Which Alpha Would You Choose?

Western Asset

Executive Summary

  • If you are looking to enhance the returns of your equity portfolio without altering the risk profile of that allocation, actively-managed, short-duration fixed income, employed in a portable alpha strategy, could be your solution.
  • Portable alpha strategies allow one to seek superior returns in the markets where one can find them and then transfer those (alpha) returns to the asset class of choice. Suitable alpha sources are those markets where above-benchmark returns can be achieved reliably and without substantially altering the risk profile of the underlying (beta) position.
  • While active equity can offer positive alpha, it does so at the cost of high tracking error. Short-duration fixed income can offer alpha at lower risk.

Introduction

Are you looking to enhance the yield of your equity portfolio? Then you should have a look at fixed-income, of all places. Using the techniques of portable alpha, you could, in effect, beat the stock market by taking positions outside the stock market.

Portable alpha is a prominent theme across the investment management landscape these days. The idea is to seek superior excess returns in the markets where they can most likely be achieved and then “port” these back to the “base” position one is seeking to enhance. These strategies can be applied not only to base positions in equities, but also to positions in bonds, commodities, or any other asset group for which derivatives instruments are available.

Exhibit 1
Hypothetical Performance of Portable Alpha Strategy in Large-Cap & Short-Duration
which-alpha-would-you-choose-2006-01
Source: Russell/Mellon Analytics, Ibbotson, Western Asset

Which Alpha Would You Choose?

Exhibit 2
Distributions of Potential Alpha Sources
which-alpha-would-you-choose-2006-01
Source: Russell/Mellon Analytics, Ibbotson, CSFB Tremont, Western Asset

In this report, we will work through the basic mechanics of portable alpha strategies and then apply these mechanics to the issue of enhancing large-cap equity asset allocations via alpha positions in short-duration fixed-income. In future reports, we will examine other aspects of the portable alpha “landscape.”

I. Portable Alpha: Meaning and Mechanics

What Is Portable Alpha? Some markets are harder to beat than others. While beating the stock market is not impossible, it is difficult, and one typically does so by taking “non-market” risks. Meanwhile, other markets are “less traveled by,” often precisely because their aggregate returns are smaller than those of equities. Ironically, this same feature makes them better candidates for the achievement of superior, above-market returns. Historically, the investor has had to choose between high-return, hard-to-beat sectors or lower-return, more-beatable ones.

This is where portable alpha comes in. It allows investors to combine the best attributes of various sectors, the high expected returns of equities with the superior excess returns of fixed-income (or elsewhere). The idea is not so much to beef up the performance of low-return assets as to enhance that of any asset.

In this context, “alphas” are the excess returns within an asset class, the extent to which a fund or manager within that asset class can consistently beat the benchmark return for his class. “Beta” in this context concerns both the risk and return of a particular, base asset class, the one whose return the strategy is intended to enhance. (Yes, this usage differs from the usage of these in the academic literature.)

An ideal portable alpha strategy should preserve the riskiness of an asset class, while enhancing its total return. This combination of results leaves the investor’s basic asset allocation decision in place, while improving total performance.

Active-equity managers most often achieve superior performance by betting with or against broad stock market trends. In this sense, they add or subtract beta more than they do alpha. In contrast, fixed-income managers take risks that are generally unrelated to stock market factors, and so they do generally add alpha rather than beta. Furthermore, as we will see, the reliability of active-equity managers’ alpha, as measured by information ratios, does not match that of short-duration fixed-income managers. On both counts, fixed-income offers an attractive alternative source of alpha for equity investors.

Establishing A Portable Alpha Position. Portable alpha strategies require the use of derivatives. In order to replicate the base returns (beta) of the initial asset allocation, while freeing up funds to invest in the alpha source, a synthetic position must be created, typically in the base or beta asset. In the case of porting alpha into a large-cap equity portfolio, a position replicating the return-risk profile of the large-cap equity market can be achieved via a long position in S&P 500 futures or S&P 500 swaps.

