Residual Risk Is Calculated As Which of The Following

Residual risk is a key concept in finance and risk management. It represents the portion of risk that cannot be diversified away through portfolio diversification. Understanding how to calculate residual risk is essential for investors and financial analysts.

What is Residual Risk?

Residual risk, also known as idiosyncratic risk or non-diversifiable risk, refers to the risk that remains after accounting for systematic risk. Systematic risk is the risk that affects an entire market or sector, while residual risk is unique to a specific investment or asset.

In portfolio theory, residual risk is what cannot be eliminated through diversification. It's the risk that investors must bear even when they hold a diversified portfolio. Residual risk is often measured using the standard deviation of an asset's returns after removing the market risk.

How to Calculate Residual Risk

The most common method to calculate residual risk is by using the following formula:

Residual Risk = √(Total Risk² - Systematic Risk²)

Where:

Total Risk is the standard deviation of the asset's returns
Systematic Risk is the beta of the asset multiplied by the standard deviation of the market returns

This formula comes from the Capital Asset Pricing Model (CAPM), which separates risk into diversifiable and non-diversifiable components. The residual risk represents the portion of risk that cannot be diversified away.

Note: Residual risk is often expressed as a standard deviation, with higher values indicating greater risk. It's important to note that residual risk cannot be eliminated through diversification, so investors must be prepared to bear this risk.

Example Calculation

Let's walk through an example to illustrate how to calculate residual risk. Suppose we have an asset with the following characteristics:

Metric	Value
Total Risk (Standard Deviation)	20%
Beta	1.2
Market Risk (Standard Deviation)	15%

Using the formula for residual risk:

Systematic Risk = Beta × Market Risk = 1.2 × 15% = 18%

Residual Risk = √(Total Risk² - Systematic Risk²) = √(20² - 18²) = √(400 - 324) = √76 ≈ 8.72%

In this example, the residual risk is approximately 8.72%. This means that 8.72% of the asset's total risk cannot be diversified away, regardless of how the investor diversifies their portfolio.

FAQ

What is the difference between residual risk and systematic risk?

Residual risk is the portion of risk that cannot be diversified away, while systematic risk is the risk that affects an entire market or sector. Systematic risk can be diversified through portfolio diversification, but residual risk cannot.

How is residual risk different from total risk?

Total risk includes both systematic and residual risk. Residual risk is the portion of total risk that remains after accounting for systematic risk. It represents the unique risk of a specific investment.

Can residual risk be eliminated through diversification?

No, residual risk cannot be eliminated through diversification. It represents the unique risk of a specific investment that cannot be shared with other assets in the portfolio.

What factors affect residual risk?

Residual risk is influenced by factors specific to an investment, such as its industry, size, and management quality. These factors contribute to the unique risk profile of the investment.