# Residual Return

Last Updated :

21 Aug, 2024

Blog Author :

Aswathi Jayachandran

Edited by :

Rashmi Kulkarni

Reviewed by :

Dheeraj Vaidya

Table Of Contents

## Residual Return Meaning

Residual Return represents the return relative to beta multiplied by the benchmark return and where beta is the measure of volatility. In other words, the residual return of an asset is equal to the excess return of the asset minus beta times the excess return of the benchmark. It compares an asset’s excess returns against the beta of the return expectations set by the relevant benchmarks.

Residual returns can be positive or negative based on an investment's performance compared to the benchmark. A corporation with a positive return produces excess returns above and beyond what has been predicted by its systematic risk factors. This may indicate that the business is run by capable management that provides value through stock selection and active management.

##### Table of contents

- Residual return is the portion of a return on an investment that cannot be accounted for by its benchmark or market returns. It is the extra return a financial investment makes over and above what was predicted, given its exposure to the present systematic risk factors.
- The return can be positive or negative, depending on the investment’s performance compared to its benchmark. An investment has surpassed its benchmark if the residual return is positive. If not, it has underperformed.
- It displays the investment manager's capacity to increase value through stock selection and active management.

### Residual Return Explained

Residual return is the portion of a return on an investment that cannot be accounted for by its benchmark or market returns. It is the extra return a investment makes over and above what would be predicted from its exposure to the present systematic risk factors. Return is the additional profit an investment manager makes from taking on a systematic risk for the organization.

It displays the investment manager's capacity to increase value through stock selection and active management. Therefore, the difference between the investment's actual return and the return expected by its benchmark is known as a residual return. A residual return could be positive or negative depending on how well the investment performed compared to its benchmark. An investment is said to have surpassed its benchmark if this return is positive. If it is negative, it means investments have underperformed.

The return is useful in calculating the information ratio, which is the ratio of the expected annual volatility of the residual return to the expected annual residual returns. The information ratio reveals the opportunities available to investment managers, which they can leverage for gain. A larger information ratio reveals the potential for more active management.

### How To Calculate?

This return can be calculated by comparing the company's expected return to the investment's actual return. The investment's expected return based on its exposure to systematic risk factors must be calculated to estimate the returns. A financial model, such as the Fama-French Three Factor Model or the Capital Asset Pricing Model (CAPM), can be used to accomplish this. Hence, the residual return formula is the gap between actual and anticipated returns.

The formula for calculating it:

*Residual return = Excess return - (Benchmark's excess return * beta)*

or

*Residual return = Expected Return - Actual Return*

**Examples**

Here are some examples that explain the concept in detail.

**Example #1**

Let us assume Dan is an investor. The investment he made has an actual return of 15% and an expected return of 10% based on its exposure to systematic risk factors.

Residual Return = 15% - 10% = 5%

Therefore, the return will be 5%.

**Example #2**

Let us assume David is an investment manager. He has a portfolio of stocks with a beta of 1.5 and a benchmark return of 10%. According to the Capital Asset Pricing Model (CAPM), the portfolio's anticipated return is calculated using the following formula:

*Expected Return = Risk-free rate + Beta x (Market return - Risk-free rate)*

The portfolio's expected return is as follows, assuming a market return of 20% and a risk-free rate of 4%:

**Expected Return = 4% + 1.5 x (20% - 4%) = 28%**

Assume his portfolio generated a 30% return. The following formula can be used to determine the return:

*Residual return = Actual Return - Expected Return*

** = 30% - 28% = 2%**

Thus, David's portfolio generated a positive residual return of 2%, indicating he could add value through thoughtful stock selection and active portfolio management.

### Residual Return vs Active Return

Both residual and active returns are indicators of an investment's performance, but they are computed differently and interpreted in different ways. Some differences are:

Key Points | Residual Return | Active Return |
---|---|---|

Concept | It is the portion of a return on an investment that cannot be accounted for by benchmark or market returns. | The difference between an investment's actual return and its benchmark or market index is the active return. |

Significance | It measures a manager's portfolio return against a portfolio exposed to identical betas. | Active return compares the risk of the manager's portfolio return with the benchmark return. |

Formula | Actual Return - Expected Return | Portfolio Return (P) - Benchmark (B) |

### Frequently Asked Questions (FAQs)

**1. Is residual return the same as alpha?**

An investment's performance in relation to a benchmark or market index is measured by its alpha. It measures how well an investment performs compared to its benchmark or market index. On the other hand, residual return compares an investment's performance to its benchmark over and above its exposure to risks.

**2. What is the expected residual return?**

It is the rate of residual return expected against specific investments. The expected residual return is the average amount of additional return that an investment is anticipated to produce over and above the figure forecasted based on its exposure to systematic risk factors.

**3. What is the relationship between residual return and investment portfolio construction?**

An investment portfolio is constructed based on an investor’s risk tolerance, transaction costs, financial needs, risk variance, and residual and active return projections.

**4. What do benchmarks mean when calculating residual return?**

Benchmarks indicate the returns that can be logically and reasonably expected on an investment portfolio based on the systematic risks chosen by an investment manager. It helps compute the residual and active risks of investing in specific instruments.

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