The total return on the synthetic beta position will typically fall short of that of the underlying, cash beta position. The difference between these two returns is known as the funding cost of the beta position. For beta positions in various classes of market-traded securities, arbitrage will ensure that this funding cost is approximately LIBOR, the risk-free rate. If the spread between cash and futures prices for the S&P 500 differed by more or less than LIBOR, an arbitrageur could long or short S&P futures, take the opposite position in the cash S&P, and invest/fund the difference in LIBOR. The relevant LIBOR instrument in this case is that with the same maturity date as the delivery date of the S&P 500 futures contract. For other asset classes, funding costs can differ from LIBOR, depending on the storability of the underlying asset.1

On the alpha side of the portable alpha strategy, the total return on the alpha source can be split up into the return on its benchmark and returns in excess of this benchmark (in other words, the actual alpha). The total return on the portable alpha strategy, then, can be written as:

We call the last term, in parentheses, the basis risk of the portable alpha position (similar to the basis risk on a hedge). It is clear from (1) that alpha sources can add to overall return and risk both through the characteristics of their alpha performance and also through their basis risk. As seen earlier, for beta positions in exchange-traded securities, funding costs will typically be LIBOR. So asset classes with a LIBOR benchmark will provide a “cleaner” alpha source for these than others, since basis risk then essentially disappears. (For other potential alpha sources, we could always take LIBOR as their benchmark, in order to simplify analysis of the portable alpha position, but that would bias analysis of the alphas, tracking errors, and information ratios for these assets, as discussed in Flannery [2000].)

The portable alpha literature defines the variability (standard deviation) of the alpha returns as the tracking error of the alpha position: the extent to which the alpha returns differ regularly from those of their benchmark. So, the variability or riskiness of an aggregate portable alpha strategy will differ from that of the underlying (cash) beta position due to the extent of tracking error, to the variability of the basis risk, and to the interaction (covariance) of these terms with the beta position and with each other.

For example, the total return on a strategy porting alpha from fixed-income to a large-cap beta position would be the return on the cash S&P plus the fixed-income manager’s alpha. Basis risk would be virtually zero if the manager is benchmarked to LIBOR, the funding cost for this strategy. Based on expression (1), the strategy will outperform the S&P 500 whenever the fixed-income manager beats LIBOR, whenever he produces positive alpha.

Suitable Alpha Sources. Any alpha source will experience some tracking error. An ideal alpha source should exhibit both minimal tracking error relative to the magnitude of its average alpha and also minimal effects on the risk characteristics of the aggregate portable alpha strategy. The former property describes the reliability of excess returns from the alpha source. The latter property describes whether or not the alpha source is affecting overall asset allocation (whether it is truly adding alpha or actually affecting beta).

In this sense, portable alpha “strategies” are more “tactics” than they are strategy. An investment manager’s strategic decision is his asset allocation, and portable alpha is a tactical decision intended to enhance the characteristics of one or more aspects of this strategy. Still, we will adhere to the industry norm and refer to these as portable alpha “strategies,” rather than portable alpha “tactics.”

Let’s put some meat on the bones of this analysis. For a strategy porting returns from short-duration fixed-income into a beta position in large-cap equity, over Q4 1995 through Q3 2005, the mean return on the S&P 500 (beta) was 949 basis points per year (bpy), with a standard deviation of 2272 bpy.2 Over this same period, the median-performing short-duration fixed-income manager produced an alpha of 104 bpy, and the median standard deviation of alpha (tracking error) was 194 bpy. The median correlation of short-term fixed-income alpha with the total return on the S&P was -0.69. For these positions, both the funding cost and alpha benchmark are 3-month LIBOR, so there is essentially no basis risk for this strategy.

