Why Zero Correlation Cannot Lower Risk Below the Lower-Volatility Asset

Summary

The document considers whether combining a strategy with 20% annualized volatility and one with 15% volatility, when their returns have zero correlation, can produce a portfolio with volatility below 15%. The accepted response uses the portfolio variance relationship and explains that covariance depends on correlation and the assets’ standard deviations.

With zero correlation, the combination does not gain the offsetting movements needed to fall below the volatility of the less volatile holding. The explanation says that negative correlation is required for one position’s movement to counteract the other’s. This is a conceptual answer, not a worked numerical portfolio calculation: it provides no allocation weights or empirical evidence, and does not discuss estimation error, changing correlations, or other portfolio constraints.

Key ideas

• Portfolio volatility depends on both constituent volatilities and their covariance.
• Zero correlation provides no offsetting covariance benefit between the two holdings.
• Negative correlation is needed for the combination to fall below the less volatile holding’s volatility.
• The answer gives a qualitative explanation without specifying portfolio weights.

Tags

# Can adding an uncorrelated high vol strategy to a low vol portfolio result in a portfolio with even lower volatility?


# Can adding an uncorrelated high vol strategy to a low vol portfolio result in a portfolio with even lower volatility?












Let's say I have fund A with 20% annualized volatility and portfolio B with 15% annualized volatility. If A and B have 0 correlation, can the combination of these funds have volatility < 15% ? Are there any papers explaining this?

## Answer by Brumder (score 1, accepted)

https://quant.stackexchange.com/a/21093

The total volatility of a portfolio is calculated as follows:

Recall that Cov(a,b) is just (Correlation a,b)/(StD A * StD B). So in this case, no the portfolio could not have a total volatility of less than 15%. For this to happen, we would need negative correlation between the two assets.

Think of volatility in this case as the amount of movement in portfolio value. Only by having some degree of negative correlation between assets could one return offset the other (from a theoretical standpoint) on the same day and cause the price swing of the total portfolio to be less wild than the least volatile holding.

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