In uncertain markets, low correlation investments may help a stock portfolio as long as they provide returns without substantially higher risk. While correlation coefficients are a starting point, understanding the beta of the security is also important. My previous article looked at several investments that had low correlations to the SPDR S&P 500 Index ETF. The following table shows these securities and two additions from the comments section from the previous article with their associated correlation coefficients.

**Low Correlation Securities**

Ticker | Name | Correlation 36 months |

SPY | S&P 500 Index Trust ETF | 100% |

PCY | PowerShares Emerging Mkts Sovereign Debt | 48% |

XLU | Utilities Select Sector SPDR | 45% |

MCD | McDonald's Corp. | 37% |

PCG | PG&E Corp. | 31% |

GLD | SPDR Gold Shares ETF | 16% |

LQD | iShares iBoxx $ Invest Grade Corp Bond | 8% |

TIP | iShares Barclays TIPS Bond | -15% |

SHY | iShares Barclays 1-3 Year Treasury Bond | -32% |

VXX | iPath S&P 500 VIX ST Futures ETN | -81% |

*Source:* *Yahoo!Finance* *for split and dividend adjusted prices, Author calculations. Three year correlations are based upon monthly returns of the securities listed. Data has been updated to include recent prices and so will not exactly match correlations in the previous article.*

Beta is one measure of risk that is often discussed in constructing investment portfolios. It is often referred to as a measure of systematic risk of a given security. Investopedia defines beta as:

A measure of the volatility, or systematic risk, of a security or a portfolio in comparison to the market as a whole. Beta is used in the capital asset pricing model (CAPM), a model that calculates the expected return of an asset based on its beta and expected market returns. Beta is calculated using regression analysis.

*Source:* *Investopedia*

In mathematical terms, beta is the ratio of the covariance of a security to that of the market relative to the variance of that given security. This math simplifies down to beta being the product of the correlation between the security and the market and the ratio of the security's volatility to the market's volatility. The following table shows the betas for some common securities:

**Implied Beta of Select Securities**

Ticker | Correlation 36 months | Volatility 36 months | Ratio | Implied Beta |

SPY | 100% | 4.4% | 1.0x | 1.0 |

PCY | 48% | 2.3% | 0.5x | 0.2 |

XLU | 45% | 2.9% | 0.7x | 0.3 |

MCD | 37% | 3.4% | 0.8x | 0.3 |

PCG | 31% | 3.9% | 0.9x | 0.3 |

GLD | 16% | 5.3% | 1.2x | 0.2 |

LQD | 8% | 1.5% | 0.3x | 0.0 |

TIP | -15% | 1.2% | 0.3x | (0.0) |

SHY | -32% | 0.2% | 0.1x | (0.0) |

VXX | -81% | 20.3% | 4.6x | (3.7) |

*Source:* *Yahoo!Finance* *for split and dividend adjusted prices, Author calculations. Three year correlations, volatility, and implied beta are based upon monthly returns of the securities listed. Implied beta is the ratio of the volatilities (fourth column) multiplied by the correlation (second column).*

This table shows that correlation and volatility might not have any relationship. Furthermore, PCG has a low correlation, but comparable monthly volatility to SPY, resulting in a beta of almost 1. GLD has a low beta due primarily to its very low correlation, despite a higher volatility than SPY. While VXX has a very negative correlation to the market, it also has an exceptionally high volatility. This combination provides significant potential for reducing a portfolios volatility. However, it should also be noted that it has performed very poorly over the past 36 months.

With an understanding of beta and both correlation and volatility, one can estimate the impact on a portfolio's beta from the addition of one of these investments. One can consider the shift from SPY to a portfolio consisting of 50% SPY and 50% of the other security. The new portfolio volatility is based on a mathematical calculation using the volatility of SPY and the select security, the correlation coefficient, and the weights of SPY and the other security.

**Portfolio Volatility Reduction**

Ticker | Correlation Coefficient | Volatility | 50/50 Portfolio Volatility | Volatility Impact |

SPY | 100% | 4.4% | 4.4% | 0.0% |

PCY | 48% | 2.3% | 2.9% | -1.5% |

XLU | 45% | 2.9% | 3.1% | -1.3% |

MCD | 37% | 3.4% | 3.3% | -1.1% |

PCG | 31% | 3.9% | 3.4% | -1.0% |

GLD | 16% | 5.3% | 3.7% | -0.7% |

LQD | 8% | 1.5% | 2.4% | -2.0% |

TIP | -15% | 1.2% | 2.2% | -2.2% |

SHY | -32% | 0.2% | 2.2% | -2.2% |

VXX | -81% | 20.3% | 8.5% | 4.1% |

*Source:* *Yahoo!Finance* *for split and dividend adjusted prices, Author calculations.*

Once can see that despite the high negative correlation of VXX, its very large volatility does not help improve the overall portfolio volatility. In contrast, if VXX had a volatility equal to 4.4%, that of SPY, the actual volatility impact would have been almost 3% less instead of 4% more. That is the impact of a negative correlation. However, the overwhelming volatility of VXX offsets that benefit. It is also clear to see that both volatility and correlation can reduce overall portfolio volatility. For example, GLD has an above market volatility (5.3% vs. 4.4%) but helps reduce portfolio volatility due to its low correlation. LQD and TIP have larger impacts since they have both low volatility and low correlations. TIP has a negative correlation.

One benefit of adding these types of investments to a portfolio is to create a stable portfolio with minimal swings. However, for adherents to the capital asset pricing model, low betas also correspond to low returns. So once again, there is a trade off that investors have to make. My follow up article to this one will look at some of these select investments with respect to the Sharpe Ratio to compare their returns to the standard deviation of the excess return.

**Disclosure: **I am long SPY. I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.

**Disclaimer: **This article is for informational and educational purposes only and shall not be construed to constitute investment advice. Nothing contained herein shall constitute a solicitation, recommendation or endorsement to buy or sell any security.