Midterm II. Monday, August 3. 2 hours

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Jennifer McGee
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1 Sa Facisco State Uivesity ichael Ba ECON 85 Summe 5 idtem II oday, August 3 hous Name: Istuctios. This is closed book, closed otes exam.. No calculatos o ay kid ae allowed. 3. Show all the calculatios. 4. I you eed moe sace, use the back o the age. 5. Fully label all gahs. Good Luck

2 Notatio o ea-vaiace Potolios with Risky Assets Asset etus: ea vecto o asset etus: Covaiace matix o asset etus: Potolio weights o isky assets: Vecto o oes: Risk-ee etu: Shae o wealth ivested i isk-ee asset:

3 . (3 oits). Coside a otolio cosistig o isky assets ad a isk-ee asset with etu. a. Usig the matix otatio o age, exess the etu o a otolio with actio ivested i the isk-ee asset ad vecto o weights o isky assets. Deote this etu by. ' b. Usig the matix otatio o age, exess the mea etu o a otolio with actio ivested i the isk-ee asset ad vecto o weights o isky assets. Deote this mea etu by. ' c. Usig the matix otatio o age, exess the vaiace o etu o a otolio with actio ivested i the isk-ee asset ad vecto o weights o isky assets. Deote this vaiace by. ' d. Usig the matix otatio o age, wite the utility maximizatio o a ivesto with mea-vaiace utility uctio u (, ), who is choosig otolios cosistig o isky assets ad a isk-ee asset. max ' ', s. t. ' O substitutig the budget costait ito the objective ad the boowig costait: max'( ) '

4 e. I ode to id otimal otolios o mea-vaiace ivestos, we use the atlab Otimizatio Toolbox uctio quadog.m. This uctio solves oblems o the om: mi.5*x'*h*x + '*x x subject to: A*x <= b Aeq*x = beq lb <= x <= ub The uctio is the used as ollows: x = quadog(h,,a,b,aeq,beq,lb,ub,x,otios); How would you ewite the otimal otolio selectio oblem i the evious sectio, so that it mas ito the om equied by quadog.m? Sice quadog.m solves miimizatio oblems, the otolio selectio oblem ca be witte as: mi ' ( )' Fidig the maximum o ay uctio (x) is the same as idig the miimum o (x).. What ae the objects i the model (otimizatio oblem) that coesod to the ollowig objects i the atlab CL.m ogam? Object i atlab CL.m Object i the model x H * ( ) 3

5 . (4 oits). The ext two igues coesod to some iacial maket. CL 5% 5% 3% 3% SL % a. Illustate the isk-ee etu o 3% o both igues above. b. Illustate the mea etu o the maket otolio o 5% o both igues above. c. Suose that the stadad deviatio o the etu o the maket otolio is %. Illustate this value o oe o the above igues (you eed to decide which oe), ad calculate the Shae Ratio. SR 5% 3%. % d. Iteet the meaig o the Shae Ratio you oud i the last sectio. SR. meas that alog the CL (otimal otolios), o evey % icease i the stadad deviatio o a otolio, the ivestos ae comesated with a.% icease i exected etu. e. Calculate the sloe o the SL. 5% 3% % 4

6 . Calculate the Beta o a asset i that has covaiace with maket otolio o Cov ( i, ).5%. Cov(, ).5% i i.5 Va( ) % Obseve that Va( )... g. What should be the exected etu o the asset i the evious sectio, based o the CAP? i ( ) 3%.5(5% 3%) 6% i h. Coside a otolio with mea etu 4% ad stadad deviatio o 6%. Is this this a otimal otolio? Povide a bie oo. A yes o o guess, without oo, will ot ea oits. The CL cotais all the otimal otolios, ad give by: SR 3%. I otolio was otimal, the it would be located o the CL. But luggig 6% i the CL gives: 3%. 6% 4.%, so otolio is below the CL, ad caot be otimal. It has smalle exected etu tha otimal otolios with the same isk. Alteatively, luggig 4% i the CL gives: 4% 3%. 5%. Oce agai, we see that otolio is below the CL, with 6%. It has highe isk tha otimal otolios with the same exected etu. i. The CL cotais (cicle the coect aswe): i. All ossible otolios o existig assets. ii. All otimal otolios. j. The SL cotais (cicle the coect aswe): i. All ossible otolios o existig assets. ii. All otimal otolios. 5

7 3. ( oits). oeygoewild.com is a hedge ud with otolio ad Beta isk.5. Suose that the isk-ee etu is % ad the mea etu o the maket otolio is %. a. Accodig to the CAP, what is the exected etu o the hedge ud s otolio? ( ) %.5(% %) 6% b. Suose that the otolio maages o oeygoewild.com oveestimate the mea etus o all isky assets by %. What is the Alha that the comay will eot o its ow otolio? The comay s estimate o the maket exected etu is ~ %. %, ad the comay s estimate o its ow otolio exected etu is ~ 6%. 7.%. Based o these estimates, we have: ~ ( ~ 7.% %.5(% %).% 7% ) 6

8 7 4. ( oits). Suose that ivestos ca ivest i a isk-ee asset with etu, ad two isky assets, with adom etus, mea ad covaiace o etus:, Ivestos have mea-vaiace utility uctio ), ( u. a. Wite the oblem o a active ivesto, who wats to id his otimal otolio. The etu, the mea ad the vaiace o such otolios ae: The otimal otolio oblem is: :.. ] [ max,, BC s t

9 8 b. Deive the ist ode ecessay coditios o otimal shaes i the isky assets. Ate substitutig the budget costait ito the objective uctio, the oblem simliies to: ] [ ) ( ) ( max, F.O.C. ] [ ), ( ] [ ), ( u u

10 5. ( oits). Suose that Qua is a assive ivesto, ad divides his iacial wealth betwee the isk-ee asset ad the maket otolio. Qua has meavaiace eeeces ove asset etus with utility uctio is u (, ). Let the actio o his wealth ivested i isk-ee asset be, the etu o the isk-ee asset is, ad the etu o maket otolio is, with mea ad vaiace. a. Wite Qua s utility maximizatio oblem, ad id the otimal shae ivested i the maket otolio:. Qua s otolio has the ollowig ate o etu, mea ad vaiace: ( ) ( ) ( ) Thus, his utility maximizatio oblem is: max ( ) ( ) The ist ode coditio o otimal is: Solvig o : ( ) ot 9

11 b. Povide a bie ecoomic ituitio about the esult you oud i the last sectio. I aticula, discuss how his ivestmet decisio deeds o the excess etu o the maket otolio, o the degee o his vaiaceavesio, ad o the vaiace o the maket otolio. Fo Qua, the maket otolio is the oly isky asset available. The highe is the excess etu o the isky asset (highe ), the moe will Qua ivest i it. The moe isk- avese he is (highe ) ad the highe is the isk o the maket otolio (highe ) the less will Qua ivest i the isky asset.

Final exam. Friday, August hours

Final exam. Friday, August hours San Fancisco State Univesity Michael Ba ECON Summe 3 Final exam Fiday, ugust 6 hous Name: Instuctions. This is closed book, closed notes exam.. No calculatos o any kind ae allowed. 3. Show all the calculations..