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Why Efficient Frontier Portfolios May Lack High-Risk, Low-Return Points

Article Quant Q&A · Author: Matt Bart
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Summary

The document asks whether portfolio plots built from combinations of several stocks are plausible and why they show few portfolios with both low returns and high standard deviation. The portfolios use weekly return and volatility estimates, with the asset set expanded across successive graphs. The response considers the absence of points in the high-risk, low-return region rather than evaluating the code or the estimates behind the plots.

Its explanation is that investors generally require higher expected returns to accept greater risk, so combinations with substantial volatility and very poor returns may be uncommon in the plotted set. The answer regards the graphs as reasonable and treats the increasing clustering as consistent with the example. This is an intuitive generalization, not a guarantee about every asset universe or sample period. The document gives no detailed portfolio optimization method, covariance analysis, or evidence that the inputs and calculations are correct.

Key ideas

  • The example plots portfolio weekly return against weekly standard deviation.
  • Adding assets can change the set of attainable portfolio combinations and the appearance of the plotted cloud.
  • The response links higher risk with investors requiring higher expected returns, offering a reason high-risk, low-return portfolios may be sparse.
  • The answer is a qualitative assessment and does not validate the underlying data or calculations.

Tags

Portfolio constructionRisk managementEquities
Full text
# Efficient Frontier Graph


# Efficient Frontier Graph












I'm writing some C code to create different portfolios using a few stocks that are given as inputs. I am having some trouble trying to find if these results are correct. My biggest hesitation is that the are no data points in the bottom right quadrant of the graph. I would expect that there be more points with lower return but higher standard deviation.

Some notes: The x axis is standard deviation (weekly) The y axis is return (weekly)

The first graph is GOOG, VIX, TSLA The second graph is GOOG, VIX, TSLA, BA The third graph is GOOG, VIX, TSLA, BA, NFLX

Obviously these stocks may not be the best combination in terms of covariance together. However the more stocks that I add to the portfolio the more of a cluster that it becomes.

So two questions:

- Do these graphs look like reasonable graphs?

- Why aren't there more points with a low return and high standard deviation?

## Answer by AdB (score 1)

https://quant.stackexchange.com/a/45055

- Yes, your graphs look pretty reasonable to me.

- In general, you would expect returns to be increasing in standard deviation. Basically, the more risk you take on, there higher returns you require. This is why, in general, it is hard to find stocks with a lot of risk and very low returns. That is exactly what you see here.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.