Portfolio Performance Analysis and Risk Assessment

This assignment focuses on evaluating the performance and risk of an investment portfolio. It requires calculating various financial metrics such as portfolio return, beta, Sharpe ratio, and Treynor ratio. The analysis also delves into risk assessment by examining components like RP risk (Risk Premium), investor risk, manager risk, selectivity risk, and diversification risk. The assignment culminates in presenting a comprehensive assessment of the portfolio's overall performance and its associated risks.

Portfolio Management
1

TABLE OF CONTENTS
INTRODUCTION...........................................................................................................................3
1. Calculating beta, systematic and unsystematic risk, sharpe and trenyor ratio of 10 stocks
pertaining to S&P 500 in spreadsheet \........................................................................................3
2. Selecting four companies by using Treynor Black methodology............................................4
3.Calculating expected monthly risk, return, Beta, Sharpe and Treynor ratios of optimized
portfolio.......................................................................................................................................4
4. Carry out a Fama decomposition of returns............................................................................5
5. Preparing report for providing information to the client.........................................................7
CONCLUSION................................................................................................................................9
REFERENCES..............................................................................................................................10
1.................................................................................................................................................11
2.................................................................................................................................................12
3.................................................................................................................................................15
4.................................................................................................................................................17
2

INTRODUCTION
Portfolio management refers to the selection of right investment tools in appropriate
proportion that helps in generating optimal returns. In the recent times, with the motive to
generate suitable return and balance or mitigate the risk level investors make focus on investing
money in portfolio rather than individual security Thus, effective portfolio management is highly
required to minimize risk and maximize return within the specific time frame. In this context, by
undertaking several tools and techniques investors or portfolio manager can manage securities
more effectually. The present report is based on the scenario of 10 different companies
pertaining to S&P 500. In this, report will provide deeper insight about the specific and
systematic, beta, sharpe as well as treynor ratio of concerned securities. Besides this, it also
entails the manner in which Treynor Black methodology assists is selecting suitable securities for
building optimal portfolio. It also depicts how Fama decomposition assists in calculating risk at
different levels and thereby aid in decision making.
1. Calculating beta, systematic and unsystematic risk, sharpe and trenyor ratio of 10 stocks
pertaining to S&P 500 in spreadsheet \
Monthly outcome
Particul
ars
S&
P
500
ret
ur
n
Goo
dyea
r
Tire
&
Rub
ber
Intern
ational
Busine
ss
Machi
nes
Intern
ational
Paper
McDo
nalds
Corp
Navist
ar
Intern
ational
Me
rck
&
Co 3M
Pro
ctor
&
Ga
mbl
e
Phi
lip
Mo
rris
Prim
erica
Beta 1.0 0.99 0.27 -0.36 -0.16 -0.13
0.6
9
-
0.2
8
-
0.10
-
0.2
6 -0.25
System
atic risk
3.4
2%
3.42
% 0.92% -1.23%
-
0.54% -0.44%
2.3
6%
-
0.9
8%
-
0.34
%
-
0.8
8%
-
0.86
%
Specific
risk
0.4
8%
7.53
% 8.12% 6.39% 6.26% 13.00%
6.2
8%
5.0
0%
5.93
%
7.3
2%
9.05
%
3

