How to Calculate Portfolio Beta?

Portfolio beta is commonly used to assess the risk of investment portfolios. Investors typically strive to diversify their investment portfolios by investing in a diversified investment vehicle. By diversifying the investment portfolios, they are able to reduce risks.

In this article, we cover the definition of portfolio beta, how to calculate it with example and interpretation. Therefore, let’s dive in!

What is Portfolio Beta?

In the concept of investment, there are two types of risk associated with the investment. These are diversifiable risk and non-diversifiable risk. These two risks together form a total risk of an investment or portfolios. Diversifiable risk is commonly called non-systematic risk while the non-diversifiable risk is commonly called systematic risk.

Portfolio beta is a measure of the non-diversifiable risk of portfolios or securities. It is the weighted average of betas of each individual investment or asset. This risk cannot be reduced by implementing diversification. Therefore, investors shall need to carefully assess before deciding on any investment vehicles.

The market beta is equal to 1.00. Typically, any assets or securities with a beta greater than 1.00 are considered as high-risk assets or securities. In contrast, if the beta is less than 1.00, that’s mean such assets or securities are at low risk than the market. However, for a risk-free asset, its beta is equal to 0.

How to Calculate Portfolio Beta of Investment Portfolio?

In order to calculate the portfolio beta, we need to know the beta of each asset. Then, we calculate by multiplying the beta of each asset with its proportion of that asset value and add up together. By doing so, we get a weighted average beta of the whole investment portfolios or securities.

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Below is the formula that we use to calculate the portfolio beta:

Portfolio Beta (βp) = WA × βA + WB × βB + WC × βC + ……… + WN × βN

 Where:

WA is the proportion of the portfolio’s total value of asset A

βA is the beta of asset A

WB is the proportion of the portfolio’s total value of asset B

βB is the beta of asset B

WC is the proportion of the portfolio’s total value of asset C

βC is the beta of asset C

WN is the proportion of the portfolio’s total value of asset N

βN is the beta of asset N

Example

ABC Fund is a large portfolio management company. It has two portfolios to assess the levels of risk in order to make investment decisions. Both portfolio A and portfolio B have five assets to be invested. The below table summarizes the beta of each asset as well as its proportion value in percentage term of each portfolio:

AssetsPortfolio A
Proportion (W)
Portfolio A
Beta (β)
Portfolio B
Proportion (W)
Portfolio B
Beta (β)
110%1.5015%0.80
225%1.0010%1.00
325%1.2025%0.85
420%1.4530%0.70
520%1.2020%1.20
Total100% 100% 

We can calculate the portfolio beta of both portfolio A and B by using the below formula:

βp = WA × βA + WB × βB + WC × βC + ……… + WN × βN

From the table above, we can calculate the portfolio beta as follow:

βp (A) = 10% × 1.50 + 25% × 1.00 + 25% × 1.20 + 20% × 1.45 + 20% × 1.20

Therefore, Portfolio Beta A (βp) = 1.23

βp (B) = 15% × 0.80 + 10% × 1.00 + 25% × 0.85 + 30% × 0.70 + 20% × 1.20

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Therefore, Portfolio Beta B (βp) = 0.88

Thus, from the calculation above, we get portfolio beta A and B at 1.20 and 0.88 respectively.

Interpretation and Analysis

As mentioned above, if a portfolio has a beta of greater than 1.00, it would be considered as low risk. This means that the portfolio experiences changes in the rate of return which is equal to the changes in the expected rate of return of the market. In other words, if it experiences a 10% increase, it would tend to experience a 10% increase of return as well.

In contrast, if the market return decrease by 10%, the return of the portfolio of beta +1.00 would also decrease by 10%.

From the calculation above, portfolio A has a greater than 1.00 beta. This means that portfolio A is a high risk and high return portfolio. Conversely, portfolio B has a beta of less than 1.00. That’s mean, portfolio B is a low risk and low return portfolio.

Conclusion

Portfolio beta is a good measure to assess the levels of risk of investment portfolios. It enables investors as the basis before deciding to invest in any assets or portfolio. 

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