Question

In: Finance

1. The change from a straight to a kinked capital allocation line reflects:

 

1. The change from a straight to a kinked capital allocation line reflects:

A) reward-to-volatility ratio decreasing.

B) lending rate exceeding borrowing rate.

C) investors risk tolerance decreasing.

D) increase in the portfolio proportion of the risk-free asset.

For the following 5 questions: You invest $100 in a risky asset with an expected rate of return of 15% and a standard deviation of 15% and a T-bill with a rate of return of 5% (and a standard deviation of 0).

2. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 13%?

  1. 20% and 80%
  2. 25% and 75%

C) 80% and 20%

D) 75% and 25%

3. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 8%?

  1. 67% and 33%

B) 53% and 47%

  1. 27% and 73%
  2. 47% and 53%

4. A portfolio that has an expected return of 23% is formed by

  1. borrowing $40 at the risk-free rate and investing the total amount ($140) in the risky asset.
  2. borrowing $80 at the risk-free rate and investing the total amount ($180) in the risky asset.
  3. borrowing $60 at the risk-free rate and investing the total amount ($160) in the risky asset.
  4. borrowing $85 at the risk-free rate and investing the total amount ($185) in the risky asset.

 

5. The slope of the CAL formed with the risky asset and the risk-free asset is equal to

A) 0.5667.

B) 0.6667.

C) 0.7667

D) 0.4667.

 

6. Given the capital allocation line, an investor's optimal complete portfolio is the portfolio that

            A) maximizes expected return

            B) minimizes standard deviation risk

            C) maximizes both risk and return

            D) maximizes expected utility

Solutions

Expert Solution

1) The change from a straight to a kinked capital allocation line reflects

A) reward-to-volatility ratio decreasing.(Answer)

In a kinked capital allocation line,the borrowing rate exceeds the lending rate. In such a case, the reward to volatility ratio(Sharpe ratio) or the slope of the Capital allocation line will be decreasing.

2)Let x be the weight of Risky asset and (1-x) be the weight of T bill

By the problem,

Weight of risky asset* return of risky asset + Weight of riskless asset* return of riskless asset = expected return

or, x*15 + (1-x)*5 = 13

solving for x, we get x = 0.8 or 80%

Weight of risky asset = 80%

Weight of T bill = 20%

C) 80% and 20% (Answer)

3) Let x be the weight of Risky asset and (1-x) be the weight of T bill

Standard deviation = sqrt(weight of risky asset^2 * Standard dev of risky asset^2)

or 0.08 = sqrt(x^2*0.15^2)

or 0.08 = 0.15x

or x = 8/15 = 0.53 or 53%

B) 53% and 47% (Answer)

4) Let x be the weight of Risky asset and (x-1) be the weight of T bill ... (Since it is borrowing portfolio X is greater than 1)

By the problem, x*15 + (x-1)*5 = 23

solving for x, we get x = 1.8 or 180%

Weight of risky asset = 180%

B) borrowing $80 at the risk-free rate and investing the total amount ($180) in the risky asset.(Answer)

5)The slope of the CAL formed with the risky asset and the risk-free asset is equal to

= (Return of risky asset - return of risk free asset) / Standard deviation of risky asset

=(0.15 - 0.05)/ 0.15

= 0.6667

B) 0.6667.(Answer)

6)Given the capital allocation line, an investor's optimal complete portfolio is the portfolio that

D) maximizes expected utility , because that will maximise the risk and return.(Answer)


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