Alpha and Beta are two very commonly used Greek terms. Hedge funds, in particular, use these terms day in and day out. Even the media uses these words as if everyone knows what they are. Sometimes, you wonder how much gibberish you have to put up with investment professionals. Fortunately, you do not need a degree in rocket science to understand what most of these terms mean. They are relatively simple concepts. Both Alpha and Beta are closely related. And investment professionals use them for various purposes such as measuring risk, constructing portfolios, and evaluating investment performance. This post focus on the last point.

## How We Get The Returns Matter

More often than not, people place too much emphasis on absolute returns. But a higher return doesn’t necessarily translate to better performance. If you read my earlier article on Risk-Adjusted Returns, you will know what I mean.

For instance, an investment manager can leverage up and buy a basket of S&P 500 stocks. In a bull market where stocks are up year on year, he is going to outperform the S&P 500 in absolute terms. But in reality, it is no big deal to leverage up your risks and get a higher return than the market in good times. What we want to know is whether he is delivering more bang for the buck which he isn’t in this case. Anyone can do what he does. So if we don’t delve any deeper other than looking at the outcomes, we might credit this manager prematurely with some superior skills.

On the other hand, another investment manager selects stocks and constructs his own portfolio from the S&P 500 stock universe. He does not use any leverage and underperforms the S&P 500. At this point, I think most will be quick to judge him as incompetent. But that is not a fair assessment. Because we do not know what risks he took and what is driving his returns. He may well be taking a much lower risk than the market and is delivering more than what is expected of those risks.

So where do Alpha and Beta fit in all these? Alpha and Beta are simply another way to present risk and return for a more objective assessment. Let's see how it works.

## Alpha and Beta – Segregating Passive And Active Returns

Let's say we manage a portfolio of stocks that are selected from the S&P 500 constituents. So what drives the returns for this portfolio? Intuitively, we can break it down into 2 components – a passive return component from the risk exposure to the market; and an active return component from the value we add through our investment strategy. We can nicely sum this up as follows:

where Rp is the portfolio return, Rm is the market return and Rf is the risk-free rate. This is just an extension of the famous Capital Asset Pricing Model (CAPM).

From this, it should not be too difficult to guess what Alpha and Beta mean. Let’s talk about Beta first. Beta is a measure of the portfolio’s risk exposure to the market. In return, the portfolio receives proportionally a market risk premium i.e. the excess returns the market gives over the risk-free rate (Rm – Rf). If the portfolio has a Beta of 1, then it will move 1% for every 1% move in the market. And if the Beta is 0.5, then the portfolio will move 0.5% for every 1% move in the market. Now, any other difference in the portfolio return not explained by these market movements and the risk-free rate is attributed to the investment manager’s skills or strategy. And that is Alpha.

## How Do We Calculate Alpha and Beta?

Alpha and Beta can be statistically estimated as linear regression parameters using historical data. Let's rearrange the earlier equation.

If we perform a regression on this, Beta is the slope or gradient of the fitted line. It tells us the sensitivity of the portfolio returns to the market. And Alpha is the intercept. A positive alpha suggests that the manager might have some skills as he is adding value. And of course, a negative alpha indicates otherwise.

## A Simple Fictional Illustration

To see how we can use Alpha and Beta to assess investment managers, I created 3 fictional investment managers A, B, and C. They are all equity managers dealing in the same market. But each has his own risk preference, stock selection, and weighting methodology. So in the end, all 3 produce distinct results. We do not know their exact methodology and neither do we know their portfolio composition. Let's say all we have is the market and their monthly return series. Based on those, we can run a regression and estimate their respective Alpha and Beta. See the table below.

##### Making Sense Of the Numbers

Manager A is aggressive. He runs the highest Beta. His portfolio may be concentrated in high-beta stocks or he could be using leverage to amplify his returns. This is also why he has an absolute total return higher than the market and the rest of the managers. But don’t rush to make him the champion. Because his Alpha is negative, suggesting he may lack critical stock selection and portfolio construction skills. If Managers B and C are using the same level of risk as he does, they can both beat him hands down.

Manager B appears to be the most conservative. He has the lowest absolute return of 30% among the 3. But before you dismiss him, he is actually also the one giving us the most bang for the buck. During this period, he is only using a quarter of the risk A takes and half of what C uses. In addition to that, he is the only one with positive Alpha and is ahead by a good margin. This indicates Manager B may have better skills than both A and C.

Manager C looks closely tied to the market with a Beta of 1 and a slightly lower absolute return and Alpha. A possible scenario is that he is just replicating the market. This would explain why his Beta is close to 1.0. And the slight underperformance can be due to fees and any other associated costs.

