2.42 Investment reports and correlations

Investment reports often include correlations. Following a table of correlations among mutual funds, a report adds, “Two funds can have perfect correlation, yet different levels of risk. For example, Fund A and Fund B may be perfectly correlated, yet Fund A moves 20% whenever Fund B moves 10%.” Write a brief explanation, for someone who does not know statistics, of how this can happen. Include a sketch to illustrate your explanation.