# How to Use An Efficient Frontier Graph

Risk and return are the two main performance metrics of a portfolio. Return is how much your investment gained in value over the time period, which is the reason you invested in the first place. Risk is how bumpy the journey was on your road to those gains. In some ways, risk is the cost of the return.

For any given portfolio you can measure its level of expected risk and its level of expected return over a time period. Expected return is typically measured by its long-term annual return while expected risk is typically measured by its long-term standard deviation.

If you blend securities together, you can create a large set of different portfolios. You can then calculate each portfolio’s expected return and expected risk. The risk and return numbers can then be graphed to create an efficient frontier.

With expected return on the Y-axis, the higher a point is on the graph the more expected return it has. With the expected risk on the X-axis, the farther to the right a point is the more volatility you’d expect that portfolio to have.

To be on the efficient frontier, a portfolio needs to have the highest expected return for its expected risk. Visually these efficient portfolios are the highest dots on the graph with no less-risky portfolios (dots to the left) higher than it.

These portfolios are the most efficient portfolios because if you can achieve the same expected return without as much volatility that would obviously be superior since withdrawing from an overly volatile portfolio risks running out of money. Efficient frontier graphs do not pick a portfolio for you though, as the level of risk you are willing to take depends on your financial goals and withdrawal needs.

Although an efficient frontier graph can feel like a guidebook where the science is telling you in what you should consider investing, there is more artistry to portfolio construction than made apparent by this simple tool.

Efficient frontier graphs can only be created using historical data and past performance has little if anything to do with future returns.

Take Energy as an example. It’s long-term historical data has suggested that it deserves a place in efficient portfolios for decades.

With years of high energy prices and stellar returns, efficient frontier analysis consistently included large amounts of Energy in its portfolios. Using the monthly returns for S&P 500 Energy Index from its earliest available date on Morningstar (October 31, 1989), efficient frontier data consistently suggested that Energy increases the expected return of efficient portfolios. By June 30, 2014, efficient frontier graphs suggested that for a portfolio over the prior 25 years to be on the efficient frontier, it required some amount allocated to Energy.

Then, Energy set its last high in June 2014. Since then, Energy has seen a gradual decline. Now, in the midst of the COVID-19 pandemic, Energy has been hit especially hard.

Past performance is simultaneously all we have to predict the future and has little to do with what happens in the future. If we follow the historical data without any artistry, we would find ourselves with strange and concentrated allocations, like 50% invested in Footwear (a big winner of the past decade).

To be useful, efficient frontiers should be tested across multiple time periods with as much data as is available.

Furthermore, the final portfolio that you correctly design may not even be one of the ones recommended by the data. An odd blend of the historical winners may be the most efficient historically, but will Footwear really continue to be a winner going forward?

Our fifth rule in safeguarding your money is understanding your investment strategy. Although a narrative is not required to justify investing in something, having a reason why this investment will do well in the future is certainly comforting.

There are many ways to tell the story of the high and low market returns of both Footwear and Energy. Which story you elect to tell will sometimes determine whether it earns a place in your portfolio or not.

While an efficient frontier graph cannot hand you a perfect asset allocation, it remains a useful tool in analyzing what the past can tell us about a wide variety of investments.

Photo by rishi on Unsplash