Question

# Ms. Bessie, manager of Everchanging Mutual Fund, know he fund currently is well diversified and that...

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.

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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