Question

Your portfolio consists of two assets: $1000 is invested in an ETF with an expected return of 15.4% and $7,350 in a bond fund with expected returns of 4.3%.

How much in $, should you transfer from bonds to the ETF so that you will obtain a portfolio with an overall expected return of 15.1%?

Answer 1

Total amount invested in the portfolio = $1000 + $7350 = $8350

Let w_E is the weight of the ETF in the portfolio and w_B is the weight of the bond in the portfolio so that the expected return on the overall portfolio is 15.1%

Required return on portfolio = 15.1%

Expected return on portfolio is calculated using the Formula:

E[R_P] = w_E*E[R_E] + w_B*E[R_B]

Expected return on ETF = E[R_E] = 15.4%

Expected return on Bond = E[R_B] = 4.3%

15.1% = w_E*15.4% + w_B*4.3%

w_B = 1 - w_E

15.1% = w_E*15.4% + (1 - w_E)*4.3%

15.1% = w_E*15.4% + 4.3% - w_E*4.3%

15.1% - 4.3% = 11.1%*w_E

10.8% = 11.1%*w_E

w_E = 10.8%/11.1% = 97.2972972972973%

w_E = Amount invested in ETF/Total amount invested = 97.2972972972973%

Amount required to be invested in ETF = 97.2972972972973% * 8350 = $ 8124.32432432433

Current amount inveted = $1000

Therefore, amount that should be trasferred from bonds to ETF = 8124.32432432433 - 1000 = $7124.32432432433

Answer (in $) -> 7124.32432432433