Fmt Company

7/23/2019 Fmt Company

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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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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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5/14

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

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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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results

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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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results

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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*+


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graphs

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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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