Alpha: Alpha Adventures: Blending Alpha with Treynor Ratio for Superior Selection

1. Introduction to Alpha and the Treynor Ratio

In the realm of investment, the pursuit of superior portfolio performance is akin to an alchemist's quest for gold. Among the tools at the disposal of modern financial alchemists are two potent metrics: Alpha and the Treynor Ratio. Alpha, a measure of an investment's performance on a risk-adjusted basis, serves as a beacon, guiding investors to securities that yield returns beyond those predicted by the capital asset pricing model (CAPM). The Treynor Ratio, on the other hand, illuminates the risk-adjusted returns of a portfolio, considering the systemic risk represented by its beta. Together, these metrics empower investors to not only chase but also capture the elusive specter of market-beating returns.

From the perspective of a portfolio manager, Alpha is the scorecard that reflects their prowess in stock selection and timing. A positive Alpha indicates that the manager has added value, outperforming the market index, while a negative Alpha suggests underperformance. For individual investors, Alpha offers a lens through which to view the effectiveness of their investment choices against the broader market's ebb and flow.

The Treynor Ratio, named after Jack L. Treynor, is a complementary tool that sharpens the focus on risk. Unlike the Sharpe Ratio, which uses total risk, the Treynor Ratio exclusively considers systemic risk, which cannot be diversified away. This makes it particularly useful for diversified portfolios where unsystematic risk is minimal.

Here's an in-depth look at these concepts:

1. Understanding Alpha:

- Alpha is often represented as a single number (like +3.0 or -2.0) which signifies how much an investment has returned in comparison to the benchmark index.

- For example, an Alpha of +3.0 means the investment has outperformed its benchmark index by 3% after adjusting for risk.

2. Calculating Alpha:

- The formula for Alpha is: $$ \alpha = R_i - (R_f + \beta_i (R_m - R_f)) $$

- Where:

- \( R_i \) is the return of the investment

- \( R_f \) is the risk-free rate

- \( \beta_i \) is the investment's beta

- \( R_m \) is the return of the market

3. The Significance of Treynor Ratio:

- The Treynor Ratio is calculated by taking the difference between the return of the portfolio and the risk-free rate, divided by the portfolio's beta.

- A higher Treynor Ratio indicates a portfolio is earning more return per unit of systemic risk.

4. Calculating Treynor Ratio:

- The formula for the Treynor ratio is: $$ TR = \frac{R_p - R_f}{\beta_p} $$

- Where:

- \( R_p \) is the return of the portfolio

- \( R_f \) is the risk-free rate

- \( \beta_p \) is the portfolio's beta

5. Alpha and Treynor Ratio in Practice:

- Consider a mutual fund with a return of 15%, a beta of 1.2, and a market return of 10%. If the risk-free rate is 3%, the fund's Alpha would be 2%.

- If the same fund has a Treynor Ratio of 10, it means it has generated 10 units of return for every unit of market risk taken.

By blending Alpha with the Treynor Ratio, investors and portfolio managers can refine their strategies for superior security selection. This dual approach allows for a more nuanced understanding of performance, distinguishing between luck and skill, and between genuine market-beating tactics and mere exposure to systemic risk. In the end, the integration of these metrics into the investment process can be the difference between a portfolio that merely floats with the market tide and one that sails ahead, capturing the winds of excess returns.

2. Understanding Market Excess Returns

In the quest for superior investment strategies, the concept of alpha has long stood as a beacon for portfolio managers and individual investors alike. Alpha, or α, represents the ability of a portfolio to outperform the market on a risk-adjusted basis. It's the excess return that isn't explained by the market's movements, encapsulating the unique value brought by a portfolio manager's skill and strategy. However, alpha doesn't operate in isolation; it's part of a broader narrative that includes market risks, investor behavior, and economic cycles.

To truly understand alpha, one must delve into the intricacies of market excess returns. These are the returns that surpass the benchmark index or expected return based on the market's overall performance. They are the holy grail for investors seeking to beat the market. But capturing these elusive returns requires a blend of art and science, intuition and analysis, and a keen understanding of the Treynor ratio.

