Introducing The Efficient Frontier

Introducing The Efficient Frontier

Last week we looked at the jelly bean chart and how it can visually describe the periodic (annual, in this case) returns of various market asset classes over time. This week we introduce a different framework based on the return vs. risk trade off facing investors at every decision point. A rational investor wants more portfolio return (Rp) for a fixed level of risk or less portfolio risk (Sp) for a fixed level of return. In an ideal world, we desire both more return AND less risk. The chart shown below shows this basic trade off.

 

Source: JQR Capital

Return / Risk Framework

The 11 asset classes shown in the jelly bean chart from last week are one way to split up the investment universe. That chart consisted of one cash asset class, five bond asset classes, and five stock asset classes. For this post, we start by first simplifying our investment universe into two main asset classes: bonds (as measured by the ICE BofA US Corporate Index) and stocks (as measured by the Wilshire 5000 Index). The expected portfolio return [E(Rp)] in the next investment cycle is equal to the weight (0% to 100%) of bonds (Wb) multiplied by the expected return of the bonds [E(Rb)] plus the weight (again, 0% to 100%) of stocks (Ws) multiplied by the expected return of the stocks [E(Rs)].

 

E(Rp) = Wb * E(Rb) + Ws * E(Rs)

 

The expected portfolio risk - as measured by standard deviation - over the next investment cycle is calculated with weights and risks for the bond (b) and stock (s) portions of the portfolio. The key ingredient to this expected portfolio risk calculation is the correlation [E(RHObs)] between the bond returns and the stock returns.

 

E(Sp) = SQRT [Wb^2 * E(Sb)^2 + 2 * Wb * Ws * E(Sb) * E(Ss) * E(RHObs) + Ws^2 * E(Ss)^2]

 

The chart below shows how bonds and stocks have historically moved in the same direction (positive return) over long periods of time, but may have moved in opposite directions over some shorter periods of time. It is important to note that each of the asset class returns differs dramatically from their longer term average (Rb = 7.39% and Rs = 11.82%) over the past 40 years.

 

Source: JQR Capital

Asset Correlation Matters

The correlations between asset classes are what create what is described as the efficient frontier. If bonds and stocks were expected to move in the same direction during the next investing cycle, their expected return correlation would be +1.00. If they were expected to move in the opposite direction during the next investing cycle, their expected return correlation would be -1.00. Over the last 40 years, the annual return correlation between stocks and bonds has been roughly +0.46. This means that for any annual investing cycle, the bonds and stocks tend to move in similar different directions in their long-term path to positive returns - and personal wealth. The primary benefit to investors of combining lower correlated assets into one portfolio is the higher return / risk tradeoff results in a smoother “ride” over time toward higher wealth.

 

Source: JQR Capital

 

Source: JQR Capital

 

Source: JQR Capital

 

JQR Capital offers you a complimentary one hour consultation to “Find Your Bearings” in your lifelong voyage to find your own private island. Please click the link shown below.

 

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Disclaimer

Past performance is no guarantee of future results. Any investment involves some amount of risk and may not be suitable for all — or any — individuals. You should consult with your investment advisor before acting on this — or any — financial information.

References

https://www.investopedia.com/terms/s/sharperatio.asp

https://fred.stlouisfed.org/


Copyright © JQR Capital Management, LLC 2024


Location: 23 Foxridge Rd, West Hartford, CT 06107, USA

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