Correlation and Diversification in Portfolio Management – Descriptive Questions and Answers
Course: Investment Management / Portfolio Management
Topic: Correlation, Portfolio Risk and Diversification
1. Define the coefficient of correlation. Explain the meaning of correlation coefficients of +1, 0, and -1 in the context of portfolio management.
Answer:
The coefficient of correlation (ρ) is a statistical measure that indicates the degree and direction of the linear relationship between the returns of two securities. It ranges from −1 to +1.
ρ = +1 (Perfect positive correlation):
The returns of the two securities move exactly in the same direction and in fixed proportion. When one security’s return increases (or decreases), the other security’s return increases (or decreases) by a proportional amount. Diversification benefits are minimal because losses and gains tend to occur simultaneously.
ρ = 0 (No correlation):
There is no systematic linear relationship between the returns of the two securities. Movements in one security do not provide information about movements in the other. Some diversification benefit exists because the random movements of one security are not closely tied to those of the other.
ρ = −1 (Perfect negative correlation):
The returns of the two securities move exactly in opposite directions. When one security’s return goes up, the other’s return goes down by a proportional amount. This provides the maximum possible diversification benefit and, in theory, can completely eliminate portfolio risk under certain weight combinations.
In summary, the lower the correlation between assets, the greater the potential reduction in portfolio risk through diversification.
2. Discuss how the coefficient of correlation affects portfolio risk. Why do investors prefer securities that are not perfectly positively correlated?
Answer:
Portfolio risk depends not only on the individual risks (standard deviations) of the securities but also on how their returns move relative to one another, as captured by the correlation coefficient.
- When securities have a high positive correlation, their returns tend to rise and fall together. In such a case, combining them produces limited diversification benefits and the overall portfolio risk remains relatively high.
- When securities have low or negative correlation, poor performance in one asset may be offset by better performance in another. This reduces the variability of portfolio returns and therefore lowers portfolio risk.
Investors prefer securities that are not perfectly positively correlated because combining such assets can reduce unsystematic (asset-specific) risk without necessarily reducing expected returns. This improves the overall risk–return profile of the portfolio.
3. An investor is considering two securities. Explain how the portfolio risk would differ if the correlation coefficient between the securities is +1, 0, and -1.
Answer:
When correlation (ρ) = +1:
The two securities move perfectly together. The portfolio standard deviation becomes the weighted average of the individual standard deviations. No diversification benefit exists, and portfolio risk cannot be reduced by combining the two securities.
When correlation (ρ) = 0:
The two securities move independently. Their returns are uncorrelated, so some diversification benefit is achieved. The portfolio standard deviation is lower than the weighted average of individual standard deviations, meaning portfolio risk is reduced.
When correlation (ρ) = −1:
The two securities move perfectly in opposite directions. This is the ideal case for diversification. With appropriate portfolio weights, it is theoretically possible to construct a portfolio with zero standard deviation (no risk), even though each individual security is risky.
Therefore, as correlation decreases from +1 towards −1, portfolio risk decreases and diversification benefits increase.
4. Why is correlation considered an important factor in diversification? Support your answer with suitable examples.
Answer:
Diversification aims to reduce portfolio risk by combining assets whose returns do not move exactly together. Correlation is important because it quantifies the degree to which assets move together or in opposite directions. The lower the correlation between assets, the greater the potential risk reduction.
Example 1:
Investing only in airline stocks may not provide significant diversification because these stocks are exposed to similar economic factors such as fuel prices, travel demand, and regulatory changes. Their returns tend to move together (high positive correlation).
Example 2:
Combining airline stocks with pharmaceutical stocks may reduce risk because the two industries are affected by different factors. A downturn in travel may not coincide with a downturn in healthcare demand. Correlation between these sectors is likely to be lower, so diversification benefits are higher.
Thus, investors seek assets with low or negative correlations to maximize diversification benefits and improve the portfolio’s risk–return trade‑off.
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