Advanced Portfolio Management
ADMS 4501 – Winter 2012 – Lois King
Lecture 3 – Chapter 6 – Review of MPT – Jan 19
An Introduction to Portfolio Management
- Some background assumptions.
- Markowitz Portfolio Theory
- Efficient Frontier and Investor Utility
- As an investor you want to maximize the returns for a given level of risk.
- Your portfolio includes all of your assets and liabilities.
- The relationship between the returns for assets in the portfolio is important.
- A good portfolio is not simply a collection of individually good investments.
- Definition of risk
Risk means the uncertainty of future outcomes.
For instance, future value of investment in Google’s stock is
uncertain so the investment is risky.
On the other hand, purchase of a six-month Certificate of Deposit
(CD) or Guaranteed Investment Certificate (GIC) has a certain
future value; the investment is not risky.
Risk is measured by the probability of an adverse outcome.
For instance, there is 40% chance you will receive a return less
Background Assumptions: Risk Aversion
- Given a choice between two assets with equal rates of return, risk-averse
investors will select the asset with the lower level of risk.
o Many investors purchase insurance for; life, automobile, health and
o Yield on bonds increases with risk classifications.
- Not all investors are risk averse
o It may depend on the amount of money involved.
Markowitz Portfolio Theory
- Quantifies risk.
- Derives the expected rate of return for a portfolio of assets and an expected risk
- Shows that the variance of the rate of return is a meaningful measure of portfolio
- Derives the formula for computing the variance of a portfolio, showing how to
effectively diversify a portfolio. - Assumptions
o Consider investments as probability distributions of expected returns over
some holding period.
o Maximize one-period expected utility, which demonstrate diminishing
marginal utility of wealth.
o Estimate the risk of the portfolio on the basis of the variability of expected
o Base decisions solely on expected return and risk.
o Prefer higher returns for a given risk level. Similarly, for a given level of
expected returns, investors prefer less risk level to more risk level.
- Using these five assumptions, a single asset or portfolio of assets is considered
to be efficient if no other asset or portfolio of assets offers higher expected return
with the same (or lower) risk, or lower risk with the same (or higher) expected
Alternative Measures of Risk
- Variance or standard deviation of expected return.
- Range of returns.
- Returns below expectations.
o Semi-variance – a measure that only considers deviations below the
o These measures of risk implicitly assume that investors want to minimize
the damage from returns less than some target rate.
- Advantages of using standard deviation
o Somewhat intuitive.
o Correct and widely recognized risk measure.
o Used in most of the theoretical asset pricing models.
Expected Rate of Return
- For an individual asset
o It is equal to the sum of the potential returns multiplied with the
corresponding probability of the returns.
Expected Rate of Return – Portfolio