Understanding beta and alpha

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Beta basics

For most investors, beta is the number they want to beat—or buy. It’s provided by an index, but beta is much richer and more complex.

In his 1955 doctoral dissertation, Harry Markowitz established the notion that a diversified portfolio of stocks could smooth fluctuations among individual stocks, providing those stocks weren’t closely correlated. Markowitz’s three principal achievements were correlation analysis, diversification as a risk-dampening measure, and the definition of risk as volatility.

Those achievements are summarized in the notion that there’s an efficient frontier beyond which diversification adds no boost to returns.

That was step one in modern portfolio theory. Step two was the articulation of beta. That goes back to the work of William Sharpe, among others. His Capital Asset Pricing Model established the market portfolio as the sum of all risky assets. And instead of analyzing the correlation of individual stocks to each other, his model looked at their correlation to the market portfolio.

Beta, said Sharpe, is the variability of an individual security’s returns against the market return—usually a benchmark such as the S&P 500. But in popular parlance, it’s come to stand in for the market return itself. CAPM involves more than that.

Securities have to be evaluated against a risk-free asset like a treasury bill. The result is the capital markets line, which tracks a portfolio starting with a risk-free asset and slopes upward as riskier assets are introduced until it reaches a portfolio of risky assets only. The higher the risk, the higher the reward.

Simple theory; the reality is less so. “There are a few different ways to define beta, but really, it’s a description of the risk/return characteristics of a particular asset class,” says Michael Cooke, head of distribution, PowerShares Canada.

“It captures the performance characteristics of a particular market or asset class, for example equities or fixed income, and it is representative of the total invested capital in that particular market. So, in theory, it’s reflective of the beliefs and expectations of every market participant about the future prospects of individual securities, and in aggregate it reflects the market portfolio.”

Adds Rotman School of Finance professor Eric Kirzner, “A high-beta stock is expected to be more volatile than the market. When the market is strong, a high-beta stock [tends to] go up more than the market; and when the market is weak, a high-beta stock [tends to] go down more than the market.”

But, he notes, in practice, betas are not the best way to pick individual stocks.

“Beta is not a terrific measure for individual stocks. Although the Capital Asset Pricing Model shows that there is a strong relationship between return and volatility, betas are quite unstable for individual stocks. So using beta for individual stocks is probably not a very powerful tool.”

Kirzner says it works much better on a portfolio level when the beta of that portfolio can be benchmarked against a relevant index.

Built-in unpredictability

All the same, Tyler Mordy, director of research and co-CIO at HAHN Investment Stewards, comments, “I love what Andrew Lo at MIT says—that finance suffers from physics envy. We would like our models to be as predictive as they are in physics. You labour in this business for a while and you realize that humans run financial markets. So things aren’t as predictive.”

He finds price variability too restrictive a definition of risk. “If you think about short-term variability and you look back, even if you took a broad-based volatility measure five years ago […] volatility was heading lower right into the financial crisis.”

Beta may not be predictive on the risk front. But there are also problems on the return front, particularly when stock market beta is compared to the beta of other asset classes. Here, stocks are assumed to be riskier, and therefore should fetch a risk premium.

But, “if we’re going to capture that positive risk premium,” says Cooke, “we have to buy assets when they’re cheap and sell them when they are expensive. In fact, the opposite holds in the market-capitalization-based portfolio,” because it forces you to do the opposite.

The performance of emerging market bonds and stocks since 1994 offers a good example. Emerging-market stocks return 5.6% annualized, making it look like the additional risk was compensated.

But that wasn’t the case, he notes. “Money-market instruments in emerging markets annualized 7.3% a year. In other words, I underperformed cash by 170 basis points per annum—a very stark example of a negative risk premium.”

The disappointing returns, Cooke says, stem from investors’ perception of beta. “A lot of foreign investors view emerging markets [through the lens of] a local bank, utility, cement manufacturer, pharmaceutical company, or energy company.”

So much so, Cooke says, that “The top 10 stocks in the Russian stock market count for 81% of the total market capitalization of the index. That wouldn’t be a problem if equity markets in general, and emerging markets in particular, were efficient. But history has shown they’re not.

“During the same period, not once did the top 10 stocks in any emerging market index collectively outperform the rest of the market over a subsequent five-year period. And yet that’s where the cap-weighted index is putting most of investors’ capital.”

