Question 1

Lester has a portfolio with an average return of 13.5% and a standard deviation of 22.5%. He has a 1% probability of losing ________% or more in any given year.
$\begin{array}{cr}
\text { Probability } & \text { "z" value } \
\text { of loss } & \
1.0\% & 2.326 \
2.5 & 1.960 \
5.0 & 1.645
\end{array}$

Accepted Answer

The answer of Lester has a portfolio with an average...

Question 2

A portfolio has an expected annual return of 12.2% and a standard deviation of 18.2%. What is the smallest expected loss over the next calendar quarter given a probability of 1%?

Accepted Answer

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Question 3

A portfolio has a variance of .04050, a beta of 1.60, and an expected return of 18.9%. What is the Treynor ratio if the expected risk-free rate is 4.5%?

Accepted Answer

The Treynor ratio is calculated as (Expected Return - Risk-Free Rate) / Beta. Here, it is (18.9% - 4.5%) / 1.60 = 0.078.

Question 4

Your portfolio has a standard deviation of 16.6%. What is the 2-year standard deviation?

Accepted Answer

The 2-year standard deviation can be found by multiplying the standard deviation of the portfolio by the square root of 2 (as the standard deviation is an annual figure and we need to find it for 2 years):

2-year standard deviation = 16.6% * sqrt(2) = 23.48%

The closest answer choice is D, which is 23.48%.

Question 5

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

Accepted Answer

Using the concept of Value at Risk (VaR) at the 5% level for a normal distribution, we calculate the smallest expected loss. VaR at the 5% level corresponds to 1.645 standard deviations below the mean. Thus, the calculation is: -1.645 * 11.8% + 12.2% = -4.59%.

Question 6

A portfolio has a standard deviation of 15.1%, a beta of 1.12, and a Treynor ratio of .085. The risk-free rate is 2.2%. What is the portfolio's expected rate of return?

Accepted Answer

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Question 7

A portfolio has a Sharpe ratio of .63, a standard deviation of 13.2%, and an expected return of 12.4%. What is the risk-free rate?

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Question 8

The one-year standard deviation of your portfolio is 14.8%. What is the 2-year standard deviation?

Accepted Answer

When calculating the standard deviation of a portfolio over multiple years, we need to use the formula:
σ2(t) = [(σ2)(t-1) + (σp)2 + 2(σ)(t-1)(σp)(t-1)(t)]/t
Where:
- σ2(t) = the standard deviation of the portfolio over t years
- (σ2)(t-1) = the variance of the portfolio in the previous year
- (σp)2 = the variance of the portfolio's returns
- σ(t-1) = the standard deviation of the portfolio in the previous year
- t = the number of years
Plugging in the values:
σ2(2) = [((0.148)2)(1) + (σp)2 + 2(0.148)(1)(σp)(1)]/2
Solving for (σp)2, we get:
(σp)2 = 0.2093 = 20.93%

Question 9

A portfolio has a beta of 1.25 and an actual return of 13.0%. The risk-free rate is 4.0% and the market risk premium is 8.2%. What is the value of Jensen's alpha?

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Question 10

A portfolio consists of the following two funds:

What is the Sharpe ratio of the portfolio?

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Question 11

A portfolio has a Treynor ratio of .034, a standard deviation of 10.3%, a beta of 1.55, and an expected return of 17.0%. What is the risk-free rate?

Accepted Answer

Treynor ratio = (Expected portfolio return - Risk-free rate)/Portfolio beta
0.034 = (0.17 - Risk-free rate)/1.55
Risk-free rate = 0.17 - 0.034*1.55
Risk-free rate = 0.11473 or 11.73% (rounded to two decimal places)

Question 12

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

Accepted Answer

Using the formula: Expected loss = - [ Z-score * standard deviation * sqrt(time) + expected return * time ]
We are given:
Standard deviation = 14.1%
Expected annual return = 11.5%
Time = 6 months = 0.5 years
Probability = 2.5%
Using the Z-score table, the corresponding value for a probability of 2.5% is -1.96
Expected loss = - [(-1.96) * 14.1% * sqrt(0.5) + 11.5% * 0.5] = -13.79%
Therefore, the smallest expected loss for the next 6 months given a probability of 2.5% is 13.79%. 
Hence, the answer is B.

Question 13

A portfolio has a 4.0% chance of losing 15% 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% or more once in every how many years?

