FRM一级模考

FRM一级模拟题

1. Which of the following best describes the relationship between leverage,margin calls, position size, and liquidity as presented in the Long-Term CapitalManagement case?

a. Leverage allows a firm to establish large positions than can generate largemargin calls and force, liquidations that can exacerbate declining marketprices.

b. Leverage can help offset the risk of being unable to meet large margin callsgenerated from large positions, thereby increasing a firm's liquidity.

c. Margin calls create leverage that can force a firm to assume illiquid positionseven in small trades.

d. Margin calls decrease the liquidity of a position unless the firm uses leverageto decrease the size of a hedg

e.

解析：a

LTCM assumed an enormous degree o(levernge, in part. because financial insumtionswith which they dealt waived margin requirements. ]heir balance sheer, leverage wasmagnified by the economic level of the positions they assumed. As a result, theirpositions were extremely large. particularly in relation m the limited liquidity in some ofthe markers. When changes in asses prices created significant marked-marker losses,LTCM did not have the equity en sneer the margin calls due to their high degree ofleverage. They were therefore forced so liquidate large illiquid positions, which movedmarker prim in such a way as to create more margin calls and more forced liquidation.

2. For the past four years, the returns on a portfolio were 6%, 9%, 4%, and 12%.The corresponding returns of the benchmark were 7%, 10%, 4%, and 10%.The minimum acceptable return is 7% and the mean squared deviation from theminimum return is 2.5. The portfolio's Sortino ratio is:

a. 0.4743.

b. 0.2143.

c. 0.5303.

d. 0.6700.

解析：a

The benchmark nmcoaan not important here. The avenge of the portfolio returns i.

(6+9+4+12)/4=31/4=7.75.

3. A portfolio manager manages a $10 million portfolio that has a beta of 1.0relative to the S&P 500. The S&P 500 futures are trading at 1,100 and themultiplier is 250. He would like to hedge exposure to market risk over the nextfew months. Suppose that at the maturity of the futures contract, the marketindex is trading at 1,090 and the portfolio has experienced a 1% decline invalue. Evaluate the following statements:

I. The appropriate hedge for the portfolio is a long position in 36 contracts.

II. The net impact of the market decline on the appropriately hedged portfoliois a gain of $10,000.

a. Only statement I is correct.

b. Only statement II is correct.

c. Both statements are correct.

d. Neither statement is correct.

解析：d Neither statement is correct. The appropriate number of contracts for the hedge is:

= βportfolio ×36250$100,1000,000,10$0.1Pr ≈⎪⎭⎫ ⎝⎛⨯⨯=⎪⎪⎭

⎫ ⎝⎛⨯multiplier ice futures alue portfolioV contracts However, since the manager is long the portfolio, he will want to take a short position inthe 36 contracts.

Change in value of portfolio =-0.01($10,000,000) = -$100,000.

Change in value of futures position = 36(1,100 - 1,090)($250) = +$90,000.

Net payoff = -$100,000 + $90,000 = -$10,000. The net impact is a loss of $10,000.

4. Given the following 1-year transition matrix, what is the probability that an Aaarated firm will default over a 2-year period?