2. Selecting four companies by using Treynor Black methodology
Treynor Black methodology is highly undertaken by investors and analysts for an active
portfolio management. Hence, according to Treynor Black methodology, optimal portfolio is
developed by an analyst through doing alpha forecast. In this, considering the alpha value weight
is assigned to the individual securities. Such model entails that when higher the alpha of security
then high weight is given to the same. On the other side, lower weight is assigned to the volatile
securities whose performances are highly influenced from firm specific news.
Weig
ht
6.0
0% 3.50% 7.00% 4.00% 1.00%
2.0
0%
23.5
0%
23.5
0%
18.8
2%
10.68
%
100.
00%
Go
ody
ear
Tire
&
Rub
ber
Internat
ional
Busine
ss
Machin
es
Internat
ional
Paper
McDo
nalds
Corp
Navista
r
Internat
ional
Me
rck
&
Co 3M
Proc
tor
&
Ga
mbl
e
Phil
ip
Mor
ris
Prim
erica
Alpha
0.5
4% 1.15% 1.45% 1.90% 0.69%
1.2
3%
1.42
%
2.07
%
1.93
%
3.41
%
Interpretation: Tabular presentation shows that alpha value of 5 companies, out of 10, is
high such Mc-d, 3M, P&G, PM and Primerica is high in comparison to others. Besides this,
through using solver function weights are assigned or given to the individual securities. Hence,
by taking into consideration the weight or alpha value four securities have selected such as Mc-d,
3M, P&G, PM and Primerica. Such optimal portfolio will prove to be beneficial for firm and
helps in meeting goals.
3.Calculating expected monthly risk, return, Beta, Sharpe and Treynor ratios of optimized
portfolio.
Considering the Treynor Black methodology, optimized portfolio has created through
including 3M, P&G, Phillip Morris and Primerica. The below depicted table shows that risk and
return associated with the portfolio of 4 securities account for .15% & 1.67% respectively. In
addition to this, beta related to such portfolio is -.24 significantly. This aspect clearly exhibits
that volatility risk associated with such securities are relatively lower over others. Thus, it can be
depicted that investor will get suitable return from investment through facing low risk.
4

Portfolio assessment
Portfolio
elements
Return Beta Sharpe ratio Treynor ratio Risk
1.67% - 0.24 0.374 -0.0458 0.15%
Return Beta Sharpe
ratio Treynor
ratio Risk
-30.00%
-20.00%
-10.00%
0.00%
10.00%
20.00%
30.00%
40.00%
Portfolio evaluation
Outcome
4. Carry out a Fama decomposition of returns
Under Fama decomposition, risk is breaking down into two terms such as manager and
investor’s risk. It helps in assessing the portion of excess returns which in turn presented by
portfolio beta and market risk premium. In the case of optimal market portfolio Rp risk accounts
for -0.00298 respectively that is highly lower.
Fama decomposition of returns
RP risk: βp (Rm – RFR)
β -0.24
Rm 1.29%
RFR 0.05%
RP risk
-0.24 (0.0129 – 0.0005) = -
0.00298
5

RP investor risk = βT (Rm – Rf)
βt 1
Rm 1.29%
Rf 0.05%
RP investor risk = 0.0124
RP manager risk = (βi - βT) (Rm – Rf)
βi -0.24
βt 1
Rm 1.29%
Rf 0.05%
RP manager risk -0.0154
 Investor’s risk: From assessment, it has identified that investor’s risk implies for the
premium which will be generated by the investors when portfolio beta is equal to the
targeted one. In the context of for securities portfolio, βp and βi accounts for -.24 & 1
significantly. Thus, in this situation, premium will be attained by the investor at targeted
beta is positive such as 0.0124 respectively.
 Manager’s risk: This measure helps in ascertaining the part of risk premium when
manager takes different level of risk rather than the target beta. Thus, premium of
portfolio will be negative such as -0.0154 if investor takes extra risk other than targeted.
Selectivity
RP selectivity: Rp total – Rp risk
RP total 0.0124
RP risk -0.00411
RP selectivity 0.01538
6

RP diversification (Rm – RFR) [σi / σm - βi]
Rm 1.29%
RFR 0.05%
σi 0.15%
σm .48%
βp -0.22
Rp diversification 0.0068
 Rp selectivity: It highlights the portion of excess return that is not highlighted or
presented through the means of portfolio beta and market risk premium (Fama
decomposition, 2017). Through applying the model of Fama decomposition, it has found
that portion of excess return is positive 0.01538.
 Rp diversification: Such measure presents difference which take place between the return
should have been generated as per CML and SML. In the case of perfectly diversified
portfolio it is equal to zero. The above mentioned table presents zero value of Rp which
in turn indicates that selected portfolio is highly diversified and helps in managing risk
more effectively.
5. Preparing report for providing information to the client
Overview: On the basis of cited case situation, client won £10 million through lottery and
now he is willing to invest such amount in shares or securities with an objective to get higher
returns. However, due to the lack of knowledge pertaining to security market client approached
analyst who have expertise in this field.
To
Mr. Jackson
Date: 29th November 2017
Subject: Investment analysis
7

