Asset allocation across risky and risk-free portfolios
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Complete portfolio: The entire portfolio including risky and risk-free assets
Ex) Portfolio with two risky assets (A and B) and a risk-free asset (F)
Market value of A = $113,400
Market value of B = $96,600
Market value of F = $ 90,000
Market value of the portfolio = $300,000
Market value of the risky asset = $210,000
Weight of A in risky asset = 113,400/210,000 = 0.54
Weight of B in risky asset = 96,600/210,000 = 0.46
Weight of risky asset in the portfolio (y)
= 210,000 / 300,000 = 0.70
Weight of risk-free asset in the portfolio (1-y)
= 90,000 / 300,000 = 0.30
Weight of A in the portfolio
= 113,400/300,000 = (113,400/210,000)(210,000/300,0000) = 0.54*0.70=0.378
Weight of B in the portfolio
= 96,600/300,000 = (96,600/210,000)(210,000/300,0000) = 0.46*0.70=0.322
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Suppose the investor decides to decrease risk by reducing the exposure to the
risky portfolio from y = 0.7 to y=0.56
Have to leave the proportion of each asset in the risky portfolio unchanged
Market value of the risky asset = $300,000*0.56 = $168,000
Market value of A = $168,000*0.54 = $90,720
Market value of B = $168,000*0.46 = $77,280