WEEK 8 CONTENT REVIEW

Risk

Uncertainty about an investment's future returns, including the possibility of gains or losses.

Risk-Return Relationship

Investors require higher expected returns for taking on greater risk; higher returns are not guaranteed.

Systematic Risk

Market-wide risk that cannot be eliminated through diversification; examples include recessions, inflation, and interest rate changes.

Nonsystematic Risk

Company-specific risk that can be reduced through diversification; examples include product recalls or losing a major customer.

Diversification

Investing in multiple assets to reduce nonsystematic risk; it does not eliminate systematic risk.

Sigma (Standard Deviation)

Measures the total volatility or variability of an investment's returns around their average.

Beta

Measures an investment's sensitivity to overall market movements; used to measure systematic risk.

Sigma vs. Beta

Sigma measures total volatility, while beta measures sensitivity to market movements.

Market Beta

The market portfolio has a beta of 1.0.

Beta Greater Than 1

The stock is more sensitive to market movements than the market.

Beta Between 0 and 1

The stock is less sensitive to market movements than the market.

Negative Beta

The investment tends to move opposite the market.

Beta of 0

The investment has no sensitivity to market movements as measured by beta.

Beta of 1.5

The stock is approximately 50% more sensitive to market movements than the market.

Beta Formula

Covariance(stock returns, market returns) / Variance(market returns).

Beta on a Regression Graph

Beta is the slope of the regression line relating stock returns to market returns.

Beta Regression Axes

Y-axis = stock returns; X-axis = market returns.

Excel SLOPE Formula

=SLOPE(stock_returns,market_returns); calculates beta with stock returns first.

Excel STDEV.S

=STDEV.S(range); calculates sample standard deviation.

Excel VAR.S

=VAR.S(range); calculates sample variance.

Excel COVARIANCE.S

=COVARIANCE.S(stock_range,market_range); calculates sample covariance.

Portfolio Beta

The weighted average of the individual stocks' betas.

Portfolio Beta Formula

Sum of (portfolio weight × individual stock beta).

Excel SUMPRODUCT

=SUMPRODUCT(weights_range,betas_range); calculates portfolio beta.

Portfolio Kelley Weights

Stock A = 20%; Stock B = 20%; Stock C = 30%; Stock D = 30%.

Capital Asset Pricing Model (CAPM)

Calculates the return investors require based on systematic risk.

CAPM Formula

Required return = Risk-free rate + Beta × Market risk premium.

Risk-Free Rate

The return on a nearly risk-free investment; the lecture uses the current 1-year Treasury yield for CAPM.

Market Risk Premium (MRP)

The extra return investors require for holding the market portfolio rather than a risk-free investment.

Market Risk Premium Formula

Historical average market return − historical average Treasury return.

Current vs. Historical Treasury Rates

Use the current Treasury yield as CAPM's starting risk-free rate; use historical Treasury averages when calculating historical MRP.

Higher Beta in CAPM

When MRP is positive, a higher beta produces a higher required return.

Security Market Line (SML)

A graph showing the relationship between beta and the CAPM required return.

SML Axes

X-axis = beta; Y-axis = required return.

SML Slope and Intercept

Slope = market risk premium; Y-intercept = risk-free rate.

Undervalued Stock

Forecasted return exceeds CAPM required return; the stock plots above the SML.

Overvalued Stock

Forecasted return is below CAPM required return; the stock plots below the SML.

Fairly Valued Stock

Forecasted return equals CAPM required return; the stock plots on the SML.

Project Beta vs. Company Beta

Use the project's beta to calculate its required return when its risk differs from the company's overall risk.

IRR Decision Rule

For a conventional project, accept if IRR exceeds the risk-adjusted required return; reject if IRR is lower.