To state these ideas formally, we extend the mean–variance utility function to include security characteristics besides risk and expected return.
Let:
n = the number of risky securities in the market
= the n -element vector of expected excess returns (in excess of r f )
Ψ = the n × n variance–covariance matrix of returns on the risky securities
= the n -element vector of investor i ’s allocations to the risky securities 29
λi = the risk aversion parameter of investor i
p = the number of characteristics (besides risk and expected excess return)
C = n × p matrix of characteristics of the securities
= p -element vector of investor i ’s attitudes toward the characteristics
Note that in the NET model, the elements of are usually negative, reflecting various degrees of dislike, but can be positive. By allowing for positive values, this model can be generalized to include characteristics that investors like—that is, popular characteristics.
For clarity, we start with the mean–variance utility-maximization problem for investor i :
Investor i ’s problem is to maximize by his or her choice of —that is, through portfolio selection.
The utility function in Equation 4.1 contains a benefit and a penalty . One might extend this utility function to account for additional attitudes toward characteristics in various ways: as an adjustment or new term representing the benefit or as an adjustment or new term for the penalty. Here, we choose to include a new term that adds to (or subtracts from) the total benefit:
From the first-order condition of this problem, we have
We can interpret this condition in terms of IDS’s ideas. The right-hand side of Equation 4.3 shows how “each investor will have his own particular utility function, according to which he translates all asset characteristics, including all risks, into [marginal] costs” (p. 24). The marginal risk costs are given by , and the marginal nonrisk costs are given by . The sum of these two terms is investor i ’s demand for capital market returns. The left-hand side of Equation 4.3 is the supply of excess capital market returns and is not specific to any individual. The investor holds the portfolio that equates the demand for capital market returns to the supply of capital market returns. In the next chapter, we show how aggregating this condition across investors leads to an asset pricing formula that includes market risk and nonrisk characteristics that could be frictional or behavioral, thus fulfilling the objective of NET and going beyond it.
Issues That the NET Framework Can Address
IDS discussed a number of issues that the NET framework can address. In the following subsections, we quote them on specific issues.
Financial Intermediation.
The NET framework can readily be expanded to include repackaging opportunities on the part of issuing firms or financial intermediaries. The role of the financial intermediary is to repackage the pricing characteristics so as to reduce investor costs. One way intermediaries accomplish their task is by making the markets for pricing characteristics more complete. By unbundling asset characteristics, for example, they increase the likelihood that those investors with lower costs for a particular characteristic will hold that characteristic in their portfolios. Another way intermediaries reduce investor costs is by optimal bundling of asset characteristics to take advantage of economies of scale.
Investors perceive financial intermediaries as additional asset offerings, whereas issuers perceive them [the intermediaries] as additional investors. Assuming perfect competition, intermediaries act to maximize aggregate investor surplus by minimizing the sum of all investor costs … across all assets for all the pricing characteristics. (pp. 26–27) [Emphasis in original.]
Risk Characteristics. IDS described the various risks covered in their approach thus:
The CAPM states that only one risk-pricing characteristic exists—namely, market risk. APT provides for multiple risk-pricing characteristics, and treats each risk as orthogonal to all of the others, so that the market payoffs are additive. The NET framework does not directly take sides in this controversy but does allow for multiple pricing characteristics. We focus here on four of the most intuitive types of risk—beta (market), inflation, real interest rate, and residual risk.
Market, or beta, risk is the risk that the return of an asset will fluctuate with the market portfolio’s return. According to CAPM, beta risk is the only risk that affects expected return. It is assumed that the rational investor will diversify away (at no cost) all other risks. In the NET framework, as noted, each investor translates risks into costs by assigning a price at which he is indifferent between buying and not buying more of the risk.
Inflation risk is the risk that an asset’s real value will fluctuate because of unanticipated changes in the inflation rate. This risk is best exemplified by a long-term government bond, which is relatively free of most other pricing characteristics. The bond is a nominal contract, and its yield to maturity consists of three components—the expected inflation rate, the expected real interest rate, and the risk premium (if any) associated with inflation and real interest rates. Although the market anticipates all three components over the bond’s life, unanticipated changes in current and expected inflation rates cause variations in the bond’s real return.
