Chapter 6Chapter 6

The Returns and Risks from The Returns and Risks from InvestingInvesting

• Define “return” and state its two components.• Explain the relationship between return and risk.• Identify the sources of risk.• Describe the different methods of measuring

returns.• Describe the different methods of measuring

risk.• Discuss the returns and risks from investing in

major financial assets in the past.

Learning ObjectivesLearning Objectives

• Asset valuation is a function of both return and risk At the centre of security analysis Return is the reward for undertaking the

investment The realized risk-return tradeoff is based on

the past The expected future risk-return tradeoff is

uncertain and may not occur

Asset ValuationAsset Valuation

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

dividends (income component of the security’s return)

• “Yield” measures relate income return to a price for the security

• Issuer makes the payments in cash to the security holder

Capital Gain (Loss): Price appreciation or depreciation

• The change in price of the security over some period of time

• Total Return = Yield + Capital Gain (Loss)

Return ComponentsReturn Components

Example: Calculating yields and price Example: Calculating yields and price changeschanges

• Assume that an investor buys 100 shares of a stock for $40, holds it for one year and then sells it at $50. During that year the investors receives a dividends of $0.01 per share every 4 months.

• Calculate the yield and the capital gain (loss) for the investor.

RiskRisk

• Risk is the chance that the realized (actual) return for an investment will be different from the expected return

• Investors are concerned that the realized return will be less than the expected return

• The greater the variability between the expected and realized return, the greater the risk

• Although, investors may receive on average their expected returns on risky assets in the long-run, they fail to do so in the short-run

• Interest Rate Risk Affects market value

and resale price

• Market Risk Overall market

effects

• Inflation Risk Purchasing power

variability

• Business Risk

• Financial Risk Tied to debt financing

• Liquidity Risk Time and price

concession required to sell security

• Exchange Rate Risk• Country Risk

Potential change in degree of political stability

Risk SourcesRisk Sources

Risk SourcesRisk Sources

• Interest Rate Risk • Is the variability in a security’s return resulting from

changes in the level of interest rates

• Affects bonds more directly than common stocks and is a major risk faced by bondholders

• Market Risk• Is the variability in returns resulting from fluctuations in

the overall market

• All securities (especially common stocks) are exposed to market risk

Risk SourcesRisk Sources• Inflation Risk• Also known as purchasing power risk

• Is related to interest rate risk since interest rates generally rise as inflation increases (inflation premiums)

• Business Risk• The risk of doing business in a particular industry or

environment

• For example, Shell Canada faces unique problems as a result of developments in the global oil situation

Risk SourcesRisk Sources• Financial Risk• Is associated with the use of debt financing by

companies (financial leverage)

• The larger the proportion of assets financed by debt (as opposed to equity), the larger the variability in returns, the larger the risk

• Liquidity Risk• Is the risk associated with the particular secondary

market in which the security trades

• A T-bill has little or no liquidity risk, whereas a small OTC stock may have a large liquidity risk

Risk SourcesRisk Sources• Exchange Rate Risk• Is the variability in returns on securities caused by

currency fluctuations

• Also called currency risk

• Country Risk• Also called political risk

• With more investors investing internationally, the political, and therefore economic, stability and viability of a country’s economy need to be considered

• Two general types: Systematic (market) risk

• Pervasive, affecting all securities, cannot be avoided

• Interest rate or market risk or inflation risk Non-systematic (non-market) risk

• Unique characteristics specific to a security• Total Risk = General Risk + Specific Risk

=Market Risk + Issuer Risk = Systematic Risk + Non-

Systematic Risk

Risk TypesRisk Types

• Total Return (TR) compares performance over time or across different securities

• Total Return is a percentage relating all cash flows received during a given time period, denoted CFt +(PE - PB), to the start of period price, PB

B

BEt

P)P(PCFTR

B

BEt

P)P(PCFTR

Measuring ReturnsMeasuring Returns

Measuring ReturnsMeasuring Returns

• CF_t = cash flows during measurement period t (Cash flows for a bond comes from interest payments

received, and for a stock it comes from dividends received)

• P_E = ending or sale price• P_B = beginning or purchase price

B

BEt

P)P(PCF

TR

B

BEt

P)P(PCF

TR

Measuring ReturnsMeasuring Returns

• The total return concept is valuable as a measure of return because:

1- It is all-inclusive, measuring the total return per dollar of the original investment

