32.4.1 Transferring Systematic Risk with Derivatives

Consider an investment strategy involving small-cap U.S. equities that is expected to generate ex ante alpha through active management. At times, the large-cap and small-cap segments of the U.S. equity markets have diverged substantially in terms of returns. Therefore, an investor with a benchmark of the S&P 500 would be concerned about using the small-cap strategy due to its different systematic risk. Portable alpha would be the ability to invest in the small-cap strategy to receive its alpha while hedging the small-cap exposure from the strategy and replacing that risk with the risk of the S&P 500, typically using derivatives.

For example, the systematic risk of a U.S. small-cap position might be hedged with a short position in futures contracts on a corresponding index, such as the Russell 2000. Simultaneously, the manager could establish long positions in futures contracts on the S&P 500 to ensure that the total portfolio has the desired exposure to the benchmark. The key here is that the actively managed portfolio of small-cap stocks must be expected to generate a positive alpha relative to its benchmark, the Russell 2000.

An important issue in managing the risk of porting the alpha is determining the appropriate sizes for the futures positions. Futures contracts on indices are usually based on a multiple of the underlying index value. For example, if a futures contract on the XYZ index is trading at $2,000, and the futures contract on that index represents a multiple of 500 times the index, then the notional value of the futures contract is $1 million per contract. If the XYZ index rises $10, ignoring changes in the basis, the long position in the futures contract gains $5,000 per contract ($10 × 500), and the notional value of the contract rises to $1,005,000. An investor with a $10 million position in the XYZ index who wishes to hedge would enter a short position in XYZ index futures contracts with a total notional value of $10 million. If the contract price is $2,000, then the hedged position would use 10 contracts.

However, the size of the hedge position also depends on the beta of the position being hedged. Specifically, the target notional value to hedge the systematic risk exposure of a cash position is equal to the size of the position to be hedged multiplied by the beta of the position being hedged (relative to the index), as depicted in Equation 32.1:¹

(32.1)

For example, to hedge a $10 million portfolio with a beta of 1.2 relative to the XYZ index requires a notional value of the futures contract of $12 million (assuming that the XYZ futures contract has a beta of 1.0 relative to the XYZ index and setting the basis equal to zero for simplicity).

The number of contracts in the hedge is found by dividing the notional value of the desired futures position by the product of the index value and the multiplier related to the futures contract (Equation 32.2):

(32.2)

Having hedged the undesirable systematic risk of the position, a portfolio manager would then need to establish exposure to the benchmark. For example, a portfolio manager porting a small-cap alpha-generating strategy into a fund with an investment mandate of tracking the S&P 500 index would need to establish positions to both hedge the small-cap risk and take on the systematic risk of the S&P 500. This would require a short position in a futures contract on a small-cap index and a long position in a futures contract on the S&P 500 index.

32.4.2 Applying Portable Alpha

The laying off of the small-cap risk and the layering on of the S&P 500 risk with futures contracts could be accomplished through a swap, through options, or even through long and short cash positions in the indices using cash products such as ETFs.

Using futures, the investor (1) invests cash in the small-cap strategy for the positive alpha that it is perceived to offer; (2) takes a short position in a small-cap index, such as the Russell 2000, using a derivative such as a futures contract; and (3) takes a long position in a derivative on the S&P 500, to bring the total position into conformity with the benchmark (the S&P 500).

What is the net return of a ported strategy? Ideally, the total return to this strategy is the combined return of the S&P 500 index and the performance of the active small-cap fund relative to the performance of the Russell 2000 Index (i.e., its alpha). To the degree that the actively managed small-cap portfolio is not perfectly correlated with its benchmark, the Russell 2000, there will be some tracking error, and therefore the total risk of the portfolio is likely to exceed the total risk of the S&P 500 index.

Portable alpha is usually discussed in the context of a particular fund with a particular strategy. The fund manager might promote the fund as being appropriate for investors with a variety of objectives by demonstrating the extent to which the fund's alpha can be ported to the various benchmarks. Not all alpha is portable. In the case of a fund manager with expertise in selecting small, underpriced private equity deals, there may not be a way for the manager to purchase the attractive deals and hedge or lay off the risk of the sector. Short selling and derivatives are not readily available on all investment opportunities or sectors. In this case, the alpha and the strategy cannot be ported. To attempt to enjoy the alpha of the strategy, the investor would have to bear the systematic risks of the strategy (i.e., the systematic risks of being in small private equity deals).

