Consider the following information: Rate of Return if State Occurs State of Econ
ID: 2766126 • Letter: C
Question
Consider the following information:
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
0.72
0.11
0.29
0.17
Bust
0.28
0.17
0.07
0.11
Requirement 1:
What is the expected return on an equally weighted portfolio of these three stocks? (Do not round your intermediate calculations.)
Requirement 2:
What is the variance of a portfolio invested 20 percent each in A and B and 60 percent in C? (Do not round your intermediate calculations.)
Consider the following information:
Rate of Return if State Occurs
State of Economy
Probability of
State of Economy
Stock A
Stock B
Stock C
Boom
0.72
0.11
0.29
0.17
Bust
0.28
0.17
0.07
0.11
Explanation / Answer
This portfolio does not have an equal weight in each asset. We first need to find the return of the portfolio in each state of the economy. To do this, we will multiply the return of each asset by its portfolio weight and then sum the products to get the portfolio return in each state of the economy. Doing so, we get:
For equally weighted portfolio of these three stocks weight of each stock=1/3
=.3333
Boom: E(Rp) = .34(.11) + .33(.29) + .33(.17) = .1892or 18.92%
Bust: E(Rp) = .34(.17) + .33(.07) + .33(.11) = .1172 or 11.72%
And the expected return of the portfolio is:
E(Rp) = .72(.1892) + .28(.1172) = .0.1690or 16.9%
Variance of a portfolio invested 20 percent each in A and B and 60 percent in C
Boom: E(Rp) = .2(.11) + .2(.29) + .6(.17) = .182or 18.2%
Boom: E(Rp) = .2(.17) + .2(.07) + .6(.11) = .114or 11.4%
E(Rp) = .72(.182) + .28(.114) = 0.163or 16.3%
sp2 = .72(.163– .182)2 + .28(.163– .114)2
sp2=.72(-.000361)+.28(0.002401)
sp2=-.00025992+0.00067228
sp = (0.00041236).5 = .0203 or 2.03%
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