Introduction: In this, all the potential securities have analyzed for the creation of suitable or
optimal portfolio. In addition to measure the volatility of different securities beta value has
analyzed. Besides this, to select profitable securities for portfolio Treynor Black methodology
has been used. Thus, such report entail portfolio in which client need to invest money.
Main Body:
Evaluation of monthly outcome: By doing analysis of return, it has assessed that companies
which are offering higher returns include Goodyear Tyre and Rubber, IBM, MC-D, Merk & Co,
3M, P&G, PM and Primerica. In addition to this, it has assessed from beta evaluation that low
level of risk is associated with the securities of Mc-D, 3M, P&G, PM and Primerica. Considering
such aspect, it can be stated that by investing money in such securities firm can generate suitable
returns at low risk.
Referring appendix 1, it can be presented that monthly returns of 3M, P&G, Phillip Morris and
Primerica accounts for 1.05%, 1.95%, 1.60% & 3.09% respectively. It shows that all such four
stocks are performing well in the security market. In addition to this, Goodtyre & Rubber, IBM
and Mc D are also offering higher returns to the investors. Along with this, specific risk
associated with the securities of 3M, P&G, Phillip Morris and Primerica is neither too high nor
too lower as compared to other securities of New State fund of Carolina. By analyzing monthly
prices of share and applying slope tool on the same it has assessed that Good Year Tire and
Rubber, Merck & company comes under the category of risky securities. Along with this, as
compared to other business units beta value of International Business Machine is higher.
Outcome of analysis shows that beta values of the concerned companies are negative except
Good Year Tire & Rubber, IBM and Merck & Co. Thus, it can be presented that out of 10, low
or negligible risk is associated with the securities of 7 firms.
Selection of Main four companies
With the motive to generate high return, client is willing to invest money in the securities or four
companies out of several. Moreover, inclusion of large number of companies makes the portfolio
highly messy and complex. In this regard, Treynor Black model is highly significant which in
turn provides assistance in building active portfolio (Bessler, Opfer and Wolff, 2017). Such model
lays high level of emphasis on assessing or determining optimal combination of passively and
actively managed assets in an investment portfolio. At the time of doing allocation of resources,
8

as per trenyor black methodology, investors consider both systematic and unsystematic risk.
Moreover, both kind of risk has major impact or influence on the returns associated with the
securities. Thus, by considering both kinds of risks firm helps in making selection of suitable
securities. In addition to this, such model considers weight and alpha value while choosing some
companies for the creation of optimal portfolio. By using such methodology or model firm can
contribute in the active portfolio management (law Juszczuk and et.al., 2016). According to such
model, less weight is assigned or given to the security that has high or more unsystematic risk.
Theory and model of active portfolio management highly supports to the securities that has low
risk and return over the riskier one.
Thus, referring all such aspects of active portfolio management, four companies such as 3M,
P&G, Phillip Morris and Primerica accounts is suggested to the investor. Such portfolio will
provide investors with suitable returns at minimum risk level (refer appendix 2 & 3). The main
criteria that is considered while making selection of such securities is higher weight. Appendix 2
& 3 clearly shows that higher weights are assigned to 3M, P&G, PM & Primerica such as 23.5%,
23.5%, 18.8% and 10.68% respectively. Besides this, alpha value of all such four securities is
also higher over others. In this way, by using specific criteria’s four companies have chosen for
the creation of suitable portfolio (Guerard Jr, 2016). By investing money in such portfolio
significant value addition can be done in money at low risk level.
Further, considering the outcome of portfolio assessment, it can be stated that beta value is -0.24
respectively which shows that risk level is highly low and negligible. Further, results show that
in against to .15% risks investor will get 1.67% return. This aspect shows that investor will get
optimal return from such concerned portfolio. In addition to this, average return which will be
generated by the investor in excess of the risk free rate accounts for .37 respectively. Thus, by
taking into account the outcome of overall assessment or evaluation it can be depicted that
proposed portfolio will prove to be fruitful for the client from investment perspective. Thus, by
investing the amount, won through lottery, in active market portfolio investor can get suitable or
optimal return.
Fama Decomposition
In addition to this, outcome of Fama decomposition clearly shows that investor will generate
positive return in both cases such targeted beta and varied risk (Cederburg and O'DOHERTY,
2016). Along with this, Rp diversification = 0, which in turn presents that portfolio includes
9

