Question

Ms. Bessie, manager of Everchanging Mutual

Fund, know he fund currently is well diversified

and that it has a CAPM beta of 1.0. The risk-free

rate is 8% and the CAPM risk premium [E(Rm –

Rf] is 6.2%. She has recently become aware of

APT measures of risk and knows that there are

(at least) two factors: Industrial Production κ1

and inflation κ2. The equation for APT is

E(Ri) – Rf = [k1-Rf] bi1 + [k2-Rf] bi2

E(Ri) = 0.08 + [0.05]bi1+ [.11]bi2

a) If the portfolio’s current sensitivity to the

Industrial production factor is bp1 is -.5 what is

the sensitivity to the inflation factor.

b) If she rebalances her portfolio to keep the

same expected return but reduce exposure to

inflation to 0 (i.e bp2 = 0) what will the

sensitivity to the industrial production factor.

Answer #1

CAPM Equation:

E(Ri)=Rf+Beta*(E(Rm-Rf))

Beta=1.0

Rf=8%

(E(Rm-Rf))=6.2%

E(Ri)=8+1.0*6.2=14.2%=0.142

E(Ri)=0.08+0.05*bi1+0.11*bi2

(a).E(Ri)=0.142

bi1=-0.5

0.142=0.08+0.05*(-0.5)+0.11*bi2

0.142=0.08-0.025+0.11*bi2

0.142=0.055+0.11bi2

0.11bi2=0.055-0.142=-0.087

bi2=-0.087/0.11=-0.79091

Sensitivity to the inflation factor=-0.79(Rounded to two decimals)

(b).

Exposure to Inflation =0

E(Ri)=0.08+0.05*bi1

0.142=0.08+0.05*bi1

0.05*bi1=0.142-0.08=0.062

bi1=0.062/0.05=1.24

Sensitivity to Industrial production factor=1.24

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