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Chapter 6

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Ryerson University

Finance

FIN 521

Eric Terry

Fall

Description

Chapter 6: An Introduction to Portfolio Management
One basic assumption of the portfolio theory is that investors want to maximize their returns from your total set of
investments for a given level of risk
Your portfolio should include all your assets and liabilities, not only your marketable securities but also your car, house,
and less marketable investments such as coins, stamps, art, antiques, and furniture
Risk Aversion: portfolio theory assumes that investors are risk averse, meaning that given a choice between two assets
with equal returns, investors will select the asset with the least risk
- Most investors are risk averse because they purchase various types of insurance, including life insurance, car
insurance, and health insurance
- Also the difference in promised yield (the required return) for different grades of bonds with different degrees of
credit risk
Risk: the uncertainty of future outcomes or the probability of an adverse outcome
Markowitz Portfolio Theory: developed by the Nobel Prize Laureate Harry Markowitz who derived the expected return
for a portfolio of assets and an expected risk measure
- Showed that the variance of the rate of return was a meaningful measure of portfolio risk under a reasonable set of
assumptions
- He derived that the formula for computing the variance of the portfolio
- This portfolio variance formula not only indicated the importance of diversifying investments to reduce the total
risk of a portfolio but also showed how to effectively diversify
- Assumptions regarding investors behaviour:
1. Investors consider each investment alternative as being represented by a probability distribution of expected
returns over some holding period
2. Investors maximize one-period expected utility, and their utility curves demonstrate diminishing marginal
utility of wealth
3. Investors estimate the risk of the portfolio on the basis of the variability of expected returns
4. Investors base decisions solely on expected return and risk, so their utility curves are a function of expected
return and the expected variance (or standard deviation) of returns only
5. For a given level of risk, investors prefer higher returns to lower returns. Similarly for a given level of
expected return, investors prefer less risk to more risk
- Under these assumptions, a single asset or portfolio of assets is considered to be efficient if no other asset or
portfolio of assets offer higher expected return with the same (or lower) risk or lower risk with the same (or
higher) expected return
ALTERNATIVE MEASURES OF RISK:
Best known measure of risk is the variance or standard deviation of expected returns
- It is a statistical measure of the dispersion of returns around the expected value whereby a larger variance or
standard deviation indicates greater dispersion (the greater the uncertainty of future returns)
Range of returns: assumed that a larger range of expected returns, from the lowest to the highest, means greater
uncertainty regarding future expected returns
Semi variance: a measure that only considers deviations
- An extension of the semi variance measure only computes expected returns below zero (that is, negative returns),
or returns below the returns of some specific asset such as T-bills, the inflation rate, or a benchmark
- Minimize the damage (regret) from returns less than some target rate
Always use the variance or standard deviation of returns because:
1. This measure is somewhat intuitive
2. It is a correct and widely recognized risk measure
3. It has been used in most of the theoretical asset pricing models
Expected Return: for a portfolio of investments is simply the weighted average of the expected return for the individual
investments in the portfolio
- Weights are proportion of total value for the individual investment
( ) ∑ Standard Deviation of Returns for an Individual Investment:
- Variance, or standard deviation, is a measure of the variation of possible rafrom the expected
return ( ) as follows:
∑, ( )-
√∑ , ( )- √
Standard Deviation of Returns for a Portfolio:
- Covariance of Returns: is a measure of the degree to which two variables move together relative to their
individual mean values over time (covariance of the rate of returns rather than prices or some other variable)
o Affected by the variability of the two

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