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8/17/2019 fmt company.xlsx
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Page 1
Table of correlations
Asset A Asset B Things in dark
Asset A 1.0000 0.369 Things in light
Asset B 0.369 1.0000 Things in yello
Things in red
Table of e%pected returns and risk&'return( )isk
Asset A *0.00+ *,.00+
Asset B 1,.00+ 33.00+
Table of co$ariances
Asset A Asset B
Asset A -.,+ 3.1+
Asset B 3.1+ 10.,9+
Proporition of !ealth in$ested inAsset A 10.,0+
Asset B /111.1+
Total 0.396-0*3 'this is a 2#T)A2T for "#ol$er"4 this cell B*3 must be
'it is the constraint that the total proportions of our !ealt
This bit is used to nd the risk of the portfolio
Asset A Asset B
Proportion 10.,0+ /111.1+ These number
Asset A 10.,0+ 1-.,*9+ /.-*10+ proportion of
Asset B /111.1+ /.-*10+ 13.*9+ co$ariance of
&%pected return on the portfolio of all 3 assets
10.1+'it you are minimi8ing risk for a gi$en return you should t
this cell4 B34 is %ed//at !hate$er le$el of return you !a
return for a %ed risk4 you should tell "#ol$er" to ma%imi
)isk associated !ith the portfolio of all 3 assets
.+'if you are minimi8ing risk for a gi$en return you should t
this cell4 B0. f you are ma%imi8ing return for a %ed risk
tell "#ol$er" that this cell is %ed.(
2o! use "sol$er" to either minimi8e the risk for a gi$en return
'ie minimi8e B3- for a prescribed $alue of B3( or
ma%imi8e return for a gi$en risk 'ie4 ma%imi8e B3 for a gi$en
$alue of B3-(.
n both cases B*3 should be constrained to e5ual 14 this is the
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condition that our "total !ealth" is in$ested in the assets.
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Page 3
grey are input parameters
grey are computed intermediate things
! are labels
re "#ol$er" inputs or outputs
orced to e5ual one(
must e5ual one(
s are a table of4 for instance
7 proportion of B 7
and B
ll "#ol$er" that
t. f you are ma%imi8ing
e this cell
ll "#ol$er" to minimi8e
you should
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8/17/2019 fmt company.xlsx
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Table of correlations
Asset A Asset B Things in dark
Asset A 100.00+ 36.9+ Things in light
Asset B 36.9+ 100.00+ Things in yello
Things in red
Table of e%pected returns and risk on the risky assets&'return( )isk
Asset A *0.00+ *,.00+
Asset B 1,.00+ 33.00+
Asset 33.00+ 0.00+
)iskfree rate 1.00+ The return on the risk free asset
Table of co$ariances for the risky assets
Asset A Asset B Asset onstruct co$
Asset A -.,00+ 3.133+ 0.0000+ such as co$ar'
Asset B 3.133+ 10.,900+ 0.0000+Asset 0.0000+ 0.0000+ 0.0000+
Proporition of !ealth in$ested in purely risky assets
Asset A 0.*61 2ormally these $alues are set by "#ol$er" b
Asset B 0.093 reset them to "sensible" $alues and then re
Asset 0.-, fails to nd a solution 'eg4 B*31:34 B*1
Total 1.0000 'this is a 2#T)A2T for "#ol$er"4 this cell B*3 must be
'it is the constraint that the sum of the proportions of our
This bit is used to nd the risk of the portfolio of purely risky assets
Asset A Asset B Asset
Proportion *.61+ 9.3+ -.,+ These number
Asset A *.61+ 1.*3-+ 0.13,6+ 0.0000+ proportion ofAsset B 9.3+ 0.13,6+ 0.09,9+ 0.0000+ co$ariance of
Asset -.,+ 0.0000+ 0.0000+ 0.0000+
&%pected return on the portfolio of all 3 risky assets
*6.03+
)isk associated !ith the portfolio of all 3 risky assets
13.*+
;arket Price of )isk ' #lope of the apital ;arket
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grey are input parameters
grey are computed intermediate things
! are labels
re "#ol$er" inputs or outputs
riance matri% using formulae
A4B(risk'A(7risk'B(7correl'A4B(
ut it may be necessary to
/run "#ol$er" if "#ol$er"
:34 B*1:3 (
orced to e5ual one(
!ealth must e5ual one(
s are a table of4 for instance
7 proportion of B 7and B
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results
Page -
Building an e?cient frontier using &%cel and sol$er is an ine?cient process.
>ou ha$e to either ma%imi8e the return gi$en a le$el of risk 'this is best for large risks
or minimi8e the risk for a gi$en le$el of return 'this is best for small risks and returns(
for a lot of possible le$els of risk and return. &ach specic le$el of risk or return re5uire
a separate sol$er run. This takes a great deal of time.
