The Basics of Risk and Return Corporate Finance Dr. A. DeMaskey

Learning Objectives u Questions to be answered: – What is risk? – How is risk measured? – What is the relationship between risk and return?

What Are Investment Returns? u Investment returns measure the financial results of an investment. u Returns may be historical or prospective (anticipated). u Returns can be expressed in: – Dollar terms – Percentage terms

What Is Investment Risk? u Typically, investment returns are not known with certainty. u Investment risk pertains to the probability of earning a return less than that expected. u The greater the chance of a return far below the expected return, the greater the risk.

Probability Distribution Rate of return (%) Stock X Stock Y Which stock is riskier? Why?

Measuring Stand-Alone Risk u Expected Rate of Return u Standard Deviation u Coefficient of Variation

Measuring Stand-Alone Risk u Standard deviation measures the stand- alone risk of an investment. u The larger the standard deviation, the higher the probability that returns will be far below the expected return. u Coefficient of variation is an alternative measure of stand-alone risk.

Portfolio Risk and Return u Portfolio Return, k p u Portfolio Risk,  p – Covariance – Portfolio Variance – Portfolio Standard Deviation – Correlation Coefficient ^

Two-Stock Portfolio u Two stocks can be combined to form a riskless portfolio if r = u Risk is not reduced at all if the two stocks have r =  In general, stocks have r  0.65, so risk is lowered but not eliminated. u Investors typically hold many stocks. u What happens when r = 0?

# Stocks in Portfolio ,000+ Company Specific (Diversifiable) Risk Market Risk 20 0 Stand-Alone Risk,  p  p (%) 35 Diversifiable Risk versus Market Risk

u Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification. u Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.

Conclusion u As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio. u  p falls very slowly after about 40 stocks are included. The lower limit for  p is about 20% =  M. u By forming well-diversified portfolios, investors can eliminate about half the riskiness of owning a single stock.

How Is Market Risk Measured For Individual Securities? u Market risk, which is relevant for stocks held in well-diversified portfolios, is defined as the contribution of a security to the overall riskiness of the portfolio. u It is measured by a stock’s beta coefficient, which measures the stock’s volatility relative to the market.

How Are Betas Calculated? u Run a regression with returns on the stock in question plotted on the Y axis and returns on the market portfolio plotted on the X axis. u The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.

How Are Betas Interpreted? u If b = 1.0, stock has average risk. u If b > 1.0, stock is riskier than average. u If b < 1.0, stock is less risky than average. u Most stocks have betas in the range of 0.5 to 1.5. u Can a stock have a negative beta?

The Capital Asset Pricing Model (CAPM) u CAPM indicates what should be the required rate of return on a risky asset. – Beta – Risk aversion u The return on a risky asset is the sum of the riskfree rate of interest and a premium for bearing risk (risk premium).

Security Market Line (SML) u The CAPM when graphed is called the Security Market Line (SML). u The SML equation can be used to find the required rate of return on a stock. u SML: k i = k RF + (k M - k RF )b i – (k M – k RF ) = market risk premium, RP M – (k M – k RF )b i = risk premium

Expected Return versus Market Risk Which of the alternatives is best? Expected SecurityreturnRisk, b HT 17.4% 1.29 Market USR T-bills Collections

Portfolio Risk and Return u Calculate beta for a portfolio with 50% HT and 50% Collections. u What is the required rate of return on the HT/Collections portfolio ?

SML 1 Original situation Required Rate of Return k (%) SML New SML  I = 3% Impact of Inflation Change on SML

k M = 18% k M = 15% SML 1 Original situation Required Rate of Return (%) SML 2 After increase in risk aversion Risk, b i  RP M = 3% Impact of Risk Aversion Change

Drawbacks of CAPM u Beta is an estimate. u Unrealistic assumptions. u Not testable. u CAPM does not explain differences in returns for securities that differ: – Over time – Dividend yield – Size effect