32.4.3 Numerical Illustrations of Portable Alpha

Consider an investor with $100 million to invest with a benchmark of large-cap U.S. stocks. The expected return for large-cap stocks is 9.2% per year and, for simplicity, the riskless interest rate is assumed to be zero. The investor puts $100 million into a hedge fund with substantial exposure to small-cap stocks. The hedge fund is expected to earn an alpha of 1.4% per year and to have a beta with respect to the small-cap stock index of 0.40.

To implement the concept of portable alpha, when placing $100 million into the hedge fund, the investor takes long positions in S&P 500 equity futures contracts with the same exposure as $100 million invested in the S&P 500, and takes short positions in futures contracts on a small-cap stock index, with exposure equivalent to the fund's exposure to small stocks adjusted for the beta and of the opposite sign.

What is the expected return of this strategy, ignoring fees and assuming no dividends? Let's estimate the expected return from each of the three components:

1. From $100 million in the hedge fund: +small-cap return + $1.4 million
2. From long futures position in the S&P 500 index: +$9.2 million
3. From short futures position in the small-cap index: −small-cap return

Note that the long systematic risk exposure to the small stock index in the hedge fund is offset by the hedging position in the small-stock futures contracts. The net result is that the full portfolio should earn an expected return of $10.6 million, or 10.6% (9.2% on the $100 million of the money in the S&P 500 index fund and 1.4% on the $100 million in the hedge fund).

Return to the example from the beginning of this section of an investor with $100 million to invest with a benchmark of large-cap U.S. stocks that implemented a long futures position in the S&P 500 index and a short position in a small-cap index. How many contracts would be required in each futures position?

The number of contracts in the futures positions in this example is determined by the size of the contracts, the size of the position being managed, and the betas. Suppose that the small-stock index trades at $1,000 and a futures contract on that index specifies payments based on 500 times the value of the index. Further, suppose that the large-cap S&P 500 index trades at $1,500 and a futures contract on that index specifies payments based on 500 times the value of the index.

Recall that the beta with respect to the small-cap stock index was estimated to be 0.40. To lay off the systematic risks of the small stocks in the $100 million hedge fund, the investor should take a short position in $40 million notional value of futures contracts on the small-cap index as determined using Equation 32.1, with the portfolio size to be hedged as $100 million and the portfolio beta as 0.40. The number of contracts is found through Equation 32.2, using the notional size determined in the previous step, divided by the product of the notional value of each contract: $40 million/($1,000 × 500). The result is a short position in the futures contracts on the small-cap index equal to 80 contracts. To take on the risk of large stocks as an overlay of risk for the $100 million in the hedge fund, the investor should take a long position of 133 contracts in the futures contracts on the S&P 500 index, found as the size of the position being hedged divided by the notional value of each contract, then rounded: $100 million/($1,500 × 500). It is assumed that the desired beta of the portfolio is 1.0 and that the beta of the S&P 500 is 1.0.

If the beta of the hedge fund differed from 0.40, the size of the hedging position in futures contracts would expand or contract proportionately. For example, if the beta of the hedge fund with the small-cap index had been 0.80, the $100 million position would respond to the index by the same dollar amount as an $80 million position with a beta of 1.0. Thus, the number of short futures contracts to lay off the risk would be ($100 million × 0.80)/(500 × $1,000) = 160 contracts.

32.4.4 Challenges with Porting Alpha

Implementing a portable alpha program is a complex process, and if it is not done carefully, the end result will turn out to be very different from what was expected. In the previous section, the porting of alpha was demonstrated under idealized conditions.

Portable alpha requires identification of a favorable alpha to be ported, the estimation of the beta of the strategy to be hedged, and the construction of the hedge that offsets the beta risk of the manager's strategy and takes on the beta risk of the benchmark.

