Efficient frontier: the best mixes for each risk

Written by the Tactfolio research teamPublished 4 min read

The efficient frontier is the set of portfolio mixes that had the highest return for each level of risk. This efficient frontier tool loads real past prices for up to 8 US stocks or ETFs. It draws every possible mix and marks the best ones. It needs a free account, because it uses our price data.

  • Each dot on the chart is one mix of your tickers. Up means more return. Right means more risk.
  • The frontier is the top edge of the dots. Any mix below it had less return for the same risk.
  • Mixing assets that do not move together can lower risk without giving up return.
  • The tool marks the lowest-risk mix and the mix with the best Sharpe ratio.
  • It shows the past. The frontier of the next 10 years will look different.

How to use the efficient frontier tool#

Type 2 to 8 tickers, separated by commas, and pick a period. Set a risk-free rate, which is about what cash pays. Then press Calculate. The chart shows the frontier as a line, with your tickers as labeled dots. The table under it lists the two marked mixes and their weights.

The tool only uses mixes that own each ticker or not. It never borrows or sells short. The weights always add up to 100%.

The starting tickers are examples. They are not advice.

How does the efficient frontier work?#

Every mix has a return and a risk. The return is the average of the tickers’ returns, weighted by how much you own. The risk is harder, because it depends on how the tickers move together.

return of mix = sum of (weight × average return)
risk of mix   = √(sum over every pair of: weight A × weight B × covariance of A and B)
covariance    = correlation × volatility of A × volatility of B

Risk here is volatility: how much the yearly return swings. When two assets have a low correlation, their swings partly cancel out. So the mix swings less than the average of its parts.

The tool finds the mix with the highest return for each level of risk. Those mixes form the frontier. Harry Markowitz described this idea in 1952. It later won him a share of the Nobel Prize in economics.

A worked example#

Say a stock fund returned 8% a year with 16% volatility. A bond fund returned 4% with 6% volatility. Their correlation was 0.

StocksBondsReturnRisk
0%100%4.0%6.0%
20%80%4.8%5.8%
40%60%5.6%7.3%
60%40%6.4%9.9%
80%20%7.2%12.9%
100%0%8.0%16.0%
  1. All bonds had 6% risk. Adding 20% stocks raised the return to 4.8% and cut the risk to 5.8%.
  2. The lowest-risk mix was about 12% stocks and 88% bonds. It returned about 4.5% with about 5.6% risk.
  3. Holding all bonds was not efficient. A mix with some stocks did better on both counts.
  4. Past the lowest-risk mix, each step up in return costs more risk. You pick where you are comfortable.

What the frontier leaves out#

  • The future. The frontier uses past returns. A small change in them can move the best mix a lot.
  • Bad streaks. Volatility treats a sudden crash and a slow slide the same. Check the max drawdown too.
  • Costs and taxes. Trading and taxes lower what you keep.
  • Rebalancing. The math assumes you reset the weights every month. Real portfolios drift between rebalances.

Common mistakes with the efficient frontier#

  • Treating the best past mix as the plan. It is the best mix for a period that is over.
  • Using a short period. Three good years for one asset can make it look like it belongs in every mix.
  • Ignoring how much the weights jump. If one more year of data flips the mix, the result is not stable.
  • Forgetting that risk is more than volatility. A calm asset can still fall hard once.

Try it on Tactfolio#

The frontier shows a mix at one moment. A real strategy has to hold and rebalance that mix through time. In the Tactfolio strategy builder you can backtest a mix with rebalancing on decades of prices. The asset correlation tool shows the numbers behind the chart. The portfolio optimizer picks one mix for your goal and limits. Learn more about the Sharpe ratio and portfolio rebalancing. Every tool is on the free trading calculators page.

Common questions#

What is the efficient frontier in simple terms?#

It is the line of best choices. For each amount of risk, it shows the mix that earned the most. Any mix below the line could have earned more for the same risk.

What is the best point on the efficient frontier?#

There is no single best point for everyone. The lowest-risk mix suits someone who hates swings. The best Sharpe ratio mix earned the most per unit of risk. Your own point depends on how much swing you can live with.

Why do I need an account for this tool?#

The tool loads years of real daily prices for each ticker. That data is part of Tactfolio, so it needs a free account. The other calculators on this site work with no sign-up.

Why does the frontier change when I change the period?#

Returns and correlations differ from one period to the next. A frontier built on a boom looks very different from one built on a crash. Try a few periods to see how steady the result is.

Is modern portfolio theory still useful?#

Yes, as a way to think. It shows why spreading money across assets that do not move together can lower risk. But its inputs come from the past, so treat its exact weights as rough.

Sources

Understand the numbers