Why Average Returns Do Not Determine Stock Correlation
Summary
The document explains that two stocks’ average returns do not determine their correlation. Correlation measures how paired returns move together over observations, while averages describe each series’ central value. The example gives two return series with means of 5% and 2% whose correlations can differ, including zero and one, demonstrating that the same averages are compatible with different co-movement.
It also points out that the question can be ambiguous about the observation period and what it means for one stock to return a stated amount. Even a fixed return for one series does not establish a unique correlation with another series; the pattern of paired observations matters. The examples are illustrative rather than an empirical study, and the document does not provide a correlation-estimation procedure or discuss sampling uncertainty. Its central lesson is to use aligned return observations to assess dependence instead of inferring correlation from average performance.
Key ideas
- Average returns do not determine the correlation between two assets.
- Correlation depends on the paired pattern of returns across observations.
- The same means can coexist with different correlation values.
- A statement about returns needs a defined time period and observation structure to support correlation analysis.
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Full text
# Correlation between 2 stocks # Correlation between 2 stocks If Stock A returns 5% on average in year Y And Stock B returns 2% on average in year Y Does this mean that correlation is 40%? ## Answer by rbm (score 3) https://quant.stackexchange.com/a/25970 Does this mean that correlation is 40%? No. Very simple example (in R). Let A and B be stocks with returns `stockA` and `stockB`. Consider following example: ``` stockA = c(0.05, 0.04, 0.05, 0.06) stockB = c(0.01, 0.02, 0.03, 0.02) mean(stockA) mean(stockB) cor(stockA, stockB) stockA = c(0.04, 0.05, 0.05, 0.06) stockB = c(0.01, 0.02, 0.02, 0.03) mean(stockA) mean(stockB) cor(stockA, stockB) ``` giving ``` > mean(stockA) [1] 0.05 > mean(stockB) [1] 0.02 > cor(stockA, stockB) [1] 0 > > stockA = c(0.04, 0.05, 0.05, 0.06) > stockB = c(0.01, 0.02, 0.02, 0.03) > mean(stockA) [1] 0.05 > mean(stockB) [1] 0.02 > cor(stockA, stockB) [1] 1 ``` ## Answer by horseless (score 1) https://quant.stackexchange.com/a/25971 The answer is no. First, the question is ambiguous about what year Y is. Is year Y actually 2015? Knowing those returns in one year says nothing about correlation. Second, if it means that if Stock A goes up 5% then Stock B will go up by 2%, then that also says nothing. What if Stock A goes down. Does stock B go up or down? Additionally, look at the averages. Create a series of every year Stock A goes up by exactly 2%. Then one can create any correlation you want, positive or negative, by playing with the Stock B returns. For example lots of small negative returns, and one large positive gets a negative correlation at the same time as a 2% average. [for example, in time series terms, A is up 2% exactly each time, but B goes from 1 to .9, .8, .7, .6, and then up to .95. The return is about 2% but the correlation would be negative 0.4 rather than positive 0.4]
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