So index construction may capture a stock’s market capitalization, but not its economic footprint or weight in the real economy.

There are two issues here. CAPM refers to all risky assets. But not all are represented on an investable index. One example would be privately held companies.

The other problem is finding a better representation of the economic weight of tradable companies that are components of an investable index.

“There’s something practitioners call the beta puzzle,” explains Mordy. “The Capital Asset Pricing Model suggests that higher-beta stocks should have higher returns. Empirical evidence suggests that it’s actually the opposite.”

Like Cooke, he argues capitalization-weighting is driven by high valuations, and valuations need more attention as a risk factor if investors are using beta as a proxy for risk.

“Value stocks tend to outperform growth stocks over the very long term because the valuation is reverting back to the mean and you get a free ride there,” says Mordy, “whereas growth stocks are typically pricing in that future growth and eventually revert back to more of a fair value. It’s the same concept with expensive assets in high-growth emerging markets.”

One response to the beta puzzle is to construct low-volatility portfolios. But Kirzner says the answer actually lies in asset allocation.

He says buying equities and looking to make them highly defensive is generally a questionable strategy. “You can go for lower beta and higher beta, but if you make it overly defensive why would you even be buying equities?” If you’re looking for an overly defensive position you’d be better served by increasing your fixed-income or cash components.

As Mordy puts it, “If we put in the equity component, I still want to have something that is going to perform close to the market. I don’t see the point of buying an equity portfolio with low expected returns and low volatility. I’d rather adjust the asset allocation.”

As for what you’re buying, even a poorly constructed index may work. On the other hand, a well-constructed index may be deceptive. “The problem with a lot of indices is that they can end up with very high concentration to individual stocks and sectors,” Kirzner says.

“The S&P/TSX might be a well-constructed index, but it’s not a particularly well-diversified index. Buying the S&P/TSX, especially the 60, [means] 70% is in three sectors: energy, gold and the banks.”

That, arguably, dilutes Markowitz’s principle that diversification reduces risk—in the late 1990s and early 2000s, the TSX 60 became heavily weighted to just one stock, Nortel.

With concentration can come another problem. Beta has “got this backward-looking aspect to it, which doesn’t account for changes in the business cycle and macro-economic regime shifts,” Mordy points out.

“A lot of the nose-to-the-grindstone stock-picker types would suggest you can ignore the big macro events and ignore bubbles and boom to bust.” He thinks stocks are in the third period of a secular bear market that began in 2000.

There are lots of ways beta may be an accurate measure of stocks and the market, but there’s much it does not answer.

Ultimately, says Cooke, “Beta is not necessarily a great way to invest. It’s a misperception that’s been widely fostered, with the growing popularity of index products, but there’s more to indexing and building a market-based portfolio that still preserves the attributes investors are looking for: low cost, transparency, tax efficiency and liquidity.”

The true cost of beta

There are two components of an active portfolio’s return. Beta is passive and stems from simply being invested in the market. The other, alpha, stems from a manager’s skill in selecting investments that will add return above what the market gives on its own.

Beta drivers

Classical beta is the standard beta that measures the exposure of a security or portfolio relative to a major index and serves as a measure of the security’s or portfolio’s exposure to systematic risk in the equity market. But beta is actually a continuum that starts with the pure classical beta and continues on to include other types of beta.

Classical beta has zero active return and a corresponding zero active risk exposure. As we move up along the continuum, active risk exposure increases, as does the possibility of active return. Here are some of the betas we find along that continuum.

Bespoke beta is a measure of exposure to local risks such as sector, country and style. (Style is beta, not alpha.) Sector-specific ETFs, such as iShares XEG, that cover the Canadian energy industry are good examples of local beta products, as are country or region ETFs such as Vanguard’s Emerging Markets ETF, as well as ETFs that cover a specific capitalization or style subset of the market.

Alternative beta is a measure of exposure to unusual systematic risks. Examples of alternative beta would be exposure to foreign currencies, commodities and real estate. Alternative betas expand systematic risk exposure beyond typical stock and bond portfolios.

Fundamental beta is meant as an alternative to the usual capitalization-weighted index. These indexes weight stocks within the index based on factors such as the price/book or dividend ratio.

Claymore’s suite of RAFI Fundamental Indexes is a good example of fundamental beta, as are ETFs invested exclusively in high dividend-paying stocks.