securities that help in balancing the risk level prominently (refer appendix 4). By applying Fama
decomposition model, it has found that client will generate positive return at targeted beta such
as 0.0124 respectively. Further, it has asserted from the evaluation that if client takes extra risk
then return will be negative. Apart from this, outcome of Rp selectivity and diversification are
also favorable (Seddeke and Rahman, 2016). Thus, by undertaking concerned and diversified
portfolio client would become able to attain investment goals.
Conclusion: At the end of report, it can be summarized that by client should go with the optimal
portfolio which in turn helps in diversifying the risk level to a great extent. Further, by summing
up this report, it can be presented that such optimal portfolio will offer positive return to the
investor at different volatility level. Thus, by investing money, won through lottery, such as £10
million pound in optimized portfolio client would become able to get desired level of returns.
Sincerely
Security analyst
CONCLUSION
From the above report, it has been concluded that by making assessment or evaluation of
beta, systematic and unsystematic risk as well as sharpe and treynor ratio manager can take
suitable decision for upcoming time period. Besides this, it can be inferred that 3M, P&G, Phillip
Morris and Primerica are highly suitable which in turn helps in creating optimal portfolio. It can
be seen in the report that alpha and weight of such securities are higher over others. Considering
all such aspects out of 10 such 4 securities have been selected. Along with this, beta of all such
securities is highly lower which in turn shows that risk level is low. Further, it has been
articulated that relative optimized portfolio with 4 securities will offer suitable returns at low
risk. It can be summarized from the evaluation that Fama decomposition helps in assessing in
manager’s and investor’s risk as well as diversification & net selectivity.
10

REFERENCES
Books and Journals
Bessler, W., Opfer, H. and Wolff, D., 2017. Multi-asset portfolio optimization and out-of-sample
performance: an evaluation of Black–Litterman, mean-variance, and naïve diversification
approaches. The European Journal of Finance. 23(1). pp.1-30.
Cederburg, S. and O'DOHERTY, M. S., 2016. Does it pay to bet against beta? on the conditional
performance of the beta anomaly. The Journal of finance. 71(2). pp.737-774.
Guerard Jr, J.B. ed., 2016. Portfolio Construction, Measurement, and Efficiency: Essays in
Honor of Jack Treynor. Springer.
law Juszczuk, P. and et.al., 2016. Market Collective Wisdom Discovery for Portfolio
Investments. International Journal of Information and Management Sciences. 27(2). pp.87-
102.
Seddeke, B. and Rahman, A. M., 2016. Evaluation of Portfolio Performance of the Investment
Corporation of Bangladesh’s Mutual Funds. Global Journal of Management And Business
Research. 16(6).
Online
Trenyor Black model. 2017. [Online]. Available through: <
http://breakingdownfinance.com/finance-topics/modern-portfolio-theory/treynor-black-
model/>.
Fama decomposition. 2017. Online]. Available through: <
http://www.performance-metrics.eu/papers/measure/Fama_1972_Short_Description.pdf>.
11

