Question 1

A portfolio has a variance of 0.04050,a beta of 1.60,and an expected return of 14.3 percent.What is the Treynor ratio if the expected risk-free rate is 5.5 percent?
A) 0.055
B) 0.063
C) 0.367
D) 0.498
E) 0.512

Accepted Answer

Treynor ratio = (0.143 − 0.055) / 1.60 = 0.0550

Question 2

A portfolio has a Sharpe ratio of 0.74,a standard deviation of 18.0 percent,and an expected return of 15.9 percent.What is the risk-free rate?
A) 1.98 percent
B) 2.36 percent
C) 2.58 percent
D) 3.09 percent
E) 3.15 percent

Accepted Answer

0.75 = ( 0.159 - r_f) / 0.18; r_f = 2.58 percent

Question 3

Trailer Co.stock has an expected return of 12.2 percent and a standard deviation of 11.8 percent.What is the smallest expected loss over the next month given a probability of 5 percent?
A) −4.59 percent
B) −6.09 percent
C) −7.27 percent
D) −11.49 percent
E) −13.77 percent

Accepted Answer

Smallest loss = (0.122 × 1 / 12) − 1.645 × (0.118 × √1 / 12) = −4.59 percent

Question 4

Mike's portfolio has a two-year expected return of 21.70 percent.What is the expected return for one year?
A) 10.85 percent
B) 12.50 percent
C) 13.33 percent
D) 14.22 percent
E) 15.34 percent

Accepted Answer

Annual return = 0.2170 / 2 = 10.85 percent

Question 5

A portfolio has a 4.0 percent chance of losing 15 percent or more according to the VaR when T = 1.This can be interpreted to mean that the portfolio is expected to have an annual loss of 15 percent or more once in every how many years?
A) 1.0
B) 2.0
C) 25
D) 50
E) 100

Accepted Answer

To find the time horizon, we need to use the formula: 
Time horizon (in years) = 1 / Probability of the loss event happening
In this case, the probability is 4.0 percent or 0.04. So, 
Time horizon = 1 / 0.04 = 25 years 
Therefore, the portfolio is expected to have an annual loss of 15 percent or more once in every 25 years.

Question 6

High Mountain Homes has an expected annual return of 16.1 percent and a standard deviation of 20.3 percent.What is the smallest expected loss over the next month given a probability of 2.5 percent?
A) −6.64 percent
B) −8.67 percent
C) −10.14 percent
D) −12.12 percent
E) −15.13 percent

Accepted Answer

Smallest loss = (0.161 × 1 / 12) − 1.96 × (0.203 × √ 1 / 12) = −10.14 percent

Question 7

A portfolio has an expected annual return of 15.7 percent and a standard deviation of 19.6 percent.What is the smallest expected loss over the next calendar quarter given a probability of 1 percent?
A) −15.11 percent
B) −16.23 percent
C) −16.49 percent
D) −18.08 percent
E) −18.87 percent

Accepted Answer

Smallest loss = (0.157 × 0.25) − 2.326 × (0.196 × √0.25) = −18.87 percent

Question 8

A stock has an annual standard deviation of 14.1 percent and an expected annual return of 11.5 percent.What is the smallest expected loss for the next 6 months given a probability of 2.5 percent?
A) −8.90 percent
B) −13.79 percent
C) −14.57 percent
D) −15.38 percent
E) −16.67 percent

Accepted Answer

Smallest expected loss = (0.115 × 0.5) − 1.96 × (0.141 × √0.5) = −13.79 percent

Question 9

A portfolio consists of the following two funds.  What is the Sharpe ratio of the portfolio?
A) 0.422
B) 0.547
C) 0.648
D) 0.721
E) 0.798

Accepted Answer

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Question 10

Your portfolio has a standard deviation of 24.1 percent.What is the two-year standard deviation?
A) 31.87 percent
B) 34.08 percent
C) 36.55 percent
D) 39.48 percent
E) 41.15 percent

Accepted Answer

Two-year standard deviation = 0.0241 × √2 = 34.08 percent

Question 11

A portfolio has a 3-year standard deviation of 18.1 percent.What is the one-year standard deviation?
A) 6.39 percent
B) 8.69 percent
C) 10.45 percent
D) 11.80 percent
E) 12.33 percent