Active beta, also called enhanced indexing, tries to earn excess return in the markets using quantitative strategies resulting in portfolios whose return is mainly beta-driven, but use long/short strategies to a varying extent. 130/30 products belong to this type of beta. The beta of 130/30 (or any combination ranging from 0/100 to 200/100) is always 1, as with the market, but may allow for more alpha generation through their reduced short-selling restrictions. These are sometimes called beta 1 products.

Bulk beta includes the typical actively managed mutual fund. Although we would expect an “active” mutual fund to have a healthy dose of alpha in its performance, the majority of the typical mutual fund’s return is generated by factor exposure (beta) rather than active return factors (alpha). Bulk beta investments are highly correlated to their benchmarks. Also, since these products are basically packaged systematic risk exposure, they have access to the whole of the underlying market’s liquidity and therefore have a large capacity for AUM.

Beta first, then alpha

Alpha is the excess return that one is left with once all the beta-driven return has been accounted for. Let’s look at an example of a fund manager who beat the S&P/TSX beta-driven return by 2.39%. What if the manager was mostly invested in small cap stocks? Is the S&P/TSX index still an appropriate benchmark?

A better benchmark would be a small cap index. But given that alpha derives its value from what has been determined as beta factors, changing the reference beta means that we will wind up with a different result for alpha. The return of the S&P/TSX Canadian Small Cap Index for the year was 38.53% in 2010, which is the more relevant beta-driven return we should be looking at in evaluating the manager. A small cap manager with a 20% return would have greatly underperformed the appropriate benchmark.

The average return of small cap managers covered by Globefund in 2010 was 26.22%, or 12.41% under the benchmark. So, comparing firm size is a very important return factor that should be considered in defining a portfolio’s beta and therefore the manager’s skill in generating alpha. In this particular case, the manager could be seen as skillfully generating 2.39% of added return, or as a not-so-skilful manager trailing his benchmark by 18.53%.

Perhaps our portfolio manager does stick with large cap stocks, but has a value-oriented management style. He looks for securities he believes have temporarily fallen out of favour, or whose true value has not yet been discovered by the markets and whose price is consequently below what he considers to be the fair value.

For the year 2010, the S&P/TSX Canada Select value and growth indexes respectively had a return of 16.67% and 19.30%. The appropriate benchmark return for our manager in this case would be 16.67%, rather than the S&P/TSX’s 17.61%.

In this instance, choosing the wrong benchmark actually underestimated the manager’s skill at generating alpha-driven return.

Alpha is a tricky thing to measure properly. Its correct measurement depends on being able to identify all the beta-driven performance factors beforehand. Unidentified beta drivers can be mistakenly interpreted as manager skill. In addition, alpha is not static. Some investment strategies that had once been considered as alpha have been found to be previously unidentified beta, such as firm size and style. For example, a value manager may have beaten the S&P/TSX Composite over a number of years, but how did he fair against the Dow Jones Canadian Select Value Index?

Alpha drivers

So how does one go about getting alpha? The only way is to get off the benchmark and loosen investment constraints such as limits on short selling, portfolio concentration, and types of markets and securities allowed in the portfolio. In theory, the fewer the constraints, the more opportunity the manager has to generate extra return. Of course, that also means more things can go wrong (negative alpha).

Alpha drivers fall within six categories. The first two categories of alpha drivers could very well be found in portfolios like that of our Canadian equities manager.

Long/short investments. These investments give the portfolio manager more ability to generate alpha from both long and short positions. By being both long and short, the manager eliminates, or at least diminishes, total market exposure, thus lowering the portfolio’s beta. If the manager is perfectly market neutral (fully hedged), the only return left is alpha. The aforementioned 130/30, in which the manager is long 130% and short 30%, is classified as a beta driver given the resulting beta of 1.

So perhaps our manager is short as well as long in his equity positions, therefore lowering his beta — maybe even all the way down to zero. The lower his beta, the bigger the portion of his 20% return attributable to selection skill. Or perhaps the manager is long individual stocks, but is also short the market as a whole through the sale of futures contracts on the index. Here again, his beta could be brought down to zero, and his 20% return totally attributable to selection skill. In this case, his skill would be present only on the long equity side of the portfolio, given that the short side is pure negative beta.

