FINA3361 WIN2022
CHAPTER 12
RISK AND RETURN
CHAPTER 12:
Why do some assets offer a higher return compared to others? Common sense tells us that the assets that
offer a higher return must have a higher risk. This logic appeals to our common sense in that we know we
cannot get something for nothing.
É There is a trade-off between risk and return. Assuming investors are risk adverse, they must be induced to
oÉ¥É ÉÉ
hold risky assets by offering a higher expected return.
In this chapter you will learn how to measure risk and return for an individual assets and portfolios. Once
we have done that, we will establish a relationship between risk and return. This will allow us to determine
the kind of the return a rational investor should demand to invest in a risky security.
☒É ,
Always
$ returns and % returns: • risk averse
higher return
-
Income component—direct cash payments such as dividends or interest Take risk with
-
Price change—loosely, capital gain or loss
to measure return
on
① How
Total dollar return = dividend income + capital gain (or loss)
☒ É -
individual assets
portfolio of assets
The return calculation is unaffected by the decision to cash out or hold securities. -
BE
% Return refers to the rate of return per dollar invested. risk on
② How to measure
zÉ É Percentage Return = Dividend Yield + Capital Gains Yield - individual assets
assets
t v
portfolio of
Dividend Yield = Dt+1 /Pt Capital Gains Yield = (Pt+1 – Pt)/Pt
-
/i
③ Establish relationship
¥
-
always toro -
caribe -
toro
to predict .
Measuring return ⑨ Use relationship
Example 1:
Assume we have the following observations on stock A. Calculate the % return you earned each month on
your investment. Remember a return is nothing more than what you make in the numerator divided by
what you put in (or what you invested). So, in the example below your numerator will consist of capital
gains (or loss) plus the dividend whenever applicable. The denominator will be the starting price.
Date Value Dividend
31-Dec 20
31-Jan 21
28-Feb 20
31-Mar 22 1.2
30-Apr 23
31-May 21
30-Jun 24 1.2
Calculating arithmetic and geometric means:
You can calculate arithmetic or a geometric average; the one you choose will depend upon the results you
desire. The arithmetic average return tells us the return we obtained in an average/typical year over a given
period. The geometric average return tells us the average compound return per year over a given period.
Unless otherwise stated the calculated return is always an arithmetic average.
Example 2:
Estimate the arithmetic and geometric averages for the following: 4.3%, 3.2%, 5.6%, 10.5%, and -7.6%.
MISHRA 1
, Example 1
Del Jan feb Mar Apr Allay June
A 1 1 I 1 I 1
$20 21 20 22 23 21 24
$1.20 $1.20
th Po
01-123-221
☐ 'an
Kelvin in Jan Pekin in Apr
-
:
: =
to
22
=
0+21-20 = 4.55%
20
5% Kelvin in May :
Ot 121-237
23
Rennin Feb : 01-20-21 = -8.7%
21
= -4.76^1 . Kelvin in June =
I -20 t (24-21)
21
Return in Mar : 1.201-(22-20) = 20^1 .
20
= 16-1 .
I =
5%1--4 -76%+16%1-4.551
.
.
t -
8.7% 1- 20%
6
=
5.348%
Arithmetic average : In a typical month , average is 5.348% .
Geometric average : 4.85% fu :pvl1tHt
^
↳ looks at beg and end
.
GM
, * If not specified do arithmetic Avg .
Makeup
,
Question
i. : i
200 100 200
Return for 41 : 100 -
200 Return for 41 : 200 -
100
200 100
= -50% =
100 %
Arithmetic Avg : = -50%1-100 %
2
=
25%1 ,
when to use arithmetic Avg : To predict what the renin might be
in the tune
'
'
Typical year return
Geometric Average
i. : i
200 100 200
•
Investment horizon doesn't matter
•
What annual renin snald I room for the $200 to become $200
t
fV= PV ( Itr )
200=200 ( Itf)
2 <
Use this if we knew FV and PV
'
I = ( Itr )
I = 11th
r = 0 %
,,
•
All you need : Beg .
and End .
amounts .
•
Avg .
renin earned each year
GM : 11th ) ( Ith ) -
I
=
,
111--0.5 ) ( 1H ) - I
-
-
fl -
I
=
0%
, Exampled :
① Arithmetic Avg : 4.3%1-3.2%+5.61 . t 10.5%1--7.61
5
= 3.2% • sthroot because 5
years
② Geometric mean :
5,111-4.3%1111-3 -2%11111-5.6%1 11+10.5%111 -7.6%)
-
I
=
3.02258%
Arithmetic mean Geometric mean ALWAYS
CHAPTER 12
RISK AND RETURN
CHAPTER 12:
Why do some assets offer a higher return compared to others? Common sense tells us that the assets that
offer a higher return must have a higher risk. This logic appeals to our common sense in that we know we
cannot get something for nothing.
