e your answer in the space provided or on a separate sheet of paper. isbils are
ID: 2820496 • Letter: E
Question
e your answer in the space provided or on a separate sheet of paper. isbils are currently returning an aoua ealc oisl and ou have th floin information on two stocks (suppose correlation between stocks A and B is 65%): Stock Expected return d Deviation ur goal is to create a portfolio of these twostocks and T-Bils wit.an a) Calculate what percent of the portfolio should be invested in each stock(WA& W-) b) Calculate the standard deviation of your portfolio. c) Calculate the Sharpe ratio of the portfolio. 05% and keep20%invested in T-Bills. [PLEASE SHOW YOUR WORK CLEARLY!
Explanation / Answer
Answer)
Expected return from portfolio (Er ) = WA * RA + WB * R B + WT * RT ------------(1)
Where , WA ,WB ,WT , RA, RAB , RT = weight and return from A,B and T-Bill.
As per question , Er = 18% ,
WT = 0.20 => WA + WB =1 - WT = 0.80
=> WA = 0.80- WB
By Putting the value of WA ,WB ,WT , RA, RAB , RT in eq(1)
18% = (0.80 - WB) *10% + WB * 14% + 0.20* 4%
=> WB = 0.023 =2.3%
=> WA = 0.80- WB = 0.777= 77.7%
Answer B)
Standard Deviation = (WA2 * SA2 + WB2* S B2 + WT2* ST2 + 2 * WA * WB *CovAB ) ^ 0.5
Where , WA ,WB ,WT , SA, SB , ST = weight and standard deviation from A,B and T-Bill
as ST , COVBT and COVAT = 0 , as T-bill is risk free asset , with standard deviation =0 .
CovAB = SA * SB * rAB , where , rAB = corelation between A & B.
CovAB = 0.18*0.24*0.65 = 0.02808
Standard Deviation = (WA2 * SA2 + WB2* S B2 + WT2* ST2 + 2 * WA * WB *CovAB ) ^ 0.5
= 14.0124%
Answer 3)
Sharpe ratio = {Portfolio return – Risk free return} / Standard Deviation
= 0.18 -0.0 4 / .140124 = 0.999 = 1.
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