Question

If an investment has 35 percent more nondiversifiable risk than the market portfolio, its beta will be: a. 35 b. 1.35 c. 0.35

Short answer

The beta is 1.35, matching option b.

Step-by-step solution

Understanding Beta and Nondiversifiable Risk

The beta (b2) of an investment measures its nondiversifiable risk in relation to the market as a whole. A beta of 1 means the investment's risk is the same as the market's, whereas a beta greater than 1 indicates more risk, and less than 1 indicates less risk.

Applying the 35% More Risk

Since the investment has 35% more nondiversifiable risk than the market, which has a beta of 1 by definition, we add this additional risk to the market's beta: \[ \beta = 1 + 0.35 = 1.35 \]

Choosing the Correct Option

The calculated beta of 1.35 matches option b. Therefore, the investment's beta is 1.35, indicating it is riskier than the market by 35%.

Key concepts

Nondiversifiable Risk

Nondiversifiable risk, also known as systematic risk, is the type of risk that cannot be eliminated through diversification. It is inherent to the entire market or a segment of the market. This risk affects a large number of assets and is usually influenced by factors such as economic changes, political events, or natural disasters. Unlike diversifiable risk, which can be reduced by diversifying a portfolio, nondiversifiable risk impacts all investments across the board.
Investors need to understand nondiversifiable risk because it sets the baseline of risk that cannot be avoided. It represents the minimum level of risk that must be accepted when investing in the market. It's measured by the beta coefficient, which tells us how much an individual asset or portfolio moves in relation to the broader market.

Market Portfolio

The market portfolio is a theoretical bundle of all possible investments in the world, with each asset being weighted proportionally to its market value. It acts as a benchmark for assessing the performance of individual assets or portfolios.
The concept of the market portfolio comes from modern portfolio theory and is essential in understanding investment returns and risk. The market portfolio is assumed to have a beta of 1, which means it represents the standard level of market risk. If an investment has a beta of 1, it moves in tandem with the market.

• A beta greater than 1 implies the investment is more volatile than the market.
• A beta less than 1 suggests less volatility compared to the market.

The Capital Asset Pricing Model (CAPM) uses the market portfolio to calculate the expected return of an asset based on its beta.

Investment Risk

Investment risk refers to the uncertainty associated with the returns that an investment might generate. This risk is a fundamental concern for investors who wish to protect their investments while achieving potential returns.
Investment risk encompasses several types of risks, including market risk, credit risk, and interest rate risk. By understanding these risks, investors can make informed decisions about which assets to include in their portfolios. Beta is often used in assessing investment risk, especially concerning stock investments, because it gauges an asset's level of market risk.
Managing investment risk effectively involves diversifying assets across various sectors and industries, thus minimizing exposure to adverse events that might affect certain segments more than others. While diversifiable risks can be mitigated through diversification, nondiversifiable risks, measured by beta, must be inherently accepted.

Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is a foundational finance theory that helps investors make more informed decisions about their investments. CAPM aims to determine an investment's expected return based on its risk relative to the market. The model incorporates the risk-free rate, the expected market return, and the investment's beta.
CAPM formula is expressed as:
\( \text{Expected Return} = \text{Risk-Free Rate} + \beta \times (\text{Market Return} - \text{Risk-Free Rate}) \)
This formula helps investors understand the expected return on an investment while considering its risk. It highlights the relationship between an asset's level of risk and its expected rate of return, assisting in asset valuation and investment decision-making. CAPM stands as a valuable tool for investors, as it provides a systematic approach to evaluating the risk-reward trade-off of different investments within a portfolio.