(GAR)
GAR essentially converts HPR to an equivalent effective per period rate
I.e. the
compound annual return
FIN2200 Fall 2014 – Lecture 5
5
𝑅𝑅
𝑡𝑡
=
𝐷𝐷
𝑡𝑡
+
𝑃𝑃
𝑡𝑡
− 𝑃𝑃
𝑡𝑡−1
𝑃𝑃
𝑡𝑡−1
=
𝐷𝐷
𝑡𝑡
𝑃𝑃
𝑡𝑡−1
+
𝑃𝑃
𝑡𝑡
− 𝑃𝑃
𝑡𝑡−1
𝑃𝑃
𝑡𝑡−1
1 +
𝐻𝐻𝑃𝑃𝑅𝑅
1
,
𝑇𝑇
=
1 +
𝑅𝑅
1
1 +
𝑅𝑅
2
… (1 +
𝑅𝑅
𝑇𝑇
)
1 +
𝐺𝐺𝐺𝐺𝑅𝑅
1
,
𝑇𝑇
= (1 +
𝐻𝐻𝑃𝑃𝑅𝑅
1
,
𝑇𝑇
)
1
𝑇𝑇
�
=
1 +
𝑅𝑅
1
1 +
𝑅𝑅
2
… (1 +
𝑅𝑅
𝑇𝑇
)
1
𝑇𝑇
�

Returns Example: Self Study Example 1: Calculate total realized returns given the following information a)P0=$50, Div1=$2, P1=$55.50
b)P0=$20, Div1=$0.25, P1=$12.75
c)P0= $30, Div1=$1, Capital Gain=$5 (
d)P0= $130, Div1=$0, Capital Loss=$128
Example 2: Find the holding period return and geometric average rate of return for stocks A and B given the following annual returns a)Yr.1, 12%; Yr.2, 20%; Yr.3, -15%; Yr.4, 6%; Yr.5, -10%
b)Yr.1, 100%; Yr.2, 300%, Yr.3, 0%; Yr.4, -50%; Yr.5, -75%
FIN2200 Fall 2014 – Lecture 5
6

Historical Returns and Standard Deviation
Mean (average) return
is the
arithmetic average rate of return
in periods
1
to
T
and is calculated as follows :
Where
R
t
is the realized return of a security in year
t
Sample variance
is a measure of the
squared deviations from the mean
in
periods
1
to
T
and is calculated as follows:
Sample standard deviation
in periods
1
to
T
is just the square root of the
sample variance:
FIN2200 Fall 2014 – Lecture 5
7
(
)
1
2
1
1
1
=
=
+
+
+
=
∑
T
T
t
t
R
R
R
R
R
T
T
Var[
R
]
=
𝑆𝑆𝐷𝐷
[
𝑅𝑅
] =
Var[
R
]

Historical Returns and Standard Deviation: Self Study Example: Consider the returns for the following stocks: Stock A: Yr.1, 12%; Yr.2, 20%; Yr.3, -15%; Yr.4, 6%; Yr.5, -10% Stock B: Yr.1, 100%; Yr.2, 300%, Yr.3, 0%; Yr.4, -50%; Yr.5, -75% a)Find the mean returnsfor stocks A and B b)Find the sample variance and standard deviation for stocks A and B using the information above: Answers:
FIN2200 Fall 2014 – Lecture 5
8

Outline – Risk, Return, and Portfolio Theory
0.
Introduction
1.
Measures of Risk and Return
A.
Historical Returns and Standard Deviation
B.
Returns and Standard Deviation with Risk
C.
Correlation and Covariance with Risk
2.
Portfolio Risk and Return
A.
Portfolio Measures of Risk and Return
i.
Portfolio Weights
ii.
Expected Portfolio Returns
iii.
Portfolio Variance and Standard Deviation
B.
Portfolio Diversification
i.
Diversifiable Versus Non-Diversifiable Risk
3.
Choosing Efficient Portfolios (Portfolio Theory)
A.
Portfolios of Risky Securities
i.
Mean-Variance Analysis
ii.
The Markowitz Efficient Frontier
B.
Risky Securities Plus a Risk-Free Asset
i.
The Tangent Portfolio
ii.
(Another) Separation Theorem
iii.
The Capital Market Line (CML)
FIN2200 Fall 2014 – Lecture 5
9