Efficient Frontier Definition
The efficient frontier, also known as the portfolio frontier, is a set of ideal or optimal portfolios that are expected to give the highest return for a minimal level of return. This frontier is formed by plotting the 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 on the y-axis and the standard deviation as a measure of risk on the x-axis. It evinces the risk-and return trade-off of a portfolio. For building the frontier, there are three important factors to be taken into consideration:
- Expected return,
- Variance/ Standard Deviation as a measure of the variability of returns also known as risk and
- The covariance of one asset’s return to that of another asset.
This model was established by the American Economist Harry Markowitz in the year 1952. After that, he spent a few years on the research about the same, which eventually led to him winning the Nobel Prize in 1990.
Example of the Efficient Frontier
Let us understand the construction of the efficient frontier with the help of a numerical example:
Assume there are two assets, A1 and A2, in a particular portfolio. Calculate the risks and returns for the two assets whose expected return and standard deviation are as follows:
| Particulars | A1 | A2 |
|---|---|---|
| Expected Return | 10% | 20% |
| Standard Deviation | 15% | 30% |
| Correlation Coefficient | -0.05 |
Let us now give weights to the assets, i.e., a few portfolio possibilities of investing in such assets as given below:
| Portfolio | Weight (in %) | |
|---|---|---|
| A1 | A2 | |
| 1 | 100 | 0 |
| 2 | 75 | 25 |
| 3 | 50 | 50 |
| 4 | 25 | 75 |
| 5 | 0 | 100 |
Using the formulae for Expected Return and Portfolio Risk i.e.
Expected Return = (Weight of A1 * Return of A1) + (Weight of A2 * Return of A2)
Portfolio Risk = √ [(Weight of A12 * Standard Deviation of A12) + (Weight of A22 * Standard Deviation of A22) + (2 X Correlation Coefficient * Standard Deviation of A1 * Standard Deviation of A2)],
We can arrive at the portfolio risks and returns as below.
| Portfolio | Risk | Return |
|---|---|---|
| 1 | 15 | 10 |
| 2 | 9.92 | 12.5 |
| 3 | 12.99 | 15 |
| 4 | 20.88 | 17.5 |
| 5 | 30 | 20 |
By using the above table, if we plot the risk on X-axis and the Return on Y-axis, we get a graph that looks as follows and is called the efficient frontier, sometimes also referred to as the Markowitz bullet.
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In this illustration, we have assumed that the portfolio consists of only two assets A1 and A2, for the sake of simplicity and easy understanding. We can, in a similar fashion, construct a portfolio for multiple assets and plot it to attain the frontier. In the above graph, any points outside to the frontier are inferior to the portfolio on the efficient frontier because they offer the same return with higher risk or lesser return with the same amount of risk as those portfolios on the frontier.
From the above graphical representation of efficient frontier, we can arrive at two logical conclusions:
- It is where the optimal portfoliosOptimal PortfoliosPortfolio optimization refers to the strategic process of making improvements or positive changes to the investor's portfolio containing various assets. The Sharpe ratio helps to analyze the returns from an optimal portfolio.read more are.
- The efficient frontier is not a straight line. It is curved. It is concaved to the Y-axis.
However, the efficient frontier would be a straight line if we are constructing it for a complete risk-free portfolio.
Assumptions of the Efficient Frontier Model
- Investors are rational and have knowledge about all the facts of the markets. This assumption implies that all the investors are vigilant enough to understand the stock movements, predict returns, and invest accordingly. That also means that this model assumes all investors to be on the same page as far as knowledge of the markets is concerned.
- All investors have a common goal, and that is to avoid the risk because they are risk-averse and maximize the return as far as possible and practicable.
- There are not many investors who would affect the market price.
- Investors have unlimited borrowing power.
- Investors lend and borrow money at a risk-free interest rate.
- The markets are efficient.
- The assets follow a normal distributionNormal DistributionNormal 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.
- Markets absorb information quickly and accordingly base the actions.
- The decisions of the investors are always based on expected return and standard deviation as a measure of risk.
Merits
- This theory portrayed the importance of diversification.
- This efficient frontier graph helps investors choose the portfolio combinations with the highest returns with the least possible returns.
- It represents all the dominant portfolios in the risk-return space.
Drawbacks/Demerits
- The assumption that all investors are rational and make sound investment decisions may not always be true because not all investors would have enough knowledge about the markets.
- The theory can be applied, or the frontier can be constructed only when there is a concept of diversification involved. In a case where there is no diversification, it is sure that the theory would fail.
- Also, the assumption that investors have unlimited borrowing and lending capacity is a faulty one.
- The assumption that the assets follow a normal distribution pattern might not always stand true. In reality, securities may have to experience returns that are far away from the respective standard deviations, sometimes like three standard deviations away from the mean.
- The real costs like taxes, brokerage, fee, etc. are not taken into consideration while constructing the frontier.
Conclusion
To sum up, the efficient frontier displays a combination of assets that has the optimal level of expected return for a given level of risk. It is dependent on the past, and it keeps changing every year; there is new data. After all, the figures of the past need not necessarily continue in the future.
All the portfolios on the line are ‘efficient,’ and the assets which fall outside the line are not optimal because either they offer a lower return for the same risk or they are riskier for the same level of return.
Although the model has its own demerits like the non-viable assumptions, it has been earmarked to be revolutionary at the time it was first introduced.
Recommended Articles
This has been a guide to what is an efficient frontier and its definition. Here we discuss an example of an efficient frontier with the graph. You can learn more from the following portfolio management articles –
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very informative.
Thanks for your kind words!