Key Points

1. A portfolio’s overall risk and return is more important than the risk and return of individual investments

2. The Modern Portfolio Theory (MPT) can be used by risk-averse investors to construct diversified portfolios that maximise returns while limiting risks

3. The construction of an efficient portfolio puts emphasis on assets that have negative correlations with each other.

## What is the Modern Portfolio Theory (MPT)?

The modern portfolio theory was pioneered by Nobel Prize winner Harry Markowitz with the 1952 publication of his essay “Portfolio Selection” in the Journal of Finance. Since then the modern portfolio theory has become one of the most popular investment strategies in the world.

The 4 important concepts of the modern portfolio theory are: risk–return, diversification, negative correlation, and the efficient frontier.

## The relationship between risk and return

All investments involve some level of risk (whether it is volatility, business risk, etc.) which can have a negative impact on your returns. In other words, there is no guaranteed returns or absolute safety for any investments.

The MPT assumes that every investor is risk averse. While it is good to have higher returns, limiting risks is essential to building an efficient portfolio, and this means finding the right balance between risk and reward.

The basic relationship between risk and return is that the higher the potential risk, the higher the potential return is. Different asset classes rank differently on the risk spectrum (Certificate deposits have very low risks but low returns, while equities have higher potential returns but higher risks).

According to the MPT, an efficient portfolio would be one that maximises potential returns while limiting the risks to an acceptable level. This is achieved through the diversification of assets that have negative or low correlations with each other.

## Diversification of assets

Diversification is an essential element in achieving an efficient portfolio that balances the risks and rewards.

There are different ways of diversification, you might diversify *within* asset classes (eg. different sectors of equities), or *between* different asset classes (eg. a combination of stocks, bonds, and real estate). In general, a portfolio with more diversification will be less risky.

The composition of assets and level of diversification depend on the risk appetite and goals of the investor. An efficient portfolio aims to have the *lowest possible risk for a given level of expected return*, this concept is called the efficient frontier, which forms the basis of the modern portfolio theory.

## The role of negative correlation in diversification

When constructing a portfolio, it is often useful to look for negative correlations between assets. For example, if you hold an S&P 500 ETF (eg. VOO), it might be good to diversify into gold (eg. GLD) as it has a negative correlation with the stock market. As seen from the graph below, when stocks (blue) go up, gold (orange) tends to go down and vice versa. While long term return of gold is lower than the stock market, adding gold to the portfolio reduces its volatility.

It is generally a good idea to look for negative correlations between assets or sectors within an asset class as it allows an investor to hedge against volatility or business risk from a particular asset.

## The Efficient Frontier and how the Modern Portfolio Theory (MPT) can be applied

The efficient frontier, proposed by Harry Markowitz, is the foundation of the MPT. The efficient frontier puts portfolios on a graph of return (x axis) and risk (risk is considered the equivalent of standard deviation in MPT) (y axis). We can create an upward sloping graph that connects all of the most efficient portfolios, a template of the graph can be found on the CFI website.

Essentially, a portfolio with a return of 10% but lower standard deviation (eg. 8.5%) would be considered more efficient than one with the same return (10%) but higher standard deviation (eg. 9.7%).

Shown on a graph, this means that any portfolio that is beneath the curve is not maximising its return for its level of risk taken.

## Limitations of the Modern Portfolio Theory (MPT)

One of the criticisms of the MPT is the use of standard deviation as the equivalent of risk. This leads to a situation where two portfolios with the same return and same variance are considered equally efficient, but one might in reality have a higher downside risk. One portfolio might have the variance due to more frequent small losses while the other might have the same variance due to rare massive declines. In this situation while their efficiency appear to be the same, one of the portfolios actually have a higher downside risk than the other.

The MPT also makes a set of assumptions that may not be true in real life, for example, it assumes that asset returns result in a normal distribution but in reality, asset returns often vary a lot from the mean.

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