NISM Series X-A Chapter 16: Portfolio Performance Measurement and Evaluation Practice Questions

Question 1

A fund has a portfolio return of 15.00%, a risk-free rate of 5.00%, and a portfolio beta of 1.25. Calculate the Treynor Ratio for this fund.

Accepted Answer

0.08. As per section 16.4.2, the Treynor Ratio formula is: 
Treynor Ratio (T) = (Rp – Rf) / Bp
Where:
Rp = Portfolio return = 15.00% = 0.15
Rf = Risk-free return = 5.00% = 0.05
Bp = Portfolio beta = 1.25
T = (0.15 - 0.05) / 1.25
T = 0.10 / 1.25
T = 0.08

Question 2

All of the following are stated characteristics of a good benchmark EXCEPT:

Accepted Answer

It must consist of a fixed set of components that never change to ensure consistency.. Section 16.5.1 lists several characteristics of a good benchmark, including clearly defined constituents/weights, investability, consistency with investment approach, same risk-return profile, and measurable performance. The text does not state that a benchmark must consist of a fixed set of components that never change; in fact, section 16.5.3 implies that changes in components can occur and need to be reviewed ('The benchmark should not be witnessing huge changes in its components otherwise this would need to be reviewed for its effectiveness.')

Question 3

In the Information Ratio (IR = (Rp – Rb)/Stdev (p-b)), what does the denominator, Stdev (p-b), represent?

Accepted Answer

The active risk of the portfolio, which is also referred to as tracking error.. The text states: 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns. ... It has to be noted that active risk is nothing but tracking error of the portfolio.'

Question 4

A portfolio has an annualized return of 12%, an annualized standard deviation of 8%, and the risk-free rate is 5%. Calculate the Sharpe Ratio for this portfolio.

Accepted Answer

0.875. As per section 16.4.1, the Sharpe Ratio formula is: 
Sharpe Ratio = (Rp - Rf) / Sigma p
Where: 
Rp = Return of the portfolio = 12% (0.12)
Rf = Risk-free return = 5% (0.05)
Sigma p = Standard deviation of return on the portfolio = 8% (0.08)
Sharpe Ratio = (0.12 - 0.05) / 0.08
Sharpe Ratio = 0.07 / 0.08
Sharpe Ratio = 0.875

Question 5

Using the same portfolio data as in the Sharpe Ratio example (annualized return = 10.50%, risk-free rate = 5.50%), if the beta of the fund is 1, what is its Treynor Ratio?

Accepted Answer

0.05. As per section 16.4.2, the Treynor Ratio formula is T = (Rp - Rf) / Beta_p.
Rp = 10.50%
Rf = 5.50%
Beta_p = 1
Treynor Ratio = (10.50% - 5.50%) / 1 = 5.00% / 1 = 0.05

Question 6

A portfolio consists of three stocks: Stock X with a Beta of 1.3 and a weight of 30%, Stock Y with a Beta of 0.9 and a weight of 50%, and Stock Z with a Beta of 1.1 and a weight of 20%. What is the Beta of this portfolio?

Accepted Answer

1.06. The Beta of the portfolio is calculated as the weighted average of the individual securities' Betas.
Portfolio Beta = (Weight of X * Beta of X) + (Weight of Y * Beta of Y) + (Weight of Z * Beta of Z)
Portfolio Beta = (0.30 * 1.3) + (0.50 * 0.9) + (0.20 * 1.1)
Portfolio Beta = 0.39 + 0.45 + 0.22
Portfolio Beta = 1.06

Question 7

Tracking error is always calculated against which type of index?

Accepted Answer

Total Returns Index. As per the text, 'Tracking Error is always calculated against the Total Returns Index which shows the returns on the Index portfolio, inclusive of dividend.'

Question 8

Which of the following is NOT listed as a criterion for a good benchmark in the provided text?

