CERTIFIED FINANCIAL PLANNER CERTIFICATION
PROFESSIONAL EDUCATION PROGRAM
Investment Planning
Session 9
Risk/Return Measurements –
Sharpe, Treynor, Jensen
(alpha), and Beta Reliability
©2015, College for Financial Planning, all rights reserved.
Session Details
Module
4
Chapter(s) 3
LOs
4-6
Explain the characteristics, uses, and
limitations of stock performance measurement
indexes.
4-7
Calculate one or more stock performance
measurement indexes for given portfolio
returns and risk.
4-8
Specify relationships among various indicators
of security returns.
9-2
Investment Risk/Return Relationships
RS
Rp
Rm
Average
Returns
Returns
Coefficient of
Variation
Rp
W
Covariance
Standard
Deviation of
Portfolio
Standard
Deviation
Beta
W
Portfolio Beta
Do
g
Rp
Sharpe Index
Correlation
Coefficient (R)
Coefficient of
Determination
(R2)
Rf
Rf
Rm
Dividend
Growth
Module
Rf
Treynor Index
CAPM
(Required
Return)
Jensen Index
(Alpha)
Rp
9-3
Required Return (r)
r  rf  (rm  rf )β
9-4
Performance Measurement
• Alpha (Jensen Index)
• Treynor Index
• Sharpe Index
9-5
Alpha (Jensen)
• Alpha is widely used to measure the value
added by an active portfolio manager.
• Since beta is used in the formula, make sure
beta is reliable (R-squared of 70 or higher).
9-6
Composite Performance Measures
The Jensen Index (Alpha)
• The alpha measures whether the actual return
exceeds the return that should have been
earned based on the CAPM.
a  rp  
r

r

r

f
m
f

 β 
• Alpha is an absolute measure of return.
9-7
Alpha (Jensen)
ABC Fund has a return of 15% and a
beta of 0.90. The risk-free rate is 5%,
and the return of the market is 16%.
Has ABC provided the level of return
required for the amount of risk taken?
a  rp  rf  rm  rf β
15 - [5 + (16 – 5).90]
15 - [5 + 9.90]
15 - [14.90] = +0.10
9-8
Treynor Index
• Treynor is a relative measure
•
(use for comparison).
o the higher the better
Beta needs to be reliable.
9-9
The Composite Performance Measures
The Treynor Index
Treynor standardizes the return in excess of the
risk-free return by the portfolio’s beta.
Ti 
rp  rf
β
9-10
Treynor Calculation
You have to choose between the following two
funds; the current risk-free rate is 5%.
• Fund A: 18% return, beta of 1.3
• Fund B: 14% return, beta of 0.85
Fund A
18 – 5 = 10
1.3
Fund B
14 – 5 = 10.59
0.85
9-11
Composite Performance Measures
Sharpe
Sharpe standardizes the return in excess of the
risk-free rate by the portfolio’s standard deviation.
Sp 
rp  rf
σp
9-12
Sharpe Index
• Can be used when beta is not reliable
• Calculation is similar to Treynor—Sharpe uses
standard deviation in the denominator,
Treynor uses beta
• Relative measure used for comparison,
the higher the better
9-13
Practice Question
You are choosing among the following funds.
Which fund should you purchase?
Apple
Lemon
Apricot
Return
13%
11%
14%
Alpha
+1.2
+0.6
-0.8%
Treynor
.89
.56
.67
Beta
0.9
1.1
1.2
Sharpe
.35
.44
.23
R-squared
45
58
32
a. Apple Fund
b. Lemon Fund
c. Apricot Fund
9-14
Fund Discussion
Name
Rsquared
(R2)
Benchmark
Beta
Alpha
Vanguard 500 Index
100
S&P 500
1.00
-0.12
Davis NY
87
S&P 500
0.84
2.19
Venture A
89
Russell 1000 Value
0.82
0.84
RiverSource
93
S&P 500
0.98
-0.16
Large Value A
96
Russell 1000 Value
0.95
-1.78
First Eagle
45
MSCI EAFE
1.71
-11.45
Gold A
95
AMEX Gold Miners
0.79
3.89
Fidelity Real
39
S&P 500
1.30
2.80
Estate
98
Wilshire REIT
0.94
-.51
Source: Morningstar Principia Pro, Sept 2007
9-15
Information Ratio
New on the Board exam:
• Extension of the Sharpe ratio: The numerator is
the return of the portfolio minus the return of
the benchmark (instead of risk-free rate).
• The denominator is the standard deviation of
the difference between the returns on the
portfolio and the returns on the benchmark.
This is also a relative measure.
RP  RB
IR 
σ ER
9-16
Question 1
Which of the following are correct interpretations of the
meaning of each of the portfolio performance
measurements?
I. The higher the Treynor index is, the better the relative
portfolio performance.
II. Jensen measures absolute return relative to the amount
of risk taken, as measured by standard deviation.
III. Jensen is an absolute, not relative, measure of return.
IV. If a portfolio is not well diversified, the Sharpe index is
more representative of the risk-adjusted performance.
a. I and II only
b. I and III only
c. III and IV only
d. I, III, and IV only
e. II, III, and IV only
9-17
Question 2
You have been given the following information on the following two funds and the
market. The risk-free rate is 4%.
Fund A
Fund B
Market
16%
11%
12%
Beta
1.1
.8
1.0
Standard Deviation
20
12
15
R-squared with market
.87
.81
Realized Return
Which of the following statements are correct?
I.
II.
III.
IV.
Fund B outperformed the market as measured by the Sharpe ratio.
Fund A has a better Treynor ratio than Fund B.
Fund B has a better return than the market with 87% of the risk.
Fund A has an alpha of +3.20.
a. I only
b. I and II only
c.
II and III only
d. II and IV only
e. I, II, and IV only
9-18
Question 3
Your client has narrowed her choices down to three
different mutual funds, and you have compiled the
following data on the funds shown.
Beta
R-squared
Treynor
Sharpe
GG
.8
44
3.36
5.52
RR
.5
19
2.22
7.66
ZZ
.6
35
1.95
4.34
Which fund should you select?
a. Fund GG
b. Fund RR
c. Fund ZZ
9-19
Question 4
Jake is considering two mutual funds for purchase.
The Circus Fund has a beta of 1.2 and 3-year return
of 8.5%. The Hindsight Fund has a beta of 0.9, and
3-year return of 8%. The current market risk
premium is 5%, and the risk-free rate is 3%.
Which fund should Jake purchase, and why?
a. the Circus Fund, because it has a higher alpha
b. the Hindsight Fund, because it has a higher alpha
c. either fund, since each has the same alpha
d. neither fund, since both have negative alphas
9-20
Question 5
The return of a market index has been 11% with a
standard deviation of 18. A managed fund, Fund
America, has a return of 14% with a standard deviation
of 25. If the risk-free rate is 2%, which of the following
actions would you take?
a. Purchase Fund America since its Sharpe ratio is
higher.
b. Purchase Fund America since it has a higher return.
c. Purchase the market index because its risk is lower.
d. Purchase the market index because its risk/return
relationship is better.
9-21
CERTIFIED FINANCIAL PLANNER CERTIFICATION
PROFESSIONAL EDUCATION PROGRAM
Investment Planning
Session 9
End of Slides
©2015, College for Financial Planning, all rights reserved.