## Old Exam Questions

Risk Management and Investment Management

Professor's Note: Module 5, Risk Management and Investment Management, is relatively new to the FRM curriculum. As a result, fewer old exam questions exist for this material.

1. An analyst has compiled the following information on a portfolio:

Calculate the semi-standard deviation of the portfolio.

2. Suppose the daily returns of a portfolio and a benchmark portfolio it is replicating are as follows:

Portfolio Return (bps) Benchmark Portfolio Return (bps)

Day 1 34 30

Day 3 108 102

Day 4 70 70

What is the tracking error over the four day period?

3. Assume that a portfolio underperformed its benchmark by 2% in the most recent month. In this scenario,

A. Alpha is "-2%" as it refers to the Outperformance / Underperformance Gap.

B. Due to underperformance, Alpha is definitely negative and cannot be positive,

C. Alpha may be positive or negative depending upon Beta and Risk Free Rate.

4. Which of the following statements about the Sortino ratio are valid?

I. The Sortino ratio is more appropriate for asymmetrical return distributions.

II. The Sortino ratio compares the portfolio return to the return of a benchmark portfolio.

III. The Sortino ratio allows one to evaluate portfolios obtained through an optimization algorithm that uses variance as a risk metric.

IV. The Sortino ratio is defined on the same principles as the Sharpe ratio, but the Sortino ratio replaces the risk free rate with the minimum acceptable return and the standard deviation of returns with the standard deviation of returns below the minimum acceptable return.

5. A portfolio has an average return over the last year of 13.2%. Its benchmark has provided an average return over the same period of 12.3%. The portfolio's standard deviation is 15.3%, its beta is 1.15, its tracking error volatility is 6.5% and its semi-standard deviation is 9.4%. Lasdy the risk free rate is 4.5%.

Calculate the portfolio's Information Ratio (IR).

6. You are given the following information about a portfolio and are asked to make a recommendation about how to reallocate the portfolio to improve the risk/return tradeoff.

Asset |
Expected Return |
Standard Deviation |
Current Weight |
Covariance of portfolio and asset returns |
Marginal Return |
Marginal Risk |
Marginal Return/ Marginal Risk |
Risk Contribution |

Asset 1 |
7.10% |
17.00% |
38.70% |
1.43% |
3.10% |
13.99% |
22.17% |
5.41% |

Asset 2 |
8.00% |
40.60% |
6.20% |
2.44% |
4.00% |
23.93% |
16.71% |
1.48% |

Asset 3 |
6.70% |
44.80% |
5.50% |
2.39% |
2.70% |
23.39% |
11.55% |
1.29% |

Asset 4 |
6.90% |
21.40% |
14.60% |
1.41% |
2.90% |
13.86% |
20.92% |
2.02% |

Risk Free |
4.00% |
0.00% |
35.00% |
0.00% |

Which of the following the recommendations will improve the risk/return tradeoff of the portfolio?

A. Increase the allocations to assets 1 and 3 and decrease the allocations to assets

B. Increase the allocations to assets 1 and 2 and decrease the allocations to assets

C. Increase the allocations to assets 2 and 3 and decrease the allocations to assets

D. Increase the allocations to assets 1 and 4 and decrease the allocations to assets

7. Suppose a portfolio consists of a USD 1 million investment in Euros and a USD 4 million investment in Mexican Pesos. Additional information is given below:

• Diversified Portfolio VaR = USD 324,700

Based on the given information, the marginal VaR and the component VaR of the Euro position are closest to:

Marginal VaR |
Component VaR | |

A. |
USD 0.058 |
USD 58,446 |

B. |
USD 0.292 |
USD 292,230 |

C. |
USD 0.084 |
USD 337,688 |

D. |
USD 0.106 |
USD 422,110 |

8. Company XYZs pension fund has liabilities of USD 100 million and assets of USD 120 million. The annual growth of the liabilities has an expected valu'e of 5% with 3% volatility. The annual return of the assets has an expected value of 8% with 12% volatility. The correlation between asset return and liability growth is 0.3. What is the 95% surplus-at-risk?

A. USD 27.6 million.

B. USD 22.7 million.

C. USD 13.8 million.

### D. USD 18.1 million.

9. The DataSoft Corporation has an employee pension scheme with fixed liabilities and a long time horizon reflecting its young workforce. The fund's assets are USD

9 billion and the present value of its liabilities is USD 8.8 billion.

Which of the following statements is/are INCORRECT?

I. The present value of long-term fixed payments behaves very much like a long position in a fixed rate bond. II. Surplus at Risk is a measure of relative risk.

III. The DataSoft Corporation will be able to immunize its liabilities by investing USD 8 billion in long-term fixed rate bonds.

10. Consider a portfolio with 40% invested in asset X and 60% invested in asset Y. The mean and variance of return on X are 0 and 25 respectively. The mean and variance of return on Y are 1 and 121 respectively. The correlation coefficient between X and

. Y is 0.3. What is the nearest value for portfolio volatility?

"11. A relative value hedge fund manager holds a long position in Asset A and a short position in Asset B of roughly equal principal amounts. Asset A currently has a correlation with Asset B of 0.97. The risk manager decides to overwrite this correlation assumption in the variance-covariance based VAR model to a level of 0.30. What effect will this change in correlation from 0.97 to 0.30 have on the resulting VAR measure?

A. It increases VAR.

B. It decreases VAR.

C. It has no effect on VAR, but changes profit or loss of strategy!

### D. Do not have enough information to answer.

12. Consider a two-asset portfolio. The portfolio weight of Asset A is 0.6 and the portfolio weight of Asset B is 0.4. The value of the total portfolio is USD1 million and its standard deviation of its decimal return is 0.060606. If the betas of Asset A and Asset B are 0.8 and 1.3 respectively, the respective marginal VAR of Asset A and the component VAR of Asset B at a 95% confidence level are closest to:

13. A portfolio is composed of two securities and has the following characteristics:

• Investment in security A = USD 1,500,000

• Investment in security B = USD 3,000,000

• Correlation between security A and B = 10%

What is the closest answer for the portfolio diversified VAR at 95% confident level?

14. As one of your duties as the chief risk officer for a fund of funds, you evaluate the risk management of candidate hedge funds. In your evaluation of a newly organized two person hedge fund, which of the following is your primary consideration?

A. Risk reporting structure.

B. Investment style.

C. Assets under management.

D. Last month's return.

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