# How Do Hedge Funds Generate Positive Alpha?

The term â€śAlphaâ€ť is gaining use across the finance and investing communities, however many are not sure exactly what it means or how to calculate it. Alpha has been a term frequently used within the hedge fund and alternative asset management industries for years. We ever hear the term consistently on CNBC, Bloomberg TV, Reddit, and across the mainstream media, often with little explanation other than â€śAlpha is good.â€ť

Many investors assume that Alpha is the difference between the fund return and the benchmark return, however, the reality is that Alpha considers the difference in returns relative to the amount of risk taken. In other words, if the returns are 25 percent better than the benchmark, the S&P 500 for example, but the risk taken was 40 percent greater than the benchmark, Alpha would actually be negative.

What this means is that if the actual returns exceed the expected risk-adjusted return, then the hedge fund manager added alpha; based on the risk taken. If the actual return is lower than the expected return, then the hedge fund manager did not add alpha based on the risk taken. That said, the actual returns may have been higher than the relevant benchmark. Investors should want hedge fund managers who add alpha to returns for the risk they take not those that generate returns simply by taking additional risk.

## Jensenâ€™s Alpha Explained

Jensenâ€™s Alpha is often used as a calculation to determine the Alpha generated by a Hedge Fund Manager. Letâ€™s provide a real-world example: assume stock XYZ realized a return of 15% last year and the appropriate market index for this fund returned 12%, the S&P 500 as an example. The beta of the fund versus that same index is 1.2, and the risk-free rate is 3%. The fund’s alpha is calculated as:
Alpha = 15% – (3% + 1.2 x (12% – 3%)) = 15% – 13.8% = 1.2%.

With a beta of 1.2, the mutual fund is expected to be riskier than the S&P 500 index, and thus earn more. A positive alpha here would show that the Hedge Fund manager earned more than enough return to be compensated for the risk they took over the year. If the Hedge Fund only returned 13%, the calculated Alpha would be -0.8%. Any negative alpha suggests that the Hedge Fund manager would not have earned enough return given the amount of risk they were taking.

• The actual equation is y = a + bx + u
Where:
y is the performance of the stock or fund.
• a is alpha, which is the excess return of the stock or fund.
• b is beta, which is volatility relative to the benchmark.
• x is the performance of the benchmark, which is often theÂ S&P 500Â index.
• u is the residual, which is the unexplained random portion of performance in a given year.

As a note, Jensenâ€™s alpha uses a formula that looks almost identical to the standard Alpha, but it has one fundamental difference. Instead of comparing your returns to some market index, it determines how they size up against a theoretical expected return.

Where do the theoretical values in Jensenâ€™s alpha formula come from? Most financiers derive them using an ideal market model, such as the capital asset pricing model, or CAPM. Such models help elucidate the ties between expected asset returns and systematic risks, or the market risks intrinsic to an entire sector.

## The Relationship Between Alpha and Modern Portfolio Theory

Letâ€™s take a quick step back; in this blog post not only wanted to explain the definition of Alpha, but also what finance folks mean when they use the term. Most importantly, weâ€™ll discuss how to measure it and how Alpha benefits investors. Before we dig further into the concept of Alpha, letâ€™s touch on the basics of the Modern Portfolio Theory. Modern Portfolio Theory was developed in the 1950s and it emphasized diversification into various non-correlated assets in order to maximize portfolio expected return for a given amount of portfolio risk. Modern Portfolio Theory instructs investors as to how to find the best possible diversification strategy in order to achieve a greater expected return with the lowest possible risk to generate that return.

## What is Modern Portfolio Theory and the Efficient Frontier?

Using Modern Portfolio Theory, an investor will be able to find a combination of investments that has the best possible expected level of return for the most appropriate level of risk. This has also become known as the efficient frontier or again, finding the most â€śefficientâ€ť level of expected return for the lowest possible risk.

In an earlier blog post titled â€śThe Efficient Process Frontier,â€ť we applied the process of finding the optimal risk/reward scenario suggesting that the â€śEfficient Process Frontierâ€ť is the set of optimal processes that offer the highest expected value for a defined level of risk or the lowest risk for a given level of expected value.