1.
Monthly outcome
S&
P
50
0
ret
urn
Good
year
Tire
&
Rubb
er
Interna
tional
Busine
ss
Machi
nes
Interna
tional
Paper
McDo
nalds
Corp
Navist
ar
Interna
tional
Mer
ck
&
Co 3M
Pro
ctor
&
Ga
mbl
e
Phil
ip
Mor
ris
Prim
erica
Return
1.2
9%
1.82
% 1.49% 0.99% 1.70% 0.53%
2.11
%
1.05
%
1.95
%
1.60
%
3.09
%
Risk
3.4
5%
8.27
% 8.17% 6.51% 6.29%
13.00
%
6.71
%
5.10
%
5.94
%
7.37
%
9.09
%
Beta 1.0 0.99 0.27 -0.36 -0.16 -0.13 0.69
-
0.28
-
0.10
-
0.26 -0.25
Systema
tic risk
3.4
2%
3.42
% 0.92% -1.23%
-
0.54% -0.44%
2.36
%
-
0.98
%
-
0.34
%
-
0.88
%
-
0.86
%
Specific
risk
0.4
8%
7.53
% 8.12% 6.39% 6.26%
13.00
%
6.28
%
5.00
%
5.93
%
7.32
%
9.05
%
Alpha
0.0
%
0.539
%
1.146
%
1.450
%
1.905
%
0.694
%
1.22
8%
1.42
0%
2.07
2%
1.92
7%
3.41
5%
Annualized outcome
S&
P
500
retu
rn
Good
year
Tire
&
Rubb
er
Interna
tional
Busine
ss
Machi
nes
Interna
tional
Paper
McDo
nalds
Corp
Navist
ar
Interna
tional
Mer
ck
&
Co 3M
Pro
ctor
&
Ga
mbl
e
Phil
ip
Mor
ris
Prim
erica
Return
16.6
4%
24.1
2%
19.45
%
12.53
%
22.46
% 6.56%
28.5
1%
13.4
2%
26.0
2%
20.9
4%
44.1
3%
Risk
11.9
6%
28.6
4%
28.30
%
22.54
%
21.77
%
45.05
%
23.2
5%
17.6
6%
20.5
7%
25.5
3%
31.5
0%
Beta 1.0 0.99 0.27 -0.36 -0.16 -0.13 0.69
-
0.28
-
0.10
-
0.26 -0.25
Systema
tic risk
11.8
4%
11.8
4% 3.20% -4.27%
-
1.87% -1.51%
8.19
%
-
3.38
%
-
1.17
%
-
3.05
%
-
2.99
%
Specific
risk
1.68
%
26.0
8%
28.12
%
22.13
%
21.69
%
45.02
%
21.7
6%
17.3
3%
20.5
4%
25.3
5%
31.3
6%
Alpha 0% 7.65 15.00 18.48 25.06 8.66% 17.1 18.1 27.6 25.1 48.2
12

% % % % 1% 2% 5% 9% 8%
2.
Correl
ation
matrix
S&
P
500
ret
urn
Good
year
Tire
&
Rubb
er
Interna
tional
Busines
s
Machin
es
Interna
tional
Paper
McDo
nalds
Corp
Navista
r
Interna
tional
Me
rck
&
Co
3
M
Pro
ctor
&
Ga
mbl
e
Phil
ip
Mo
rris
Prime
rica
S&P
500
return 1 0.11 -0.15 -0.08 -0.07 0.18
-
0.1
5
-
0.
07
-
0.15
-
0.1
2 -0.09
Goody
ear
Tire &
Rubber
0.1
1 1 0.05 0.31 0.37 0.33
0.2
8
0.
25 0.23
-
0.0
2 0.04
Interna
tional
Busine
ss
Machin
es
-
0.1
5 0.05 1 0.30 0.31 0.14
0.2
9
0.
20 0.20
0.1
0 0.14
Interna
tional
Paper
-
0.0
8 0.31 0.30 1 0.19 0.29
0.3
3
0.
41 0.28
0.0
7 0.02
McDon
alds
Corp
-
0.0
7 0.37 0.31 0.19 1 0.19
0.3
4
0.
20 0.54
0.1
0 -0.02
Navista
r
Interna
tional
0.1
8 0.33 0.14 0.29 0.19 1
0.1
5
0.
07 0.19
0.1
0 0.14
Merck
& Co
-
0.1
5 0.28 0.29 0.33 0.34 0.15 1
0.
30 0.58
0.0
7 0.02
3M
-
0.0
7 0.25 0.20 0.41 0.20 0.07
0.3
0 1 0.36
-
0.0
1 0.06
Proctor
&
Gambl
e
-
0.1
5 0.23 0.20 0.28 0.54 0.19
0.5
8
0.
36 1
-
0.1
3 -0.19
13

