In review of our calculations, we can see the covariance in correlation for both of these stocks versus the S&P 500 are aligned Microsoft's positive covariance means the stock returns moving the same direction as the market returns and vice versa for fnv's negative relationship. However, covariance does not clearly show us to what degree this is, why most investors prefer correlation due to its standardized indication of strength and how it remains unaffected by changes in Dimensions locations and scale here. The correlation shows a stronger positive relationship for msft at 0.7. The fnv's negative relationship of negative 0.1.

These figures could easily be compared to similar data samples for other stocks.

The correlation Matrix above illustrates the correlation factor between different pairs of assets. Obviously the correlation between the same asset is 1.0 a perfect correlation some pairs of assets such as small stocks and large stocks have a strong correlation of 0.8 other pairs of assets have weaker correlations such as long-term corporate bonds and treasury bills, which have a correlation factor of just 0.16.

Other pairs of assets have a negative correlation. So they will move in opposite directions such as treasury bills and small stocks negative correlations can be very helpful for hedging purposes correlations within a portfolio are important to understand as the cumulative Factor exposures of individual assets can change when combined factors have generally had low correlations with each other intended to perform. Well at different parts of the economic cycle.

A diversified strategy can navigate more types of Market environments and potentially lower overall volatility. However, correlations can be volatile in different Market environments. They can change quickly and often in times of Market stress at the worst possible time the diversifying aspect of combining factors with different risk and return characteristics and low correlations help investors, whether the storm during adverse market conditions.

The above formula is intimidating at first, but it is calculating the variance of the portfolio and then taking the square root to give us the standard deviation of the portfolio.

First We Take the variance of each individual asset weighted by the percentage of that asset in the portfolio squared then we add it to the product of the weights asset correlation, the individual asset standard deviations multiplied by two you can see it just isn't the risk of the individual assets the first part of the formula which contributes to the risk of the portfolio. It is also the interaction of the assets to each other the correlation.

A portfolio of four assets will not only have four weights but also have six correlation terms five assets will have 10 correlation terms variance is not a particularly easy statistic to interpret on its own. So most analysts calculate the standard deviation, which is simply the square root of variance.

Here the S&P 500 and Microsoft both have positive standard deviations 5.3 and 6.0 respectively.

However, the portfolio correlation is 0.7. And this means that rather than being the weighted average of the two standard deviations. The overall portfolio standard deviation is slightly below the weighted average at 5.2.

In contrast fnv has a standard deviation of 6.7. However, when combined together in an equally weighted portfolio, the portfolio standard deviation is 4.0 lower than both individual assets. The portfolio standard deviation is affected by both the individual assets, but also by the negative correlation Where the assets returns typically change in different directions resulting in a lower overall portfolio therefore risk.

If both assets and the portfolio have the same standard deviation, then there will be no benefits to diversification. If the correlation is below one, then the standard deviation of the portfolio will be less than the weighted average of the assets as the correlation between the assets declines. Then the diversification benefits will increase if the correlation is negative one, then we have a perfect hedge as one asset goes up. Then the other asset will decline in the standard deviation of the portfolio is zero the same as the risk-free rate.

The chart below shows the portfolio risk in return for four correlation values in a range of Weights of 0 to 100% for each asset in a two asset portfolio portfolio risk grows with each successive increase in the correlation value for each level of expected return with the greatest risk, when the correlation equals positive 1 the curve nature of a portfolio of assets is recognizable in all investment opportunity sets except at the extremes where correlation equals negative one or positive one while the expected return varies with asset weights. It is unaffected by the correlation in only the portfolio risk changes in other words because of diversification as correlations decline the investor can obtain lower portfolio risk without sacrificing return at the extremes where 100% is invested in either asset A or B. The Portfolio risk is unaffected by the correlation coefficient because you are only investing in one asset.

In the previous example, you can see by adding assets which aren't closely correlated helps diversify risk and reduce the overall portfolio volatility adding more assets will continue to reduce the volatility. However, there comes a point when adding more Investments to a portfolio ceases to make a meaningful difference. It is also not just individual assets which help reduce volatility.

You can break down the portfolio into industry exposure broad asset classes or geographical regions.

Combining asset classes that are highly correlated typically serves little purpose as they perform in-kind unfortunately many assets have high positive correlations. The challenge in diversifying risk is to find assets that have correlations much lower than positive 1 the primary objective for optimal portfolio management is to reduce risk without sacrificing returns.