DATE

10.06.2022

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**The Beta** of an asset or portfolio **can be used as a statistic to make investment decisions** based on the estimates of the returns we can expect depending on the risks.

If the factors that have determined the fluctuations in the past are reproduced in the future market (systematic risks), under normal market conditions, Beta is a statistic that **can help us to also estimate the theoretical returns expected for a given asset or portfolio of assets’** **risk.**

To** estimate the expected returns** of an asset or portfolio** using Beta**, we will use **two methodological approaches** that are very intuitive and easy to apply. The first will give us the expected returns and the second will give us the range of the variation for a given probabilistic scenario:

Beta allows us to estimate the long-term returns we can expect for a given asset based on its systematic risks (under normal conditions of the market).

To do this **we will use the CAPM (Capital Asset Pricing Model)**. A model that has been widely questioned due to numerous assumptions made in its formula. However, because of its simplicity, it is the most widely used model in corporate finance and is also, in many cases, the main model for estimating expected returns in the vast majority of business schools in corporate finance courses.

The CAPM model was developed by the 1990 Nobel Prize winners Sharpe and Lintner. It is a model that **allows** us to easily and intuitively** estimate** the** returns that we can expect for a financial asset** or portfolio **under normal financial markets conditions based on its systematic risks.**

This model is based on the principle that the market only rewards systematic risk-taking through returns because it believes that since unique risks are easily eliminated by adequate diversification, the investor is diversified.

The version of** the CAPM formula** we use for estimating long-term returns is as follows:

*Expected return on a financial asset = (return on a risk-free financial asset) + (the additional return we should expect from that asset because of the level of risk it has relative to the market).*

The logic of the formula is that the return we can expect for an asset with risk is higher than that for an asset without risk, and that the additional return we should expect for the risk of that asset is proportional to the return that the market as a whole has over risk-free assets.

**For the first part of the sum** we will use the data that informs us of the returns that we can expect for a financial asset with the lowest possible risk to serve as a better estimator for the risk-free asset. For example, German Government short-term debt securities or US Treasury debt securities (for Europe and the US respectively).

**For the second part**, let’s break it down to see what data we need:

- The return we should expect from that asset because of the level of systematic risk it has in respect to the market = Beta of the financial asset x market risk premium.
- The Market Risk Premium is the historical extra return that financial markets have on historical returns of risk-free assets.

For a non-professional investor with a long-term vision, it’s an **easy and intuitive way** to get **an approximation of the returns we can expect** from a financial asset or portfolio (an Investment Fund, for example) depending on the risk we want or are willing to take.

Beyond precision – which never exists when we want to estimate expected returns – this tool helps us make better-informed investment decisions. This knowledge **allows us to avoid getting into scams or high-risk investments** with promises of unrealistic returns.

Let’s take a practical example, with data produced from historical series. If the Beta of an Mutual Fund investing in the US stock market, and whose benchmark index is the S&P 500, is 1.4. (It is 40% more volatile than the S&P 500 Index):

- Analysing historical 3 months US Treasury Bill returns and weighing the data of the last 10 years over the entire historical series, the result is 1.9% (approximately 2%). We will use this data as a better approximation of the returns of a risk-free asset, knowing that it can change gradually as interest rates evolve.
- The historical “extra-yield” of the S&P 500 relative to the 10-year US Treasury bonds is 4.47% (approximately 4.5%).
- The approximate Mutual Fund`s return we could expect over a long-term outlook and under normal market conditions is:

2% + (1.4 x 4.5%) = 8.3%.

Based on the volatility of the market index that represents an asset or a portfolio of assets (for example, an Investment Fund), the Beta also allows us to estimate the expected long-term return ranges under normal market conditions.

This tool is also based on the principle that the market rewards only via returns, the assumption of systematic risks only, as single risks are considered to be easily eliminated.

First of all, we should know that **volatility informs us of the dispersion of returns around the average return in a year**, taking into account 68% of the possible cases. This means that, if we are interested in using volatility as a measure of risk, there are 32% of cases that are not covered by the volatility statistic (16% for positive cases and 16% for negative cases).

**If we know the historical average return** of the index representing a financial asset or product (for example, an Investment Fund) **and its volatility, using the Beta** of the financial asset or product, **we can calculate the expected returns of this asset based on its (systematics) risk.**

For example, based on the usual information of an Mutual Fund`s report, knowing that:

- The Beta for the Mutual Fund is, for example, 0.8.
- Its historical average return is, for example, 6.5%.
- The volatility of the index used as a benchmark is, for example, 18%.
- We can estimate that, with a 68% probability, the returns of this Mutual Fund could be between -9.2% (0.8 x (6.5% – 18%)) and +19.6% (0.8 x (6.5% + 18%).

- What is the Beta coefficient in finance?
- How is Beta interpreted?
- How to measure risks with Beta?
*How to estimate returns with Beta? (current post)*

José Luís Álvarez – CEO HollyMontt

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