The Basics of Risk and Return

Corporate Finance

Dr. A. DeMaskey

Learning Objectives

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

return?

What Are Investment Returns?

Investment returns measure the financial results of an investment.

Returns may be historical or prospective (anticipated).

Returns can be expressed in:– Dollar terms– Percentage terms

What Is Investment Risk?

Typically, investment returns are not known with certainty.

Investment risk pertains to the probability of earning a return less than that expected.

The greater the chance of a return far below the expected return, the greater the risk.

Probability Distribution

Rate ofreturn (%) 50150-20

Stock X

Stock Y

Which stock is riskier? Why?

Measuring Stand-Alone Risk

Expected Rate of Return

Standard Deviation

Coefficient of Variation

Measuring Stand-Alone Risk

Standard deviation measures the stand-alone risk of an investment.

The larger the standard deviation, the higher the probability that returns will be far below the expected return.

Coefficient of variation is an alternative measure of stand-alone risk.

Portfolio Risk and Return

Portfolio Return, kp

Portfolio Risk, p

– Covariance– Portfolio Variance– Portfolio Standard Deviation– Correlation Coefficient

^

Two-Stock Portfolio

Two stocks can be combined to form a riskless portfolio if r = -1.0.

Risk is not reduced at all if the two stocks have r = +1.0.

In general, stocks have r 0.65, so risk is lowered but not eliminated.

Investors typically hold many stocks. What happens when r = 0?

# Stocks in Portfolio

10 20 30 40 2,000+

Company Specific (Diversifiable) Risk

Market Risk

20

0

Stand-Alone Risk, p

p (%)35

Diversifiable Risk versus Market Risk

Diversifiable Risk versus Market Risk

Market risk is that part of a security’s stand-alone risk that cannot be eliminated by diversification.

Firm-specific, or diversifiable, risk is that part of a security’s stand-alone risk that can be eliminated by diversification.

Conclusion

As more stocks are added, each new stock has a smaller risk-reducing impact on the portfolio.

p falls very slowly after about 40 stocks are included. The lower limit for p is about 20% = M .

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? 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.

It is measured by a stock’s beta coefficient, which measures the stock’s volatility relative to the market.

How Are Betas Calculated?

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.

The slope of the regression line, which measures relative volatility, is defined as the stock’s beta coefficient, or b.

How Are Betas Interpreted?

If b = 1.0, stock has average risk. If b > 1.0, stock is riskier than average. If b < 1.0, stock is less risky than average. Most stocks have betas in the range of 0.5

to 1.5. Can a stock have a negative beta?

The Capital Asset Pricing Model (CAPM)

CAPM indicates what should be the required rate of return on a risky asset.– Beta– Risk aversion

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)

The CAPM when graphed is called the Security Market Line (SML).

The SML equation can be used to find the required rate of return on a stock.

SML: ki = kRF + (kM - kRF)bi – (kM – kRF) = market risk premium, RPM

– (kM – kRF)bi = risk premium

Expected Return versus Market Risk

Which of the alternatives is best?

Expected

Security return Risk, b

HT 17.4% 1.29

Market 15.0 1.00

USR 13.8 0.68

T-bills 8.0 0.00

Collections

1.7 -0.86

Portfolio Risk and Return

Calculate beta for a portfolio with 50% HT and 50% Collections.

What is the required rate of return on the HT/Collections portfolio?

SML1

Original situation

Required Rate of Return k (%)

SML2

0 0.5 1.0 1.5 2.0

1815

11 8

New SML I = 3%

Impact of Inflation Change on SML

kM = 18%

kM = 15%

SML1

Original situation

Required Rate of Return (%) SML2

After increasein risk aversion

Risk, bi

18

15

8

1.0

RPM = 3%

Impact of Risk Aversion Change

Drawbacks of CAPM

Beta is an estimate. Unrealistic assumptions. Not testable. CAPM does not explain differences in

returns for securities that differ:– Over time– Dividend yield– Size effect