UNDERSTANDING
RISK AND RETURN
CHAPTER TWO
Practical Investment Management
Robert A,Strong
2 - 2Strong C2 – Understanding Risk and Return
Introduction
? A dollar today is worth more than a dollar
tomorrow.
? A safe dollar is worth more than a risky
dollar.
? People have different degrees of risk
aversion,Some are more willing to take a
chance than others.
? A tradeoff exists between risk and return.
2 - 3Strong C2 – Understanding Risk and Return
Holding
period =
return
Ending Beginning
value value Income
Beginning value
_ +
Holding Period Return
? The simplest measure of return is the
holding period return.
2 - 4Strong C2 – Understanding Risk and Return
Buy 100 shares
at $25 per share
Time
Sell the shares
at $30 per share
Dividend of
$0.10 per share
Example,
Holding period return = = 20.4%$30 - $25 + $0.10
$25
Holding Period Return
2 - 5Strong C2 – Understanding Risk and Return
? Holding period return is independent of the
passage of time.
? When comparing investments,the periods
should all be of the same length.
? When there are stock splits or other
corporate actions,care should be taken to
ensure that the correct value is used for
calculating the holding period return.
Holding Period Return
2 - 6Strong C2 – Understanding Risk and Return
Current yield is annual income
divided by current price.
Example,
For a stock selling for $40 and expected to
pay $1 in dividends over the next year,
current yield = $1 / $40 = 2.5%,
Yield and Appreciation
Dividend yield is used for stocks
whose income comes exclusively
from dividends.
2 - 7Strong C2 – Understanding Risk and Return
Appreciation is the increase in
value of an investment
independent of its yield.
Example,
When a stock bought at $95 rises to $97.50,
it has appreciated by $2.50,or
$2.50 / $95 = 2.6%,
Yield and Appreciation
It excludes accrued interest,as
well as increases in value which
are due to additional deposits.
2 - 8Strong C2 – Understanding Risk and Return
P × ( 1 + r )n = F
where P = present value (i.e,price today)
F = future value
r = interest rate per period
and n = number of periods
The Time Value of Money
? The time value of money is the notion that
a dollar today is worth more than a dollar
tomorrow.
2 - 9Strong C2 – Understanding Risk and Return
? The current price of any financial asset
should be the present value of its expected
future cash flows.
The Time Value of Money
Example,
P × ( 1 + 0.0919 )4 = $1,000
? P = $703.50
What is the most that an investor would pay for
a zero coupon bond which matures in 4 years'
time,and has a redemption value of $1,000?
The interest rate is 9.19%,
2 - 10Strong C2 – Understanding Risk and Return
? Many securities pay more than one cash flow
over their lives,In particular,an annuity is a
series of equal and evenly spaced payments.
? A convenient expression for the present value
of an annuity is:
The Time Value of Money
where C = coupon or periodic payment
? ? ??
?
?
?
?
?
?? n
r1 r
1
r
1 CP
2 - 11Strong C2 – Understanding Risk and Return
The Time Value of Money
Insert Figure 2.1 here.
2 - 12Strong C2 – Understanding Risk and Return
Compounding
? Compounding refers to the earning of
interest on interest that is earned previously.
where r = annual interest rate
n = number of compounding periods per year
and t = investment horizon in years
nt
n
r1PF
?
?
??
?
? ??
2 - 13Strong C2 – Understanding Risk and Return
? The more frequent the compounding,the
greater the interest earned.
Compounding
2 - 14Strong C2 – Understanding Risk and Return
? A truly risky situation must
involve a chance of loss.
Risk vs,Uncertainty
2 - 15Strong C2 – Understanding Risk and Return
Dispersion and the Chance of Loss
? There are 2 aspects to risk - the average
outcome and the scattering of the possible
outcomes about this average.
? A common measure of statistical
dispersion is variance,The standard
deviation is the square root of the variance.
? ??
?
??
n
1i
2
i xx)i(p r o bV a r ia n c e
2 - 16Strong C2 – Understanding Risk and Return
Dispersion and the Chance of Loss
Insert Figure 2-3 here.
2 - 17Strong C2 – Understanding Risk and Return
The Problem with Losses
? Big losses - a large one-period loss can
overwhelm a series of gains
? Small losses - can be a problem too if they
occur too often
? Risk and the time horizon - as the time
horizon increases,the probability of losing
money decreases but the amount of money
that may be lost increases.
2 - 18Strong C2 – Understanding Risk and Return
Small Losses
Insert Figure 2-4 here.
2 - 19Strong C2 – Understanding Risk and Return
Risk Aversion and Rational People
? A safe (certain) dollar is worth more than a
risky dollar.
? A rational person will choose a certain
dollar over a risky dollar.
