2007 FRM － Mock Exam 模考试题 (21 - 25)

21. Synthetic collateralized debt obligation (CDO) tranches are structured securities whose performance depends on the number of defaults in a portfolio of credit default swaps (CDS) .A typical synthetic CDO with an equity, mezzanine, senior tranche, and super senior tranche is shown below. Each of the tranches receives a contractual spread in exchange for absorbing losses in the portfolio. For instance, the equity tranche receives a 1,250 bps running spread in exchange for absorbing losses form 0% to 3%.

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CDO tranche size and structure

	Tranche	Size	Notional (in millions USD)	Spread over LIBOR
Equity	0%-3%	3%	30	12.50%
Mezzanine	3%-6%	3%	30	2.50%
Senior	6%-9%	3%	30	0.90%
Super Senior	9%-100%	91%	910	0.20%

Which of the following statements is correct?

a. The equity tranche holder is short a call option with a strike price of USD 30 million written on the value of the portfolio of CDS.

b. The super senior tranche holder is short a put option with a strike price of USD 90 million written on the value of the portfolio of CDS.

c. The mezzanine tranche holder is short a put option with a strike price of USD 60 million written on the value of the portfolio of CDS.

d. The senior tranche holder is long a put option with a strike price of USD 60 million written on the value of the portfolio of CDS.

22. Which of the following sentences best describes the volatility smile in equity options?

a. Actual volatility is higher for in-the-money options than for out-of-the-money options, possibly because the volatility is stochastic for longer maturity options.

b. Implied volatility derived from the Black-Scholes model is higher for in-the-money options than for at-the-money-options, possibly because the Black-Scholes model assumes there are jumps in underlying equity prices.

c. Implied volatility derived from the Black-Scholes model is higher for out-of-the-money options than for at-the-money-options, possibly because the Black-Scholes model assumes constant volatility.

d. Implied volatility derived from the Black-Scholes model is higher for at-the-money options than for in-the-money options, possibly because the Black-Scholes model assumes constant volatility.

23. Consider the following homogeneous reference portfolio in a synthetic collateralized debt obligation:

·Number of reference entities: 100

·Credit default swap (CDS) spread: 150 bps

·Recovery rate in case of default: 50%

Assume that defaults are independent. On a single name the annual default probability is constant over five years and obeys the relation: CDS Premium = (1- Recovery rate) * Annual Default Probability

What is the expected number of defaulting entities over the next five years, and which of the following tranches would be entirely wiped out (loses 100% of the principal invested) by the expected number of defaulting entities?

a. 14 defaults and a [3% - 14%] tranche would be wiped out

b. 3 defaults and a [0% - 1%] tranche would be wiped out

c. 7 defaults and a [2% -3%] tranche would be wiped out

d. 14 defaults and a [6% -7%] tranche would be wiped out

24. A hedge fund manager has to choose a risk model for a large “equity market neutral” portfolio. Many of the stocks held are recent IPOs. Among the following alternatives, the best is

a. A single index model with no specific risk, estimated over the last year.

b. A diagonal index model with idiosyncratic risk, estimated over the last year.

c. A model that maps positions on industry and style factors.

d. A full covariance matrix model using a very short window.

25. You are given the following information about firm A:

·Market value of asset at time 0 = 1000

·Market value of asset at time 1 = 1200

·Short-term debt = 500

·Long-term debt = 300

·Annualized asset volatility = 10%

According to the KMV model, what are the default point and the distance to default at time 1?