80 Corporate Finance
Set the level of investment in Stock 1 at Re 1 and solve for the rest.
INV 1 = Re 1
INV 2 = Re 0.624857
INV 3 = Re –1.157143
INV 4 = Re –0.485714The arbitrage portfolio would be:
Expected return Prod. sens Infl. sens
Stock INV INV expret INV sensit (P) INV * sensit (I)
1 1.0 13.0 0.20 2.0
2 0.643 17.361 1.929 0.129
3 –1.157 –18.512 –1.157 –1.157
4 –0.486 –9.720 –0.972 –0.972
0 2.129 0 0The activity of buying the first two stocks will drive up their prices and bring their returns in line with
their sensitivities. Similarly short-selling the remaining will drive down their prices. In other words, arbitrage
will bring returns of stocks to their equilibrium levels. The factors that affect security returns themselves are
identified through factor analysis.
WHAT ABOUT BONDS?
Although the Capital Asset Pricing Model is used to estimate expected return from stocks, it is supposed to
be applicable to any asset. What about bonds? Would the CAPM explain the cross section of bond
returns? Gebhardt et al. (2001) find that both bond market factors like default risk beta and term risk beta
and bond characteristics like bond rating and duration largely explain the variation in the cross section of
bond returns.^9 One source of risk for corporate bonds arises from unexpected changes in the term structure of
interest rates. The other source of risk arises from changes in default risk in response to changing economic
conditions. They take the difference between the monthly return on a portfolio of long term government
bonds and 1 month T-bill return as proxy for term risk and the difference between the monthly return on
a value weighted market portfolio of all investment grade bonds with at least ten years to maturity and the
monthly return on long term government bonds as proxy for the default risk. To estimate default and
term betas they run the following two-factor regression:
rit – rft = α + βd DEFt + βt TERMt + utwhere
rit – rft = excess return on corporate bonds,
DEFt and TERMt are default risk and term risk factors, and
βd and βt are factor loadings (beta) for the two risk factors.
(^9) Some of these concepts are discussed in the chapter on debt markets.