Topic II.b: The Portfolio Effect
Learning outcome:

Define and describe the portfolio effect
In this chapter, the concept of portfolio formation moves beyond the risky and risk-free asset
combinations of the previous chapter to include combinations of two or more risky assets. The
concept of risk reduction via diversification created by combining securities with different return
patterns is introduced. The student is introduced to analytical tools that are used to create the
lowest risk portfolio that meets a target expected return. After finding the best diversified
combinations the risk free asset is combined with the risky portfolio. The capital allocation line
that is tangent to the so called efficient frontier of best diversified portfolios will dominate all
risky portfolios, regardless of the level of risk aversion. As in Chapter 5, investors will optimally
vary their asset allocation decision according to their risk tolerance by varying the amount they
invest in the tangency portfolio and the amount invested in the risk free asset. See Text figure
6.6. The single factor index model is introduced; this model predicts stock returns based upon
both the firm-specific and market risks of the security. Firm-specific risk may be eliminated by
adding more securities to the portfolio. In a diversified portfolio, firm-specific risk is eliminated,
and thus beta (systematic or market risk) becomes the relevant risk measure of the portfolio
(Bodie et al, 2010).
A portfolio is a collection of assets. When investing in a portfolio, it is inaccurate to consider the
risk of each asset individually, rather should we focus on the co-movement between asset
returns. While the relationship between portfolio return and each asset's return is associative,
this is not the case for the relationship between portfolio risk and each asset's risk. Intuitively,
one can easily foresee that when you hold many securities together, you may earn profits with
some and lose with other. Bottom line, the variability of the portfolio returns is much lower than
the average variability (risk) of each asset held individually. This is really what the complicated
variance equation means: the average risk of a portfolio of many assets is the average risk of
each asset's risk less the propensity of each asset's performance to offset each other's effect.
Naturally, the lower the correlation coefficient (ri,j), the greater the risk reduction: this
phenomenon is known as diversification. The question is to what extent can an investor
beneficiate from this diversification effect. Well, it is usually accepted that more than 20
securities provide increasing diminishing utility to further diversify. Thus, a limited portfolio
effect occurs because of the risk reduction accompanying diversification. The size of the
portfolio effect is therefore inversely related to the correlation between a given asset's returns and
those of the rest of portfolio. This finding is at the essence of what is called modern portfolio
theory and further suggest that efficient investing lies in the ability to find securities and markets
which returns are poorly related. For example, historical global bond portfolio correlations
between domestic rates of return in U.S. and foreign bond markets demonstrate that the low
positive correlations give U.S. investors opportunities for risk reduction through global
diversification. The same conclusion can be reached with Global Equity Portfolio correlations
with US equity markets.