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Case Alex Sharpe's Portfolio Essay

1224 words - 5 pages

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Case 2: Alex Sharpe’s portfolio |
8.5.2014 |

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Tehtävä 1.
CAPM kaava on:

Osakkeen tuotto-odotus E(Ri) = 10,25 %
Riskittömän sijoituskohteen tuotto Rf = 6 %
Markkinaportfolion tuotto-odotus E(Rm) = 14,5 % (riskitön korko + riskipreemio)

Sijoittamalla nämä yllä olevaan kaavaan saadaan:
10,25 % = 6 % + β(14,5 % - 6 %)
josta saadan betan β arvoksi 0,5.
Kun osakkeen tuottojen ja markkinaportfolion välinen kovarianssi kaksinkertaistuu, β-kerroin kaksinkertaistuu, kun markkinaportfolion varianssi ei muutu. Betan kaksinkertaistuessa osakkeen riskipreemio puolittuu.
Kun β kerrotaan kahdella ja luvut sijoitetaan samaan kaavaan, saadaan osakkeen tuotto-odotukseksi ...view middle of the document...

Tästä voidaan päätellä, että sen beta – kerroin on luultavimmin korkein vertailujoukosta. Hasbron keskimääräinen tuotto (0,87 %) on Reynoldsin matalampi mutta myös Hasbron volatiliteetti on pienempi (8,12 %).
Molempien osakkeiden keskihajonta on viiden vuoden tarkasteluajanjakson aikana laskenut kohtuullisen suuristakin luvuista lähemmäs S&P 500 indeksin vaihtelua. Indeksiin verrattuna yritysten osakkeiden keskimääräinen tuotto on korkeampi mutta toisaalta osakkeiden volatiliteetti on huomattavasti korkeampi. Tämä selittyy sillä, että indeksiin vaikuttaa suuri joukko eri osakkeita. Eri alojen ominainen vaihtelu tasoittuu, kun indeksillä on suuri hajautuminen.
Keskimääräisen tuoton laskemiseen käytimme geometrista keskiarvoa aritmeettisen keskiarvon sijaan, sillä käytössämme oli toteutuneita tuottoprosentteja aiemmilta vuosilta. Tällöin geometrinen keskiarvo kuvaa menneisyyden keskimääräisiä tuottoja aritmeettista paremmin.

Tehtävä 2.
Jos Sharpella olisi ollut sijoitusajanjakson aikana portfoliossaan 99 % S&P 500:aa ja 1 % Reynoldsia, portfolion arvo olisi vuoden 2007 Tammikuussa kasvanut (1+0,510 %)5 eli 2,57 prosenttia. Jos portfoliossa 1 % olisi Hasbroa, olisi portfolion arvo kasvanut (1+0,504 %)5 eli 2,55 prosenttia. Tämä on laskettu käyttäen portfolion tuoton odotusarvoa, joka on laskettu osakkeiden geometrisista keskiarvoista painottaen ne osakkeiden suhteellisella määrällä portfoliossa. Geometrista keskiarvoa käytetään, koska tehtävässä arvioidaan portfolion nykyistä arvoa historiallisen datan perusteella.

Hasbron korrelaatio on korkea (62,79 %) suhteessa S&P 500 indeksiin, josta johtuen portfolion volatiliteetti nousee suuremmaksi, kuin Reynolds & S&P 500 portfoliolla. Vaikka Hasbron oma keskihajonta onkin Reynoldsia pienempi. Hasbron kurssi vaihtelee enemmän samaan suuntaan S&P 500 kanssa, eivätkä ne kumoa toistensa vaikutusta.

Tässä tilanteessa Reynolds olisi parempi valinta, koska portfolion tuoton odotusarvo (0,510 %) olisi suurempi kuin S&P Hasbron, ja volatiliteetti on pienempi. Tämä havainto on ristiriitainen ensimmäisen tehtävän havaintojen kanssa, jossa Reynolds on yksittäisenä osakkeena riskisempi. S&P 500 pienentää Reynoldsin riskisyyttä portfoliossa. Tässä tilanteessa, kun yhdistetään kaksi osaketta, niiden keskeisellä korrelaatiolla on vaikutusta tuoton odotusarvoon ja portfolion riskisyyteen.

Jos Sharpella olisi ollut sijoitusajanjakson aikana portfoliossaan 99 % S&P 500:aa ja 1 % Reynoldsia, portfolion volatiliteetti olisi ollut 3,605. Hasbron tilanteessa olisi portfolion hajonta 3,629. Tästä nähdään, että osakkeiden yhdistäminen portfolioksi voi pienentää tuottojen vaihtelua pienemmäksi, kuin mitä yksittäisten osakkeiden vaihtelu on. Esimerkiksi näin on käynyt S&P 500 ja Reynoldsin portfoliolla. Hasbron ja S&P 500 tilanteessa volatiliteetti laskee, mutta jää lievästi S&P 500 omaa keskihajontaa suuremmaksi.

Tehtävä 3.
Beta saadaan laskettua kaavalla:
βi=σimσm2,
jossa σim on osakkeen ja S&P 500...

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