# Understanding Returns Generating Models and Beta | CFA Level I Portfolio Management

## Introduction to Return Generating Models and Beta

In this lesson, we’ll explore return generating models – multifactor models, the market model, and dive into beta. You’ll learn what beta is, how to calculate it, and how to interpret it.

## Return Generating Models

In general, return generating models are used to estimate expected returns on risky securities based on specific factors. They can be classified as:

• Macroeconomic factors (e.g. GDP growth, inflation, consumer confidence)
• Fundamental factors (e.g. earnings, earnings growth, firm size, research expenditures)
• Statistical factors (based on past return data of the asset)

## Multifactor Models

Multifactor models often use macroeconomic and fundamental factors to estimate returns. Examples of these models include the Fama-French model and the Carhart model.

### Fama-French Three-Factor Model

The Fama-French model is a popular multifactor model that estimates the sensitivity of security returns to three factors:

1. Market risk: The excess return on the market portfolio
2. Size risk: The difference in returns between small and large firms (firm size)
3. Value risk: The difference in returns between high and low book-to-market ratio firms

### Carhart Four-Factor Model

The Carhart model is an extension of the Fama-French model, adding a fourth factor:

1. Momentum risk: The difference in returns between stocks with high and low past performance (price momentum)

Together, the four factors in the Carhart model do a relatively good job of explaining return differences for U.S. equity securities over the period for which the model has been estimated. For CFA Level I, you don’t need to know how to calculate all these factors, but you should be aware of them.

## Single-Factor Model and the Market Model

The single-factor model considers only one risk factor, estimating sensitivity to that factor. A special case is the single-index model, where the single factor is the excess return on the market. The market model is a simplified form of the single-index model.

EXAMPLE

If the beta of a stock against the market is 0.6, the risk-free rate is 4%, alpha will be 1.6. If the market return for the year is 7%, the expected return of the stock is 5.8%. If the actual return of the stock for the year is 8%, the abnormal return is 2.2%.

## Estimating Beta

To estimate the beta of an asset, you can use two approaches:

1. Estimate beta by regressing returns on the asset on those of the market index.
2. Calculate it based on the covariance of the asset’s return with the market return, divided by the variance of the market return. Alternatively, you can use correlation.

EXAMPLE

Plumber Inc is a US-listed company whose stock has a standard deviation of returns of 36% for the past 20 years. The average return and standard deviation of returns of the S&P500 index for the past 20 years are 8% and 18%, respectively. If the correlation of returns of Plumber stock with the market is 0.4, estimate the beta of the stock.

βi = ρi,m  x (σi/σm) = 0.4 x (36/18) = 0.8

## Wrapping Up

And that’s a wrap! In this lesson, we’ve learned about return generating models, multifactor models, the market model, and beta. We’ve also learned how to estimate beta using different methods. In the next lesson, we’ll take the concept of beta further to develop the Capital Asset Pricing Model (CAPM).

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