Chapter 6

The Returns and Risks The Returns and Risks from Investingfrom Investing

• Function of both return and risk– At the centre of security analysis

• How should realized return and risk be measured?– The realized risk-return tradeoff is

based on the past– The expected future risk-return

tradeoff is uncertain and may not occur

Asset Valuation

• Returns consist of two elements:– Yield: Periodic cash flows such as

interest or dividends (income return)• “Yield” measures relate income return to

a price for the security

– Capital Gain or Loss: Price appreciation or depreciation

• The change in price of the asset

• Total Return = Yield + Price Change

Return Components

• Two general types:– Systematic (market) risk

• economy wide factors that impact returns

– Non-systematic (non-market) risk• Unique characteristics specific to a

security

• Total Risk measured by volatility• Systematic risk measured by beta

Risk Types

Measures Describing a Return Series

• Arithmetic mean, or simply mean

• Geometric mean defined as the n-th root of the product of n return relatives minus

nX

X nX

X

1)TR1)...(TR1)(TR1( n/1n21 1)TR1)...(TR1)(TR1( n/1n21

• Risk is the chance that the actual outcome will be different than the expected outcome

• Standard Deviation measures the deviation of returns from the mean

s

X Xn 1

2 1/2

s

X Xn 1

2 1/2

Measuring Risk

• Premium is additional return earned or expected for additional risk

• Equity risk premium is the difference between stock and risk-free returns

• Bond default premium is the difference between the return on long term corporate bonds and long term government bonds

• http://www.smartmoney.com/onebond/index.cfm?story=yieldcurve

Risk Premiums

Series Geom

Mean

Arithm

Mean

Standard

Deviation

Canadian Common Stocks

10.32% 11.53% 16.36%

US CommonStocks

12.09% 13.5% 17.67%

Long-term Government of Canada Bonds

6.07% 6.46% 9.39%

T-bills 5.20% 5.28% 4.36%

Inflation (CPI) 3.97% 4.05% 3.63%

Annual Total Returns (1938-2003)