Portfolio concentration. Concentrated portfolios make large bets on a few securities. Traditional mutual fund managers usually seek diversification in order to minimize tracking error relative to their benchmark, resulting in bulk beta.

Concentrated portfolios such as corporate governance and private equity funds assume greater tracking error in an attempt to produce larger active return. How many securities does our portfolio manager hold? 60? 10? Do these securities belong in the S&P/TSX’s investment universe?

The other alpha driver categories require that we move away from a stock-only portfolio, so our manager probably would not apply these in this case.

Absolute return investments. This manager’s objective is to seek alpha in any opportunities that present themselves. The absolute return manager is unconstrained in investment style or strategy, buying and shorting just about anything under the sun. Her main objective is to always have positive returns over a certain time interval.

Segmented markets. These are markets most investors never get involved with. Commodities, junk bonds, and the pink sheet market (penny stocks) are usually off limits to institutional investors due to liquidity or quality constraints. These markets may provide opportunities to find alpha since they are less crowded and less efficient.

Nonlinear return distributions. The stock market’s returns are considered to follow a roughly normal (bell curve) distribution, with outlier or extreme events expected to be few and far between. Strategies such as merger arbitrage, event-driven strategies, or trend-following managed futures aim to reflect a return profile resembling what you would find in the options market, such as buying out of the money calls going for a long shot, or covered-call writing, which is akin to collecting insurance premiums monthly.

Alternative beta exposure. A manager can expand the systematic risk exposure beyond the typical stock and bond portfolio. Exposure to asset classes such as currencies, commodities, real estate and even volatility — taken individually – is considered beta. But alpha is achievable, either through strategic and timely selection among them, or simply by actively seeking out these betas, which are classified as alternative relative to the typical stock/bond factor exposure. Each alternative asset class has its beta, as described in the above section covering the various forms of beta. Yet exposure to these alternative asset classes and their risk factors, relative to the classic 60/40 portfolio, is considered to be alpha generated through a better beta.

Alpha and beta separation

The distinction between alpha and beta (in its various forms) should interest investors beyond its theoretical considerations.

Beta is more predictable than alpha. If the markets fall and a portfolio’s return is solely determined by market exposure, or pure beta, the portfolio’s value will fall by the exact amount the market does. If the portfolio is managed actively, who is to say whether the manager will outperform or underperform the market? Alpha can only be determined after the fact and requires the investor take a leap of faith.

Unfortunately, persistence of skill among active managers is hard to find. From one period to the next, an active manager can easily outperform or underperform the market. This unpredictability can add risk to the investor’s portfolio.

The second important distinction is cost. Alpha is much more expensive than beta in terms of management fees and trading cost. If the investor is paying alpha-like fees, we would hope he is getting equivalent management effort.

Here, the notion of bulk beta is important. Mutual funds promise superior returns through active management and as a result charge high management fees. The average Canadian large cap equity fund’s MER is about 2.50%.

Of course, one has to consider the embedded commission trailer that the advisor receives from that, which is usually around 1% and should probably not be considered when discussing fees for managing the portfolio. This leaves management fees of 1.50%, not including the Trading Cost Ratio, which varies between 0.01% and 0.40%, depending on portfolio turnover. But since most mutual funds are really bulk beta products, shouldn’t they be priced as such?

The cost of beta is now known through the proliferation of index-tracking ETF products in the retail marketplace. Access to market risk can cost as little as 0.07%, as with BetaPro’s HXT ETF, which tracks the S&P/TSX 60 index, or 0.06% for Vanguard’s S&P 500-tracking ETF, or 0.24% to buy the American bond market through iShares’ Barclays Aggregate Bond fund.

For the first time, investors have at their disposal different alternatives for accessing the markets, and they can weigh the pros and cons of each. Indeed, if expensive active mutual funds were once the primary way for investors to have access to market beta, they now have a low cost through index-based ETFs. Would you really want to pay 21 times that amount for an index-hugging bulk beta mutual fund that has no potential for generating excess return?

Accurate pricing of beta and the resulting alpha/beta separation will most probably have a major impact on the asset management industry and on the way it offers its asset management solutions to the investor. A possible indication that such changes are already under way is that mutual fund AUM numbers worldwide, in the United States and here in Canada have not yet reached pre-crisis levels, while ETF AUMs keep on growing.

