Question

Please explain with great detail as I want to understand this.

1)An investor develops a portfolio with 25% in a riskfree asset with a return of 6% and the rest in a risky asset with expected return of 9% and standard deviation of 6%. The standard deviation for the portfolio is:

(a) 20.3%. (b) 4.5%. (c) 0.0%. (d) 27.0%.

2)An investor has a portfolio with 60% in a riskfree asset with a return of 5% and the rest in a risky asset with an expected return of 12% and a standard deviation of 10%. Respectively, the expected return and standard deviation of the portfolio are (a) 10.5%. (b) 9.7%. (c) 11.4%. (d) 12.6%.

3)If the proportion invested in the riskfree asset is -.4, the proportion invested in the risky portfolio is: (a) -1.4.    (b) 0.6.   (c) 0.0.   (d) 1.4.   (e) -0.6.

Answer 1

1). Standard Deviation of the Portfolio with risk-free asset = [W²_risky x ²_risky]^1/2

= [0.75² x 0.06²]^1/2

= [0.5625 x 0.0036]^0.5

= 0.002025^0.5

= 0.045, or 4.50%

Hence, Option "B" is correct.

2). E(Rp) = (W_risk-free x R_risk-free) + (W_risky x R_risky)

= (0.6 x 5%) + (0.4 x 12%) = 3% + 4.8% = 7.8%

Standard Deviation of the Portfolio with risk-free asset = [W²_risky x ²_risky]^1/2

= [0.4² x 0.10²]^1/2

= [0.16 x 0.01]^0.5

= 0.0016^0.5

= 0.04, or 4%

3). W_portfolio = W_risk-free + W_risky

1.00 = -0.40 + W_risky

W_risky = 1.00 + 0.40 = 1.40

Hence, Option "D" is correct.