Coefficient of Variation

Week 8

Coefficient of variation (CV): a standardized measure of dispersion about the expected return, tells how much risk we face per unit of return (chose the one with lowest CV)

Correlation coefficient, is a measure of the extent to which two securities’ returns tend to move together[pic 1]

• Describe the goodness of fit about linear relationship between two variables

[pic 2]

Portfolio return is the weighted average of the expected returns of the individual assets

Risk attitudes

• A risk adverse investor tries to maximize his return and minimize his risk
• A risk neutral investor tries to maximize his return but does not care about the risk
• A risk seeking investor tries to maximize his return and maximize his risk

Diversification: strategy designed to reduce risk by spreading the portfolio across many investors (systematic/unsystematic risk)

[pic 3]

Week 9

Diversification and portfolio risk

• As more shares are added, each new share has a smaller risk-reducing impact
• By forming portfolios, we can eliminate some of the riskiness of the individual shares

Markowitz Portfolio Theory (MPT)

1. Investors consider each investment alternative as being presented 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 risk level, investors prefer higher returns to lower returns.  Similarly, for a given level of expected returns, investors prefer less risk to more risk.

Efficient frontier

[pic 4]

• The section of the opportunity set above the minimum variance portfolio is the efficient frontier

Capital Market Line (CML)

[pic 5]

• Introducing a risk0free asset, the opportunity set for investors is expanded and results in a new efficient frontier
• The CML represents the efficient set of all portfolios that provides the investor with best possible investment opportunities when a risk-free asset is available
• The important facts

1. Risk-free asset has a standard deviation od zero
2. The minimum variance portfolio lies on the boundary of the feasible set at a point where the variance is at a minimum
3. The optimal portfolio lies on the feasible set and on a tangent from the risk-free asset

Beta β

• A measure of a security’s systematic risk
• Measures the responsiveness of a security to movements in the market portfolio

• If beta = 0, the expected return if risk-free
• If beta = 1, stock is as risky as the market
• If beta > 1, stock is riskier than the market
• If beta < 1, stock is less risky than the market

Security Market Line (SML)

[pic 6]

• Represent CAPM, describe the linear relationship between expected returns for individual securities and systematic risk
• In equilibrium, all securities must be priced that their returns lie on the SML
• If inflation rises, it will shift the SML to the left
• If risk aversion increased, it will increase the market premium by the same amount

What’s the difference between SML and CML?

Week 10

Cost of capital: the rate of return the firm must earn to maintain its market value and attract investors, estimated

• On an after-tax basis
• At a point in time
• Based on expected future values
• Holding business and financial risk fixed

• Cost of capital is the RRR on the three main types of financing

• Cost of debt (YTM)
• Cost of equity
• Cost of preference shares

Cost of debt

1. Find the YTM
2. Covert to an annual cost of debt
3. Find the after-tax cost of debt ki (1 – T)

Cost of preference shares

• Preference shares generally pay a constant dividend every period forever (perpetuity)
• kp = D1 / P

Cost of capital

1. Dividend Growth Model (DGM)

Advantage: easy to understand and use

Disadvantage:

• Only applicable to companies currently paying dividends
• Not applicable if dividends are not growing at a reasonably constant rate
• Extremely sensitive to the estimated growth rate (1% increase in g will lead to 1% increase in the cost of capital)
• Does not explicitly consider risk

1. SML or CAPM

Advantages:

• Explicitly adjusts for systematic risk
• Applicable to all companies

Disadvantages:

• Have to estimate the expected market risk premium
• Have to estimate beta
• Relying on the past to predict the future, which is unreliable