One would certainly expect expensive, low-value-added bulk beta products to be the first to feel the squeeze, but the changes may go beyond simply correctly pricing expensive beta products.

We may see specialization of firms: some will come up with new ways of creating beta, while others will strive to generate attractive and sustainable alpha. More and more, the investor will demand genuine alpha efforts in return for alpha-type fees. Investors will get beta at its true price.

Alpha’s residual nature

Alpha is what is left after we’ve accounted for the beta portion of a manager’s return— it’s a residual value. Indexes have been published from the early days of market trading, either by the exchanges themselves or by publishing companies such as Dow Jones and Standard & Poor’s, so these references became the benchmarks to beat. Thus, one popular notion of alpha is that of a manager beating the S&P 500, or the S&P/TSX Composite Index, for example.

The CAPM tells us that in the context of an efficient market, stock picking doesn’t work. If you want more return, you need to take on more risk (in the form of leverage). Any risk-adjusted return above this is called “abnormal return,” or alpha. In CAPM terms, return is tied to the notion of exposure to the market in general and represented by the linear regression model.

CAPM: E(R_p) = Rf + B x (R_m-R_f)

Where:

• R_p: The portfolio return
• E(R_p): The expected portfolio return as per CAPM
• R_f: the risk-free rate
• B: the manager’s Beta, or leverage factor

(R_m-R_f): the risk premium expected from investing the market.

CAPM is a single-factor equilibrium model for which the risk factor is market risk. In efficient markets, a manager’s return should be 100% dictated by and limited to exposure to the market risk factor. In other words, R_p = E(R_p).

In an efficient market—a market whose general conditions do not allow for added return through manager skill—a manager’s return is solely dependent on the extent of his beta (given a constant risk-free rate and a constant market risk premium), or exposure to the underlying risk factor.

So if a manager’s return in the last twelve months came in at 1% above his benchmark, the efficient market hypothesis tells you that’s because he took on more risk. If expected market return is 7% and the risk-free rate is 2%:

E(R_p) = 2% + 1 x (7%-2%) = 7%

If the manager’s return over twelve months is actually 8%, and his beta is 1.2 (he is leveraged 1.2 to 1):

E(R_p) = 2% + 1.2 x (7%-2%) = 8.0%

In this case the manager has not generated any skill-based return, as the actual portfolio return is equal to the expected portfolio return given a beta of 1.2:

R_p– E(R_p) = 8.0 – (2% + 1.2 x (7%-2%)) = 8.0 – 8.0 = 0

In other words, apart from the risk free rate, the manager’s return is completely explained by the degree of exposure to the market risk factor. There is no leftover return that needs explaining. If there were, under single-factor CAPM, we call that residual return alpha and attribute it to manager skill.

[α]_p = R_p– E(R_p)

Where:

[α]_p = Jensen’s alpha

R_p = Funds’ realized return

E(R_p) = Funds’ expected return

What if the manager’s beta is 1? In this case, CAPM is not able to explain all of the manager’s performance. There is a residual return that remains unexplained after taking into account the manager’s CAPM beta exposure and risk-free rate. That variable would be the ever-sought-after excess return, alpha, α_p:

E(R_p) = R_f + [α]_{p + B x (Rm-Rf)}

Our example above would look more like this:

8.0 – (2% + 1.0 x (7%-2%))

8.0 -7.0 = 1

[α]_p = R_p– E(R_p)

1 = 8%-7% = [α]_p

Notice that the manager has produced a return of 1% above the return expected under CAPM, and has done so without taking on additional beta.

But what if there are other risk factors to be considered? What if in addition to being exposed to the market risk factor, the manager is in fact specialized in small-cap stocks, which are riskier than large caps? Then the expected portfolio return, E(Rp), would look something like:

E(R_p) = R_f + B₁ x (R_m-R_f) + B₂ x (R_S– R_B)

So now we have two betas. The general market beta, and an additional beta for the additional risk factor taken on by investing in small-cap stocks versus safer large-cap stocks (Small minus Big, or SMB).

Let’s assume the risk premium of owning small-cap stocks versus large-cap stocks is 1% per year. Plugging in the manager’s numbers would look like:

E(R_p) = 2% + 1 x (7%-2%) + 1 x (8%-7%)

E(R_p) = 8%

We see that expanding the value of beta actually reduces what was considered alpha under single-factor CAPM to zero.

