Quant View -- Investing by the Numbers -- Archives: March '08 Stating the Obvious

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March 2008
Alpha Seekers and Beta Managers
Alpha Isn't the Only Way to Beat the Market

"The superior man...does not set his mind either for anything, or against anything; what is right he will follow."
-- Confucius (551 BC - 479 BC)
The Confucian Analects

HE ACTIVE VS. PASSIVE management debate really boils down to the likelihood of consistently beating an unmanaged index. For active management to succeed, market timing, sector weighting, and security selection must offer the potential to beat the benchmark. Managers who profess to do this tout their ability to add value over and above that of passively investing in the market.

This is the result of Modern Portfolio Theory which postulates that a portfolio's return is the result of market and non-market factors:

Rp = α + (βp * Rm) + є
Where:
Rp = Portfolio Return
Rm = Market Return
α = Portfolio Alpha
βp = Portfolio Beta
є = Regression Error Term

This is essentially a one factor model where the portfolio's beta is the variable and its alpha is the constant. The market return is the independent variable and the portfolio's return is the dependent one. The error return for the regression is typically minimal and is often overlooked when evaluating the portfolio's performance.

Beta is a measure of the portfolio's sensitivity to the market. A portfolio with a beta of 1.0 will move in tandem with the market while one with a beta of 1.2 will move 20% more while one with a beta of .70 will move 30% less. Beta affects expected return in both directions, both up and down.

Alpha is the part of the portfolio's performance that differs from what is projected by its beta-adjusted market return. It can be either positive or negative. This is where active managers say they add value, by creating and/or increasing positive alpha.

 

More Than One Way to Add Value
You hear very little about beta. After all, it's fairly easy to increase or decrease your market risk exposure based upon the securities you buy or sell in your portfolio. To make things even easier, there are mutual funds and ETFs that provide increased multiples of market risk. By combining them with money market instruments, you can create a portfolio with just about any imaginable level of market risk.
ALPHA & BETA
Two Components of Return
Alpha (α)
A measure of a fund's risk-adjusted return. Alpha can be used to directly measure the value added or subtracted by a fund's manager. It is calculated by measuring the difference between a fund's actual returns and its expected performance given its level of market risk as measured by beta. An alpha of 1.0 means the fund produced a return 1% higher than its beta would predict. An alpha of -1.0 means the fund produced a return 1% lower.
Beta (β)
A measure of an investment's volatility relative to a chosen benchmark. For stocks or stock funds, the benchmark is usually the S&P 500. For bonds or bond funds, it is Treasury bills. The beta of the benchmark is always 1.00. So a stock fund with a beta of 1.00 has experienced up and down movements of roughly the same magnitude as the S&P 500. Meanwhile, a fund with a beta of 1.25 is expected to do 25% better than the S&P in an up market and 25% worse in a down market. Generally speaking, the higher the beta, the more risky the investment.
Source: SmartMoney.com

Alpha, on the other hand, offers value over that which would be predicted by market risk and return. It's where managers claim to earn their keep by giving investors more than they can get from passive index investing. Archive Index

As opposed to beta, you hear a lot about alpha. Managers compete on their ability to generate it and investors go out of their way to find those that do. Whether by astute stock-picking, prescient trading, or timely allocation, active managers believe (or at least want you to believe) they can add value while maintaining a steady level of market risk.

Every year there are some successes and some are able to generate alpha for longer periods of time. Some strategies are quantitative, some rely on concentrated portfolios, and often rely on substantial trading. Whatever the process, active managers work for every bit of alpha they create.

But you can use beta to beat the market, too, and arguably, there's a lot more beta out there to work with. You rarely hear about this alternative.

When you look at the equation above, it's natural to view beta as a fixed value. In other words, if you're looking at a five-year return, you'd plug in one number for beta that represents the market risk for the portfolio for the entire period. The same goes for the other factors as well. But just as the market return varies from day to day and month to month, the beta can vary as well. This is where an active manager can add value.

