【FRM风险管理】债券与基础衍生品试题及解答-金程FRM

【FRM风险管理】债券与基础衍生品试题及解答

行业资讯 | 2020-05-26

今天金程FRM小编给大家推出，债券与基础衍生品试题及解答，本篇问题共6道有关债券与基础衍生品的试题，希望可以帮助大家！

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Q-1.Pear,Inc.is a manufacturer that is heavily dependent on plastic parts shipped from Malaysia.Pear wants to hedge its exposure to plastic price shocks over the next 7½months.Futures contracts,however,are not readily available for plastic.After some research,Pear identifies futures contracts on other commodities whose prices are closely correlated to plastic prices.Futures on Commodity A have a correlation of 0.85 with the price of plastic,and futures on Commodity B have a correlation of 0.92 with the price of plastic.Futures on both Commodity A and Commodity B are available with 6-month and 9-month expirations.Ignoring liquidity considerations,which contract would be the best to minimize basis risk?

A.Futures on Commodity A with 6 months to expiration

B.Futures on Commodity A with 9 months to expiration

C.Futures on Commodity B with 6 months to expiration

D.Futures on Commodity B with 9 months to expiration

Solution:D

In order to minimize basis risk,one should choose the futures contract with the highest correlation to price changes,and the one with the closest maturity,preferably expiring after the duration of the hedge.

Q-2.The hedge ratio is the ratio of derivatives to a spot position(or vice versa that achieves an objective such as minimizing or eliminating risk.Suppose that the standard deviation of quarterly changes in the price of a commodity is 0.57,the standard deviation of quarterly changes in the price of a futures contract on the commodity is 0.85,and the correlation between the two changes is 0.3876.What is the optimal hedge ratio for a 3-month contract?

A.0.1893

B.0.2135

C.0.2381

D.0.2599

Solution:D

The optimal hedge ratio can be determined by the formula:

Q-3.On Nov 1,Jimmy Walton,a fund manager of a USD 60 million US medium-to-large cap equity portfolio,considers locking up the profit from the recent rally.The S&P 500 index and its futures with the multiplier of 250 are trading at 900 and 910,respectively.Instead of selling off his holdings,he would rather hedge two-thirds of his market exposure over the remaining 2 months.Given that the correlation between Jimmy’s portfolio and the S&P 500 index futures is 0.89 and the volatilities of the equity fund and the futures are 0.51 and 0.48 per year respectively,what position should he take to achieve his objective?

A.Sell 250 futures contracts of S&P 500

B.Sell 169 futures contracts of S&P 500

C.Sell 167 futures contracts of S&P 500

D.Sell 148 futures contracts of S&P 500

Solution:C

The optimal hedge ratio is the product of the coefficient of correlation between the change in the spot price and the change in futures price,and the ratio of the volatility of the equity fund and the futures.

Two-thirds of the equity fund is worth USD 40 million.The optimal hedge ratio computed:

h=0.89×(0.51/0.48)=0.945

Computing the number of futures contracts:

N=0.945×40,000,000/(910×250)=166.26≈167,round up to nearest integer.

Q-4.The current value of the S&P 500 index futures is 1457,and each S&P futures contract is for delivery of 250 times the index.A long-only equity portfolio with market value of USD 300,100,000 has beta of 1.1.To reduce the portfolio beta to 0.75,how many S&P futures contract should you sell?

A.288 contracts

B.618 contracts

C.906 contracts

D.574 contracts

Solution:A

This is as in the previous question,but the hedge is partial,i.e.for a change of 1.10 to 0.75.So,

Q-5.Two companies,C and D,have the borrowing rates shown in the following table.

According to the comparative advantage argument,what is the total potential savings for C and D if they enter into an interest rate swap?

A.0.5%

B.1.0%

C.1.5%

D.2.0%

Solution:C

The difference of the differences is(12%–10%)–[LIBOR+1%–(LIBOR+0.5%)]=1.5%.

Q-6.Consider the following 3-year currency swap,which involves exchanging annual interest of 2.75%on 10 million US dollars for 3.75%on 15 million Canadian dollars.The CAD/USD spot rate is 1.52.The term structure is flat in both countries.Calculate the value of the swap in USD if interest rates in Canada are 5%and in the United States are 4%.Assume continuous compounding.Round to the nearest dollar.

A.$152,000

B.$145,693

C.$131,968

D.$127,818

Solution:C

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