R-B-Ch.7 Introduction to Portfolio Management - Points to Refresh

Reilly and Brown's Investment Analysis and Portfolio Management

Chapter 7 - An Introduction to Portfolio Management

A good portfolio is not simply a collection of individually good investments.
The relationship between the returns for assets in the portfolio is important.



Your portfolio includes all of your assets and liabilities.

As an investor you want to maximize the returns for a given level of risk.

Given a choice between two assets with equal rates of return, most investors will select the asset with the lower level of risk.

Definition of Risk

1. Uncertainty of future outcomes
or
2. Probability of an adverse outcome


Markowitz Portfolio Theory

Quantifies risk
Shows that the variance of the rate of return is a meaningful measure of portfolio risk

Derives the expected rate of return for a portfolio of assets.

Derives the formula for computing the variance of a portfolio, showing how to effectively diversify a portfolio

Assumptions

1. Investors consider each investment alternative as being presented by a probability distribution of expected returns over some holding period.(Investors determine or know the probability distribution).

2. Investors minimize 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 risk level, investors prefer higher returns to lower returns. Similarly, for a given level of expected returns, investors prefer less risk to more risk.

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 return.

Expected Rates of Return
For an individual asset can be estimated by summing of the potential returns multiplied with the corresponding probability of the returns. In this case the analyst has to estimate multiple returns and probality of each of the potential returns. Such an estimation process will give the variance of the return also.

In practice I recommend using target price based expected return.

For a portfolio of assets - weighted average of the expected rates of return for the individual investments in the portfolio will be the expected return of the portfolio.
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statistics Concepts used in this chapter
Variance

Variance is a measure of the variation of possible rates of return Ri, from the expected rate of return [E(Ri)]

Standard deviation

Standard deviation is the square root of the variance


Covariance of Returns

A measure of the degree to which two variables “move together” relative to their individual mean values over time

Correlation

The correlation coefficient is obtained by standardizing (dividing) the covariance by the product of the individual standard deviations



It can vary only in the range +1 to -1.

A value of +1 would indicate perfect positive correlation. This means that returns for the two assets move together in a completely linear manner.

A value of –1 would indicate perfect correlation. This means that the returns for two assets have the same percentage movement, but in opposite directions
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Estimation Issues


Estimates required

Expected returns
Standard deviation
Correlation coefficients among all pairs of the entire set of assets
With 100 assets, 4,950 correlation estimates

Estimation risk refers to potential errors

With assumption that stock returns can be described by a single market model, the number of correlations required reduces to the number of assets

Single index market model:

Ri = ai + bi*Rm + ei

Ri = return on a security
bi = the slope coefficient that relates the returns for security i to the returns for the aggregate stock market
Rm = the returns for the aggregate stock market
ei = error term