You invest $10,000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 20% and a standard deviation of 21% and a treasury bill with a rate of return of 5%. How much money should be invested in the risky asset to form a portfolio with an expected return of 8%?
Risky asset Expected return = 20%
Risk-free rate of return = 5%
Desired portfolio expected return = 8%
Portfolio expected return = (weight of Risky asset * Exp. return of Risky asset) + (Weight of Risk free asset * Exp. return of risk free asset)
Assume weight of risk free = x, risky = 1-x
8 = ( (1-x) * 20) + (x * 5)
8 = 20 - 20x + 5x
-12 = -15x
x = 12/15 = 0.80
So, weight of risk free asset = 0.80,
Weight of risky asset = 1-0.80 = 0.20
Amount invested in risk-free asset = 10000 * 0.80 = $8,000
Amount invested in risky asset = 10000 * 0.20 = $2,000
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