## What Is Portfolio Beta?

Portfolio Beta is a metric (or indicator) that investors use to measure the volatility associated with a particular portfolio. Its primary goal is to determine the portfolio’s market risk relative to the whole market or a particular index.

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Source: Portfolio Beta (wallstreetmojo.com)

The implications of portfolio beta equations became visible in the mid-20th century. American economist Harry Markowitz presented the modern portfolio theory, suggesting the use of beta in risk estimation. The value obtained indicates the volatility of that particular portfolio. Thus, it became easy for investors to optimize risk and multiply returns.

##### Table of contents

### Key Takeaways

- Portfolio beta is a financial metric used to measure the overall volatility of an entire investment portfolio, considering all the stocks held within it.
- The concept of beta in portfolio management originated in the mid-20th century, notably with Harry Markowitz’s introduction of the modern portfolio theory.
- The formula for calculating portfolio beta involves the cumulative sum of individual stock beta values multiplied by their respective weights within the portfolio.
- Stock beta assesses the volatility of individual stocks, while portfolio beta concentrates on evaluating the overall volatility of an entire portfolio, encompassing all its constituent stocks.

### Portfolio Beta Explained

Portfolio beta is a crucial concept of portfolio management among investors. It measures the volatility linked with a portfolio to the overall market. As a result, it becomes easy to estimate the risk of a particular investment. Also, it makes a vital component of the Capital Asset Pricing Model (CAPM). Thus, any positive or negative beta value can determine whether a portfolio is highly risky or not. Likewise, investors can curate the stocks that perform well to give higher returns. However, the rate of return usually depends on the portfolio beta coefficient value.

Generally, the market portfolio beta coefficient can be positive, negative, or near zero. Each value depicts the risk level associated with and the direction of the portfolio. So, if the beta value is positive, it indicates that the portfolio moves in the same direction as the market. It means that the portfolio is more sensitive or on par with the market performance. Thus, if the market spikes up, even the portfolio will react the same.

However, if the value is highly negative, it indicates that the portfolio moves in the opposite direction to the market. It means that there is a subtle risk associated with this stage. The beta value acts inversely to the current market condition. Thus, if the market is moving forward, the portfolio may see a downturn. This reaction may occur due to several reasons, including business deals, revenue figures, or any potential news.

Lastly, if the portfolio beta equation gives a zero coefficient, it depicts a less volatile situation. It means, at this stage, the portfolio is less sensitive to the market. Any movement of the market will not affect the portfolio. As a result, the stocks will perform near the market performance.

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### Formula

After understanding the different beta values, let us look at the formula used to calculate portfolio beta coefficient:

Here, *β* refers to the Greek letter that defines the beta of the entire portfolio, and *ω* represents the weight assigned to each stock. The weight is a specific percentage allotted to each stock based on certain factors, with more volatile stocks potentially having a higher weight.

However, it is important to note that this formula is an aggregate representation of stock beta. Therefore, it is necessary to find the individual beta for each stock and utilize the above formula.

When calculating the individual beta for stocks, consider the total number of shares. Multiply the total shares by the corresponding price, sum all the stock values to obtain the total value of the portfolio, and determine the beta value for each stock by taking a percentage of the entire portfolio.

### Examples

Let us look at some examples for comprehending the concept in a better way.

#### Example #1

Suppose Suzanne is a portfolio manager with over six years of experience managing portfolios for more than 50 clients. Each client has a unique budget and risk tolerance, and Suzanne employs CAPM to allocate stocks, ensuring the overall portfolio delivers the expected returns. To assess the risk, she analyzes the beta of each portfolio. Consider client – John’s portfolio:

Company | Total shares | Price | Total stock value | Stock percentage (%) | Weight | Beta |
---|---|---|---|---|---|---|

