MIT Sloan School of Management
J. Wang
15.407
E52456
Fall 2003
Problem Set 7: Portfolio Choice
Due: November 25, 2003
1.
(BKM) Which statement(s) about portfolio diversiﬁcation is correct?
(a) Proper diversiﬁcation can reduce or eliminate systematic risk.
(b) Diversiﬁcation reduces the portfolio’s expected return because it reduces the port
folio’s total risk.
(c) As more securities are added to a portfolio, total risk would typically be expected
to fall at a decreasing rate.
(d) The riskreducing beneﬁts of diversiﬁcation do not occur meaningfully until at least
30 individual securities are included in the portfolio.
2.
Consider the following scenario: There are an inﬁnite number of stocks in the economy,
and each of them has a annual volatility (standard deviation) of 30%. The covariance
between any two stocks are 0.01. The riskfree rate is 5%.
(a) What is the magnitude of the systematic risk in the stock market?
(b) Assuming perfect market (no trading cost, short sell allowed, etc) is it still possible
for some stocks in the market to have diﬀerent expected returns?
3.
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 Fall '03
 Wang
 Standard Deviation, Capital Asset Pricing Model, Modern portfolio theory, Risk in finance, Riskfree interest rate

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