Accepted Answer

The benchmark is composed of at least 50 constituents.. The text lists criteria for a good benchmark: 'The identity of constituents and their weights in the benchmark are clearly defined.', 'The benchmark is investable...', 'The benchmark is consistent with the portfolio’s investment approach.', 'The benchmark is having the same risk-return profile as the portfolio', 'The performance of the benchmark is measurable.' The number of constituents is not mentioned as a criterion

Question 9

An investor holds a poorly diversified portfolio. Which risk-adjusted return measure would be more appropriate for evaluating its performance, and why?

Accepted Answer

Sharpe Ratio, because it adjusts return for total portfolio risk, which includes both systematic and unsystematic risk relevant for poorly diversified portfolios.. According to section 16.4.3, 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios.' This is because Sharpe Ratio uses total risk (standard deviation), which captures both systematic and unsystematic risk, both of which are significant in a poorly diversified portfolio

Question 10

According to the text, which type of risk can be diversified away?

Accepted Answer

Unsystematic risk, linked to sector-specific factors.. Section 16.3.6 states, 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Systematic risk cannot be diversified away

Question 11

What is the primary cause of tracking errors between a portfolio and its target benchmark?

Accepted Answer

Mismatches between the portfolio's risk profile and the benchmark's risk profile.. According to the text, 'Tracking errors primarily arises due to mismatches between portfolio’s risk profile and the benchmark’s risk profile.'

Question 12

An investor holds a poorly diversified portfolio and wishes to evaluate its performance. Which risk-adjusted return measure would be most suitable for this investor?

Accepted Answer

Sharpe Ratio. The text states, 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios'. Therefore, Sharpe Ratio is suitable for a poorly diversified portfolio

Question 13

For an investor whose wealth is not adequately diversified, which risk-adjusted return measure is generally more suitable for evaluating portfolio performance?

Accepted Answer

Sharpe Ratio, because it adjusts return to the total portfolio risk.. The text states: 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios'. This is because Sharpe Ratio adjusts return to total portfolio risk (standard deviation), which includes unsystematic risk relevant to an undiversified investor

Question 14

What is tracking error in the context of portfolio performance measurement?

Accepted Answer

The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.. As per section 16.3.5, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' Option A describes tracking difference, C describes Beta, and D describes Credit risk

Question 15

What is defined as the standard deviation of the difference between the portfolio and its target benchmark portfolio total return?

Accepted Answer

Tracking error. Tracking error is defined as the standard deviation of the difference between the portfolio and its target benchmark portfolio total return. Tracking difference is a simpler point-to-point difference, while systematic and unsystematic risks are different categories of risk

Question 16

What is the key distinction between Tracking Error and Tracking Difference?

Accepted Answer

Tracking Error is the standard deviation of return differences between a portfolio and its benchmark, while Tracking Difference is the simple point-to-point difference between index return and fund return.. Section 16.3.5 states: 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' It also states: 'Tracking difference is layman’s approach - just the simple point-to-point difference between index return and fund return.'

Question 17

A fund has a portfolio return (Rp) of 12.00%, a risk-free rate (Rf) of 4.00%, and a portfolio Beta (Bp) of 1.5. Calculate the Treynor Ratio for this fund.

Accepted Answer

0.053. As per section 16.4.2, the Treynor Ratio formula is T = (Rp - Rf) / Bp.
Given:
Rp = 12.00% = 0.12
Rf = 4.00% = 0.04
Bp = 1.5
Treynor Ratio = (0.12 - 0.04) / 1.5
Treynor Ratio = 0.08 / 1.5
Treynor Ratio ≈ 0.0533

Question 18

In the Information Ratio formula, IR = (Rp – Rb) / Stdev (p-b), what does the denominator 'Stdev (p-b)' primarily represent?

Accepted Answer

The active risk or tracking error of the portfolio.. The text states: 'The denominator could be considered as a measure of the amount of residual (unsystematic) risk that the investor incurred in pursuit of those excess returns. The numerator is often referred to as the active return on the portfolio whereas denominator is referred to as the active risk. It has to be noted that active risk is nothing but tracking error of the portfolio.'