1. The role of Risk-Adjusted returns:

The Treynor Ratio is pivotal in this context. It measures the returns earned in excess of the risk-free rate per unit of market risk taken. It's given by the formula:

$$ \text{Treynor Ratio} = \frac{\text{Portfolio Return} - \text{Risk-Free Rate}}{\text{Beta}} $$

This ratio helps investors understand if the excess returns of a portfolio are due to smart investment decisions or a result of taking on too much risk.

2. Market Efficiency and Alpha:

The efficient Market hypothesis (EMH) posits that it's impossible to consistently achieve higher returns than the market average because stock prices always incorporate and reflect all relevant information. Alpha challenges this notion by representing the skill of the portfolio manager in generating returns that beat the market.

3. behavioral Finance insights:

Behavioral finance teaches us that markets are not always rational, and human emotions often drive investment decisions. This can lead to mispricings that skilled investors can exploit to generate alpha.

4. Quantitative Models:

Quantitative models, such as the Capital asset Pricing model (CAPM), attempt to predict returns and assess the performance of a portfolio against the market. These models are essential for understanding the relationship between risk and return and for isolating alpha.

5. real-World examples:

Consider the case of a technology-focused mutual fund that achieved a 20% return in a year when the overall market grew by 10%. If the risk-free rate is 2%, and the fund's beta is 1.5, the Treynor Ratio would be:

$$ \text{Treynor Ratio} = \frac{20\% - 2\%}{1.5} = 12\% $$

This indicates that the fund has provided a 12% excess return per unit of market risk, which is a strong indicator of alpha.

Decoding alpha is about peeling back the layers of market performance to reveal the core of active management prowess. It's about understanding that while the market provides the canvas, the strokes of genius that define excess returns are the result of a meticulous blend of risk management, market insight, and the courage to deviate from the herd. The Treynor Ratio, in this blend, serves as a critical tool for distinguishing between luck and skill in the pursuit of alpha. It's a journey that requires patience, discipline, and an unwavering commitment to the art of investment.

3. Measuring Risk-Adjusted Returns

In the quest for superior investment strategies, blending the concept of alpha with the Treynor ratio can be a game-changer for portfolio managers and individual investors alike. The Treynor Ratio, a cornerstone in modern portfolio theory, serves as a beacon, guiding investors in assessing the risk-adjusted returns of their portfolios. Unlike raw returns, which can be misleading, the Treynor Ratio provides a more nuanced view by considering the volatility of the portfolio relative to the market as a whole, represented by its beta. This ratio is particularly insightful when juxtaposed with alpha, a measure of the excess return on an investment relative to the return of a benchmark index.

1. Understanding the Treynor Ratio:

The Treynor Ratio is calculated by taking the difference between the return of the portfolio and the risk-free rate, divided by the portfolio's beta:

$$ Treynor\ Ratio = \frac{Portfolio\ Return - Risk-Free\ Rate}{Portfolio\ Beta} $$

This formula encapsulates the essence of risk-adjusted performance, highlighting how much excess return is generated for each unit of market risk taken.

2. Alpha and the Treynor Ratio:

Alpha represents the value that a portfolio manager adds to or subtracts from a fund's return. A positive alpha indicates that the fund has outperformed its benchmark index after adjusting for risk, while a negative alpha suggests underperformance. When alpha is analyzed alongside the Treynor Ratio, investors gain a clearer picture of whether the excess returns are a result of smart investment choices or simply a byproduct of taking on more market risk.

3. Practical Application:

Consider a portfolio with a return of 12%, a risk-free rate of 3%, and a beta of 1.2. The Treynor Ratio would be:

$$ Treynor\ Ratio = \frac{12\% - 3\%}{1.2} = 7.5\% $$

If this portfolio has an alpha of 2%, it indicates that the manager is effectively generating returns above the expected outcome based on market risk.

4. Diverse Perspectives on the Treynor Ratio:

From the viewpoint of a conservative investor, a high Treynor Ratio might signal a well-optimized portfolio that aligns with their risk tolerance. Conversely, a risk-seeking investor might prioritize portfolios with high alphas, even if the Treynor Ratio is lower, seeking aggressive growth opportunities.

5. Limitations and Considerations:

The Treynor Ratio is not without its limitations. It assumes that investors are only concerned with market risk, overlooking other forms of risk such as liquidity or sector-specific risks. Additionally, it relies on the beta being a stable and accurate measure of market risk, which may not always hold true in turbulent market conditions.

