, set off the loss due to fall in the share prices. As someone rightly said, ”Every portfolio benefits from bonds; they provide a cushion when the stock market hits a rough patch.”

**Assumptions:**

Every theory that is put into practice works only with certain assumptions. The MPT assumes that:

- Investor decides to invest only on the basis of 2 parameters-Risk and Return.
- All the sets of variances, covariance and expected return are known in advance.
- Investor has a single time horizon.
- Investor prefers more to less. Thus, at a given level of income investor will always prefer those assets that give them higher returns.
- Investor dislikes risk.
- Markets are efficient and there are no transaction costs and taxes.
- There is unlimited buying and selling in the market including the short selling.
- Investors can hold their assets in fractions as well.

**How does it work?****Step** **1:** To find the optimal portfolio, one needs to find the opportunity set which is a set of all possible combinations of assets that are taken.

**Step 2:** The next task is to find the efficient frontier which is nothing but removing all the inefficient parts of the opportunity set.

**Step 3:** The last step is to find an efficient portfolio which is the point of tangency of the indifference curve and the efficient frontier.

This is how the efficient portfolio is identified. The above diagrams tell the efficient portfolio in case of 2 assets. It may happen that an investor has more than 2 assets in his portfolio. In such a case, Lagrangian Multiplier is used to identify the different proportion of assets that are to be invested to maximize portfolio returns.

**Uses of MPT:**

- It helps investors construct portfolios to maximize returns while limiting risk as much as possible.
- It also helps in diversification thus reducing considerate risk.

**Criticisms to ****the theory:**

No theory is without its faults or naysayers, and Modern Portfolio Theory is no exception.

- Experts say that technical analysis gives a better picture.
- There are investors who prefer to manage their portfolio by actively trading and maximizing returns.

Even with the above flaws, MPT is widely used in managing portfolios and maximizing returns.

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