Inflation risk arises when one side explicitly or implicitly contracts in nominal, instead of real, terms. For this pricing characteristic to be nonzero, at least one side must have negative inflation risk costs and be willing to pay the other side to create these risks. The inflation risk premium may be positive for investors in the stock market and for holders of short-term, and possibly long-term, bonds. Other assets likely to contain a nonzero amount of inflation risk include real estate, gold, and any other assets whose real returns are correlated (positively or negatively) with unanticipated changes in the inflation rate. (pp. 27–28)
The authors went on to put real interest rate risk into the NET context:
The real interest rate is the difference between the instantaneous nominal interest rate (on a characteristic-free bond) and the instantaneous inflation rate. Since real interest rate changes are unanticipated, the investor who rolls over a series of short-term bonds receives an uncertain return in real terms. The investor in long-term bonds can lock in the real rate over the bond’s life but incurs inflation risk in the process. It is, of course, possible to construct a long-term contract in real terms [TIPS are such contracts. 30 ] and avoid both inflation and real interest rate risk for any given time horizon. (pp. 28–29)
They then described residual risk in the NET context:
Residual risk is the risk resulting from lack of diversification in a portfolio. Assuming that the risks already described account for an asset’s undiversifiable risk, residual risk is the one remaining risk factor. We propose that residual risk, like the other risk factors, may be an ex ante pricing factor.
In CAPM, the rational investor perfectly diversifies so as to eliminate entirely all residual risk. NET assumes that it is costly to diversify. The factors that make perfect diversification either impossible or suboptimal are related to non-risk pricing characteristics. For example, many investors wish to own their residences outright. The large unit size of other real estate investments, along with the high cost of creating divisibility mechanisms such as condominiums and limited partnerships, imposes high costs on investors seeking diversification. Thus, most investors do not hold a diversified real estate portfolio—that is, one that is spread over various geographical locations and types of land and structures. (p. 29)
The authors concluded their litany of risks by addressing human capital:
Human capital is subject to even more extreme constraints on diversification. Once acquired, human capital cannot readily be sold and is usually rented out for wages in the labor market. It follows that one cannot easily buy a portion of another person’s human capital in order to diversify within the ass
et class. (p. 29)
Idiosyncratic risk is usually uncompensated in asset pricing theory. But some investments may be difficult to diversify, such as an owner-occupied house or human capital. In such cases, idiosyncratic risk itself may merit a risk premium. We focus on stocks in this book, but even in the pure equity case, an entrepreneur’s concentrated position may have its value reduced by the entrepreneur’s need to consider the total risk, rather than simply the beta risk, of his or her investment. Closely held companies may also be illiquid. This combination may lower valuations considerably, leading to high but volatile expected returns that are hard to realize.
Taxability. IDS then addressed nonrisk costs, one example of which is taxes:
Taxability often has a substantial impact on an asset’s cost of capital. The taxability characteristic is inherently complex because of the intricacies of the U.S. (and other countries’) taxation systems. This complexity consists of (1) the stepwise (“tax bracket”) and multiplicative attributes of the tax function; (2) the fact that taxes on a given asset are contingent on the performance (effect on income) of other assets in one’s portfolio; (3) the differential treatment of ordinary income and capital gains; (4) special tax laws, such as those allowing depreciation much faster than the useful life of certain assets; and (5) multiple taxing authorities. These attributes cause the tax costs for the same asset to differ across individuals. The general principle is that highly taxable assets are lower priced—i.e., have a higher before-tax expected return—than less highly taxed assets.
For example, municipal bonds, whose coupons are free of U.S. federal income taxes, yield 20 to 50 percent less than fully taxable corporate bonds of comparable risk. A similar relationship has been suggested for high dividend versus low dividend stocks. Constantinides [1983] provides a personal tax equilibrium that includes the timing option for the realization of capital losses and the deferral of capital gains. Most of these and other tax-related theoretical results can be introduced into the general NET framework because NET does not specify actual investor costs.
Real estate, venture capital, hedging portfolios, and leasing arrangements provide special opportunities for financial intermediaries to separate out tax characteristics and repackage them for the appropriate clienteles. After repackaging, many investments may be tax shelters having negative tax rates.