Beta has evolved through time as new risk-factor models have been identified. Eugene Fama and Kenneth French expanded the original single-factor model to a three-factor model that includes a size factor (R_S – R_B) as well as a book-to-market factor (R_H– R_L, or high book value minus low book value):

E(R_p) = R_f + B₁ x (R_m-R_f) + B₂ x (R_S – R_B) + B₃ x (R_H– R_L)

Mark Carhart later demonstrated the Fama and French model did not capture return attributable to the one-year return momentum of a stock. The Carhart four-factor model takes the Fama and French three-factor model and adds a momentum risk factor (Winners minus Losers, or R_W– R_L):

E(R_p) = R_f + B1 x (R_m-R_f) + B₂ x (R_S– R_B) + B₃ x (R_H– R_L)

Proliferation of ETFs

Since alpha is a residual return once all sources of beta are accounted for, any expansion of beta will make alpha more rare.

The slicing and dicing of various market betas such as size, value, sector concentration, style, geography, momentum and asset class, combined with the arrival to market of ETFs tracking these various risk factors, are steadily pushing alpha-chasing and accompanying fees to the sidelines, or at least giving them a complementary role in portfolio building as opposed to the central objective.

The investor and advisor can build high-performing and low-cost portfolios consisting of diversified factor exposure and go from there. Taking each of the above factor models, we can find at least one corresponding low-cost ETF offering exposure to the appropriate risk factor:

Market risk premium: Vanguard S&P 500 ETF: VOO (0.06%)

Small minus big: iShares Russell 2000 ETF: IWM (0.26%)

Three-factor model: iShares Russell 2000 value ETF: IWO (0.40%)

Strong momentum stocks:

PowerShare DWA technical leaders portfolio ETF: PDP (0.70%)

In these cases, what was once considered alpha and priced accordingly is now considered unrecognized beta, and priced at a much lower level.

As previously mentioned, beta occurs on a continuum from pure or classical beta to more complex risk-factor exposure. The cost of more complex beta, unsurprisingly, is higher than the cost of classical beta.

But while there’s nothing wrong with paying extra for genuine alpha-generation effort, there is no reason for the investor to pay alpha-like fees for a product that delivers beta, classical or not.

Alpha versus beta

Should investors spend time choosing the best manager, or diversifying?

Investors can gain access to TSX return for as little as 0.07%. In contrast, most hedge funds charge 2% of capital and a 20% performance fee. The average active Canadian large-cap fund MER is about 1.50%, excluding advisor compensation.

Yet study after study shows the majority of mutual funds simply generate beta. Why should the investor pay 150 bps for beta when he can get it for 7 bps?

Alpha and beta also have different impacts on portfolio performance and volatility. When building a portfolio, selecting among active managers adds little value both in terms of performance and volatility reduction. On the other hand, diversifying across various asset classes and risk-premium exposures has considerable impact.

Let’s start with a TSX-benchmarked portfolio. We are looking for either a potential for increased return or a potential for increased diversification; preferably both. So is it easier to gain potentially higher return and/or diversification (through greater return dispersion between the portfolio’s constituent parts) by manager selection within an asset class—alpha, or by selecting between various asset classes—beta?

Betting on alpha

On the mutual fund side, Standard and Poor’s Indices versus Active (SPIVA) 2010 report tells us 19.64% of Canadian large cap managers beat the TSX over a 12-month period, 10.94% over a three-year period, and 2.53% over the five-year period. For the five-year period, the average mutual fund return is 3.88%, versus 6.51% for the TSX.

Being less expensive than their Canadian counterparts, funds in the U.S. have fared better. Over the one-, three- and five-year periods, 34.28%, 42.35% and 38.17% of actively managed funds outperformed the S&P 500. For the five-year period, the median fund performance is 1.89%, versus 2.29% for the S&P 500.

Mutual funds in both Canada and the U.S. basically track their benchmark, minus fees. So we look to the institutional side, where fees aren’t so egregious and where alpha generation efforts can be taken more seriously. (Institutional managers post returns gross of management fees, so they are taken out of the equation.)

Let’s look at the five-year performance of large-cap managers on the Mercer Pooled Fund Survey. As of December 2010, the median large-cap pooled fund five year performance was 6.54%, just 0.03% higher than the TSX.