2- It facilitates the comparison of assets returns over a specified period, whether the comparison is of different assets (stocks vs. bonds) or different securities within the same asset (several common stocks)

• Total Return can be either positive or negative When calculating a cumulative wealth index or a

geometric mean (cumulating or compounding), negative returns are a problem

• A Return Relative solves the problem because it is always positive

RR CF PPt E

B

1 TR RR CF PPt E

B

1 TR

Measuring ReturnsMeasuring Returns

Example: Total return and return Example: Total return and return relativerelative

• Problem 4 pg 181• Calculate the TR and return relative for:• A preferred stock bought for $70 per share, held

one year during which $5 per share dividend are collected, and sold for $63

• A bond with a 12% coupon rate bought for $870, held for two years during which interest is collected, and sold for $930

• To measure the level of wealth created by an investment rather than the change in wealth, returns need to be cumulated over time

• Cumulative Wealth Index, CWIn, over n periods, =

)1)...(2

1)(1

1(0

CWI n

TRTRTRWIn

)1)...(2

1)(1

1(0

CWI n

TRTRTRWIn

Measuring ReturnsMeasuring Returns

Measuring ReturnsMeasuring Returns

• CWI_n = the cumulative wealth index as of the end of period n

• WI_0 = the beginning index value, typically $1

(The cumulative effect of returns over time are measured given some stated beginning amount, such as $1)

• TR_1…n = the periodic TRs in decimal form

Example: Cumulative wealth index Example: Cumulative wealth index

Year TR%

1999 31.42598

2000 7.52756

2001 -12.60567

2002 -12.32439

2003 26.32534

Calculate the cumulative wealth index for the S&P/TSX Index total returns shown above (assume that the beginning index value is equal to $1)

Example in book pg 163

Measuring ReturnsMeasuring Returns

• The values for the cumulative wealth index can be used to calculate the rate of return for a given period

• TR_n = (CWI_n / CWI_n-1) – 1

• Example

Use the CWI in years 2002 and 2003 to calculate TR for year 2003. (pg 164)

• International returns include any realized exchange rate changes If foreign currency depreciates, returns are

lower in domestic currency terms and vice versa

• Total Return in domestic currency =

1For.Curr. of Val.Begin

For.Curr. of Val.EndRR

1

For.Curr. of Val.BeginFor.Curr. of Val.End

RR

Measuring International ReturnsMeasuring International Returns

Example: Example: International ReturnsInternational Returns

• (Pg 164 & 165) Consider a Canadian investor who invests in US Steel (which trades on NYSE) at $30 US when the value of the US dollar stated in Canadian dollars is $1.37. One year later, US Steel is at $33 US and the stock paid a dividend of $0.20 US. The US dollar is now at $1.4, which means that the Canadian dollar depreciated against it.

• Calculate the TR to the Canadian investor in US dollars

• Calculate the TR to the Canadian investor in Canadian dollars after currency adjustment

• TR, RR, and CWI are useful for a given, single time period

• What about summarizing returns over several time periods (i.e., a series of returns)? Arithmetic mean and geometric mean

• Arithmetic mean, or simply mean, is the sum of each of the values being considered divided by the total number of values

nX

X nX

X

Measures Describing a Return Measures Describing a Return SeriesSeries

Arithmetic MeanArithmetic Mean

• When should the arithmetic mean be used when talking about stock returns?

• Arithmetic mean should be used when describing the average rate of return without considering compounding

• It is the best estimate of the rate of return for a single period, such as a year

Geometric MeanGeometric Mean

• Geometric mean is the compound rate of return over time

• When should the geometric mean be used when talking about stock returns?

• It is a better measure of the change in wealth over more than a single period

• Over multiple periods the geometric mean indicates the compound rate of return or the rate at which the invested dollar grows, taking into account the variability in returns.

• Arithmetic mean does not measure the compound growth rate over time Does not capture the realized change in

wealth over multiple periods Does capture typical return in a single period

• Geometric mean reflects compound, cumulative returns over more than one period

Arithmetic Versus GeometricArithmetic Versus Geometric

• Geometric mean defined as the n-th root of the product of n return relatives minus one, or G =

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

n21

Geometric MeanGeometric Mean

Example: Arithmetic and Geometric Example: Arithmetic and Geometric MeanMean

Year TR%

1987 6.23

1988 10.62

1989 21.20

1990 -14.81• Calculate the arithmetic and geometric mean

Arithmetic and Geometric MeanArithmetic and Geometric Mean• The geometric mean will always be less than the

arithmetic mean (unless the values are identical) because it reflects the variability of the returns