Suppose the portfolio had an alpha of 1.2. If it maintained this throughout the period, it would climb 20% more than the market, but would also decline 20% more, too. What if the manager didn't try to keep a steady beta but instead altered it to meet market conditions? In this case he might allow it to rise to 1.2 when the overall market was moving up, but might try to move it below 1.0 when the market was in decline. This would allow the portfolio to capture more of the market gains and less of its losses.

At the end of the five-year period, the portfolio would have a single beta value, but that would be a function of the various levels throughout the period. If the strategy was successful, the portfolio would outperform the index, but as a result of beta management.

Is this market timing? Absolutely. The attempt to adjust beta to changing market conditions is definitely a form of market timing, but then what active management strategy isn't? In and of itself, a beta management strategy is not inherently riskier than an alpha seeking approach. The real difference is simply the risks being targeted.

 

Case Study
In an effort to see how the two approaches stacked up, we devised a simple case study. Imagine on New Year's Eve 1997 (before 4:00pm EST) your crystal ball magically revealed to you the list of mutual funds that would have the best alpha and beta managers over the next ten years. If you bought the funds of both, which would have the best returns?

The alpha managers are easy to determine: They're the ones with the highest alpha values over the ten-year period. The beta managers are little more difficult to detect. Since their beta value is a moving target, it alone is not a sufficient means of locating them.
Chart 1
RETURNS BY QUINTILES
High Alpha Funds vs.
High Beta Spread Funds
Ten Years Ending December 31, 2007
Graph -- High Alpha Funds vs. High Beta Spread Funds Return Quintiles, 10-Years Ending December 31, 2007
Data Source: Morningstar
Returns by quintile for high alpha funds (beta managers) and high up market ratio/down market ratio spread funds (beta managers) were almost identical over the ten years ending December 31, 2007.
Chart 2
FIRST QUINTILE FUNDAMENTALS

High
Alpha Funds
High Beta
Spread Funds
Relative Standard Deviation 105.61% 115.42%
Beta 0.98 1.04
Batting Average 56.09% 55.75%

Instead, we used the spread between their funds' up and down market ratios. We calculated the up market ratio for each fund by considering each month in the 120 month period in which the fund's benchmark index was up. By dividing the fund's gain by that of the index, we arrived at the up market ratio for that month. The average of the corresponding value for all up months in the 10 year period, yields the fund's 10-year up market ratio. A similar calculation for months in which the benchmark index declined produced the down market ratio.

Finally, we subtracted the down market ratio from the up market ratio for each fund. This spread offered a reading on the degree to which the manager allowed beta to rise and fall with changing market conditions. Our assumption was that managers who let their funds' betas fluctuate to a high degree were allowing -- if not causing -- this to happen. It wasn't merely a chance occurrence. Notice, however, this simple calculation doesn't necessarily reflect how successful the approach was, only the magnitude of the variation.

We divided each set of funds into quintiles, the alpha managers sorted by alpha, the beta managers sorted by the up market/down market spread. We then compared the returns for each quintile.

Somewhat surprisingly, the results were almost identical. The alpha managers had a slight return edge in the first quintile (6.4% vs. 5.7%), but the beta seekers led in the other four. All in all, the results were quite similar. The results are presented graphically in Chart 1.

The other fundamentals of the two approaches weren't that different, either. Chart 2 shows the relative standard deviation, beta, and batting average for the first quintile of each. As you'd expect, the beta and relative standard deviation are slightly higher for the beta managers, but not significantly so. The batting average is roughly the same.

So what to make of this? It's possible that the two groups of managers were just one in the same. In other words, the alpha seekers may have really just been manipulating beta to beat the market. It's certainly not unheard of, just think back to the 1990s when everyone thought they were god's gift to investing. So many investors were "beating the market" because they loaded up on high beta tech stocks. Could the alpha seekers have been doing something similar over the past ten years?

On the other hand, this is just one ten-year snapshot. It may be something of a coincidence that the results are so similar. Had we considered any other ten-year period, the data may have been dramatically different.

At the very least, it's enough to make you stop and think. If alpha's so hard to find and there are so many ways to manage beta, is the pursuit of alpha really worth it? Makes you wonder.



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