Question 19

A portfolio has an annualized return of 12.0% and an annualized standard deviation of 8.0%. If the risk-free rate of return is 4.0%, what is the Sharpe ratio for this portfolio?

Accepted Answer

1.00. The Sharpe Ratio formula is: S = (Rp - Rf) / Sigma p
Where:
Rp = Return of the portfolio = 12.0%
Rf = Risk-free return = 4.0%
Sigma p = Standard deviation of return on the portfolio = 8.0%

S = (12.0% - 4.0%) / 8.0%
S = 8.0% / 8.0%
S = 1.00

Question 20

A portfolio has generated a return of 30% with a standard deviation of 35%. The market portfolio has generated a return of 20% with a standard deviation of 25%. The treasury bill rate is 5%. Using the M2 measure, what is the risk-adjusted return of the portfolio (rp*)?

Accepted Answer

22.86%. To calculate the M2 risk-adjusted return (rp*), we first need to adjust the portfolio's risk to match the market's risk.
1. Calculate the proportion of the portfolio (P) to hold to match the market's standard deviation:
   Proportion in P = (Market's Standard Deviation) / (Portfolio's Standard Deviation)
   Proportion in P = 25% / 35% = 5/7 ≈ 0.714286
2. Calculate the proportion to hold in the risk-free asset (T-bills):
   Proportion in T-bills = 1 - Proportion in P = 1 - (5/7) = 2/7 ≈ 0.285714
3. Calculate the risk-adjusted return (rp*):
   rp* = (Proportion in P * Return on Portfolio) + (Proportion in T-bills * Risk-free rate)
   rp* = (5/7 * 0.30) + (2/7 * 0.05)
   rp* = (1.50/7) + (0.10/7)
   rp* = 1.60/7 ≈ 0.22857
   rp* ≈ 22.86%

Question 21

What is the primary difference between 'tracking error' and 'tracking difference' as described in the text?

Accepted Answer

Tracking error is the standard deviation of the difference between portfolio and benchmark total return, while tracking difference is the simple point-to-point difference between index and fund return.. As per section 16.3.5, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' and 'Tracking difference is layman’s approach - just the simple point-to-point difference between index return and fund return.'

Question 22

A portfolio has generated a return of 30% with a standard deviation of 40%. The market portfolio returned 20% with a standard deviation of 25%. The treasury bill rate is 5%. Using the Modigliani and Modigliani (M2) Measure, if the portfolio's risk is adjusted to match the market's standard deviation, what is the adjusted return of the portfolio (rp*)?

Accepted Answer

20.63%. As per section 16.4.6, the M2 measure adjusts the risk of the portfolio to match the market portfolio's standard deviation by levering or de-levering.
1. Determine the proportion of the portfolio (P) and T-bills (Rf) to match market volatility:
   Market's standard deviation = 25%
   Portfolio's standard deviation = 40%
   Proportion in Portfolio (P) = Market's std dev / Portfolio's std dev = 25% / 40% = 0.625
   Proportion in T-bills = 1 - Proportion in Portfolio = 1 - 0.625 = 0.375
2. Calculate the adjusted portfolio return (rp*):
   rp* = (Proportion in P * Return of Portfolio) + (Proportion in T-bills * Risk-free rate)
   rp* = (0.625 * 0.30) + (0.375 * 0.05)
   rp* = 0.1875 + 0.01875
   rp* = 0.20625 = 20.625%
Rounding to two decimal places, this is 20.63%

Question 23

According to the text, what primarily causes tracking errors?

Accepted Answer

Mismatches between the portfolio’s risk profile and the benchmark’s risk profile.. The text states: 'Tracking errors primarily arises due to mismatches between portfolio’s risk profile and the benchmark’s risk profile.'

Question 24

A portfolio consists of Stock X with a beta of 1.3 and Stock Y with a beta of 0.9. If Stock X makes up 70% of the portfolio and Stock Y makes up 30%, what is the beta of the portfolio?