It follows that a large-cap-based portable alpha strategy employing as an alpha source a hypothetical short-term fixed-income manager with median performance on all these counts over 1995-2005 would have had an expected return of 1053 bpy (the sum of the two returns), with a standard deviation of 2116 bpy, 155 bpy less than that of the S&P 500 index.3 These results are as shown in Exhibit 1.

Turning this trade around, it would not make sense to use active equity as an alpha source for a beta position in short-duration fixed-income. The tracking error and basis risks so introduced would be so large as to dominate that of the aggregate position. That is, such a strategy would deliver essentially the same risk/return characteristics as the opposite direction strategy described just above, porting fixed-income onto an equity beta. While such characteristics are little different from those of a large-cap equity position, they are dramatically different from those of a short-duration fixed-income portfolio. Like a “tail wagging the dog,” the active equity position would effectively become the beta of such an aggregate position, and so it would not be a suitable “alpha” source for a “beta” allocation based in short-term fixed-income.

II. Whose Alpha is it anyway? Active Equity vs. Short Fixed-Income as Alpha Sources

So where should an investor look for alpha sources for his equity allocation: active-equity or short-duration fixed-income? Compare the alphas on active equity with those of aggregate portable alpha strategies porting fixed-income to large-cap equity bases. Both of these “aggregate” positions can be benchmarked against the S&P 500. In both cases, their excess returns relative to the S&P 500 boil down to just the alphas of the respective managers themselves.4 So the fair and accurate comparison between active equity and short-duration fixed-income as alpha sources is between the excess return (alpha) characteristics of active equity managers and of short-duration fixed-income managers. How have these alphas behaved?

Alpha From Active Equity. For active equity managers, Hill and Thierens (2004) (hereafter H&T) found that the typical (median) large-cap active equity manager delivered negative alpha over 1990-2003. Regular reports from the Standard & Poor’s Index Versus Active (SPIVA) group also find that active equity managers, on average, underperform the market indices. Of course, the typical equity manager would disagree with that. More pertinent to our analysis, H&T’s and SPIVA’s findings are based on the performance of sector-wide returns, and so they do not provide direct information on the riskiness or reliability of the alphas provided by individual managers.

To provide a different perspective, we analyzed the alphas of a group of individual active-equity managers: the 461 equity managers currently reporting performance to Russell/Mellon Analytics and included in the latter’s “Equity Accounts Universe.” We analyzed these data over a Q4 1995-Q3 2005 sample period, the full range over which individual managers’ data are available from Russell. We also broke that sample into two sub-periods: during and after the bull market in stocks, our “break point” being September 2000.5 (The S&P 500 peaked in August 2000.) We calculated the alphas of these managers by comparing their performance to that of the total return on the S&P 500, as reported by Ibbotson & Associates. Results are shown in Exhibit 3.

Exhibit 3
Performance of Active-Equity Managers' Alpha (Gross of Fees)
which-alpha-would-you-choose-2006-01
Source: Russell/Mellon Analytics, Ibbotson, Western Asset

Our findings on average manager performance differ somewhat from those of H&T and SPIVA, our estimates of typical manager alpha being positive and theirs negative. In spite of technical differences between their methodology and ours,7 the main source of this difference would seem to accrue from the different samples employed and from the different roles of survivorship bias in each tally. Both H&T and we find managers performing best against the benchmark after the end of the bull market. With their sample containing nearly six more years of bull-stock-market experience and ours containing nearly two more years of post-bull-market experience, that raises our estimate of “median” active-equity alpha.

Meanwhile, both their data and ours suffer from selection bias: we are receiving performance data only from those managers choosing to report to Russell/Mellon, and better-performing managers are more likely to do so. However, our data also reflect a survivorship bias. H&T analyze returns for all managers reporting in a given quarter, and even if a manager ceases to exist or to report, his results will still be part of the H&T summary data for past quarters. The data we received for 1995-2005 are only for those managers still reporting results, and those survivors are also more likely to be the better-performing ones.

