FRM Questions and Answers : Foundations of Risk Management

FRM Questions and Answers

Greetings to all FRM candidates. We hope that you are following the other Doubt & Question (D&A) discussions as well. They are bound to come of use to you, especially at this crucial juncture. The FRM Level I Exam is on November 16, 2013, which is right around the corner!

Discussions like these are precise and to the point, hence not making you waste time!

In today’s discussion, we will be covering four questions pertaining to Foundations of Risk Management in FRM.

So without further ado, let’s get right to it!

Topics Covered in this discussion on Foundations of Risk Management:

Question 1

The AT&T pension fund reports total assets worth $19.6 billion and liabilities of $17.4 billion. Assume the surplus has a normal distribution and volatility of 10% per annum. The 95% surplus at risk over the next year is

a. $360 million

b. $513 million

c. $2,860 million

d. $3,220 million

Answer 1:

The answer is $360 million.

The fund’s surplus is the excess of assets over liabilities, which $19.6 – $17.4 = $2.2 billion.

The surplus at risk at the 95%level over one year is, assuming a normal distribution, 1.645 × 10%× $2,200 = $360 million. Answer b) is incorrect because it uses a 99% confidence level. Answers c) and d) are incorrect because they apply the risk to the liabilities and assets instead of the surplus.

One student, Judy, asked a question on Immunization, which is very important from the exam perspective. Check it out!

Question 2

A pension plan reports $12 billion in assets and $10 billion in present value of the benefit obligations. Future pension benefits are indexed to the rate of inflation. To immunize its liabilities, the plan should

a. Invest $12 billion of assets in fixed-coupon long-term bonds

b. Invest $10 billion of assets in fixed-coupon long-term bonds

c. Invest $10 billion of assets in cash

d. Invest $10 billion of assets in Treasury Inflation-Protected Securities

My solution was:

Answer 2:

The answer is Invest $10 billion of assets in Treasury Inflation-Protected Securities.

Immunization occurs when assets are invested so as to perfectly hedge changes in liabilities. So, the amount to invest is $10 billion, which is the value of liabilities. In this case, we are told that the pension payments are indexed to the rate of inflation. Because the liabilities are tied to inflation, immunization requires that the assets should react in a similar way to inflation. This can be achieved with Treasury inflation-protected securities (TIPS).

Another topic that may seem confusing is Sharpe Ratio and Treynor Ratio, which comes under Portfolio Management Read the following question to see if you are thorough with your answer!

Question 3

Kalpesh argues with Jayesh that the Sharpe Ratio and the Treynor ratio are similar with only some difference. He lists the following difference.

I.Sharpe uses the standard deviation, Treynor uses beta

II.S is more appropriate for well diversified portfolios, T for individual assets

III.For perfectly diversified portfolios, S and T will give the same ranking, but different numbers (the ranking, not the number itself, is what is most important)

Which of these arguments is/are correct

a. I and II only

b. I and III only

c. I only

d. All of the above

Answer 3:

The correct answer is all of the above.

Question 4

Assume that a hedge fund provides a large positive alpha. The fund can take leveraged long and short positions in stocks. The market went up over the period. Based on this information,

I. If the fund has net positive beta, all of the alpha must come from the market.

II. If the fund has net negative beta, part of the alpha comes from the market.

III. If the fund has net positive beta, part of the alpha comes from the market.

IV. If the fund has net negative beta, all of the alpha must come from the market.

a. II and III only

b. II and IV only

c. IV only

d. III only

Answer 4:

The answer is III only. Because the market went up, a portfolio with positive beta will have part of its positive performance due to the market effect. A portfolio with negative beta will have in part a negative performance due to the market. Answer I is incorrect because the fund manager could still have generated some of its alpha through judicious stock-picking. Answers II and IV are incorrect because a negative beta combined with a market going up should lead to a decrease, not an increase, in the alpha.