How Low Correlation Improves Portfolio Diversification

Summary

The document explains why two assets can offer portfolio benefits even when they have identical means and standard deviations. Their individual return statistics describe only the first two moments of each asset; they do not capture how the assets move together. When correlation is below one, combining assets can reduce portfolio volatility relative to the same expected return and thereby improve the Sharpe ratio, under the stated assumptions.

The discussion extends the intuition to portfolios of multiple assets, where lower average correlation generally supports diversification. It also notes that maximizing the Sharpe ratio through numerical portfolio optimization tends to favor assets with low or negative correlations. The answer is conceptual rather than empirical: it provides no market data, optimization details, or treatment of estimation error, transaction costs, constraints, or changing correlations. Its conclusions therefore describe a theoretical diversification benefit, not a guarantee of realized performance.

Key ideas

• Assets with identical means and volatilities can still diversify one another.
• Correlation describes joint movements that individual means and standard deviations do not capture.
• Combining assets with correlation below one can improve the portfolio Sharpe ratio under the stated assumptions.
• Sharpe-ratio optimization tends to assign more weight to assets with lower or negative correlations.
• The discussion does not address estimation error, trading costs, or changing correlations.

Tags

# Two assets with the same mean and standard deviation - Would there be any benefit?


# Two assets with the same mean and standard deviation - Would there be any benefit?












If I have two assets in a portfolio with the same standard deviation and mean and the correlation between the assets is 0, theoretically could there be a situation where it would be beneficial to having a portfolio like this?

## Answer by Simon (score 2)

https://quant.stackexchange.com/a/14786

It will bring diversification benefits to your portfolio. Mean and standard deviation alone only measures the first two moments of the individual asset returns, with no regards for their joint distribution and correlation structure.

Assuming the mean and volatility measurements are the same for $2$ assets with correlation $corr<1$, then combining them will improve your portfolio's Sharpe ratio. To extend it further, assuming you have $n$ assets with same mean and volatility, then combining them into a portfolio will generally be beneficial if their average correlation is less than one.

In fact, if you run a numerical optimization for these portfolio using Sharpe maximum as the objective metric, the resultant weighting scheme will favor those assets with low or negative correlation automatically.

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.