Ok, now that we are clear on what Modern Portfolio Theory, we can discuss Alpha with risk in mind. Within Modern Portfolio Theory, there are five specific risk ratios that investors can use to determine the risk-reward profile of an investment: alpha, beta, standard deviation, R-squared, and Sharpe ratio.

Letâ€™s make sure weâ€™re clear on this point one last time – Alpha is used to measure performance on a risk-adjusted basis. As an investor, we want to know if we are being compensated for the risk taken in our investment, and Alpha helps assess whether or not an investment is viable. We wonâ€™t confuse the conversation any further than to simply present Jensenâ€™s Alpha calculation that we added to the blog post above. The critical product of the calculation that investors need to focus on is the numerical value of Alpha itself.

As an example, a positive Alpha of 1.0 means the investment has outperformed its benchmark index by 1%. Similarly, a negative 1.0 alpha would indicate an underperformance of 1%. An Alpha of zero means the investment has earned the same risk-adjusted return as its benchmark. To be clear, a zero Alpha does not mean the investor has made or lost money, it simply means that they didnâ€™t earn enough profit on the investment to compensate for the risk they took.

Hedge Fund and active portfolio managers seek to generate Alpha in diversified portfolios, with diversification intended to eliminate unsystematic risk or risk that is associated with a single industry or equity. Because Alpha represents the performance of a portfolio relative to a benchmark, it has become known as the value that a manager adds to or subtracts from a fund’s return. To reiterate, Alpha is the return on an investment that is not a result of the movement in the overall market or benchmark. Thus, an Alpha of zero would again indicate that the portfolio or fund is tracking perfectly with the benchmark index and that the manager has not added or lost any additional value compared to the broad market or benchmark.

Within Modern Portfolio Theory, there are five specific risk ratios that investors can use to determine the risk-reward profile of an investment: alpha, beta, standard deviation, R-squared, and Sharpe ratio.

To wrap this section up, Alpha indicates how an investment has performed after accounting for the risk involved. The following are true:

• Alpha is lower than 0 means that the investment earned too little for the risk taken or simply that the investment was too risky for return of the investment
• Alpha is equal to 0 means the investment earned a return adequate for the risk taken
• Alpha greater than 0 means that the investment earned a return in excess of the risk taken

In addition, here are 3 Key Points to remember about the significance of Alpha:

• Alpha refers to excess returns earned on an investment above the benchmark return.
• Active portfolio managers seek to generate alpha in diversified portfolios, with diversification intended to eliminate unsystematic risk.
• Because alpha represents the performance of a portfolio relative to a benchmark, it is often considered to represent the value that a portfolio manager adds to or subtracts from a fund’s return.

## Can Ryan Eyes Empower Managers Measure Alpha Quickly & Easily?

We donâ€™t like to do commercials in our blog posts and at the risk of sounding a bit self-serving, yes, Ryan Eyes software generates a variety of risk calculations that will allow Hedge Fund managers to easily calculate Alpha.

Letâ€™s start with a risk calculation that our clients use consistently to understand the potential loss their portfolio could experience at any single point in time. Value at Risk (VaR) is a measure of the risk of loss for investments. VaR estimates how much a set of investments might lose, with a given probability, given normal market conditions, in a set time period such as a day, week, or month. VaR is typically used by funds in the financial industry to gauge the number of assets needed to cover possible losses.

For example, if a portfolio of stocks has a one-day 5% VaR of \$1 million, that means that there is a 0.05 probability that the portfolio will fall in value by more than \$1 million over a one-day period.

Ryan Eyes software handles the calculations instantly and presents the resulting analysis in a clean, dashboard format. Ryan Eyes provides the following calculations:

• VaR
• Sharpe and Sortino Ratios Drawdown
• Monte Carlo Analysis
• Shock Analysis
• Risk Triggers on the Greek values which includes theta, vega, delta, and gamma
• Portfolio Optimization
• Concentration Limits
• Hard and Soft Triggers