Chapter 10: Capital Markets and the Pricing of Risk-1
Chapter 10: Capital Markets and the Pricing of Risk
I. Estimating Risk and Return
Basic approaches:
1) peer into the future
2) look at the past and assume future will be like the past.
A. Estimates based on forecasts (Review)
Key: need probability distributions for investments
=> probability (pR) of each possible return (R)
1. Expected return: ER  R p R  R
(10.1)
=> return around which possible returns scattered
2. Variance and Standard deviation:
VarR   R p R  R  ER 2
(10.2)
SDR   VarR 
(10.3)
=> measure of how widely scattered are the possible returns
=> the higher the number, the more widely scattered the possible returns
Ex. Given the following possible returns on General Electric (GE) stock, what is the
expected return and standard deviation of returns on GE stock?
Prob
.25
.40
.35
Return
-26%
11%
44%
E[R] =
Var(R) =
SD(R) =
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Chapter 10: Capital Markets and the Pricing of Risk-2
Ex. Assume that the expected return on General Mills (GIS) is 5% and that the standard
deviation of returns on GIS is 10%.
=> General Mills has a lower expected return but less volatility than GE.
Note: if returns were normally distributed, then can compare distributions of GE and
GIS.
B. Estimates based on historical returns
Key assumption: future will be like the past
1. Realized return: Rt 1 
Div t 1 Pt 1  Pt

Pt
Pt
(10.4)
Notes:
1)
2)
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Chapter 10: Capital Markets and the Pricing of Risk-3
Ex. Assume the following prices and dividends for General Electric (GE) stock
Date Dividend
12/31 $0.00
2/25
$0.10
6/17
$0.10
9/16
$0.12
12/22 $0.14
12/31 $0.00
Price
$15.13
$15.92
$15.91
$16.23
$18.06
$18.29
What is return between 9/16 and 12/22?
R12/22 =
2. Realized return over longer periods
Key: usually think in terms of annual returns
a.
=> 1+RL = (1+RS1) (1+RS2) (1+RS3)….
(10.5b)
Note:
Ex. Returns per period (previous GE example):
Date
12/31
2/25
6/17
9/16
12/22
12/31
Dividend
$0.00
$0.10
$0.10
$0.12
$0.14
$0.00
Price
$15.13
$15.92
$15.91
$16.23
$18.06
$18.29
Return
n.a.
5.88%
0.57%
2.77%
12.14%
1.27%
1+Ryear =
=> Ryear =
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Chapter 10: Capital Markets and the Pricing of Risk-4
b.
Notes:
1) this is not in the book and not in homework from the book, but there are
some problems on old exams
2)
3)
4)
Ex.
Date Dividend
12/31
$0.00
2/25
$0.10
6/17
$0.10
9/16
$0.12
12/22
$0.14
12/31
$0.00
Price
$15.13
$15.92
$15.91
$16.23
$18.06
$18.29
Days
0
56
168
259
356
365
=> r =
3. Average Annual Returns: R 
1 T
 Rt
T t 1
(10.6)
where: T = number of historical returns
=> return around which past returns are scattered
4. Variance and Volatility of Returns
Var R  
1 T
Rt  R 2

T  1 t 1
(10.7)
Note: dividing by T-1 rather than T gives unbiased estimator
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Chapter 10: Capital Markets and the Pricing of Risk-5
Volatility = SDR   VarR 
=> gives spread of possible returns
=> the higher the volatility, the more spread out the returns
Ex. Assume that the returns on General Electric (GE) over the last 6 years were as
follows: 24%, -2%, -54%, 3%, 9%, -1%. How did the returns on GE compare to
those of General Mills (GIS) which had an average return of 9% and a standard
deviation of returns of 9%?
RGE 
Var RGE  
SD(RGE) =
5. Standard Deviation of Averages (Standard Error)
Standard Deviation of Averages (Standard Error): SE 
SD
(10.8)
N
Where:
SD = standard deviation of the observations (individual returns)
N = number of observations (size of sample)
Ex. SE (Average return on GE) =
Notes:
1)
2) the standard deviation of an average return is called the standard errror
3)
4) the bigger our sample, the more confident we are in the average we calculated
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Chapter 10: Capital Markets and the Pricing of Risk-6
II. Information, risk, and return (Review)
1) Firm-specific news: good or bad news about company itself
Risk from firm-specific news called: firm-specific, idiosyncratic, unsystematic, unique,
diversifiable risk
2) Market-wide news: about economy and thus impacts all stocks
Risk from market-wide news called: systematic, undiversifiable, market risk
Notes:
1) individual stocks contain firm-specific risk that averages out in large portfolios
2) investors will only earn a premium for systematic risk
=> no premium for firm-specific risk since diversifies away in a portfolio
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