Tutorial no. 10
Business Finance (MGT 337Y)
Rotman School of Management
November 22, 2002
a. Real GNP was lower than anticipated. Since returns are positively related to the
level of GNP returns should fall based on this factor.
Inﬂation was exactly the amount anticipated. Since there was no surprise in this
announcement, it will not affect Lewis-Striden returns.
Interest rates are higher than anticipated. Since returns are negatively related to
interest rates, the higher than expected rate is bad news. Returns should fall due
to interest rates.
The president’s death is bad news. Although the president was expected to re-
tire, his retirement would not be effective for six months. During that period he
would still contribute to the ﬁrm. His untimely death mean that those contribu-
tions would not be made. Since he was generally considered an asset to the ﬁrm,
his death will cause returns to fall.
The poor research results are also bad news. Since Lewis-Striden must continue
to test the drug as early as expected. The delay will affect expected future earn-
ings, and thus will dampen returns now.
The research breakthrough is positive news for Lewis Striden. Since it was un-
expected, it will cause returns to rise.
The competitor’s announcement is also unexpected, but it is not a welcome sur-
prise. This announcement will lower the returns on Lewis Striden.
b. Systematic risk is risk that cannot be diversiﬁed away through formation of a
portfolio. Generally, systematic risk factors are those factors that affect a large
number of ﬁrms in the market. Note those factors do not have to equally affect
the ﬁrms. The systematic factors in the list are real GNP, inﬂation and interest
c. Unsystematic risk is the type of risk that can be diversiﬁed away through port-
folio formation. Unsystematic risk factors are speciﬁc to the ﬁrm or industry.
Surprises in these factors will affect the returns of the ﬁrm in which you are in-
terested, but they will have no effect on the returns of ﬁrms in a different industry
and perhaps little effect on other ﬁrms in the same industry. For Lewis-Striden,
the unsystematic risk factors are the president’s ability to contribute to the ﬁrm,
the research results and the competitor.
a. Systematic Risk= 2.04(.048 − .035) − 1.90(.152 − .140) = 0.00372 = 0.372%
b. Unsystematic Return= −0.030(55 − 57) − 1.40(.027 − .027) = 0.06 = 6%
c. Total Return= 0.09 + 0.00372 + 0.06 = 0.15372 = 15.372%
a. Stock A:
RA = RA + βA (Rm − Rm ) + εA
RA = 10.5% + 1.2(Rm − 14.2%) + εA
RB = RB + βB (Rm − Rm ) + εB
RB = 13% + 0.98(Rm − 14.2%) + εB
RC = RC + βC (Rm − Rm ) + εC
RC = 15.7% + 1.37(Rm − 14.2%) + εC
b. RP = 0.40RA + 0.25RB + 0.35RC
= 0.40[10.5% + 1.2(Rm − 14.2%) + εA ]
+ 0.25[13% + 0.98(Rm − 14.2%) + εB ]
+ 0.35[15.7% + 1.37(Rm − 14.2%) + εC ]
= 12.945% + 1.2045(Rm − 14.2%) + 0.40εA + 0.25εB + 0.35εC
c. (i) RA = 10.5% + 1.2(12% − 14.2%) = 7.86%
RB = 13% + 0.98(12% − 14.2%) = 10.84%
RC = 15.7% + 1.37(12% − 14.2%) = 12.69%
(ii) RP = 12.945% + 1.2045(12% − 14.2%) = 10.2951%
a. V ar(Rj ) = βi2 V ar(Rm ) + V ar(εi )
σA = 0.52 (100) + 500 = 525
σB = 1.62 (100) + 100 = 356
σC = 12 (100) + 2500 = 2600
b. (i) As N → ∞, V ar(εi )/N → 0
σA = 0.52 (100) = 25
σB = 1.62 (100) = 256
σC = 12 (100) = 100
(ii) The easiest way to see which portfolio would not be held is to draw the
security market line for these securities. Security C will not be held because
point C lies below the line through A and B.
(iii) Everyone would want to sell the portfolio C, but no one would want to buy
it. Competition will bid down the price of C until its expected return is
on the security market line. The algebraic characterization of that line is
E(Ri ) = − 0.09 + ×β 0.4