Securities Analysis 3FB3 February 27 , 2014
Chapter 6: Optimal Risky Portfolios
The investment decision can be viewed as a topdown process
1. Capital allocation between the risky portfolio and the RF assets
2. Asset allocation across broad asset classes
3. Security selection of individual assets within each asset class
Capital allocation determines the investor’s exposure to risk.
The optimal capital allocation is determined by risk aversion as well as expectations for the risk
return tradeoff of the optimal risky portfolio.
Diversification can reduce risk without affecting expected returns.
6.1 Diversification and Portfolio Risk
Risk for one single stock can come from the economy (macroeconomic factors), as well as firm
specific influences. These latter factors affect only the company, not the market.
The more you diversify, the more you spread out exposure to firmspecific factors and portfolio
volatility should fall.
When all risk is firmspecific, diversification can reduce risk to arbitrarily low levels. With all
risk sources independent, and with the portfolio spread across many securities, the exposure to
any particular source of risk is reduced to a negligible level.
The reduction of risk to very low levels in the case of independent risk sources is sometimes
called the insurance principle, because of the conventional belief that an insure company
depends on the risk reduction achieved through diversification when it writes many policies
insuring against many independent sources of risk.
The risk that remains even after extensive diversification is called market risk, also called
systematic risk, or nondiversifiable risk.
The risk that can be eliminated by diversification is called unique risk, firmspecific risk, non
systematic risk, or diversifiable risk.
6.2 Portfolios of Two Risky Assets
Efficient diversification – risky portfolios that provide the lowest possible risk for any given
level of expected return.
Expected return of portfolio is weighted.
Variance is not a weighted average of the individual asset variances.
*The variance of the portfolio is a weighted sum of covariances, where each weight is the
product of the portfolio proportions of the pair of assets in the covariance term.
Variance is reduced if the covariance term is negative.
Even if the covariance term is positive, the portfolio standard deviation still is les than the
weighted average of the individual security standard deviations, unless the two securities are
perfectly positively correlated.
The SD of the portfolio with perfect positive correlation is just the weighted average of the
component standard deviations. [Type text] [Type text] [Type text]
In all other cases, the correlation coefficient is less than 1, making the portfolio standard
deviation less than the weighted average of the component SDs.
Portfolio expected return always is the weighted average of its component ERs, while its SD is
less than the weighted average of the component SDs, thus portfolios of less than perfectly
correlated assets always offer better riskreturn opportunities than the individual component
securities on their own. The less correlation, the greater the gain in efficiency.
How low can portfolio SD be? The lowest possible value of the correlation coefficient in 1,
perfect negative correlation, in which case the investor has the opportunity of creating a perfectly
For a pair of assets with a large positive correlation of returns, the portfolio SD will increase
monotonically from the lowrisk asset to the highrisk asset.
Covariance – how your stocks move together ▯correlation
Variance – how your stock moves from your mean/expected values
SD – risk
What is the minimum level to which portfolio SD can be held?
The minimumvariance portfolio has a SD smaller than that of either of the individual
component assets. This highlights the effect of diversification.
When two assets are perfectly negatively correlated, their portfolio variance and standard
deviation is zero.
Portfolio opportunity set – shows the combination of expected return and SD of all portfolios
that can be constructed from the two available assets.
Straight line shows that there is no benefit from diversification when the correlation between two
assets is perfectly positive.
Expected ROR of any portfolio is weighted average of asset expected returns. This is not the