By integrating the Treynor ratio with alpha, investors can refine their approach to portfolio selection, ensuring that they are not just chasing returns, but are also cognizant of the risks they undertake. This blend of performance metrics can lead to a more disciplined and potentially more rewarding investment experience.

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4. Combining Alpha and Treynor Ratio for Portfolio Analysis

In the realm of investment management, the pursuit of superior portfolio performance is a constant endeavor. Combining Alpha and the Treynor Ratio offers a nuanced approach to portfolio analysis, allowing investors to gauge not just the excess returns a portfolio generates over a benchmark, but also how those returns relate to the market risk taken. Alpha, a measure of performance on a risk-adjusted basis, tells us how much an investment has returned over its expected earnings based on its beta. The Treynor Ratio, on the other hand, provides insight into the returns earned in excess of the risk-free rate per unit of market risk, as measured by beta.

From the perspective of a fund manager, this combination is invaluable. It allows for a more comprehensive assessment of performance, taking into account both the ability to generate excess returns and the efficiency of risk-taking. For the individual investor, these metrics can be a guide to selecting funds that not only outperform but do so with a favorable risk-return profile.

Let's delve deeper into how these two metrics can be synergized for effective portfolio analysis:

1. Understanding Alpha: Alpha is often seen as the holy grail of investment metrics. A positive alpha indicates that the portfolio has outperformed its benchmark after adjusting for risk, which is typically what investors strive for. For example, if a mutual fund has an alpha of 1.5, it means that it has outperformed its benchmark index by 1.5% on a risk-adjusted basis.

2. Grasping the treynor ratio: The Treynor Ratio takes the portfolio's returns above the risk-free rate and divides it by the portfolio's beta. A higher Treynor Ratio suggests that the portfolio is earning more excess return per unit of market risk. For instance, a portfolio with a Treynor Ratio of 0.06 has generated 6% of excess return per unit of risk, which is considered good.

3. Combining the Two: When Alpha and Treynor Ratio are used together, they provide a more rounded view of the portfolio's performance. For example, a high alpha might be less impressive if accompanied by a low Treynor Ratio, indicating high market risk. Conversely, a high Treynor Ratio with a low alpha might suggest that the portfolio is not utilizing its risk budget effectively.

4. Practical Application: Consider a portfolio manager who is evaluating two funds. Fund A has an alpha of 2.0 and a Treynor Ratio of 0.04, while Fund B has an alpha of 1.0 and a Treynor Ratio of 0.07. While Fund A has a higher alpha, indicating better performance relative to the benchmark, Fund B has a higher Treynor Ratio, suggesting it is more efficient in terms of risk-adjusted return. The manager might prefer Fund B if they value efficiency over raw performance.

5. Limitations and Considerations: It's important to note that both Alpha and the Treynor Ratio have their limitations. Alpha does not account for systemic market risks, and the Treynor Ratio assumes a fully diversified portfolio to nullify unsystematic risk. Investors should also consider other factors such as the Sharpe Ratio, portfolio volatility, and the investment horizon.

Blending Alpha with the Treynor Ratio can lead to a more informed investment decision-making process. By considering both the raw performance and the efficiency of risk-taking, investors and portfolio managers can strive for a balance that aligns with their investment goals and risk appetite. This dual approach underscores the sophistication required in modern portfolio analysis and the ongoing quest for achieving 'alpha' in every sense of the word.

5. Alpha and Treynor Ratio in Action

In the realm of investment management, the pursuit of superior portfolio selection is often akin to an alchemist's quest for gold. It's a meticulous blend of science and art, where metrics like Alpha and the Treynor Ratio serve as critical instruments in the investor's toolkit. Alpha, representing the excess return of an investment relative to the return of a benchmark index, is the elusive treasure that active managers seek to uncover. Meanwhile, the Treynor Ratio, which measures returns earned in excess of that which could have been earned on a riskless investment per each unit of market risk, acts as a beacon, guiding investors towards risk-adjusted rewards.

From the vantage point of a fund manager, the Alpha signifies the value added or subtracted from a fund's holdings due to active management. For an individual investor, Alpha offers a glimpse into the potential for outperformance, a siren's call to those navigating the choppy waters of market volatility. On the other hand, the Treynor Ratio illuminates the path for institutional investors, enabling them to compare the risk-adjusted performance of various portfolios and thus allocate assets more efficiently.