? Risk averse persons will take risks,when
they expect to be rewarded for taking the
risks.
? People have different degrees of risk
aversion,Some are more willing to take a
chance than others.
2 - 20Strong C2 – Understanding Risk and Return
? While the returns over a long horizon may
be more uncertain,history suggests that
over long periods of time,the likelihood
that the investment will lose money is less.
Risk and Time
2 - 21Strong C2 – Understanding Risk and Return
Partitioning Risk
? Undiversifiable risk is risk that must be
borne by virtue of being in the market,
It is also known as systematic risk or
market risk,and is measured by beta.
? Diversifiable risk is also known as
unsystematic risk.
? Total risk = undiversifiable risk
+ diversifiable risk
2 - 22Strong C2 – Understanding Risk and Return
Partitioning Risk
? Business risk - the variability in a firm's
sales,or its ability to sell its product
? Financial risk - associated with the
financial structure of the firm
? Purchasing power risk - the possibility that
the rate of return on an investment will be
insufficient to offset the rise in the cost of
living
2 - 23Strong C2 – Understanding Risk and Return
Partitioning Risk
? Interest rate risk - the chance of a loss in
portfolio value due to an adverse change in
interest rate
? Foreign exchange risk - the possibility of
loss due to adverse changes in the relative
values of world currencies
2 - 24Strong C2 – Understanding Risk and Return
Partitioning Risk
? Political risk - the possibility that a
government will interfere with a firm's
preferred manner of conducting business
? Social risk - the potentially adverse impact
changing public attitudes can have on a
firm's ability to sell its product
2 - 25Strong C2 – Understanding Risk and Return
The Direct Relationship between Risk and Return
Insert Figure 2-7 here.
2 - 26Strong C2 – Understanding Risk and Return
? Empirical financial research reveals clear
evidence of the direct relationship between
systematic risk and expected return,i.e,
riskier securities earn higher returns on
average.
The Direct Relationship between Risk and Return
2 - 27Strong C2 – Understanding Risk and Return
The Direct Relationship between Risk and Return
Insert Figure 2-8 here.
2 - 28Strong C2 – Understanding Risk and Return
Risk,Return,and Dominance
? An investment alternative shows
dominance over another if it offers the
same expected return for less risk,or if the
security has a higher expected return than
another security of comparable risk.
? Equivalent assets should sell for the same
price,This is known as the law of one
price.
RISK AND RETURN
CHAPTER TWO
Practical Investment Management
Robert A,Strong
2 - 2Strong C2 – Understanding Risk and Return
Introduction
? A dollar today is worth more than a dollar
tomorrow.
? A safe dollar is worth more than a risky
dollar.
? People have different degrees of risk
aversion,Some are more willing to take a
chance than others.
? A tradeoff exists between risk and return.
2 - 3Strong C2 – Understanding Risk and Return
Holding
period =
return
Ending Beginning
value value Income
Beginning value
_ +
Holding Period Return
? The simplest measure of return is the
holding period return.
2 - 4Strong C2 – Understanding Risk and Return
Buy 100 shares
at $25 per share
Time
Sell the shares
at $30 per share
Dividend of
$0.10 per share
Example,
Holding period return = = 20.4%$30 - $25 + $0.10
$25
Holding Period Return
2 - 5Strong C2 – Understanding Risk and Return
? Holding period return is independent of the
passage of time.
? When comparing investments,the periods
should all be of the same length.
? When there are stock splits or other
corporate actions,care should be taken to
ensure that the correct value is used for
calculating the holding period return.
Holding Period Return
2 - 6Strong C2 – Understanding Risk and Return
Current yield is annual income
divided by current price.
Example,
For a stock selling for $40 and expected to
pay $1 in dividends over the next year,
current yield = $1 / $40 = 2.5%,
Yield and Appreciation
Dividend yield is used for stocks
whose income comes exclusively
from dividends.
2 - 7Strong C2 – Understanding Risk and Return
Appreciation is the increase in
value of an investment
independent of its yield.
Example,
When a stock bought at $95 rises to $97.50,
it has appreciated by $2.50,or
$2.50 / $95 = 2.6%,
Yield and Appreciation
It excludes accrued interest,as
well as increases in value which
are due to additional deposits.
2 - 8Strong C2 – Understanding Risk and Return
P × ( 1 + r )n = F
where P = present value (i.e,price today)
F = future value
r = interest rate per period
and n = number of periods
The Time Value of Money
? The time value of money is the notion that
a dollar today is worth more than a dollar
tomorrow.
2 - 9Strong C2 – Understanding Risk and Return
? The current price of any financial asset
should be the present value of its expected
future cash flows.
