Modern portfolio theory (MPT) is a theory of investment which tries to maximize portfolio expected return for a given amount of portfolio risk, or equivalently minimize risk for a given level of expected return, by carefully choosing the proportions of various assets.

The mathematical framework of MPT makes many assumptions about investors and markets.

Some are explicit in the equations, such as the use of normal distributions to model returns.

Others are implicit, such as the neglect of taxes and transaction fees.

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## What are the Key assumptions of Modern Portfolio Theory?

None of these assumptions are entirely true, and each of they compromises modern portfolio theory to some degree:

### 1. Asset Returns are (Jointly) Normally Distributed Random Variables

In fact, it is frequently observed that returns in equity and other markets are not normally distributed.

Large swings occur in the market far more frequently than the normal distribution assumption would predict.

While the model can also be justified by assuming any return distribution which is jointly elliptical, all the joint elliptical distributions are symmetrical whereas asset returns empirically are not.

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### 2. Correlations between Assets are Fixed and Constant Forever

Correlations depend on systemic relationships between the underlying assets and change when relationships change.

**For example**, one country declaring war on another, or a general market crash.

During times of financial crisis, al assets tend to become positively correlated, because they all move (down) together.

**In other words**, MPT breaks down precisely when investors are ost in need of protection from risk.

### 3. All Investors Aim to Maximize Economic Utility

This is a key assumption of the efficient market hypothesis, upon which is MPT relies, in other words, to make as much money as possible regardless of any other considerations.

### 4. All Investors are Rational and Risk Averse

This is another assumption of the efficient market hypothesis, but it is clear from behavioral economics that market participants are not rational.

It does not allow for herd behavior or investors who will accept lower returns for higher risk.

Casino gambles clearly pay for risk, and it is possible that some stock traders will pay for risk as well.

### 5. All Investors have Access to the Same Information at the Same Time

This also comes from the efficient market hypothesis.

**In fact**, real markets contain information asymmetry.

**Insider trading**, and those who are simply better informed than others.

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### 6. Investors have an Accurate Conception of Positive Returns

The probability beliefs of investors match the true **distribution of returns**.

A different possibility is that investors’ expectations are biased, causing market prices to be informationally inefficient.

This possibility is studied in the field of behavioral finance, which uses psychological assumptions to provide alternatives to the **CAPM** such as the overconfidence based asset pricing model.

### 7. There are no Taxes or Transaction Costs

Real financial products are subject both to taxes and transaction costs (such as broker fees), and taking these into account will after the composition of the optimum portfolio.

These assumptions can be relaxed with more complicated versions of the model.

### 8. Investors are Price Takers

In reality, sufficiently large sales or purchases of individual assets can sift market prices for that asset and others (via cross elasticity of demand).

An investor may not even be able to assemble the theoretically optimal portfolio if the market moves too much while they are buying the required securities.

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### 9. Every Investor has a Credit Limit

Any investor can lend and borrow an unlimited amount at the risk-free rate of interest.

### 10. All Securities can be Divided into Parcels of Any Size

In reality, fractional shares usually can not be bought or sold, and some assets have minimum order sizes.

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