Investments, tenth edition

  Factor  

  Factor Risk 

Premium  

  Factor Betas for 

Niagara Mohawk  

 Term structure 

 .425  

1.0615 

 Interest rates 

  2 .051  

 2 2.4167 

 Exchange rates 

  2 .049 

 1.3235 

 Business cycle 

 .041  

.1292 

 Infl ation 

  2 .069  

 2 .5220 

 Other macro factors 

 .530  

.3046 

 Therefore, the expected return on any security should 

be related to its factor betas as follows:   

r

f

1 .425 b

term struc

2 .051 b

int rate

2.049 b

ex rate

1 .041 b

bus cycle

2 .069 b

inflation

1 .530 b

other

  

 Finally, to obtain the cost of capital for a particular firm, 

the authors estimate the firm’s betas against each source of 

risk, multiply each factor beta by the “cost of factor risk” 

from the table above, sum over all risk sources to obtain 

the total risk premium, and add the risk-free rate. 

 For example, the beta estimates for Niagara Mohawk 

appear in the last column of the table above. Therefore, its 

cost of capital is   

 

Cost of capital

5 r

f

1 .425 3 1.0615 2 .051(22.4167)

 

2.049(1.3235) 1 .041(.1292)

 

2.069(2.5220) 1 .530(.3046)

 

5 r

f

1 .72

 

In other words, the monthly cost of capital for Niagara 

Mohawk is .72% above the monthly risk-free rate. Its annu-

alized risk premium is therefore .72%  3  12  5  8.64%.  

  *Edwin J. Elton, Martin J. Gruber, and Jianping Mei, “Cost of 

Capital Using Arbitrage Pricing Theory: A Case Study of Nine New 

York Utilities,”  Financial Markets, Institutions, and Instruments  

3 (August 1994), pp. 46–68.  

 WORDS FROM THE STREET 

of average stock returns from levels consistent with the CAPM. Fama and French jus-

tify this model on empirical grounds: While SMB and HML are not themselves obvious 

candidates for relevant risk factors, the argument is that these variables may proxy for 

yet-unknown more-fundamental variables. For example, Fama and French point out that 

firms with high ratios of book-to-market value are more likely to be in financial distress 

and that small stocks may be more sensitive to changes in business conditions. Thus, these 

variables may capture sensitivity to risk factors in the macroeconomy. More evidence on 

the Fama-French model appears in Chapter 13. 

 The problem with empirical approaches such as the Fama-French model, which use prox-

ies for extramarket sources of risk, is that none of the factors in the proposed models can 

be clearly identified as hedging a significant source of uncertainty. Black  

9

   points out that 

  

9

 Fischer Black, “Beta and Return,”  Journal of Portfolio Management  20 (1993), pp. 8–18. 

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342 

P A R T   I I I

  Equilibrium in Capital Markets

when researchers scan and rescan the database of security returns in search of explanatory 

factors (an activity often called data-snooping), they may eventually uncover past “patterns” 

that are due purely to chance. Black observes that return premiums to factors such as firm 

size have proven to be inconsistent since first discovered. However, Fama and French have 

shown that size and book-to-market ratios have predicted average returns in various time 

periods and in markets all over the world, thus mitigating potential effects of data-snooping.

  

 The firm-characteristic basis of the Fama-French factors raises the question of whether 

they reflect a multi-index ICAPM based on extra-market hedging demands or just repre-

sent yet-unexplained anomalies, where firm characteristics are correlated with alpha val-

ues. This is an important distinction for the debate over the proper interpretation of the 

model, because the validity of FF-style models may signify either a deviation from rational 

equilibrium (as there is no rational reason to prefer one or another of these firm character-

istics per se), or that firm characteristics identified as empirically associated with average 

returns are correlated with other (yet unknown) risk factors. 

 The issue is still unresolved and is discussed in Chapter 13.