* Portfolio 1 has 5.5% expected return and 15% return standard deviation. * Port

Question

* Portfolio 1 has 5.5% expected return and 15% return standard deviation. * Portfolio 2 has 8.5% expected return and 25% return standard deviation. Through- out this problem, there are no restrictions on short-selling. 26. Compute the Sharpe ratio of the Tangency Portfolio associated with the given tangency line (Hint: In an (x.y)-diagram, the slope of a straight line connecting points (xl.yl) and (x2y2) is given by (v2-y1)/(x2-x)) (a) 0.2 (b) 0.3 (c) 0.4 (d) 0.5 27. Compute the risk-free rate that is located on the given tangency line (a) 1% (b) 2% (e) 3% (d) 4% 28. Suppose that there is a seond tangency line, corresponding to a risk-free rate of 2% and a market portfolio with 6% expected return and ars return standard deviation with the risk-free rate of 2%, what is the maximum expected return that yon can generate given 25% return standard deviation? (a) 5% (b) 6% (e) 7% (d) 8% 29. (3 points) Given the usual rational preferences, suppose you wanted to form a portfolio with 25% return standard deviation. Which of the two tangency lines would you prefer, the original tangency line or the second tangency line (a) The original tangency line (b) The second tangeny line

Explanation / Answer

Sol:

26> Sharpe ratio is the slope of the tangent line (CAL).

Portfolio 1: (15%, 5.5%)

Portfolio 2: (25%, 8.5%)

Sharpe ratio = (8.5 – 5.5)/(25 – 15) = 0.30

27>

For a given slope m, the equation of a line is y – y1 = m(x – x1)

Equation of CAL

r – 5.5 = 0.3*(SD – 15)

For risk free rate, standard deviation is zero. SD = 0

r – 5.5 = 0.3*-15

r = 5.5 – 0.3*15 = 1% (this is risk free rate).

28> Risk-free asset (0, 2%); market portfolio (20%, 6%)

Sharpe ratio or slope of the line = (6 – 2) / (20 – 0) = 4/20 = 0.2

Equation of CAL: r – 2 = 0.2*(SD – 0); r = 2 + 0.2 SD

For 25% standard deviation, r = 2 + 0.2*25 = 7%

29> portfolio with 25%

For r – 5.5 = 0.3*(SD – 15) and SD = 25%, r = 5.5 + 0.3*10 = 8.5%

For r = 2 + 0.2 SD and SD = 25%, r = 7%

For same level of risk 25%, you choose tangency line with provide you higher return 8.5%

Therefore, for 25% SD, tangency line passing through (15%, 5.5%) and (25%, 8.5%) is better than line passing through (0, 2%) and (20%, 6%).

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