• The spread between the two depends on the dispersion of the distribution

• Difference between Geometric mean and Arithmetic mean depends on the variability of returns (standard deviation), s

sX1G1 222 sX1G1 222

• Returns measures are not adjusted for inflation (since they are nominal returns) Purchasing power of investment may change

over time Consumer Price Index (CPI) is a possible

measure of the rate of inflation (IF)

TR IA

TRCPI

11

1

TR IA

TRCPI

11

1

Inflation-Adjusted (Real) Returns Inflation-Adjusted (Real) Returns

Example: Inflation-Adjusted ReturnsExample: Inflation-Adjusted Returns

• (Pg 169) For the period from April 1, 1995 to March 31, 2004, the total return for small-cap Canadian common stocks for the entire period was 9% and the rate of inflation was 1.9%.

• Calculate the real (inflation-adjusted) total return for small-cap common stocks

• How much is a basket of consumer goods purchased for $1 in April 1995 worth in March 2004?

• Risk is the chance that the actual outcome will be different than the expected outcome (i.e., dispersion or variability of returns)

• Standard Deviation measures the deviation of returns from the arithmetic mean of the observations

s

X Xn 1

2 1/2

s

X Xn 1

2 1/2

Measuring RiskMeasuring Risk

Standard DeviationStandard Deviation

• s = standard deviation• X = each observation in the sample• ¯X = the mean of the observations• n = the number of returns in the sample

s

X X

n 1

2 1/2

s

X X

n 1

2 1/2

Standard DeviationStandard Deviation

• Standard deviation is a measure of the total risk of an asset or portfolio

• It is considered to be a reliable measure of variability because all the information in a sample is used

• It can be combined with the normal distribution to provide useful information about the dispersion or variation in returns.

Standard DeviationStandard Deviation

Example: Standard DeviationExample: Standard Deviation

Year TR%

1999 31.42598

2000 7.52756

2001 -12.60567

2002 -12.32439

2003 26.32534

• Calculate the standard deviation for the years 1999 to 2003. (Problem 16 pg 182)

• Premium is additional return earned or expected for additional risk Calculated for any two asset classes

• Risk premium is the part of the security’s return above the risk-free rate of return

• The risk premiums are measured as the geometric difference between pairs of return series

Risk PremiumsRisk Premiums

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

• Equity Risk Premium, ERP, =

11

1

RF

CSTR

111

RF

CSTR

or, RFTRCS or, RFTRCS

Risk PremiumsRisk Premiums

Risk PremiumsRisk Premiums

• Bond horizon premium is the difference between the return on long term government bonds and the risk-free rate as measured by the returns on T-bills

• Bond Horizon Premium, BHP, =

11

1

TBTR

GBTR

111

TBTR

GBTR

Risk PremiumsRisk Premiums

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

• Bond Default Premium, BDP, =

11

1

GBTR

CBTR

111

GBTR

CBTR

• Since 1938, cumulative wealth indexes show stock returns dominate bond returns Stock standard deviations also exceed bond

standard deviations

• Annual geometric mean return for the time period between 1938 and 2003 for Canadian common stocks is 10.32% with standard deviation of 16.36%

• The smaller differences between the geometric and arithmetic means for bonds (6.07% & 6.46%), T-bills (5.2% & 5.28%), and inflation (3.97% & 4.05%) reflect the much lower levels of variability in these series

The Risk-Return RecordThe Risk-Return Record

Series Geometric

Mean

Arithmetic

Mean

Standard

Deviation

Canadian Common Stocks

10.32% 11.53% 16.36%

US Common

Stocks12.09% 13.5% 17.67%

Long-term Government of Canada Bonds

6.07% 6.46% 9.39%

91-Day Government Canada Bonds

5.20% 5.28% 4.36%

Inflation (CPI) 3.97% 4.05% 3.63%

Annual Total Returns for Major Annual Total Returns for Major Financial Assets (1938-2003)Financial Assets (1938-2003)

The Risk-Return RecordThe Risk-Return Record

• G = the geometric mean of a series of asset returns

• ¯X = the arithmetic mean of a series of asset returns

• s = the standard deviation of the arithmetic series of returns

Thus, if we know the arithmetic mean of a series of asset returns and the standard deviation of the series, we can approximate the geometric mean of this series.

sX1G1 222 sX1G1 222