Question

Suppose the entire market consists of risky stocks A, B, C and D as well as the risk-free asset which returns 6%. Portfolios X, Y and Z are combinations of only the risky stocks (i.e. none of the portfolios have a position in the risk-free asset). Expected returns and standard deviations are given below:

	Expected return	standard deviation
stock A	12%	15%
Stock B	18%	26%
Stock C	22%	20%
Stock D	10%	8%
Portfolio X	14%	6%
Portfolio Y	21%	22%
Portfolio Z	8%	10%

(a)  Client 1 wants to invest in only one stock. If she is non-satiated and risk-averse which stock will she certainly not invest in? Choose one:  A,   B,   C,   D   and explain in 3 sentences or less.

(b) You are told that one of the portfolios involves short-selling.  Which one must it be?  Choose one:  X,   Y,   Z   and explain in 3 sentences or less.

(c)  You are told that one of the portfolios is the tangency portfolio.  Which one must it be?  Circle one:  X,   Y,   Z   and explain in 3 sentences or less.

Answer 1

SOLUTION

STEP 1

Calculation Sharpe Ratio of all stocks and Portfolios

Sharpe Ratio = Expected returns - Risk Free Return / Standard Deviation

STEP 2

Answer (A)

Since, She is non-satiated and risk-averse therefore Stock having Higher Standard Deviation (SD) shall be worst for her. Therefore it is better to not invest in the Stock B on behalf of her.

Answer (B)

Among all the portfolios, Portfolio Z is having lowest Sharpe Ratio that means it is contributing less in generation of return however bearing more risk. Therefore it is advised to shortsell the Portfolio Z.

Answer (C)

Among all the portfolios, Portfolio X is having Highest Sharpe Ratio that means it is contributing More in generation of return however bearing less risk. Therefore it is evedient that Portfolio X is the tangency portfolio in above all 3 portfolios.