Treynor-Black Model

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21 Aug, 2024

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Treynor-Black model is a portfolio optimization technique that creates an optimal mix of assets by incorporating actively and passively managed components. The model focuses on maximizing the portfolio's Sharpe ratio by optimizing its risk-adjusted return.

The model optimizes a portfolio's risk-adjusted return by considering the trade-off between expected return and tracking the degree of deviation relative to a benchmark. The whole model enhances the Treynor ratio, a performance metric also known as a reward-to-volatility ratio. Furthermore, it is based on modern portfolio theory.

What Is Treynor-Black Model?

Treynor-Black model is a portfolio optimization model focussing on including actively and passively managed components in the portfolio.
It was developed by Fisher Black and Jack Treynor in 1973 and was published in an article named "How to Use Security Analysis to Improve Stock Selection."
The model's application results in a dual-partitioned portfolio. The first portion comprises a mix of underpriced securities, and the other follows a passive index investment.
The Treynor-Black model is complex, and its reliance on accurate stock selection poses challenges for widespread adoption in investment management.

Treynor-Black Model Explained

The Treynor-Black model is an investment approach that lets investors identify and gauge the right combination of active and passive portfolio elements to maximize returns that are also adjusted for any form of market risk. Fisher Black and Jack Treynor introduced the model in an article called "How to Use Security Analysis to Improve Portfolio Selection," published in 1973. The technique is employed for active portfolio management.

The model explicitly uses the Sharpe ratio, which is an evaluation of any single investment or entire portfolio's risk-adjusted performance against the risk-free rate of return. This risk-free rate of return is commonly taken from securities or financial instruments with minimal risk, such as US treasury securities.

The Treynor-Black model divides the portfolio into two segments: an actively managed segment comprising undervalued stocks and a passive segment focusing on index funds. The passive portfolio has securities according to their market value. In the active portfolio, every security is gauged by its ratio of excess returns per benchmark index. This ratio is also known as the Treynor-Black ratio, which technically calculates the value that each investment adds to the entire portfolio.

Examples

Let us look into a few examples:

Example #1

Imagine an investor named Anna possessing a competitive advantage (proven stock-picking skills and general industry familiarity) over other market participants. When she creates a portfolio, applying the Treynor-Black model suggests aligning investment decisions with her identified edge to optimize portfolio performance and achieve competitive returns.

Anna can choose passive index funds, such as those tracking broad market indices like the S&P 500 or the Russell 2000, to fill a portion of her portfolio. Anna ensures that she benefits from overall market growth while maintaining a low-cost and relatively stable investment component by including index funds. Leveraging her edge in stock-picking skills, Anna can selectively invest in underpriced stocks that she identifies through her research and analysis.

These underpriced stocks present opportunities for potential capital appreciation if their market value eventually aligns with their intrinsic worth. Anna's ability to assess undervalued securities allows her to capitalize on mispricing opportunities and potentially generate alpha, enhancing the overall performance of her portfolio.

Example #2

Consider an asset management company, ABC Investments, utilizing the Treynor-Black model to optimize its portfolio management strategy. ABC Investments divides its portfolio into two segments: a passive segment comprising index funds that track major market indices and an active segment comprising mispriced securities.

The company allocates some of its assets to the passive segment, ensuring diversification across sectors and minimizing specific company risks. Simultaneously, ABC Investments leverages its research capabilities and investment expertise to manage the other segment actively. This will help to gain from mispriced securities and generate alpha.

Since there is no specific Treynor-Black model formula, ABC evaluates the performance of each segment using metrics such as the Sharpe ratio to assess risk-adjusted returns and the Treynor ratio to measure excess returns per unit of systematic risk. By implementing the Treynor-Black model, ABC Investments aims to optimize its portfolio's risk-return profile, balancing the benefits of passive indexing with the potential for outperformance through active management.

Advantages And Disadvantages

The advantages of the Treynor-Black model are -

The Treynor-Black model is easy to implement and more useful when some assumptions are relaxed.
The model uses less quantitative information compared to other optimization methods.
It provides monetary independence.
The relative allocation in the existing or remaining assets does not change when assets are removed or added.
The model is not very sensitive to small changes, so it is stable in terms of portfolio selection and less complex than other optimization techniques.

The disadvantages of the Treynor-Black model are -

The model's efficiency depends heavily on the ability to predict orthodox returns.
The Treynor-Black model's implementation requires a security analyst forecast, given that its properties are openly used when new forecasts are entered for optimization.
This model continuously evaluates the underlying portfolio for performance, resulting in higher exposure to outside pressures.

Frequently Asked Questions (FAQs)

1. What are the assumptions of the Treynor-Black model?

The assumptions of the Treynor-Black model are -

- The model assumes that the investor is considering the securities price efficiently. - There is a high probability of collaborative movement among security prices.
- Take less notice of the cost of buying and selling to treat the portfolio as a single-period problem.
- It also assumes that individual portfolio managers can calculate the future performance of certain securities along with the expected risk and return parameters.
- The model assumes that all returns follow a normal distribution.

2. What is the difference between the Treynor-Black and Black Litterman models?

The Treynor-Black model differs from the Black-Litterman model. The Treynor-Black model focuses on creating and maintaining two sections in the portfolio: one active and one passive elements section. It relies on an investor's ability to select index funds and underpriced stocks or securities to maximize returns. On the other hand, the Black-Litterman model aids in portfolio allocation and incorporates the investor's views of expected returns and risk tolerance. Furthermore, Fisher Black is the co-developer of both models.

3. How useful is the Treynor-Black model's information ratio in evaluating the performance of portfolio managers?

Portfolio managers use the Treynor-Black ratio to create their portfolios' risk-adjusted return and make risk management and asset allocation decisions. Additionally, portfolio managers and analysts use this to evaluate funds and compare the performance of different portfolios.