Betas can be difficult to predict. If the active manager's beta is not estimated accurately, or if the beta of the active manager's portfolio changes through time, then its systematic risk will be imperfectly hedged. This means the entire portfolio will end up having substantially different systematic risk than anticipated. The active manager's alpha is likely to be different from the anticipated alpha. The end result is that an investor in such a portable alpha program could end up with a portfolio that underperforms the passive benchmark by a substantial amount on a risk- adjusted basis.

One approach to reducing the impact of estimation risk is to port the alpha of a portfolio of active managers rather than the alpha of a single manager. This tends to reduce the estimation risk if the managers are not following identical strategies. Finally, transaction costs, higher costs of borrowing, and the price impacts of large trades are just some of the problems that could reduce the effectiveness of a portable alpha program.

A potentially more effective but also more complex approach to porting alpha is based on total portfolio risk minimization rather than targeting only the known, hedgeable, and undesirable systematic risk. The total risk minimization approach tends to lower the size of the recommended hedge position by taking into account the potential for large hedging positions to increase the portfolio's exposure to hidden or unhedgeable systematic risks.

32.5.1 Traditional Asset Allocation

In an informationally efficient market, active investment management focuses on issues other than alpha, such as risk management, liquidity, taxes, and transaction costs. However, in imperfect markets and with opportunities for ex ante alpha through areas of market inefficiency, a challenge that arises is how to best allocate among opportunities that include both alpha and beta.

In the traditional approach to portfolio allocation, the top-level decision is a long-term target allocation decision, known as the strategic asset allocation decision. The strategic asset allocation decision is the long-term target asset allocation based on investor objectives and long-term expectations of returns and risk. For the passive investment manager or indexer, the strategic asset allocation decision is the only major decision.

For active investment managers, tactical decisions are also important decisions. Tactical asset allocation is the process of making portfolio decisions to alter the systematic risks of the portfolio through time in an attempt to earn superior risk-adjusted returns. Even though tactical decisions emphasize short-term management of a portfolio's beta, it may be argued that these tactical decisions are an attempt to earn alpha from the market timing of beta exposures. In other words, systematic risk exposures are adjusted not for the purposes of earning appropriate risk premiums from bearing systematic risk but to generate alpha by bearing those systematic risks that the allocator believes are being best rewarded at each point in time.

In a traditional asset allocation approach, the weights to each asset class are specified. However, within each investment category, an active investment manager may attempt to generate alpha by selecting managers or securities with superior risk-adjusted returns. For example, if 3% of a portfolio is allocated to domestic small-cap equities, then some or all of that 3% might be allocated to active managers who attempt to find domestic small-cap equities that offer higher risk-adjusted returns than other domestic small-cap equities (i.e., ex ante alpha). In traditional investments, this typically entails security selection, whereas in alternative investments, this typically entails fund manager selection.

The traditional approach to portfolio allocation may not be optimal from a risk-return trade-off standpoint if the strategic and tactical asset allocation decisions are made with little regard for alpha opportunities. The strategic asset allocation decision generally specifies and constrains asset allocations and performance benchmarks. Without investment flexibility, the investment staff is forced to seek alpha inside rigid policy constraints and probably inside the traditional asset classes of stocks and bonds. Consequently, alpha is often wrongly sought within the most efficient markets, since the strategic benchmarks typically allocate primarily to the most efficient markets.

For example, consider PC University's endowment fund, which is restricted to investing in traditional equities and fixed-income investments. Through the years, the endowment fund has come under increased pressure to generate solid returns but has found it to be more and more difficult to identify traditional investment managers that seem to have the skill to generate consistently high returns. As a result, the directors of the fund have decided to periodically increase the allocation of the fund to equities and decrease the allocation to bonds. The directors believe that stocks offer the higher average returns that the endowment needs to generate.

By using a traditional asset allocation model, the portfolio of PC University is becoming riskier in the search for higher returns. The policy of remaining in traditional investments has limited the endowment's ability to generate alpha. The result has been a shift toward increased beta in an effort to respond to pressure to earn higher average returns. However, the higher total risk of a high-beta approach runs an increased risk of very poor returns in bear markets.

