Implementing the Tracking Portfolio Approach

If the financial manager identifies a tracking portfolio that is mean-variance efficient,

valuation is a straightforward task. For example, if the CAPM holds, simply knowing

the $5 million (market portfolio) and $5 million (risk-free asset) composition of the

Hilton casino tracking portfolio indicates that the project’s present value is $10 million.

The manager does not need to know the expected return of the market, the risk-free

return, or even the expected cash flow of Hilton to compute this present value.

This situation, however, is rare. For example, we might be able to look at traded

casino stocks and compute their average beta as .5, but how would we know that $5

million is the correct investment in the market portfolio without first estimating the

expected future cash flow and the expected return of the market portfolio?

⁵Discounting the expected cash flow at the tracking portfolio’s expected return generates the present

value only if the present value is of the same sign (positive or negative) as the expected cash flow and

both the present value and expected cash flow are nonzero.For example, as either the present value or

expected cash flow (but not both) approach zero, the expected return (i.e., the discount rate) approaches

(plus or minus) infinity. In such cases, we have to abandon the risk-adjusted discount rate method, and

instead use the certainty equivalent method (discussed later in the chapter) to generate present values.

Grinblatt764Titman: Financial	III. Valuing Real Assets	11. Investing in Risky	© The McGraw764Hill
Markets and Corporate		Projects	Companies, 2002
Strategy, Second Edition

376Part IIIValuing Real Assets

Estimating Tracking Portfolios without Expected Cash Flows orReturns.There

are a few ways to estimate a tracking portfolio without knowing expected returns or

expected cash flows. One way arises when there is perfect or almost perfect tracking.

Because tracking error that is zero or close to zero can be ignored, perfect or almost

perfect tracking has a further advantage: Afinancial manager can use any combination

of financial assets to track the investment, including those that are not mean-variance

efficient. This approach is clearly superior to the CAPM/APTapproaches, which gen-

erate substantial tracking error because of the restrictive composition of their tracking

portfolios but nevertheless imply that the tracking error has zero present value. As a

first pass, a manager should try to identify a tracking portfolio with minimum tracking

error variance and, only when this variance is large, turn to asset pricing models that

specify a tangency portfolio as the critical tracking instrument.

Using the Market Portfolio orFactorPortfolios in Computing the Tracking

Portfolio.In most cases, the existence of tracking error necessitates the use of a mar-

ket portfolio or a set of factor portfolios, combined with a risk-free asset, to track a

project. However, the specification of the appropriate mix of financial assets in the

tracking portfolio can be complicated.

Linking Financial Asset Tracking to Real Asset Valuation with the SML

Despite this complexity, it is very important to determine, as best as one can, the proper

mix of assets in the tracking portfolio, especially when there is tracking error. In this

subsection, we use the securities market line to illustrate why being careless about this

estimation can be costly.

The returns of risky zero-NPVinvestments, such as financial assets, can be graphed

as lying on the securities market line. This line (see Exhibit 11.1) is based on the risk-

expected return relation developed from the tangency portfolio discussion in Chapter 5.

EXHIBIT11.1Real Assets and the Securities Market Line

Mean
return
	Securities
R T	market line
A: positive NPV
	A**

Wealth
	B: negative NPV
created

A*: NPV = 0

r f		Beta with
		return of the
	C
		tangency
0	1	portfolio

Grinblatt766Titman: Financial	III. Valuing Real Assets	11. Investing in Risky	© The McGraw766Hill
Markets and Corporate		Projects	Companies, 2002
Strategy, Second Edition

Chapter 11

Investing in Risky Projects

377

Having a cash flow with return beta of —computed with respect to the tangency port-

folio—means that we can track the cash flow per dollar of present value with a port-

folio that has a weight of on the tangency portfolio and a weight of 1 on the

risk-free asset. In the Hilton example, the of the project return and thus the weight

on the market portfolio is ¹2

.

Positive NPVprojects plot above the securities market line at, for example, point

A. Conversely, negative NPVprojects plot below the securities market line at point

B. Expected returns on the projects in Exhibit 11.1 are computed using the cost of

initiating the project as the baseprice.Since these costs can be either above or

below the present value of the project’s future cash flows, the expected returns cal-

culated in this manner can plot above or below the securities market line. When a

project’s future cash flows are sold to the financial markets as in the Thermo Elec-

tron discussion in the opening vignette, returns are computed with the present value

as the base price. Hence, a positive NPVproject, such as point Ain Exhibit 11.1,

when spun off to the financial markets, would lie at point A*. The movement from

Ato its counterpart A* on the securities market line signifies that wealth is created

by adopting the project and spinning it off to the securities markets. This wealth

arises because the firm can sell those future cash flows for more than it costs to

produce them.

The key to recognizing a positive NPVproject is to know the project’s beta. If beta

is overestimated—for example, if the project at point Ais assumed to have a beta at

point Cand thus is erroneously interpreted as being at point A**—a positive NPVproj-

ect can mistakenly appear to have a negative NPV.It is also possible to underestimate

the betas of negative NPVprojects, which could lead to adoptions of bad projects. Thus,

it is very important to understand how to best identify the project’s beta. The next sec-

tion discusses this issue at great length.