Let's delve into some case studies that illustrate these concepts in action:

1. The High-Alpha hedge fund: Consider a hedge fund that has consistently delivered an Alpha of +5%. This indicates that the fund has outperformed its benchmark index by 5% annually, a commendable feat. However, upon closer inspection, if the fund's Treynor Ratio is lower than that of its peers, it suggests that the fund is taking on excessive market risk to achieve its returns. Investors might then be wary of the fund's risk profile, despite its attractive Alpha.

2. The Conservative pension fund: A pension fund with a modest Alpha of +1% might not seem as impressive at first glance. Yet, if its Treynor Ratio is high, it reveals that the fund is achieving superior risk-adjusted returns. For pension funds, where preserving capital and maintaining steady growth are paramount, a high Treynor Ratio can be more desirable than a high Alpha.

3. The Balanced Mutual Fund: Imagine a mutual fund that has an Alpha of 0, indicating it performs in line with the market. However, its Treynor Ratio is above average, suggesting it's providing better returns per unit of risk compared to the market. This fund might appeal to risk-averse investors who are satisfied with market returns but are keen on minimizing volatility.

Through these examples, we see that while Alpha can be a siren's call, beckoning investors with promises of high returns, it is the Treynor Ratio that often shines a light on the true merit of an investment. It's not just about how much you make, but how much you make for every ounce of risk you take. Blending Alpha with the Treynor Ratio allows for a more nuanced approach to portfolio selection, one that balances the thrill of the chase for high returns with the prudence of risk management.

6. Strategies for Maximizing Alpha with the Treynor Ratio

In the quest for superior portfolio performance, the integration of alpha and the Treynor Ratio can be a formidable strategy. Alpha, representing the excess return of an investment relative to the return of a benchmark index, is a measure of an investment's active return. On the other hand, the Treynor Ratio, which divides the excess return of a portfolio over the risk-free rate by the portfolio's beta, offers a risk-adjusted perspective. It's a nuanced dance of numbers where maximizing alpha is not just about selecting high-return assets but about choosing those that offer the greatest reward per unit of market risk.

1. Understanding Beta and Market Sensitivity: Before delving into strategies, it's crucial to comprehend that beta measures a security's sensitivity to market movements. A beta greater than 1 indicates higher volatility than the market, while a beta less than 1 suggests less volatility. For instance, if a stock has a beta of 1.5, it's expected to be 50% more volatile than the market.

2. Selecting Low-Beta High-Alpha Securities: One approach is to look for securities with a low beta but high alpha. This means they're less sensitive to market swings but still offer returns above the benchmark. For example, a utility company might have a beta of 0.7 but could be efficiently managed, resulting in an alpha of 2%.

3. portfolio Optimization techniques: Utilizing optimization models like the Sharpe Ratio or the black-Litterman model can help in blending alpha with the Treynor Ratio. These models aid in the selection of a mix of assets that maximizes return for a given level of risk.

4. Diversification Across Different Asset Classes: Diversification is key. By investing in a mix of asset classes with varying betas and alphas, investors can potentially maximize their portfolio's overall alpha while keeping the Treynor Ratio in check. For instance, combining stocks, bonds, and real estate investments can balance the risk-return profile.

5. Leveraging Derivatives for Hedging: Options and futures can be used to hedge against market volatility and improve the Treynor Ratio. For example, buying put options on stocks with high beta can protect against downside risk while allowing investors to benefit from the high alpha.

6. active Portfolio management: Active managers can dynamically adjust the portfolio's composition in response to market conditions, aiming to maintain high alpha and an optimal Treynor Ratio. This might involve rotating sectors or adjusting the weight of assets.

7. Monitoring Macroeconomic Indicators: Economic indicators like inflation rates, interest rates, and GDP growth can influence market risk and, consequently, the Treynor Ratio. Keeping an eye on these can inform timely adjustments to the portfolio.

8. Utilizing Alternative Investments: Sometimes, alternative investments like hedge funds or private equity, which might not correlate directly with market indices, can offer unique alpha opportunities while affecting the portfolio's beta in a favorable way.

Blending alpha with the Treynor Ratio requires a multifaceted approach that considers market sensitivity, risk management, and active portfolio adjustments. By employing these strategies, investors can strive for a portfolio that not only beats the benchmark but does so with a keen eye on risk-adjusted returns.