## A Real World Illustration

Now, let’s extend this to a real-world example using equity market-neutral hedge funds. These funds sell their stock selection skills and aim to deliver regardless of market conditions. Mathematically speaking, they are looking to remove the Beta and survive almost entirely on Alpha. To do this, they select good stocks to long and bad ones to short. The long positions give you a positive Beta while short positions are the reverse. When these positions are carefully calibrated, the aggregate Beta can be zeroed out. What is left then is the Alpha which largely depends on how good their stock-picking skills are. In practice, this is not easy since Beta is not a static number. But for our purpose, we will just look back historically to see how they fare.

For this study, we use the following indices:

1. HFRI Equity Market Neutral – represents market-neutral hedge funds

2. MSCI World – represents the equity market *

* Note that it is not straightforward to pick an appropriate benchmark or market for hedge funds given their wide latitude in strategies and composition. Most hedge funds adopt an absolute return target or a peer strategy benchmark.

##### 36-Month Rolling Alpha and Beta

Let's analyze the market-neutral funds over the period from January 1990 to March 2019. If you recall, I mentioned earlier that Alpha and Beta are not some everlasting static numbers. They change with the market environment. In fact, the risk-free rate is not a constant either. But well, almost nothing about the markets is constant other than change itself. So it would not make much sense for us to do a single regression over the entire 30-year period. Neither is too short a window viable since we need the numbers to get a reasonable estimate for Alpha and Beta. So let's do this on a 36 months rolling basis. For simplicity, let's also assume that the risk-free rate stays at 1% per year for this entire exercise. The plot below is what we get.

There are a few things we can establish from the chart. First, it shows us that market-neutral funds are almost true to their name. They run a fairly low Beta between -0.1 to 0.2. But there is a clear trend that their Beta is increasing. Second, they do deliver positive alpha most of the time. However, Alpha is also evidently heading south. At this moment, their Alpha is almost non-existent and the returns are driven by Beta.

##### The Regression Plots

A picture paints a thousand words. So sometimes it is also useful to look at the regression plots. We can glean useful information from it without the need to perform complicated statistical analysis. I included a longer period of data to get the plots. Basically, I did one for the first 10-year period January 1990 to December 1999 and another for the last 10-year period April 2009 to March 2019. This is just to see how things changed. The focus here is not so much on absolute Alpha or Beta numbers, but rather on the distributions.

Just by looking at the distributions of the points in the 2 plots, it is not hard to notice the difference. In the first plot, the points appear to scatter more randomly. This is in line with what market-neutral managers want to achieve i.e. returns that are not correlated with the market. But the more impressive part is the bulk of their monthly returns lies in the positive upper half of the plot. If we zoom in on the part in red, we find these guys delivering mostly positive returns even when the broad market MSCI World is down. The second plot shows a starkly different picture. The points are clearly concentrated around the fitted line with a more equitable distribution across both the positive and negative territory.

This gel with what the rolling alpha and beta show us. But why is there a deterioration in Alpha and an increase in Beta? Did the managers lose their skills? Or perhaps this is the result of overcrowding in the large and mid-cap space of developed equity markets and the only way to eke out any decent returns is by taking on Beta.

## Alpha and Beta Don’t Tell You Everything

At this point, I must mention that no single metric is perfect. All come with their own set of assumptions and none tell us the complete picture. Alpha and Beta are no exceptions.

For one, we can’t just pick any market or form a composite benchmark according to your whim for computing Alpha and Beta. For instance, we can’t use a fixed-income index as the market for a pure equity fund. It does not make any sense. A result that shows the equity fund has a low Beta against an uncorrelated fixed-income index is meaningless. And whatever Alpha we get is contaminated with passive equity market returns that are unaccounted for. The index we choose should ideally represent as closely what the funds invest in as possible.

However, knowing we need the right market does not mean we can always find it. Not all funds pursue a narrow long-only strategy within a well-defined universe. Hedge funds, in particular, run a large multitude of strategies that spans different regions, asset classes, and time frames. And these can evolve over time making benchmark selection a big challenge.

As an example, we used the MSCI World index as the market in the study for lack of a better choice. But it can be questionable whether it is a suitable benchmark, especially for the early period in the 90s. There aren’t that many market-neutral or large hedge funds during that time and I would not be surprised if many run small portfolios with concentrated names. In contrast, the MSCI World is a large diversified index with more than 1000 constituents. Their composition might turn out to be miles apart from each other.

## Parting Thoughts

What we see applies to funds with a single asset. How about funds that adopt a multi-asset strategy? Then a single-factor model no longer suffice. However, we can always extend this into a multi-factor model with each factor representing the risk premium from a particular asset class. The concept remains the same. I will leave you to take some time to digest the information. And after that, congratulations, you can add two more Greek words to your vocabulary.

This post was first published on my personal blog investmentcache.com

I will be releasing videos on alpha and beta, keep a watch for them!

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