Accepted Answer

1.18. The Beta of the portfolio is calculated by taking the weighted average beta of the individual securities. 
Portfolio Beta = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y)
Portfolio Beta = (0.70 * 1.3) + (0.30 * 0.9)
Portfolio Beta = 0.91 + 0.27
Portfolio Beta = 1.18

Question 25

A portfolio has an annualized return of 15.00% and an annualized standard deviation of 10.00%. If the risk-free rate of return is 6.00%, what is the Sharpe Ratio for this portfolio?

Accepted Answer

0.90. As per section 16.4.1, the Sharpe Ratio formula is S = (Rp - Rf) / Sigma_p.
Given:
Rp = 15.00% = 0.15
Rf = 6.00% = 0.06
Sigma_p = 10.00% = 0.10
Sharpe Ratio = (0.15 - 0.06) / 0.10
Sharpe Ratio = 0.09 / 0.10
Sharpe Ratio = 0.90

Question 26

Which type of risk, as described in the text, can be diversified away?

Accepted Answer

Unsystematic risk. The text states, 'Risks due to sector specific/company specific factors is referred as unsystematic risks. These risks can be diversified away.' Systematic risk, interest rate risk, and exchange rate risk are all forms of systematic risk which cannot be diversified away

Question 27

Which type of risk is defined as the uncertainty introduced by the secondary market of an investment, relating to the ease of converting an asset into cash at close to its economic worth?

Accepted Answer

Liquidity risk. Section 16.3.8 states, 'Liquidity risk is the uncertainty introduced by the secondary market of an investment.' and 'Liquidity is defined as ease of converting an asset into cash at close to its economic worth.'

Question 28

For which type of investor is the Treynor Ratio generally a more appropriate measure of performance compared to the Sharpe Ratio?

Accepted Answer

An investor whose wealth is already well diversified, with minimal unsystematic risk.. Section 16.4.3 states: 'The Sharpe Ratio is more suitable to evaluate a portfolio performance for an investor who has not achieved adequate diversification on his wealth as a whole, and Treynor Ratio should be used for investors who hold their wealth in well diversified portfolios'. This is because the Treynor Ratio focuses on systematic risk, which is the only risk that matters for well-diversified investors

Question 29

A portfolio consists of Stock X with a Beta of 1.3 and Stock Y with a Beta of 0.9. If Stock X makes up 70% of the portfolio and Stock Y makes up 30%, what is the Beta of the portfolio?

Accepted Answer

1.18. As per section 16.3.7, the Beta of the portfolio is the weighted average beta of the individual securities.
Portfolio Beta = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y)
Bp = (0.70 * 1.3) + (0.30 * 0.9)
Bp = 0.91 + 0.27
Bp = 1.18

Question 30

Which of the following best defines Tracking Error?

Accepted Answer

The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.. As per section 16.3.5, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.' Option A describes tracking difference, while C and D describe liquidity risk and credit risk, respectively

Question 31

A fund has an annualized return of 13.00% and a beta of 1.2. If the risk-free rate of return is 5.00%, what is the Treynor ratio for this fund?

Accepted Answer

0.0667. The Treynor Ratio is calculated as: 
Treynor Ratio = (Rp - Rf) / Bp
Where:
Rp = Portfolio return = 13.00%
Rf = Risk-free return = 5.00%
Bp = Portfolio beta = 1.2
Treynor Ratio = (13.00% - 5.00%) / 1.2 = 8.00% / 1.2 = 0.06666...
Rounded to 0.0667

Question 32

Which of the following is NOT listed as a criterion for a good benchmark?

Accepted Answer

The benchmark is actively managed to outperform the portfolio.. The text lists the criteria for a good benchmark: 'The identity of constituents and their weights in the benchmark are clearly defined.', 'The benchmark is investable...', 'The benchmark is consistent with the portfolio’s investment approach.', 'The benchmark is having the same risk-return profile as the portfolio', and 'The performance of the benchmark is measurable.' An actively managed benchmark designed to outperform the portfolio is not mentioned as a criterion

Question 33

According to the text, what is tracking error?