In summary, an asset may generate taxes (positive or negative) on income, expenses, or capital appreciation. The investor includes these tax costs in his pricing process. The complexity of the taxation system and the interaction of taxes with other pricing characteristics make it difficult to specify this pricing characteristic. Nevertheless, the magnitude of taxes is sufficiently large that it must be included in any exposition of the NET framework. (p. 29)
Marketability, Information, Search, Transaction, and Divisibility Costs. Marketability costs, referred to in more modern language as “illiquidity” or the cost to achieve liquidity, are another nonrisk cost:
We group all the entry and exit costs associated with buying or selling an asset into the category of marketability costs. The NET framework … provides no description of how an investor came to hold his particular portfolio or when or how he may rebalance his portfolio. For the NET equilibrium to be descriptive, each investor must reduce the value of his assets by a present value amount to cover these costs. These marketability costs include information, search and transaction, and divisibility costs. (pp. 29–30)
Information costs, search and transaction costs, and divisibility costs each have their own unique attributes:
Information costs are the costs that an investor must pay to learn the value of an asset. Since the NET model assumes homogeneous expectations, we have already in some sense assumed these costs away. Nevertheless, we can informally apply the NET model by suggesting that investors must pay some costs to learn what the homogeneous expectations are. In such a world, investors with comparatively lower information costs for a particular asset would tend to own that asset. For example, U.S. investors own stocks and bonds of U.S. corporations in disproportionately large quantities because of the cost of acquiring information across national boundaries. Moreover, assets that are difficult to learn about, such as stocks of small or new companies, should have higher before-cost expected returns than assets that are easier to learn about, such as large-company stocks. Finally, information costs tend to favor the large investor, since there are economies of scale in information use.
Search and transaction costs include the costs of looking for the other side of the transaction, as well as the costs of actually closing the transaction. The costs may include the bid–ask spread, the waiting time beyond the investor’s desired horizon, the possibility of having to take a price concession, the paperwork and legal costs accompanying a transaction, the cost of advertising or other efforts to locate the other party to the transaction, and the cost of any brokers or agents used to effect the transaction. These costs are treated in search and bargaining theory literature. In the NET framework, these costs are merely estimated by the investor as their present value equivalent costs.
Divisibility costs arise from the large and discrete scale of some investments, such as real estate, venture capital, large-denomination certificates of indebtedness, and certain discrete human capital decisions. Divisibility interacts with many of the other pricing characteristics. Indivisibility’s chief burden to investors may be that it forces them to take substantial residual risk. It also causes some investors to hold a suboptimal quantity of a particular investment. (p. 30)
Human capital, the authors write, can be treated like any other asset, but with its own unique characteristics:
Human capital, once acquired, is often considered nonmarketable as well as indivisible. It can be rented and, to some extent, it can be put up as collateral for loans. When invested in a business, portions of it can sometimes be sold. In the NET framework, we can regard these as high, but not insurmountable, divisibility costs. In some models, an equilibrium is arrived at in which human capital is literally treated as non-marketable. (p. 30)
In many settings, divisibility costs can be overcome:
One of the principal roles of financial intermediaries is to repackage securities in such a way as to reduce divisibility costs. A saver (small lender) would have great difficulty in finding a borrower with whom to transact and still maintain the liquidity of his savings. By pooling the savings of many persons, a bank can do exactly that. Money market funds reduce the minimum investment amount for cash instruments from $10,000 to very little. Real estate investment trusts and limited partnerships lower the size barrier for investing in large properties from the range of millions of dollars to the range of thousands or less. Each of these mechanisms for reducing divisibility costs is itself costly. For many investors, however, paying the costs of investing through a financial intermediary increases their investor surplus. (p. 30)
The authors conclude by listing other possible pricing factors:
Other miscellaneous factors may affect the price of a capital market asset. These include nonpecuniary costs or benefits, all of which we would treat as positive or negative costs. In addition, certain expenses, such as management, maintenance, and storage costs, are best treated as costs of capital rather than as decrements to cash flow. This is because they differ across investors. Because investors seek to maximize returns net of all costs and benefits, these factors should be included in the set of NET pricing factors. (p. 30)
Note the connection to our present work, which regards nonpecuniary costs and benefits as critical to asset pricing.
Asset Class Characteristics
IDS included a table of the characteristics of various asset classes that should be priced in the NET framework. We provide this table here as Exhibit 4.1 . These characteristics are classified according to being related to risks, taxability, and marketability as discussed in the preceding quotations.
Conclusion
NET is a classical p
recursor to the popularity asset pricing model because it is based on a principle for understanding how investors’ attitudes toward the nonrisk characteristics of securities affect how securities are priced in an equilibrium model. NET can easily be extended to include behavioral preferences, as we do in this book.
Although the creators of the NET framework, Ibbotson, Diermeier, and Siegel (1984) , did not develop a formal equilibrium model, they had a number of insights related to the costs of owning securities that rational investors would consider when making investment decisions. In this chapter, we showed how such costs can be incorporated into an investor utility function and how the first-order condition for maximizing that utility function matches the authors’ notion of equating the supply of and the demand for capital market returns. In the next chapter, this first-order condition is the starting point for a formal equilibrium model in which investors’ attitudes toward all characteristics, both rational and irrational, determine asset prices.
Exhibit 4.1. Asset Class Characteristics Priced in NET
a Financial intermediaries are likely to be important in reducing these costs.
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