É There is a trade-off between risk and return. Assuming investors are risk adverse, they must be induced to
oÉ¥É ÉÉ
hold risky assets by offering a higher expected return.
In this chapter you will learn how to measure risk and return for an individual assets and portfolios. Once
we have done that, we will establish a relationship between risk and return. This will allow us to determine
the kind of the return a rational investor should demand to invest in a risky security.
☒É ,
Always
$ returns and % returns: • risk averse
higher return
-
Income component—direct cash payments such as dividends or interest Take risk with
-
Price change—loosely, capital gain or loss
to measure return
on
① How
Total dollar return = dividend income + capital gain (or loss)
☒ É -
individual assets
portfolio of assets
The return calculation is unaffected by the decision to cash out or hold securities. -
BE
% Return refers to the rate of return per dollar invested. risk on
② How to measure
zÉ É Percentage Return = Dividend Yield + Capital Gains Yield - individual assets
assets
t v
portfolio of
Dividend Yield = Dt+1 /Pt Capital Gains Yield = (Pt+1 – Pt)/Pt
-
/i
③ Establish relationship
¥
-
always toro -
caribe -
toro
to predict .
Measuring return ⑨ Use relationship
Example 1:
Assume we have the following observations on stock A. Calculate the % return you earned each month on
your investment. Remember a return is nothing more than what you make in the numerator divided by
what you put in (or what you invested). So, in the example below your numerator will consist of capital
gains (or loss) plus the dividend whenever applicable. The denominator will be the starting price.
Date Value Dividend
31-Dec 20
31-Jan 21
28-Feb 20
31-Mar 22 1.2
30-Apr 23
31-May 21
30-Jun 24 1.2
Calculating arithmetic and geometric means:
You can calculate arithmetic or a geometric average; the one you choose will depend upon the results you
desire. The arithmetic average return tells us the return we obtained in an average/typical year over a given
period. The geometric average return tells us the average compound return per year over a given period.
Unless otherwise stated the calculated return is always an arithmetic average.
Example 2:
Estimate the arithmetic and geometric averages for the following: 4.3%, 3.2%, 5.6%, 10.5%, and -7.6%.
MISHRA 1
, Example 1
Del Jan feb Mar Apr Allay June
A 1 1 I 1 I 1
$20 21 20 22 23 21 24
$1.20 $1.20
th Po
01-123-221
☐ 'an
Kelvin in Jan Pekin in Apr
-
:
: =
to
22
=
0+21-20 = 4.55%
20
5% Kelvin in May :
Ot 121-237
23
Rennin Feb : 01-20-21 = -8.7%
21
= -4.76^1 . Kelvin in June =
I -20 t (24-21)
21
Return in Mar : 1.201-(22-20) = 20^1 .
20
= 16-1 .
I =
5%1--4 -76%+16%1-4.551
.
.
t -
8.7% 1- 20%
6
=
5.348%
Arithmetic average : In a typical month , average is 5.348% .
Geometric average : 4.85% fu :pvl1tHt
^
↳ looks at beg and end
.
GM
, * If not specified do arithmetic Avg .
Makeup
,
Question
i. : i
200 100 200
Return for 41 : 100 -
200 Return for 41 : 200 -
100
200 100
= -50% =
100 %
Arithmetic Avg : = -50%1-100 %
2
=
25%1 ,
when to use arithmetic Avg : To predict what the renin might be
in the tune
'
'
Typical year return
Geometric Average
i. : i
200 100 200
•
Investment horizon doesn't matter
•
What annual renin snald I room for the $200 to become $200
t
fV= PV ( Itr )
200=200 ( Itf)
2 <
Use this if we knew FV and PV
'
I = ( Itr )
I = 11th
r = 0 %
,,
•
All you need : Beg .
and End .
amounts .
•
Avg .
renin earned each year
GM : 11th ) ( Ith ) -
I
=
,
111--0.5 ) ( 1H ) - I
-
-
fl -
I
=
0%
, Exampled :
① Arithmetic Avg : 4.3%1-3.2%+5.61 . t 10.5%1--7.61
5
= 3.2% • sthroot because 5
years
② Geometric mean :
5,111-4.3%1111-3 -2%11111-5.6%1 11+10.5%111 -7.6%)
-
I
=
3.02258%
Arithmetic mean Geometric mean ALWAYS