Accepted Answer

0.1810 = σ × √3; σ = 10.45 percent

Question 12

What is the Treynor ratio of a portfolio comprised of 40 percent portfolio A,25 percent portfolio B,and The risk-free rate is 2.5 percent and the market risk premium is 8.4 percent. 
A) 0.057
B) 0.063
C) 0.076
D) 0.081
E) 0.094

Accepted Answer

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Question 13

A portfolio has a beta of 1.25 and an actual return of 13.0 percent.The risk-free rate is 4.50 percent and the market risk premium is 8.2 percent.What is the value of Jensen's alpha?
A) −0.86
B) −1.01
C) −1.14
D) −1.25
E) −1.34

Accepted Answer

Jensen's alpha = 0.130 − [0.040 + 1.25 (0.082)] = −1.25 percent

Question 14

Lester has a portfolio with an average return of 13.5 percent and a standard deviation of 22.5 percent.He has a one percent probability of losing ________ percent or more in any given year. 
A) −33.97
B) −38.94
C) −20.23
D) −5.04
E) −8.37

Accepted Answer

Loss percent = 0.135 − 2.326 (0.225) = −38.84 percent

Question 15

The one-year standard deviation of your portfolio is 14.8 percent.What is the two-year standard deviation?
A) 16.47 percent
B) 18.23 percent
C) 20.93 percent
D) 25.41 percent
E) 27.20 percent

Accepted Answer

Two-year standard deviation = 0.148 × √2 = 20.93 percent

Question 16

Your portfolio has a standard deviation of 11.7 percent.What is the two-year standard deviation?
A) 14.87 percent
B) 15.83 percent
C) 16.55 percent
D) 23.48 percent
E) 24.15 percent

Accepted Answer

Two-year standard deviation = 0.0976 × √2 = 23.48 percent

Quiz 13: Performance Evaluation and Risk Management

A portfolio has a variance of 0.04050,a beta of 1.60,and an expected return of 14.3 percent.What is the Treynor ratio if the expected risk-free rate is 5.5 percent?

A portfolio has a Sharpe ratio of 0.74,a standard deviation of 18.0 percent,and an expected return of 15.9 percent.What is the risk-free rate?

Trailer Co.stock has an expected return of 12.2 percent and a standard deviation of 11.8 percent.What is the smallest expected loss over the next month given a probability of 5 percent?

Mike's portfolio has a two-year expected return of 21.70 percent.What is the expected return for one year?

A portfolio has a 4.0 percent chance of losing 15 percent or more according to the VaR when T = 1.This can be interpreted to mean that the portfolio is expected to have an annual loss of 15 percent or more once in every how many years?

High Mountain Homes has an expected annual return of 16.1 percent and a standard deviation of 20.3 percent.What is the smallest expected loss over the next month given a probability of 2.5 percent?

A portfolio has an expected annual return of 15.7 percent and a standard deviation of 19.6 percent.What is the smallest expected loss over the next calendar quarter given a probability of 1 percent?

A stock has an annual standard deviation of 14.1 percent and an expected annual return of 11.5 percent.What is the smallest expected loss for the next 6 months given a probability of 2.5 percent?

A portfolio consists of the following two funds. What is the Sharpe ratio of the portfolio?

Your portfolio has a standard deviation of 24.1 percent.What is the two-year standard deviation?

A portfolio has a 3-year standard deviation of 18.1 percent.What is the one-year standard deviation?

What is the Treynor ratio of a portfolio comprised of 40 percent portfolio A,25 percent portfolio B,and The risk-free rate is 2.5 percent and the market risk premium is 8.4 percent.

A portfolio has a beta of 1.25 and an actual return of 13.0 percent.The risk-free rate is 4.50 percent and the market risk premium is 8.2 percent.What is the value of Jensen's alpha?

Lester has a portfolio with an average return of 13.5 percent and a standard deviation of 22.5 percent.He has a one percent probability of losing ________ percent or more in any given year.

The one-year standard deviation of your portfolio is 14.8 percent.What is the two-year standard deviation?

Your portfolio has a standard deviation of 11.7 percent.What is the two-year standard deviation?