Finance: Risk, Return, Portfolio Theory

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Definitions from RWJ: Chapters 12 and 13, and Curtis Lecture Notes on Return, Risk, and Portfolio Theory.

The excess return required from an investment in a risky asset over that required from risk-free asset.

Variance

The average squared difference between the actual return and the average return.

Standard deviation

The positive square root of the variance. Variance and standard deviation are the most commonly used measures of volatility.

Normal Distribution (bell curve)

A symmetric, bell-shaped frequency distribution that is completely defined by its mean and standard deviation.

Geometric Average Return

The average compound return earned per year over a multi-year period. Short term projected wealth level calculated using geometric averages are probably pessimistic.

Arithmetic Average Return

The return earned in an average year over a multi-year period. Long-run projected wealth levels calculated using arithmetic average should be regarded as optimistic.

Efficient Capital Market

A market in which security prices reflect available information.

Efficient Market Hypothesis

The hypothesis that actual capital markets, such as the NYSE are efficient.

Expected Return

The return on a risky asset expected in the future. The sum of the weighted probabilities of different returns.

Portfolio

A group of assets such as stocks and bonds held by an investor

Portfolio Weight

The percentage of a portfolio's total value that is in a particular asset.

Systematic Risk

A risk that influences a large number of assets. Also known as market risk. For example, inflation.

Unsystematic Risk

The risk that effects at most a small number of assets; it is also called unique or asset-specific risk. For example, oil strike by a single company.

Principle of Diversification

That by spreading an investment across a number of assets you will eliminate some, but not all, of the risk. Unsystematic risk is essentially eliminated by diversification, so a portfolio with many assets as almost no unsystematic risk.

Systematic Risk Principle

States that the expected return on a risky asset depends on that asset's systematic risk.

Beta coefficient

The amount of systematic risk present in a particular risky asset relative to that in an average risky asset.

Security Market Line

The positively sloped straight line displaying the relations between expected return and beta.

The slope of the SML. The difference between the expected return on a market portfolio and the risk-free rate.

Capital Asset Pricing Model (CAPM)

The equation of the SML showing the relationship between expected return and beta.

CAPM shows that expected return for a particular asset depends on 3 things:
1. Pure time value of money -> measured by risk-free rate

2. Reward for bering systematic risk -> measured by market risk premium

3. Amount of systematic risk -> measured by beta

The Fama-French Results

A factor model that expands on the capital asset pricing model (CAPM) by adding size and value factors in addition to the market risk factor in CAPM. This model considers the fact that value and small cap stocks outperform markets on a regular basis. By including these two additional factors, the model adjusts for the outperformance tendency, which is thought to make it a better tool for evaluating manager performance.

Fama and French attempted to better measure market returns and, through research, found that value stocks outperform growth stocks; similarly, small cap stocks tend to outperform large cap stocks. As an evaluation tool, the performance of portfolios with a large number of small cap or value stocks would be lower than the CAPM result, as the three factor model adjusts downward for small cap and value outperformance.

Continued

1. Firm size, "small firm effect"
2. The Firm's Book-to-Market Ratio (bigger is better)
3. The Firm's Price-to-Book Ratio (lower is better)

Example: