Question

Karen has the following share portfolio: 200 shares in Gippsland Nurseries Ltd (GNL); 1200 shares in Alpine Bank Ltd (ABL) and 9000 shares in River Lett Ltd (RLL). Their current market prices are: $47.90 (GNL), $21.20 (ABL) and $1.10 (RLL). Karen also has $13,500 invested at the risk-free rate of 4%. Karen's investment adviser has told her that the estimates betas of her share holdings are: 1.4 for GNL, 0.8 for ABL and 1.7 for RLL. Her investment adviser has also forecast that the market risk premium will be 7.5%. What is the beta of Karen's portfolio? What is its expected return? Karen wishes to increase her portfolio beta to the beta of the market portfolio by reducing her risk-free investment and increasing her investment in GNL. Advise Karen on what she needs to do to achieve this outcome.

Answer 1

(a) SOLUTION a) Calculation of Peta of Parttolio [weighted Avg. fe TrRIce ofeachi Shaues NUMBEN oi Shores NAME Value GNL $9580 47.90 200 $25440 21.20 1200 ह्११०० RLL 1.10 9000 Reskfree 9avestment $ 13500 Total weighted dug Béta (d)x (c) Total |019nvestmeal vestment (b) Shates weights Beta Value a/b=(c) (d) ca) 1.4 GNL 9580 •1639849 58420 0.230 58420 .4354673| 0.8 ABL 25440 0• 348 .1694625 1.7 9900 c8420 0•288 nLL Resk free •2310852 58420 Peta of Paet folio 13500 Oo867 Page 01

(b) Caleulatisi of Expected Retudn of Portfolio Gupected deturn = Risk firee Re turnt Petartlortfoleó [Meslietsetisen- Reiskfronm stalm 0.867 [7o5] 10.50% cc) 22200H aAW Current Peta af Partholis isr0.867 and we Know that Peta df Market is always ! the feta of Pertholes to 1 Karen will for snereasng need to.inerease the Weeghted Ang Beta dr GNL from 0.230 to 0-363,other things remaning coustant.ie C0.363+ •348+ o 288+ o ]= 1 Now, for increasing the eta f GNL Karen ceill need to laivest in GNL. toi the tune ofanadditinalamount of $$5567047 It wwill lead to the increase ia ralul 1 Iaveslinents in GNL Firten $ 9580 to $15147.47 02 fage