The Time Value of Money
Example,
P × ( 1 + 0.0919 )4 = $1,000
? P = $703.50
What is the most that an investor would pay for
a zero coupon bond which matures in 4 years'
time,and has a redemption value of $1,000?
The interest rate is 9.19%,
2 - 10Strong C2 – Understanding Risk and Return
? Many securities pay more than one cash flow
over their lives,In particular,an annuity is a
series of equal and evenly spaced payments.
? A convenient expression for the present value
of an annuity is:
The Time Value of Money
where C = coupon or periodic payment
? ? ??
?
?
?
?
?
?? n
r1 r
1
r
1 CP
2 - 11Strong C2 – Understanding Risk and Return
The Time Value of Money
Insert Figure 2.1 here.
2 - 12Strong C2 – Understanding Risk and Return
Compounding
? Compounding refers to the earning of
interest on interest that is earned previously.
where r = annual interest rate
n = number of compounding periods per year
and t = investment horizon in years
nt
n
r1PF
?
?
??
?
? ??
2 - 13Strong C2 – Understanding Risk and Return
? The more frequent the compounding,the
greater the interest earned.
Compounding
2 - 14Strong C2 – Understanding Risk and Return
? A truly risky situation must
involve a chance of loss.
Risk vs,Uncertainty
2 - 15Strong C2 – Understanding Risk and Return
Dispersion and the Chance of Loss
? There are 2 aspects to risk - the average
outcome and the scattering of the possible
outcomes about this average.
? A common measure of statistical
dispersion is variance,The standard
deviation is the square root of the variance.
? ??
?
??
n
1i
2
i xx)i(p r o bV a r ia n c e
2 - 16Strong C2 – Understanding Risk and Return
Dispersion and the Chance of Loss
Insert Figure 2-3 here.
2 - 17Strong C2 – Understanding Risk and Return
The Problem with Losses
? Big losses - a large one-period loss can
overwhelm a series of gains
? Small losses - can be a problem too if they
occur too often
? Risk and the time horizon - as the time
horizon increases,the probability of losing
money decreases but the amount of money
that may be lost increases.
2 - 18Strong C2 – Understanding Risk and Return
Small Losses
Insert Figure 2-4 here.
2 - 19Strong C2 – Understanding Risk and Return
Risk Aversion and Rational People
? A safe (certain) dollar is worth more than a
risky dollar.
? A rational person will choose a certain
dollar over a risky dollar.
? Risk averse persons will take risks,when
they expect to be rewarded for taking the
risks.
? People have different degrees of risk
aversion,Some are more willing to take a
chance than others.
2 - 20Strong C2 – Understanding Risk and Return
? While the returns over a long horizon may
be more uncertain,history suggests that
over long periods of time,the likelihood
that the investment will lose money is less.
Risk and Time
2 - 21Strong C2 – Understanding Risk and Return
Partitioning Risk
? Undiversifiable risk is risk that must be
borne by virtue of being in the market,
It is also known as systematic risk or
market risk,and is measured by beta.
? Diversifiable risk is also known as
unsystematic risk.
? Total risk = undiversifiable risk
+ diversifiable risk
2 - 22Strong C2 – Understanding Risk and Return
Partitioning Risk
? Business risk - the variability in a firm's
sales,or its ability to sell its product
? Financial risk - associated with the
financial structure of the firm
? Purchasing power risk - the possibility that
the rate of return on an investment will be
insufficient to offset the rise in the cost of
living
2 - 23Strong C2 – Understanding Risk and Return
Partitioning Risk
? Interest rate risk - the chance of a loss in
portfolio value due to an adverse change in
interest rate
? Foreign exchange risk - the possibility of
loss due to adverse changes in the relative
values of world currencies
2 - 24Strong C2 – Understanding Risk and Return
Partitioning Risk
? Political risk - the possibility that a
government will interfere with a firm's
preferred manner of conducting business
? Social risk - the potentially adverse impact
changing public attitudes can have on a
firm's ability to sell its product
2 - 25Strong C2 – Understanding Risk and Return
The Direct Relationship between Risk and Return
Insert Figure 2-7 here.
2 - 26Strong C2 – Understanding Risk and Return
? Empirical financial research reveals clear
evidence of the direct relationship between
systematic risk and expected return,i.e,
riskier securities earn higher returns on
average.
The Direct Relationship between Risk and Return
2 - 27Strong C2 – Understanding Risk and Return
The Direct Relationship between Risk and Return
Insert Figure 2-8 here.
2 - 28Strong C2 – Understanding Risk and Return
Risk,Return,and Dominance
? An investment alternative shows
dominance over another if it offers the
same expected return for less risk,or if the
security has a higher expected return than
another security of comparable risk.
? Equivalent assets should sell for the same
price,This is known as the law of one
price.