Accepted Answer

The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.. Tracking error is defined as the standard deviation of the difference between the portfolio and its target benchmark portfolio total return. Option A describes tracking difference, not tracking error

Question 34

A portfolio consists of two stocks: Stock X with a beta of 1.3 and Stock Y with a beta of 0.9. If Stock X makes up 70% of the portfolio and Stock Y makes up 30%, what is the Beta of the portfolio?

Accepted Answer

1.18. The Beta of a portfolio is the weighted average beta of the individual securities. 
Portfolio Beta = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y)
Portfolio Beta = (0.70 * 1.3) + (0.30 * 0.9)
Portfolio Beta = 0.91 + 0.27
Portfolio Beta = 1.18

Question 35

Which of the following is NOT a characteristic of a good benchmark for portfolio performance evaluation?

Accepted Answer

The benchmark has a significantly different risk-return profile than the portfolio to highlight manager skill.. A good benchmark should have 'the same risk-return profile as the portfolio', as stated in the text. A significantly different risk-return profile would make it an unsuitable comparison for evaluating performance

Question 36

Which of the following is NOT a characteristic of a good benchmark as per the provided text?

Accepted Answer

The benchmark exclusively consists of market-based indices to avoid customization costs.. Section 16.5.1 and 16.5.2 list characteristics of good benchmarks and discuss customized benchmarks. Options A, B, and C are explicitly mentioned as criteria for a good benchmark. Option D is incorrect because the text acknowledges that 'market-based indices may not meet the above criteria' and 'Such situation demands for appropriate customized benchmark', indicating that good benchmarks are not exclusively market-based indices

Question 37

What is the primary distinction between 'tracking error' and 'tracking difference'?

Accepted Answer

Tracking error is the standard deviation of the difference between portfolio and benchmark returns, while tracking difference is the simple point-to-point difference.. The text states, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return,' and 'Tracking difference is layman’s approach - just the simple point-to-point difference between index return and fund return.'

Question 38

Stock P has a beta of 1.3 and Stock Q has a beta of 0.9. If a portfolio is constructed with 70% invested in Stock P and 30% in Stock Q, what is the Beta of the portfolio?

Accepted Answer

1.18. As per section 16.3.7, 'Beta of the portfolio can also be calculated by taking the weighted average beta of the individual securities/investments in the portfolio.'
Portfolio Beta = (Weight of Stock P * Beta of Stock P) + (Weight of Stock Q * Beta of Stock Q)
Portfolio Beta = (0.70 * 1.3) + (0.30 * 0.9)
Portfolio Beta = 0.91 + 0.27
Portfolio Beta = 1.18

Question 39

Credit risk primarily arises in the case of which type of financial instruments?

Accepted Answer

Debt instruments. Section 16.3.9 states, 'Credit risk arises in case of debt instruments.'

Question 40

An investment portfolio consists of two stocks, Stock X and Stock Y. Stock X has a beta of 1.3 and makes up 70% of the portfolio. Stock Y has a beta of 0.9 and makes up 30% of the portfolio. What is the Beta of this portfolio?

Accepted Answer

1.18. The Beta of the portfolio is calculated by taking the weighted average beta of the individual securities. 
Portfolio Beta (Bp) = (Weight of Stock X * Beta of Stock X) + (Weight of Stock Y * Beta of Stock Y)
Bp = (0.70 * 1.3) + (0.30 * 0.9)
Bp = 0.91 + 0.27
Bp = 1.18

Question 41

A fund has an annualized return of 15%, a risk-free rate of 5%, and a portfolio beta of 1.25. Calculate the Treynor Ratio and interpret its meaning.

Accepted Answer

0.08; The fund generated 0.08 percentage points of excess return for every unit of systematic risk.. The Treynor Ratio (T) is calculated as (Rp - Rf) / Bp.
Rp = 15% = 0.15
Rf = 5% = 0.05
Bp = 1.25
T = (0.15 - 0.05) / 1.25 = 0.10 / 1.25 = 0.08
Interpretation: The text states, 'This indicates that the fund has generated 0.05-percentage point excess returns for every unit of systematic risk.' Applying this logic, 0.08 means the fund generated 0.08 percentage points of excess return for every unit of systematic risk

Question 42

According to the text, which of the following is NOT a characteristic of a good benchmark?

