How Correlation Shapes Two-Asset Portfolio Risk and Allocation

Summary

The document poses a portfolio allocation problem for two assets with stated expected returns and equal volatility, asking how the choice might change when their correlation is positive one, zero, or negative one. It raises the idea that when correlation is positive one, holding the lower-return asset may add little, while negative correlation could allow a hedge and zero correlation could call for a mean–variance analysis.

These are questions and preliminary intuitions rather than a worked solution: the text provides no allocation weights, optimization, or empirical evidence. Correlation alone does not establish that two assets have equal market beta or equal overall risk, and equal standalone volatility does not make their portfolio contributions identical. A complete allocation would require a stated objective and assumptions about expected returns, risk tolerance, constraints, and any costs. The useful lesson is that covariance affects portfolio volatility and that diversification or hedging potential depends on how assets move together.

Key ideas

• Portfolio volatility depends on the assets’ covariance as well as their individual volatilities.
• Perfect positive correlation offers no volatility reduction through diversification.
• Negative correlation can create hedging potential, with the hedge depending on position weights.
• Zero correlation can still support diversification, but an allocation requires a defined objective and constraints.
• Correlation does not by itself determine beta or prove that two assets have the same overall risk.

Tags

# Discuss how you would allocate your budget between the two assets if their correlation is 1, 0, or -1


# Discuss how you would allocate your budget between the two assets if their correlation is 1, 0, or -1












An asset A is expected to yield a $2\%$ return with a standard deviation of $1\%$, and another asset B is expected to yield a $1\%$ return with a standard deviation of $1\%$. Discuss how you would allocate your budget between the two assets if their correlation is $1$, $0$, or $-1$.

In case the correlation between A and B is $1$, I would say that A and B have almost the same Beta ( I don't know to which extent this is true ), and in that case they have almost the same systematic risk ( risk inherent to the entire market ), and since they have the same specific risk ( $1\%$ ), we can assume that they have the same overall risk. In that case B is not adding anything to our portfolio so I would put everything in A since it has a greater expected return.

In case the correlation is $-1$, I assume we need to do some hedging, but I don't really know how to compute the weights that I should allocate in my portfolio.

In case the correlation is $0$, I assume we could use Markowitz optimization for example to find the weigths.

Your help is appreciated

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