441 words - 2 pages

Quiz 3 – A

Financial Economics

Fall 2012

Name:_______________________________

Variance of a portfolio of two assets:

Equation of the Capital Allocation Line:

σp2 = x2 σ12 (1-x)2 σ22 +2x(1-x)ρ1,2 σ1 σ2

E[rP] = rf +( E[r1]- rf) σP/ σ1

Weight of asset 1 in the minimum variance portfolio with 2 assets:

x1min = σ2(σ2 – ρ1,2 σ1)/( σ12 + σ22 – 2ρ1,2σ1 σ2)

a) If you dispose of many positively correlated assets (that is, Cov(ri ,rj)>0 for all couples of assets i

and j), then by buying strictly positive amount of each asset, you can:

Obtain a portfolio that is risk-free.

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Portfolio A has an expected return of E[rA]= 20%and a standard deviation of return of σA = 20%,

Portfolio B has an expected return of E[rB] = 10% and a standard deviation of return of σB = 30%.

The correlation coefficient between Portfolios A and B is ρA,B = 0. The risk free asset has a return of

rf =1%.

c) If an investor has to choose between investing all is wealth in either portfolio A or portfolio B, then

he will choose

Portfolio A

Portfolio B

The investor is indifferent between A or B

Impossible to tell without knowing the investor’s risk aversion.

d) Consider a portfolio C composed of Portfolio A and B but not of the risk free asset. What must be

the weight of A and B if you want portfolio C to have the minimum possible risk?

{xA , xB }={1,0}

{xA , xB } ={0.2, 0.8}

{xA , xB }={0.308, 0.692}

{xA , xB }={0.8, 0.2}

{xA , xB } ={0.692, 0.308}

e) Portfolio D is composed of portfolio A and the risk free asset but not of portfolio B. The standard

deviation of Portfolio D return is equal to the standard deviation of Portfolio B. What is the

composition of portfolio D?

{xA , xf }={0,1}

{xA , xf }={0.5,0.5}

{xA , xf }={-0.5,1.5}

{xA , xf }={1.5, -0.5}

{xA , xf }={1,0}

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