Apple | 2000 | $187.44 | $374,880 | 53.5 | 1.41 | 0.75 |

Nvidia | 300 | $496.56 | $148,968 | 21.3 | 1.36 | 0.29 |

Walmart | 700 | $167.65 | $117,355 | 16.8 | 0.87 | 0.15 |

CVS Health | 100 | $68.5 | $6850 | 0.97 | 0.2 | 0.0019 |

Tesla | 200 | $237.41 | $47,482 | 6.7 | 0.6 | 0.0402 |

General Motors | 150 | $28.2 | $4230 | 0.6 | 0.001 | 0.00006 |

Total | $699,765 | 1.232 |

**Note:** The weights in the Weight column are calculated by dividing the stock percentage by 100 for a consistent unit. When Suzanne calculated the market portfolio beta coefficient, the value turned out to be 1.232, indicating a positive beta. The portfolio is highly volatile and tends to move in the same direction as the market. Any sudden market changes will likely result in a similar reaction in the portfolio.

#### Example #2

According to the Zacks Mutual Fund Rank, PGIM Jennison Focused Growth A (SPFAX) currently holds a 4 (Sell) based on factors such as size, cost, and past performance. However, there are notable positive aspects to consider. Managed by PGIM in Providence, RI, SPFAX has been in operation since June 2000 and has successfully accumulated around $739.49 million in assets. Despite a 5-year annualized total return of 11.1%, placing it in the middle third among peers, SPFAX demonstrates resilience with a 78.66% allocation to U.S. stocks and 16.99% in foreign securities.

Despite a 3-year annualized total return of -0.04%, SPFAX exhibits an active trading approach with a 49% turnover rate. Its standard deviation over the past three and five years, though higher than the category average, reflects the fund’s active management strategy. With a 5-year beta of 1.17, indicating slightly higher volatility than the market average, SPFAX can be viewed positively by investors seeking opportunities in dynamic market conditions. Despite being a load fund with an expense ratio of 1.05%, slightly above the category average, SPFAX’s strengths make it a potential choice for proactive and risk-tolerant investors.

### Importance

Portfolio beta holds a significant role in finance and portfolio management, offering valuable insights into risk tolerance. When a stock within a portfolio has a beta value exceeding 1, it indicates higher volatility compared to the market, implying potential for increased returns alongside heightened risk.

Additionally, portfolio beta helps determine the stocks’ direction relative to the market and assesses portfolio volatility, particularly in different market conditions. This beta value serves as a crucial tool for portfolio curation, allowing managers to tailor portfolios based on investors’ risk tolerance, creating a well-balanced mix that aligns with their capacity for risk.

### Portfolio Beta vs Stock Beta

Although portfolio and stock beta share similarities, they differ significantly. Let us examine these distinctions:

Basis | Portfolio Beta | Stock Beta |
---|---|---|

Meaning | It refers to the beta value calculated for the entire portfolio, | Stock beta is the measure of the volatility of individual stocks. |

Focus | Here, the prime focus stays on determining the volatility of the portfolio. | It aims to calculate the volatility of stocks and not cumulative beta. |

Formula | β_{P} = β_{1} x ω_{1} + β_{2} x ω_{2} + … + β_{n} x ω_{n} | β_{s} = Covariance/Variance |

### Frequently Asked Questions (FAQs)

**1. How to calculate the beta of a portfolio in Excel?**

Following are the ways to calculate the beta for a portfolio in an Excel worksheet. Let us look at them:

– Gather data regarding the portfolios of the clients.

– Enter the data in the cell format.

– Create columns, namely stock value, weight, and beta.

– Use the Excel formulas and calculate the beta value.

– Lastly, estimate the volatility factor with this value.

**2. What is the difference between portfolio beta and alpha?**

Although alpha and beta are primarily used indicators in stock markets, here, alpha refers to the measure for calculating excess return. In contrast, beta is the measure for calculating the risk and volatility factor.

**3. What are the limitations of portfolio beta?**

The following are the limitations of portfolio management. Let us look at them:

– It considers historical data instead of current data.

– This beta is less helpful for long-term investment calculation.

– This measure is dynamic. As a result, the calculation may be subjective to time.

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