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Can someone help me do this exam. I have answer, but I need the explaination?step by step.?


TestId: 2001

 

For each problem, choose the answer choice that best answers the question.

 

Name

 


 

___________________________________

 

1 ____________

 


 

13 ____________

 


 

2 ____________

 


 

14 ____________

 


 

3 ____________

 


 

15 ____________

 


 

4 ____________

 


 

16 ____________

 


 

5 ____________

 


 

17 ____________

 


 

6 ____________

 


 

18 ____________

 


 

7 ____________

 


 

19 ____________

 


 

8 ____________

 


 

20 ____________

 


 

9 ____________

 


 

21 ____________

 


 

10 ____________

 


 

22 ____________

 


 

11 ____________

 


 

23 ____________

 


 

12 ____________

 


 

24 ____________

 

25 ____________

 


 

TestId: 2001

 


 

TestId: 2001

 

Question 1)

 

The continuously-compounded zero rate for a bond with maturity in 0.5 years is 3.3%. The continouslycompounded zero rate for a bond with maturity in 1 year is 3.6%. The continuously compounded forward

 

rate for a loan to be made in 0.5 years and paid back in 1.5 years (1 year after the loan is made) is 3.9%.

 

What is the price of a zero-coupon bond with face value of $100 maturing in 1.5 years?

 

1)

 

2)

 

3)

 

4)

 


 

$96.37

 

$95.17

 

$94.60

 

$94.32

 


 

TestId: 2001

 

Question 2)

 

I have created a bear spread by buying a put option with a strike price of $25 and selling a put option with

 

a strike price of $20. If the price of the underlying stock at expiration is $23.50, what is the payoff of my

 

trading strategy?

 

1)

 

2)

 

3)

 

4)

 


 

$3.50

 

$1.50

 

$5.00

 

-$5.00

 


 

TestId: 2001

 

Question 3)

 

Which of the following statements regarding option Greeks is FALSE?

 

1) Holding all else equal, the vega of an at-the-money option is higher than the vega of an outof-the-money option or the vega of an in-the-money option.

 

2) Holding all else equal, the theta of an at-the-money option is much smaller in magnitude

 

than the theta of an out-of-the-money or in-the-money option.

 

3) The gamma of all options is positive.

 

4) Holding all else equal, the gamma of an at-the-money option is higher than the gamma of an

 

out-of-the-money option or the gamma of an in-the-money option.

 


 

TestId: 2001

 

Question 4)

 

Which of the following is FALSE regarding the Black-Scholes-Merton option

 

pricing model?

 

1) If N(d 1 ) is between -1 and 1 then N(d 2 ) will be greater than 1

 

in absolute value, and vice versa.

 

2) As the spot price of the underlying stock gets very high, d 1 gets

 

very large and N(d 1 ) approaches 1.00.

 

3) N(d 2 ) is the risk-neutral probability that a call option will be

 

exercised.

 

4) As the spot price of the underlying stock gets very small

 

(approaches 0), d 1 becomes negative and large in magnitude

 

and N(d 1 ) approaches 0.

 


 

TestId: 2001

 

Question 5)

 

You own a 2-month European put option with a strike price of $30 on a stock that is currently worth $35. The

 

implied volatility of the option you own is 20%. News on the stock is announced that causes investors to be

 

unsure about the future prospects of the firm. In a very short amount of time the price of the stock drops to

 

$28 and the volatility used to price the option jumps to 24%. Which of the following is true regarding the value

 

of the put option?

 

1)

 

2)

 

3)

 

4)

 


 

The value of the put option decreases.

 

The value of the put option may increase but it also may decrease.

 

The value of the put option increases.

 

The value of the put option stays the same.

 


 

TestId: 2001

 

Question 6)

 

On June 18th, an investor took a short position in 8 September wheat futures contracts when the futures

 

price was $5.36. Each contract is on 5,000 bushels of wheat. The initial margin is $1,430 per contract and

 

the maintenance margin is $1,300 per contract. On July 22nd, the investor gets a margin call requiring an

 

additional deposit of $2,000. On August 13th, the investor buys back all 8 futures contracts when the

 

futures price is $5.48. How much money did the investor make or lose on the futures trade?

 

1)

 

2)

 

3)

 

4)

 


 

Gain of $3,370

 

Gain of $600

 

Loss of $4,800

 

Loss of $3,370

 


 

TestId: 2001

 

Question 7)

 

According to the Black, Scholes, Merton option pricing model, what is the value of a 6-month European

 

call option with a strike price of $21 on a stock that is worth $19 today, pays no dividends, and has a

 

volatilty of 45%? The risk-free rate is 5%. When answering this question you may use the information

 

below.