7. Challenges and Considerations in Blending Alpha and Treynor

Blending the Alpha and Treynor Ratio presents a nuanced approach to portfolio management, aiming to balance the pursuit of excess returns with the inherent risks associated with investment choices. Alpha, representing the performance of an investment relative to a benchmark, is a measure of the active return on an investment. It is the result of active management and the ability to outperform the market. On the other hand, the Treynor Ratio, which divides excess return by beta, focuses on risk-adjusted returns and considers systemic risk. The challenge lies in harmonizing these two metrics, as they often pull in different directions—Alpha seeks to maximize returns regardless of the benchmark, while the Treynor Ratio emphasizes the importance of earning returns that compensate for the risk taken.

From an investment manager's perspective, the key considerations include:

1. Risk Tolerance Alignment: Ensuring that the blend of Alpha and Treynor aligns with the risk tolerance of the investors. For instance, a conservative investor might prioritize a higher Treynor Ratio over Alpha, seeking to minimize systemic risk.

2. Market Conditions: Understanding that market volatility and conditions significantly impact Alpha and the Treynor Ratio. During a bull market, high Alpha is often achievable; however, in turbulent times, a favorable Treynor Ratio might be more desirable.

3. Investment Horizon: Considering the time frame of the investment is crucial. short-term investments may benefit from a focus on Alpha, while long-term investments might align better with the Treynor Ratio's risk-adjusted approach.

4. Diversification: Recognizing the role of diversification in blending Alpha and Treynor. A well-diversified portfolio can mitigate unsystematic risk, allowing the Treynor Ratio to provide a clearer picture of the performance.

5. Benchmark Selection: The choice of benchmark is pivotal in calculating Alpha and can greatly influence the perceived performance. An inappropriate benchmark can lead to a misleading Alpha, affecting the blend's effectiveness.

6. Cost Considerations: Acknowledging that the pursuit of high Alpha often involves higher transaction costs and management fees, which can erode the net returns and affect the Treynor Ratio.

7. Performance Attribution: Dissecting performance to understand the sources of Alpha and the contributions of various factors to the Treynor Ratio. This analysis helps in fine-tuning the strategy.

For example, consider a portfolio manager who manages a technology-focused mutual fund. In a year when tech stocks outperform, the fund might exhibit high Alpha due to sector selection. However, if the tech sector is also high beta, the Treynor Ratio might not look as impressive. The manager must then communicate to investors the reasons behind the numbers and set the right expectations for future performance.

Blending Alpha with the Treynor Ratio requires a delicate balance and a deep understanding of both metrics. It's not just about chasing high returns or minimizing risk in isolation; it's about achieving a harmony that aligns with the investment philosophy and goals. By considering multiple perspectives and maintaining a disciplined approach, investors and managers can navigate these challenges and make informed decisions that enhance portfolio performance.

8. Tools and Techniques for Calculating Alpha and Treynor

In the quest for portfolio optimization, investors often turn to various metrics that can guide their decision-making process. Among these, Alpha and Treynor Ratio stand out as critical tools for assessing investment performance relative to risk. Alpha, a measure of an investment's performance on a risk-adjusted basis, provides insight into the manager's ability to generate returns over and above the market's. It is the excess return an investment has earned over its expected market returns given its level of risk as measured by beta. On the other hand, the Treynor Ratio, developed by Jack Treynor, is similar to the sharpe Ratio but uses beta as the risk measure, thus focusing on systemic risk. It is particularly useful when comparing the risk-adjusted returns of different portfolios.

Calculating these metrics requires a blend of historical data analysis, risk assessment, and performance measurement. Here are some in-depth techniques and tools that can be employed:

1. Alpha Calculation:

- Formula: The formula for Alpha ($\alpha$) is $$\alpha = R_i - (R_f + \beta_i (R_m - R_f))$$ where $R_i$ is the investment's return, $R_f$ is the risk-free rate, $\beta_i$ is the investment's beta, and $R_m$ is the return of the benchmark market.

- Regression Analysis: A common method to calculate alpha is through regression analysis, where the investment's returns are regressed against the returns of the benchmark index.