Thus, possible survivorship bias in our data could affect our findings on average alpha, relative to the findings of H&T and of SPIVA. However, the focus in our study is on the volatility and reliability of active-

equity managers’ alpha relative to those of short-duration fixed-income managers. There is no reason to think that possible survivorship issues should bias our findings on these scores.

Over the whole Q4 1995-Q3 2005 sample, the median value of active-equity managers’ average alpha within our sample was 136 bpy. The median standard deviation of alpha (tracking error) was 969 bpy. Both mean and tracking error were lower during the bull market and higher since.

While a 136 bpy alpha looks impressive, it is dwarfed by the tracking error. Thus, the median information ratio (average alpha over tracking error) is only 0.169, significant only at the 70% confidence level.8 The typical manager produced 17 bp of alpha for every 100 bp of risk. Both the negative correlations with the S&P 500 and performance across sub-periods indicate that active-equity managers achieve much of their “alpha” returns by moving counter to market trends, by taking regular “beta” risks.

Alpha From Short-Duration Fixed-Income. As seen already, a portable alpha strategy involving short-term fixed-income ported onto a large-cap equity beta position involves essentially no basis risk. What about the magnitude and reliability of the alpha returns the fixed-income position produces (which become the alpha returns of the aggregate portable alpha strategy)?

We examined returns for the universe of individual, short-duration fixed-income managers reporting to Russell-Mellon Analytics. As with equity managers, this dataset extends from Q4 1995 to the present. The summary results for this group are shown in Exhibit 4. The median, short-duration manager outperformed LIBOR by 104 bpy over 1995-2005.9 These alphas were generated at the “cost” of 194 bpy of tracking error. Both mean and variability of alpha were lower during the bull market and higher since. A typical information ratio for these managers was 0.54, significant at the 94% confidence level.10

As with active-equity managers, the short-duration fixed-income managers’ alpha returns were negatively correlated with their own benchmark and with the S&P 500. Unlike the alphas for equity managers, though, fixed-income managers’ alphas were accomplished by taking risks that were not counter to equity-market movements.

Exhibit 4
Short-Term Fixed-Income Managers' Alpha (Gross of Fees)
which-alpha-would-you-choose-2006-01
Source: Russell/Mellon Analytics, Ibbotson, Western Asset

Exhibit 5 compares the performance over time of alphas for “typical” equity and short fixed-income managers: for an equity manager with mean alpha and tracking error close to its sector medians and for the Western Asset U.S. Enhanced Cash Composite. The equity manager shown here produced an average alpha of 135 bpy, with an information ratio of 0.18, statistically significant at the 71% confidence level. The fixed-income manager’s average alpha was 73 bp per year, with an information ratio of 0.88, significant at the 99% confidence level. In the chart, the equity alpha returns are so volatile they visually “drown” out the alpha returns of the fixed-income manager. Don’t be swayed by these visuals. As we have emphasized, the fixed-income fund shown here exhibits a much higher information ratio than the equity fund, and it provides a comparable average return.

Exhibit 5
Historical Alpha for Typical Active-Equity & Short-Duration Fixed-Income Managers
which-alpha-would-you-choose-2006-01
Source: Russell/Mellon Analytics, Ibbotson, Western Asset

Conclusions

While the average returns of the equity managers look alluring, the academic literature correctly points out that it is return relative to tracking error (information ratio) that one should focus on (Sharpe 1994). By leveraging one’s bet on a higher information ratio investment, one could achieve the same total return with less risk (tracking error) than would accrue from an investment with higher total return but lower information ratio. The experience of the last ten years shows that short-duration fixed-income managers have produced alpha more reliably in their market than active-equity managers have in theirs. Portable alpha strategies allow one to transfer that alpha into a base position in large-cap equity.

Yes, we have compared equity managers’ performance to an S&P 500 benchmark and short-duration fixed-income managers to a LIBOR benchmark. The logic dictates that this is the correct comparison for evaluating these asset types as potential alpha sources for an equity allocation. And yes, our results are subject to selection and survivorship bias. However, there is no reason to think those biases in the datasets bias our comparison of active equity relative to fixed-income.

