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Questioning a Standard-Deviation Adjustment to CAGR

Article Quant Q&A · Author: Anon9001
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Summary

The document questions a proposed risk-adjusted compound annual growth rate formula that multiplies CAGR by one minus standard deviation. It summarizes the claim that this adjustment leaves CAGR unchanged when standard deviation is zero and reduces the adjusted value as standard deviation increases. The author contrasts the suggestion with more familiar measures such as the Sharpe and Sortino ratios and asks whether the standard deviation in the formula must be annualized.

This is a prompt for evaluating a performance measure, not a completed analysis. It supplies no calculation, comparison, market data, or conclusion about whether the formula is valid or useful. The annualization question is especially relevant because CAGR is annualized, while a volatility estimate depends on the sampling interval and scaling convention. Readers should therefore treat the quoted rule as an unverified claim in this document rather than as a validated risk-adjusted return method.

Key ideas

  • The document examines a proposed adjustment that scales CAGR by one minus standard deviation.
  • The cited description says the adjustment is unchanged at zero standard deviation and declines as standard deviation rises.
  • The author questions the measure's prevalence relative to Sharpe and Sortino ratios.
  • The document asks whether standard deviation should be annualized but gives no answer.
  • No calculations, empirical comparisons, or validation of the formula are provided.

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StatisticsRisk management
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# Is Risk Adjusted CAGR formula from Investopedia correct?


# Is Risk Adjusted CAGR formula from Investopedia correct?












https://www.investopedia.com/investing/compound-annual-growth-rate-what-you-should-know/

"A simple method for calculating a risk-adjusted CAGR is to multiply the CAGR by one minus the standard deviation. If the standard deviation (risk) is zero, the risk-adjusted CAGR is unaffected. The larger the standard deviation, the lower the risk-adjusted CAGR."

I have not seen this used widely as Sharpe/Sortino Ratio to measure risk adjisted returns hence the question. I assume the standard deviation has to be annualized.

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.