Philip
Morris
-
0.1
2 -0.02 0.10 0.07 0.10 0.10
0.0
7
-
0.
01
-
0.13 1 0.32
Covari
ance
S&
P
500
retu
rn
Good
year
Tire
&
Rubb
er
Interna
tional
Busine
ss
Machi
nes
Interna
tional
Paper
McDo
nalds
Corp
Navist
ar
Interna
tional
Me
rck
&
Co 3M
Pro
ctor
&
Ga
mbl
e
Phil
ip
Mor
ris
Prim
erica
S&P
500
return
0.00
12
0.001
2 0.0003
-
0.0004
-
0.000
2
-
0.0002
0.0
008
-
0.00
03
-
0.00
01
-
0.00
03
-
0.000
3
Goody
ear
Tire &
Rubber
0.00
03
0.006
8 0.0004 0.0017
0.001
9 0.0035
0.0
015
0.00
11
0.00
11
-
0.00
01
0.000
3
Interna
tional
Busine
ss
Machi
nes
-
0.00
04
0.000
4 0.0066 0.0016
0.001
6 0.0015
0.0
016
0.00
08
0.00
10
0.00
06
0.001
0
Interna
tional
Paper
-
0.00
02
0.001
7 0.0016 0.0042
0.000
8 0.0024
0.0
014
0.00
13
0.00
11
0.00
03
0.000
1
McDo
nalds
Corp
-
0.00
02
0.001
9 0.0016 0.0008
0.003
9 0.0016
0.0
014
0.00
06
0.00
20
0.00
05
-
0.000
1
Navist
ar
Interna
tional
0.00
08
0.003
5 0.0015 0.0024
0.001
6 0.0167
0.0
013
0.00
05
0.00
14
0.00
10
0.001
6
Merck
& Co
-
0.00
03
0.001
5 0.0016 0.0014
0.001
4 0.0013
0.0
045
0.00
10
0.00
23
0.00
04
0.000
1
3M
-
0.00
01
0.001
1 0.0008 0.0013
0.000
6 0.0005
0.0
010
0.00
26
0.00
11
0.00
00
0.000
3
Proctor
&
Gambl
e
-
0.00
03
0.001
1 0.0010 0.0011
0.002
0 0.0014
0.0
023
0.00
11
0.00
35
-
0.00
06
-
0.001
0
Philip
Morris
-
0.00
-
0.000
0.0006 0.0003 0.000
5
0.0010 0.0
004
0.00
00
-
0.00
0.00
54
0.002
2
14