We have found short-duration fixed-income managers to have provided alpha that is reliable and generally statistically significant. Furthermore, when these are employed as part of a portable alpha strategy porting returns to a large-cap equity base position, the expectations are that one could enhance the returns of that base position while adding essentially no beta (equity market risk) to that asset allocation and without having to make timing or sector bets against the aggregate equity market. An equity investor would do well to consider these strategies.

References

Flannery, Sean P., “Information, White Noise, and Garbage,” General Investing Essays and Perspectives, State Street Global Advisors, 9/15/2000.

Hill, Joanne M. and Ingrid Thierens, “When Do Active Equity Managers Add Alpha?” Index and Derivatives Perspective, Goldman Sachs Equity Derivatives Strategy Group, 7/23/2003, Updated 3/2/2004.

Sharpe, William F., “The Sharpe Ratio,” Journal of Portfolio Management, Fall 1994.

  1. Because equities are so easily “storable,” the arbitrage described here will occur, holding funding costs to LIBOR, and that is also the case for other marketable securities, which are as storable as equities. For physical commodities, storage, spoilage, and insurance is more of an issue, and the “funding costs” of these assets exhibit quite different characteristics, such as have been described, in a different context, in our reports on collateralized commodity futures contracts. We will expand on these points in a future report.
  2. The results here are a preview of findings described in the next section. All the results reported here were tabulated in terms of quarterly logarithmic (compound) returns, with final results converted to percentage bases. Quarterly returns were annualized reflecting actual experience. Quarterly results are available on request.
  3. This is calculated as the square root of the following sum: the variance of the beta position–the square of 2272 bpy–plus the variance of the portable alpha position–the square of 194 bpy–plus twice the covariance between them–2 times 2272 bpy times 194 bpy times -0.69, since the covariance between the alpha and beta returns is their correlation times their standard deviations. Finally, this amount is converted to a percentage.
  4. For the fixed-income-to-equities portable alpha strategy, the total return on the underlying beta position is that of the cash S&P 500, so subtracting this from (1) leaves only the alpha for the fixed-income managers (since there is no basis risk). For active equity managers, subtracting the return on the cash S&P 500 from their total return leaves just their alpha relative to the S&P 500.
  5. In order to annualize this set of quarterly data, we converted the results into ten four-quarter periods over Q4 1995–Q3 2005, these periods corresponding to Q4–Q3 “fiscal years.” Our break-point at September 2000 splits this period into two such five-year periods.
  6. While the Russell group provided returns data on 461 large-cap managers, many of these had reported performance for only a small number of quarters. For the whole sample, we included in our calculations only those managers that reported twenty or more quarters of performance. For each of the sub-periods, we included in our calculations only those managers that reported ten or more quarters of performance in the respective sub-period. This netted the tallies listed in the table.
  7. Again, they report the median alpha across managers at each point in time and look at the average of that over time. We compute average alphas over time for each manager and then look at median and average levels of those across managers.
  8. The information ratio times the square root of the number of observations is distributed as Student’s t, with degrees of freedom equal to the number of observations. (Sharpe [1994].) The confidence levels stated here and below are based upon this finding. For quarterly data, active-equity managers’ median information ratio was significant at the 75% confidence level, also not statistically significant.
  9. The LIBOR concept used as the benchmark was the total return on a three-month LIBOR instrument.
  10. While the Russell group provided returns data on 64 short-duration managers, many of these reported performance for only a small number of quarters, as was also the case with active equity managers. As with the active-equity managers, we included in our calculations only those managers that reported twenty or more quarters of performance. For each of the sub-periods, we included in our calculations only managers that reported ten or more quarters of performance, netting the tallies in the table.
  11. With quarterly returns, the median information ratio for this group was significant at the 98% confidence level.
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