32.5.2 The New Investment Model

In the new investment model, investments are allocated with flexibility and in the explicit context of alpha and beta management. Beta is sought through investment products that cost-effectively offer returns driven by beta so that the endowment obtains efficient economic exposure to market risk and can earn the expected risk premiums associated with bearing systematic risks. Beta risk is managed with the purpose of implementing the strategic asset allocation strategy established by the investor. Alpha is sought independently of beta. The professional investment staff can seek alpha from those investment products that are perceived to offer the best opportunities, even if those products fall outside the benchmark and traditional asset classes. Alternative assets can be highly useful with this flexible model.

In the new investment model, alpha and beta are simultaneously and efficiently managed. A high priority is attached to pursuing alpha, and tolerance for bearing idiosyncratic risks from pursuing alpha should be applied to those investment products that offer the most potential for alpha per unit of idiosyncratic risk. Alpha should be pursued in products related to less efficient markets, including hedge funds, real assets, commodities, private equity, and structured products. The management of systematic risk should be accomplished with those products that offer beta exposure efficiently, which are typically the last place to look for alpha. Key concepts in the new investment model are the ideas of the separation of alpha and beta and of portable alpha.

Returning to the example of PC University, the university altered its endowment asset allocation model in the wake of huge losses during the financial crisis of 2007 to 2009. The new asset allocation model allows greater investment flexibility, including the use of alternative investments. The allocation model seeks to enhance returns without increasing risk through higher allocations to investments offering alpha and lower allocations to traditional assets. The new investment model seeks to generate alpha wherever it can most effectively be found, usually in alternative investments. The new process explicitly prioritizes the search for alpha subject to idiosyncratic risk constraints while managing the desired beta exposures through the use of investment products that deliver the desired beta exposures in a cost-effective manner.

In summary, a traditional approach to portfolio management is focused on imposing a top-down asset allocation with specified weights to each investment category. For example, the allocation to domestic small-cap equities may be set to a target of 2%. In the new investment model, the portfolio's aggregate risks may be expressed through a benchmark; however, flexibility is provided to allow alpha to be sought where it is perceived to be most available and to allow beta to be controlled through risk management. Thus, the portfolio manager has the flexibility to have any allocation to domestic small-cap equities that is consistent with the portfolio's overall goals regarding risk exposures and the pursuit of alpha.

32.5.3 Active Risk, Active Return, and Traditional Investment Products

A passively managed portfolio, such as an indexed buy-and-hold portfolio, seeks to match the return of an index or a benchmark without engaging in active trading that attempts to generate improved performance. An actively managed portfolio involves trading with the intent of generating improved performance. Active investment management may be viewed as generating active risk and active return.

Active risk is the risk that an actively managed portfolio contains as the portfolio manager endeavors to beat the returns of a benchmark. The variation in performance can be attributed to systematic risk that differs from the benchmark and from idiosyncratic risk. Active return is the expected or consistently realized return from active management relative to a passively managed portfolio or the benchmark.

Index products take little or no active risk, extract no added value, and are not expected to generate active return. They do not attempt to exploit information to earn higher returns but passively capture the risk premium associated with a risky asset class. Included in this group are most ETFs and other replication products designed to efficiently capture systematic risk premiums.

Enhanced index products are designed to take slightly more risk than the index within tightly controlled parameters and offer a little extra return, usually on a large pool of capital. Small, consistent alpha is their objective. Next, just slightly above the enhanced indices in terms of idiosyncratic risk, are the traditional long-only active managers. It is argued that sometimes these products actually bet on pure beta but that they present an image of pursuing alpha through active management. In other words, the managers claim to exploit superior information and analysis to generate alpha without higher beta but in actuality may attempt to earn enhanced returns by taking greater beta risks than are found in the benchmark.

32.5.4 Is Alpha a Zero-Sum Game?

A zero-sum game is a market, environment, or situation in which any gains to one party must be equally offset by losses to one or more other parties. If two people are sharing a pie, it is a zero-sum game, since any part of the pie eaten by one person means less pie available for the other person. But if two people are making pies together, there can be efficiencies such that together they can make more pies than the combined number of pies they can make if they work separately. With efficiencies, the pie making would not be a zero-sum game but would be said to be synergistic. Activist investors and LBO funds can be argued to generate operational efficiencies that increase total wealth, making alternative investing a creator of wealth rather than a zero-sum game.