For the years 2009, 2008 and 2007, respectively, the median pooled fund Canadian large-cap mandate had gross five-year returns of 7.95%, 5.02% and 18.8%, versus TSX returns of 7.66%, 4.16% and 18.3%. The average alpha for those four five-year rolling periods is a slim 0.42% before management fees. If you happen to have $10 million invested, the average management fee is 45 bps (not counting custodial fees), so any added value is gone.

How did best-of-class managers fare? For the four five-year periods, top-quartile mandates beat the TSX by an average of 1.16% before fees. If you had $10 million to invest and managed to pick all top-quartile managers, you would have outperformed the TSX by 70 bps, before custodial fees.

The TSX has a historical standard deviation of 15%. To encompass 95% of all probable returns for any given year, we need to consider two standard deviations. This translates in a probable range of 30% above or below the TSX’s average annual return. Assume the historical return for the TSX is 10%, resulting in a possible return of anywhere between +40% and -20%, or a 60% range. Would you notice a 0.70% difference? It’s on the same scale as a krill hitting the backside of a whale.

Betting on diversification

Another indication that mutual funds just track their indices is how little dispersion there is between the various performance quartiles. Although not available in the Canadian SPIVA study, the U.S. study tracks the performance of the first, second and third-quartile funds in addition to the median.

For 2010, 2009 and 2008, the differences in performance between the first and third quartile for large-cap core mutual funds in the U.S. were 3.55%, 8.63% and 5.98%—for an average of barely 6%. For the three-year period ending in December 2010, 2.85% separated the first and third quartile. For pooled funds, the results are similar. For the same three years, the difference between first and third quartile is, on average, 5.79%.

The chart below shows 12 different asset classes, including the TSX. A to D are various fixed-income asset classes such as government bonds, real-return bonds, corporate bonds and so on. The other eight asset classes are non-fixed income asset classes ranging from equities to real estate to broad commodities.

Each year, asset classes are ranked from top to worst performer. The colours bounce around each year as each asset class’s performance rank varies. To maximize diversification, we should have a wide dispersion between the different rectangles each year, and always have some positive and some negative rectangles. Otherwise, all the asset classes would be moving in unison and the portfolio holding them would swing wildly.

Return dispersion between the different asset classes in any given year is much greater than the dispersion between the SPIVA and Mercer managers discussed above. The difference in returns between the top- and bottom-performing asset class varies between a low of 12.79% to a high of 57.35%, and has an average of 41.91%. This means the potential for diversification is much more substantial for beta than for alpha.

Also, in any given year, there is at least one asset class that outperforms the TSX, sometimes by as much as 42%. If you diversify the portfolio, there’s no need to guess which asset class it will be each year, as it is also impossible to guess which managers will end up in the first quartile each year. Yet forgoing those asset classes in any given year means forgoing extra return.

The 10-year period is especially favourable to the TSX. It has a compound annual growth rate (CAGR) of 5.6%versus 1.6% for EAFE stocks and -3.9% for the S&P 500. Their respective standard deviations range from 15.44% to 17.78%.

We can put beta diversification to the test by building an equal-weighted portfolio and simply rebalancing it quarterly. To make things more challenging, we can exclude any fixed-income beta, so as to have a truer comparison to being invested only in the TSX. That gives us a portfolio with eight equally weighted asset classes.

Each quarter, the portfolio is rebalanced. There is no active management or tactical call behind the individual asset classes, as they are represented by their indexes and their respective weights remain 12.50%.

That portfolio would have had a return standard deviation of 12.37%. Diversification has resulted in a portfolio that is less volatile than the individual indexes. What may be more surprising, especially given that the period we’re looking at is quite favourable to the TSX, is the equal-weighted portfolio’s CAGR comes in at 7.2%, versus 5.6% for the TSX.

In short, diversifying across beta exposures (without fixed-income) and rebalancing could have given the investor an extra return of 1.90% over the best of the three main indexes over the 10-year period.

Doing so would have also lowered risk (the standard deviation is lowered to 12.37% vs. 15.44% for the TSX). In contrast, the median managers we looked at earlier had a performance of 0.42% above the TSX (we have no information on the standard deviation) over the five-year period studied.

This lesson is compiled from articles originally produced for Advisor’s Edge Report by Scot Blythe and Guy Lalonde.