Accepted Answer

The benchmark's performance data is not always required to be measurable.. As per section 16.5.1, one of the criteria for a good benchmark is: 'The performance of the benchmark is measurable.' Therefore, option C, which states the opposite, is NOT a characteristic of a good benchmark

Question 43

Which of the following is NOT listed as a criterion for a good benchmark?

Accepted Answer

The benchmark is comprised solely of market-based indices.. Section 16.5.1 lists the characteristics of a good benchmark, which include options A, B, and C. The text also discusses customized benchmarks (16.5.2) when market-based indices are not suitable, indicating that benchmarks are not solely market-based

Question 44

A portfolio has an annualized return of 15.00%, and the risk-free rate is 5.00%. If the portfolio's Beta is 1.2, what is its Treynor Ratio?

Accepted Answer

0.0833. Treynor Ratio = (Rp - Rf) / Bp
Given:
Rp = 15.00% (0.15)
Rf = 5.00% (0.05)
Bp = 1.2
Treynor Ratio = (0.15 - 0.05) / 1.2
Treynor Ratio = 0.10 / 1.2
Treynor Ratio = 0.0833 (approximately)

Question 45

Which of the following is NOT listed as a criterion for a good benchmark?

Accepted Answer

The benchmark is designed to maximize returns regardless of risk.. Section 16.5.1 lists characteristics of good benchmarks. Options A, B, and D are all listed. Option C, 'The benchmark is designed to maximize returns regardless of risk,' is not a criterion; instead, a good benchmark should have 'the same risk-return profile as the portfolio.'

Question 46

Stock P has a beta of 1.3 and Stock Q has a beta of 0.9. If a portfolio is constructed with 70% in Stock P and 30% in Stock Q, what is the Beta of the portfolio?

Accepted Answer

1.18. As per section 16.3.7, 'Beta of the portfolio can also be calculated by taking the weighted average beta of the individual securities/investments in the portfolio.'
Portfolio Beta = (Weight of Stock P * Beta of Stock P) + (Weight of Stock Q * Beta of Stock Q)
Bp = (0.70 * 1.3) + (0.30 * 0.9)
Bp = 0.91 + 0.27
Bp = 1.18

Question 47

What is tracking error primarily defined as?

Accepted Answer

The standard deviation of the difference between the portfolio and its target benchmark portfolio total return.. As per section 16.3.5, 'Tracking error is the standard deviation of the difference between the portfolio and its target benchmark portfolio total return.'

Question 48

A portfolio has an annualized return of 12%, an annualized standard deviation of 8%, and the risk-free rate of return is 4%. Calculate the Sharpe Ratio for this portfolio.

Accepted Answer

1.00. The Sharpe Ratio is calculated as (Return of the portfolio - Risk-free return) / Standard deviation of return on the portfolio.
Sharpe Ratio = (Rp - Rf) / Sigma p
Sharpe Ratio = (12% - 4%) / 8%
Sharpe Ratio = 8% / 8%
Sharpe Ratio = 1.00

Question 49

The Sortino Ratio adjusts a portfolio's excess return to which specific type of risk?

Accepted Answer

Downside risk. The text explicitly states, 'Sortino Ratio adjusts portfolio’s excess return to the downside risk.'

Question 50

What is the primary adjustment made to a portfolio when calculating the Modigliani and Modigliani Ratio (M2) measure?

Accepted Answer

The portfolio's risk is adjusted to match the risk of the market portfolio.. The text states: 'They have adjusted the risk of the portfolio to match the risk of the market portfolio.' and 'To adjust the risk of the portfolio, they resorted to levering or de-levering.'

Ch.16: Portfolio Performance Measurement and Evaluation

What You Will Learn in This Chapter

Multiple Choice Questions (150)

Case-Based Questions (5 sets)

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