In addition to gains from efficiencies, it is important to note that entities can become better off even when total market value remains constant. Returning to the pie example, if one person is trying to lose weight and the other person needs to gain weight, the situation may no longer be a pure zero-sum game, because the two persons have substantially different preferences and can experience large and mutually beneficial gains through exchange involving another commodity. Perhaps the person needing to gain weight will trade low-calorie foods to get more pie. Similarly, an investor in a high tax bracket may be able to engage in a structured product with an investor in a low tax bracket such that both investors can be better off, even in an informationally efficient market. Another example is the role of event strategies, such as merger arbitrage, in providing liquidity and risk bearing to traditional investors who wish to avoid the high levels of idiosyncratic risk related to major events. Arbitrage strategies, such as statistical arbitrage, can provide higher liquidity and lower trading costs to all investors.

So, is investing a zero-sum game? If one investor receives a positive alpha, does it mean that another investor must bear a negative alpha? Does the sum of all positive and negative alpha performance have to be zero? This is a question that is the object of considerable debate. Sufficient conditions to make alpha a zero-sum game include the following:

• Investors have the same investment horizon.
• Investors have the same level of risk tolerance.
• Investors are allowed the same access to all asset classes (there is no market segmentation).
• Investors pay the same tax rate, or, equivalently, there is no tax.
• Investors have the same expectations about return and asset class risk premiums.
• Investments can be divided and traded without cost.

Clearly, the sufficient conditions for alpha to be a zero-sum game do not hold. Investors do indeed have different investment horizons with different liquidity needs (a pension fund versus a hedge fund, for example); have different risk tolerances (an endowment fund versus a high-net-worth investor); have different access to asset classes (many pension funds do not, or are not allowed to, invest in commodities or hedge funds); have different tax rates (a high-net-worth investor compared to a tax-exempt pension fund); and certainly have different expectations about return and risk (speculators versus hedgers). Information is costly to obtain and analyze, so there is little reason to believe that all investors reach identical expectations regarding investment risks and returns. Marginal tax rates vary tremendously among investors, providing further opportunities for investors to improve their after-tax returns without adversely affecting other investors. As a final point, investment markets are imperfect, with lumpy assets and, in some cases, high transaction costs, providing solid economic reasons that many financial transactions can be mutually beneficial.

The fact that markets are imperfect and that there are so many varied investment horizons, market segments, risk tolerances, and expectations can be argued to allow a net positive alpha to be generated across time, asset classes, and risk tolerances. Simply put, exchange takes place for the perceived benefit of both parties to the exchange. For example, a large, illiquid, and complex private equity deal may offer attractive economic opportunities to society if willing investors can be located with reasonable return requirements. One or more large, sophisticated, institutional-quality investors with proven expertise and excess liquidity may be able to analyze the project and offer financing at rates that offer alpha to the investors and enable the project to be completed. Perhaps the investors raise some of the necessary funds by borrowing money on a secured basis from other institutional investors who prefer safe, liquid, and easy-to-understand securities. The net result is that alpha received by one investor does not need to be at the expense of other investors, and therefore alpha need not be a zero-sum game.

Futures markets present a clear example of a situation that appears to be a zero-sum game, but on closer examination, one can see that there is room for some investors to earn a positive alpha without requiring other investors to earn a negative alpha. Some futures market participants use these markets to hedge their risks and to protect future incomes or costs. These participants are willing to pay a premium to investors, perhaps managed futures investors, who are able to assume these risks. Just as insurance companies can produce positive net benefits to society by providing fire insurance on homes, managed futures funds can provide positive benefits to society by bearing risks that operating firms seek to avoid.

The overview of investing in this chapter may be summarized as follows: The greatest benefits from asset allocation can be derived from the explicit consideration of ex ante alpha and beta in strategic and tactical planning. Viewing alpha and beta as distinct attributes may allow the management of alpha and beta to be optimized. The separation of the management of alpha and beta is facilitated by portable alpha: the ability to pursue a particular alpha strategy while transforming the total beta exposure to meet the preferences of the investor. Portable alpha facilitates a new investment model in which alpha can be pursued in nontraditional investments that derive alpha from those markets in which alpha can be most effectively sought, while managing beta using those products that deliver beta as cost-effectively as possible.