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Lecture 9

BU457 Lecture Notes - Lecture 9: Systematic Risk, Weighted Arithmetic Mean

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Bixia Xu

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Portfolio Diversification
The Principles of Portfolio Diversification
One way investors can lower risk for a given expected return is
to adopt a strategy of diversification, that is, to invest in a
portfolio of securities
The risk reported on by many common accounting-based risk
measures, such as debt to equity, times interest earned, or the
current ratio, can be reduced or eliminated a priori by
appropriate diversification
Assumption: all investors need information about the expected
values and riskiness of returns from investments, regardless of
the specific forms of their utility functions
Market-wide or economy-wide factors are states of nature
which affect the returns of all shares, such as levels of interest
rates, foreign exchange rates, the level of economic activity etc.
In addition to economy-wide factors, there are also firm-
specific factors, also called idiosyncratic factors, that affect
the return of one firm only
The Optimal Investment Decision
Holding the market folio, which includes some of every security
traded on the market, reduces risk
When more than one risky investment is held, the firm-specific
risks tend to cancel out
As a result, the riskiness of returns is reduced
At minimum, when the market portfolio is held, the economy-
wide factors will remain to contribute to portfolio risk
o Such non-diversifiable risk is called systematic risk
Portfolio risk can be adjusted to desired level without losing the
benefits of diversification by selling some of the market folio and
use the proceeds to buy the risk-free asset
When transaction costs are ignored, a risk-averse investor’s
optimal investment decision is to buy that combination of market
portfolio and risk-free asset that yields the best tradeoff between
expected return and risk
o Some investors may want to reduce their investment in
market portfolio and buy the risk-free assets, while others
may wish to borrow at the risk-free rate and increase their
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