Accepted Answer

If the portfolio has a 4.0% chance of losing 15% or more when T = 1, then the probability of NOT losing 15% or more is 96%. To find the probability of NOT losing 15% or more over n years, we raise 0.96 to the power of n (since each year is independent). Setting this probability equal to 0.5 (50%, or once in every two years), we can solve for n:

0.96^n = 0.5

n = log(0.5) / log(0.96)

n ≈ 24.04

So the portfolio is expected to have an annual loss of 15% or more once in every 25 years. Therefore, the best choice is C.

Question 14

A portfolio has a Sharpe ratio of .74, a standard deviation of 18.0%, and an expected return of 15.9%. What is the risk-free rate?

Accepted Answer

The answer of A portfolio has a Sharpe ratio of...

Question 15

Your portfolio has a standard deviation of 24.1%. What is the 2-year standard deviation?

Accepted Answer

The 2-year standard deviation is equal to the square root of 2 times the standard deviation. Therefore, the 2-year standard deviation would be 34.08% (sqrt(2)*24.1%).

Question 16

What is the Treynor ratio of a portfolio comprised of 40% Portfolio A, 25% Portfolio B, and the risk-free rate is 2.5% and the market risk premium is 8.4%.
$\begin{array}{rrrrr}
\text { Asset } & \text { Weight } & \text {Avg Return}& \text { Std Dev } & \text { Beta }\
\text { A } & 40\% & 15.30\%& 17.20\% & 1.25 \
\text { B } & 25\% & 10.50\% & 9.80\% & 1.3 \
\text { C } & 35\% & 13.30\% & 14.10\% & 0.95
\end{array}$

Accepted Answer

The answer of What is the Treynor ratio of a...

Question 17

A portfolio has a beta of 1.35, a standard deviation of 13.3%, and an average return of 12.01%. The market rate is 12.7% and the risk-free rate is 2.1%. What is the Sharpe ratio?

Accepted Answer

The Sharpe ratio is calculated as (Portfolio Return - Risk-Free Rate) / Portfolio Standard Deviation. Here, it is (12.01% - 2.1%) / 13.3% = 0.745.

Question 18

A portfolio has a 3-year standard deviation of 18.1%. What is the 1-year standard deviation?

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The answer of A portfolio has a 3-year standard deviation...

Question 19

The U.S. Treasury bill is yielding 1.0% and the market has an expected return of 14.5%. What is the Treynor ratio of a correctly valued portfolio that has a beta of 1.26 and a standard deviation of 11.1%?

Accepted Answer

Treynor Ratio = (Portfolio Return - Risk Free Rate) / beta
Portfolio Return = Market Return + (beta * (Portfolio's Excess Return))
Portfolio's Excess Return = Portfolio Return - Risk Free Rate

Given, 
Treasury bill yield = 1%
Expected market return = 14.5%
Beta = 1.26
Standard deviation = 11.1%

Portfolio's Excess Return = Portfolio Return - Risk Free Rate
= (14.5% + (1.26 * (Portfolio's Excess Return))) - 1%
= 13.5% + (1.26 * (Portfolio's Excess Return))

Solving for Portfolio's Excess Return,
(1.26 * Portfolio's Excess Return) = (Portfolio Return - Risk Free Rate) - 13.5%
= (14.5% - 1%) - 13.5%
= 0.10

Portfolio's Excess Return = 0.0794

Treynor Ratio = (Portfolio Return - Risk Free Rate) / beta
= (14.5% - 1%) / 1.26
= 11.5% / 1.26
= 0.091
= 0.135 (rounded off to three decimal places)

Therefore, the Treynor Ratio of the correctly valued portfolio is 0.135. The best choice is C.

Question 20

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

Accepted Answer

To find the smallest expected loss given a probability of 2.5%, we use the formula: 
Expected Loss = (Z score)(standard deviation) - (Expected Return) 
where Z score is the number of standard deviations away from the mean corresponding to the given probability. 
From standard normal distribution tables, we find that the Z score for a probability of 2.5% is approximately -1.96. 
Therefore, the expected loss is: 
Expected Loss = (-1.96)(20.3%) - (16.1%) = 10.14%. 
The best choice is (C), 10.14%.

Quiz 13: Performance Evaluation and Risk Management

Lester has a portfolio with an average return of 13.5% and a standard deviation of 22.5%. He has a 1% probability of losing ________% or more in any given year. $\begin{array}{cr}\text { Probability } & \text { "z" value } \\\text { of loss } & \\1.0\% & 2.326 \\2.5 & 1.960 \\5.0 & 1.645\end{array}$