Belo! are the results for a three asset model !here the e%pected returns and $ariance
&'return( )iskAsset A *0.00+ *,.00+
Asset B 1,.00+ 33.00+
Asset 33.00+ 0.00+
the co$ariance matri% is
Asset A Asset B market pr
Asset A -.,+ 3.1+ risk fr
Asset B 3.1+ 10.,9+
and the correlation matri% is
Asset A Asset B
Asset A 100.00+ 36.9+
Asset B 36.9+ 100.00+
e?cient frontier
risk return + of asset A + of asset B
-0.-6+ 0.00+ 100.9+ 13*.,*+
6.1+ *.00+ 96.1+ 1*3.3+
9.9+ .00+ 91.6,+ 113.,,+
.13+ 6.00+ ,-.*3+ 10.0+
,.,0+ ,.00+ ,*.--+ 9.93+
3.6*+ 10.00+ -,.3*+ ,.6+
1.11+ 11.00+ -6.09+ ,0.-*+3,.6-+ 1*.00+ -3.,6+ -.99+
36.31+ 13.00+ -1.6+ -1.*+
3.0+ 1.00+ 69.1+ 66.1+
31.91+ 1.00+ 6-.1,+ 61.-,+
*9.9*+ 16.00+ 6.9+ -.0+
*,.10+ 1-.00+ 6*.-3+ *.30+
*6.9+ 1,.00+ 60.0+ -.-+
*.13+ 19.00+ ,.*-+ *.,3+
*.0-+ *0.00+ 6.0+ 3,.10+
*3.3+ *1.00+ 3.,*+ 33.36+
**.99+ **.00+ 1.9+ *,.6*+
*3.00+ **.90+ 9.60+ *.33+*.00+ *.--+ .3,+ 1.1+
*.00+ *.-+ 3.*3+ 10.90+
*6.00+ *6.*+ 1.,+ -.1-+
*-.00+ *-.19+ 0.11+ 3.9-+
*,.00+ *-.,0+ 3,.-0+ 1.1*+
*9.00+ *,.3-+ 3-.3+ /1.63+
30.00+ *,.90+ 36.*,+ /.11+
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0.00+ 33.0+ *6.16+ /*.3-+
0.00+ 3-.31+ 1-.3+ /3.,6+
60.00+ 1.00+ 9.*+ /61.3,+
-0.00+ .9+ 1.*,+ /-,.36+
,0.00+ ,.11+ /6.6+ /9.1*+
90.00+ 1.9+ /1.**+ /111.60+
100.00+ .0+ /*1.-+ /1*,.10+110.00+ ,.,+ /*9.1+ /1.36+
1*0.00+ 61.90+ /36.96+ /160.61+
130.00+ 6.31+ /.60+ /1-6.-*+
10.00+ 6,.-1+ /*.13+ /19*.,6+
10.00+ -*.10+ /9.--+ /*0,.,-+
minimi8ed risk for a gi$en return
ma%imi8ed return for a gi$en risk
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nd returns(
s
of returns are
ice of risk 1.,66,,9
e rate 1.00+
capital market line
risk return
0.00+ 1.00+
.00+ ,.6+
,.00+ 1.93+
1*.00+ *3.39+
16.00+ 30.,+
*0.00+ 3,.31+
*.00+ .-,+short selling *,.00+ 3.*+
3*.00+ 60.-0+
36.00+ 6,.16+
0.00+ -.63+
.00+ ,3.09+
,.00+ 90.+
*.00+ 9,.0*+
6.00+ 10.,+
60.00+ 11*.9+
6.00+ 1*0.0+
no short selling 6,.00+ 1*-.,-+
-*.00+ 13.33+-6.00+ 1*.-9+
,0.00+ 10.*6+
,.00+ 1-.-*+
,,.00+ 16.1,+
9*.00+ 1-*.6+
96.00+ 1,0.11+
100.00+ 1,-.-+
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10.00+ 19.03+
10,.00+ *0*.9+
11*.00+ *09.96+
short selling 116.00+ *1-.*+
1*0.00+ **.,,+
1*.00+ *3*.3+
1*,.00+ *39.,1+13*.00+ *-.*-+
136.00+ *.-3+
10.00+ *6*.*0+
1.00+ *69.66+
1,.00+ *--.1*+
8/17/2019 fmt company.xlsx
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graphs
Page 11
0+ *+ 0+ -+
0+
*0+
0+
60+
,0+
op set border e?cient frontie
risk
return
0+
60+
,0+
op set border e?cient frontier ca
return
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graphs
Page 1*
0+ *+ 0+ -+
0+
*0+
risk
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graphs
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100+ 1*+ 10+
r assets
market line assets
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graphs
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100+ 1*+ 10+
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