03 1 06
Primer
ica
-
0.00
03
0.000
3 0.0010 0.0001
-
0.000
1 0.0016
0.0
001
0.00
03
-
0.00
10
0.00
22
0.008
2
Weig
ht
6.00
% 3.50% 7.00%
4.00
% 1.00%
2.0
0%
23.
50
%
23.5
0%
18.8
2%
10.6
8%
100.
00%
We
ight
Multi
plied
board
ed
varian
ce
Goo
dyea
r
Tire
&
Rub
ber
Intern
ationa
l
Busin
ess
Machi
nes
Intern
ationa
l
Paper
McD
onald
s
Corp
Navist
ar
Intern
ationa
l
Me
rck
&
Co 3M
Proc
tor
&
Ga
mbl
e
Phil
ip
Mor
ris
Prim
erica
6.0
0%
Good
year
Tire
&
Rubbe
r
0.00
002
0.000
00
0.000
01
0.000
00
0.000
00
0.0
000
0
0.0
000
1
0.00
002
0.00
000
0.00
000
3.5
0%
Intern
ationa
l
Busin
ess
Machi
nes
0.00
000
0.000
01
0.000
00
0.000
00
0.000
00
0.0
000
0
0.0
000
1
0.00
001
0.00
000
0.00
000
7.0
0%
Intern
ationa
l
Paper
0.00
001
0.000
00
0.000
02
0.000
00
0.000
00
0.0
000
0
0.0
000
2
0.00
002
0.00
000
0.00
000
4.0
0%
McDo
nalds
Corp
0.00
000
0.000
00
0.000
00
0.000
01
0.000
00
0.0
000
0
0.0
000
1
0.00
002
0.00
000
0.00
000
1.0
0%
Navist
ar
Intern
ationa
l
0.00
000
0.000
00
0.000
00
0.000
00
0.000
00
0.0
000
0
0.0
000
0
0.00
000
0.00
000
0.00
000
2.0
0%
Merck
& Co
0.00
000
0.000
00
0.000
00
0.000
00
0.000
00
0.0
000
0
0.0
000
0
0.00
001
0.00
000
0.00
000
23.
50
3M 0.00
001
0.000
01
0.000
02
0.000
01
0.000
00
0.0
000
0.0
001
0.00
006
0.00
000
0.00
001
15

% 0 4
23.
50
%
Procto
r &
Gamb
le
0.00
002
0.000
01
0.000
02
0.000
02
0.000
00
0.0
000
1
0.0
000
6
0.00
019
-
0.00
003
-
0.00
003
18.
82
%
Philip
Morri
s
0.00
000
0.000
00
0.000
00
0.000
00
0.000
00
0.0
000
0
0.0
000
0
-
0.00
003
0.00
019
0.00
004
10.
68
%
Prime
rica
0.00
000
0.000
00
0.000
00
0.000
00
0.000
00
0.0
000
0
0.0
000
1
-
0.00
003
0.00
004
0.00
009
Variance 0.001
Standard
deviation 3.41%
Return 1.6820%
Risk free rate 6.87%
Sharpe ratio 0.493923167
3.
E(rm) 1.29%
Rf 0.57%
erp 0.72%
σm 3.45%
Stock α β σ( e) α/σ( e)
3M 1.4%
-
0.28 5.0% 0.0819
Proctor &
Gamble 2.1%
-
0.10 20.5% 0.1009
Philip Morris 1.9% - 25.3% 0.0760
16

0.26
Primerica 3.42% -0.25
31.36
%
0.1089
(
Trenyor
Black
model,
2017)
Active
Portfolio
Sharpe Ratio Sp
0.37
4
Market Sharpe
Ratio Sm
0.20
9
Stock α β
σ( e
)
α/σ2(
e)
Wei
ght
αA (Portfolio
berta)
βA
σ
2( eA)
3M
1.4
2%
-
0.28
5.0
%
0
.28
0.49
8 0.00707
(0.
14)
0.00
062
Proctor &
Gamble
2.0
7%
-
0.10
20.
5%
0
.10
0.17
7 0.00367
(0.
02)
0.00
132
Philip
Morris
1.9
3%
-
0.26
25.
3%
0
.08
0.13
3 0.00257
(0.
03)
0.00
114
Primerica
3.4
2%
-
0.25
31.
4%
0
.11
0.19
1 0.00653
(0.
05)
0.00
36
0.5
695
1.0
000 0.0198
-
0.240
0
0.0
067
Weight of
Active
Portfolio w0 0.4907
Adjusted
weight w* 0.3051
17

Companies Return Weight Weight * return
3M 1.05% 0.498 0.53%
Proctor &
Gamble 1.95% 0.177 0.34%
Philip Morris 1.60% 0.133 0.21%
Primerica 3.09% 0.191 0.59%
Portfolio return 1.67%
Portfolio assessment
Portfolio
elements
Return Beta Sharpe ratio Treynor ratio Risk
1.67% - 0.24 0.374 -0.0458 0.15%
4.
RP risk RP investor
risk
RP manager
risk
RP selectivity Rp
diversification
Outcome -0.00298 0.0124 -0.0154 0.01538 0.0068
18