- Example: If a mutual fund returned 15% last year while the risk-free rate was 3% and the market return was 10%, with a beta of 1.2, the fund's alpha would be calculated as: $$\alpha = 0.15 - (0.03 + 1.2 \times (0.10 - 0.03)) = 0.15 - (0.03 + 1.2 \times 0.07) = 0.15 - 0.114 = 0.036$$ or 3.6%.

2. Treynor Ratio Calculation:

- Formula: The Treynor Ratio is calculated using the formula $$T = \frac{R_i - R_f}{\beta_i}$$ where $R_i$ is the investment's return, $R_f$ is the risk-free rate, and $\beta_i$ is the investment's beta.

- Risk-Adjusted Return: It measures how much return an investment has generated per unit of systemic risk.

- Example: Using the same mutual fund example, the Treynor Ratio would be: $$T = \frac{0.15 - 0.03}{1.2} = \frac{0.12}{1.2} = 0.10$$ or 10%.

These calculations, while seemingly straightforward, require accurate and up-to-date data. Investors often use financial software and databases to obtain the necessary information. Moreover, understanding the context and limitations of these metrics is crucial. For instance, Alpha assumes the market is efficient and does not account for added value through active management in an inefficient market. Similarly, the Treynor Ratio assumes the portfolio is well-diversified and only systemic risk is rewarded.

Incorporating both Alpha and Treynor ratio into portfolio analysis allows for a more nuanced approach to investment selection. By considering both the risk-adjusted performance (Alpha) and the market risk (Treynor Ratio), investors can better gauge the true value added by a portfolio manager and make more informed decisions that align with their risk tolerance and investment goals. This dual approach can be particularly powerful in markets characterized by volatility and uncertainty, where the ability to navigate risk is paramount.

9. The Future of Investment Selection with Alpha and Treynor

In the realm of investment, the pursuit of superior selection strategies is akin to the quest for the Holy Grail. The integration of Alpha and the Treynor Ratio presents a compelling approach to this quest, offering a nuanced perspective that transcends traditional metrics. Alpha, representing the excess return of an investment relative to the return of a benchmark index, is the investor's scoreboard. It quantifies the value added or subtracted by a fund manager's decisions. On the other hand, the Treynor Ratio, which adjusts returns for systematic risk, provides a lens through which the risk-adjusted performance of a portfolio can be assessed. Together, they form a powerful duo for investors seeking to navigate the turbulent waters of the market with a more informed compass.

1. Alpha's Role in Investment Selection: Alpha is often seen as the measure of a manager's prowess. A positive alpha indicates that the manager has added value, generating returns above the benchmark, while a negative alpha suggests underperformance. For example, if a mutual fund reports an alpha of +2%, it means that the fund has outperformed its benchmark index by 2% after adjusting for risk.

2. Treynor Ratio's Insight into Risk: The Treynor Ratio takes into account the beta of a portfolio, reflecting its sensitivity to market movements. A higher Treynor Ratio indicates that the portfolio is earning more excess return per unit of risk taken. Consider a portfolio with a beta of 1.2 and an excess return of 10%. If the risk-free rate is 3%, the Treynor Ratio would be calculated as (10% - 3%) / 1.2, which equals approximately 5.83%.

3. Blending Alpha and Treynor for a Holistic View: By combining Alpha and the Treynor Ratio, investors can gain a comprehensive understanding of a fund's performance. A fund might have a high alpha but also a high beta, suggesting that the excess returns are not without substantial risk. Conversely, a lower alpha accompanied by a low beta and a high Treynor Ratio might indicate a more favorable risk-adjusted performance.

4. Case Studies of Alpha and Treynor in Action: Real-world examples abound where the interplay of Alpha and Treynor has guided investment decisions. Take, for instance, the case of two funds: Fund A with an alpha of +3% and a Treynor Ratio of 4%, and Fund B with an alpha of +1% and a Treynor Ratio of 6%. While Fund A shows higher raw performance, Fund B demonstrates better risk-adjusted returns, which might be more appealing to risk-averse investors.

The future of investment selection lies in the sophisticated combination of various performance and risk metrics. Alpha and the Treynor Ratio, when used in concert, provide a more dimensional view of a fund's potential, allowing investors to make decisions that align with their individual risk tolerance and return objectives. As the investment landscape evolves, so too will the tools and analyses, but the essence of seeking alpha while managing risk will remain a constant pursuit in the art and science of investment selection.