 

N(d1)=0.4694

 

N(d2)=0.3464

 

N(-d1)=0.5306

 

N(-d2)=0.6536

 

N'(d1)=N'(-d1)=0.3978

 

N'(d2)=N'(-d2)=0.369

 

1)

 

2)

 

3)

 

4)

 


 

$2.45

 

$1.82

 

$8.19

 

$3.00

 


 

TestId: 2001

 

Question 8)

 

The current S&P 500 index level is 2,106. The 6-month continuously compounded zero rate is 4%.

 

The 6-month forward price for the S&P 500 index is 2128.23. What is the dividend yield on the S&P

 

500 index?

 

1)

 

2)

 

3)

 

4)

 


 

1.3%

 

0.0%

 

1.9%

 

1.1%

 


 

TestId: 2001

 

Question 9)

 

The current price of a stock is $20. If I believe that over the next 3 months the price of a

 

stock is going to stay very close to $20, which of the following option strategies could I use to

 

create a portfolio that will profit if my prediction is correct?

 

1)

 

2)

 

3)

 

4)

 


 

Long strangle

 

Long brass monkey

 

Long strip

 

Long butterfly spread

 


 

TestId: 2001

 

Question 10)

 

I own a 3-month straddle position comprised of European options with a strike price of $42 on a non-dividendpaying stock with market price of $45. The risk-free rate is 2% and the price of the put position in my straddle is

 

$4.31. What is the total price of my straddle position?

 

1)

 

2)

 

3)

 

4)

 


 

$7.31

 

$2.81

 

$11.83

 

$8.62

 


 

TestId: 2001

 

Question 11)

 

Which of the following regarding cross-hedging with futures contracts is TRUE?

 

1) When choosing which futures contract to use as the hedge, the best contract

 

to use is the contract that has the lowest volatility because this is the least

 

risky hedge.

 

2) When choosing which futures contract to use as the hedge, the best contract

 

to use is the contract that has the lowest hedge ratio.

 

3) When choosing which futures contract to use as the hedge, the best contract

 

to use is the contract that has the highest correlation with the asset being

 

hedged.

 

4) When choosing which futures contract to use as the hedge, the best contract

 

to use is the contract that has the highest hedge ratio.

 


 

TestId: 2001

 

Question 12)

 

Ten years ago I took a 30-year loan at a fixed interest rate of 5% per year. Now, I want to transform the

 

loan from a fixed rate loan into a floating rate loan. Which of the following will achieve my objective?

 

1) Enter an interest rate swap in which I will receive a fixed rate of interest and pay a floating

 

rate of interest.

 

2) Enter an interest rate swap in which I will receive a floating rate of interest and pay a fixed

 

rate of interest.

 

3) Buy a fixed rate bond.

 

4) Buy a floating rate bond.

 


 

TestId: 2001

 

Question 13)

 

My business will sell machinery to a foreign firm for 25 million euros in September. The current exchange

 

rate for euros is $1.18 per euro. I want to take an option position that locks in a minimum effective

 

exchange rate of $1.15 per euro in September. Which of the following positions is most appropriate?

 

1)

 

2)

 

3)

 

4)

 


 

Long position in September euro puts with a strike of $1.15

 

Short position in September euro puts with a strike of $1.15

 

Short position in September euro calls with a strike of $1.15

 

Long position in September euro calls with a strike of $1.15

 


 

TestId: 2001

 

Question 14)

 

You are using a 1-step binomial tree to price a derivative security whose payoff is

 

determined by the price of XYZ stock in 1 month. XYZ stock pays no dividends. The price of

 

XYZ stock in 1 month will be either $83.50 or $77.25. If the price of XYZ stock in 1 month is

 

$83.50, the payoff of the derivative contract will be $5.25. If the price of XYZ stock in 1

 

month is $77.25, the payoff of the derivative contract will be $10.25. What position in XYZ

 

stock, combined with a LONG position of 1 derivative contract, will produce a riskless

 

portfolio?

 

1)

 

2)

 

3)

 

4)

 


 

Long 0.8 shares

 

Short 1.25 shares

 

Short 5 shares

 

Long 1.25 shares

 


 

TestId: 2001

 

Question 15)

 

You have purchased 3 call options with a strike price of $40 for a price of $11.99 each. You also sold 2 put

 

options with a strike price of $45 for a price of $2.94. Finally, you sold 6 call options with a strike price of $50

 

for a price of $5.96. All of the options are European options with the same underlying security and same

 

expiration date. On the expiration date, the price of the undelrying stock is $43.50. What is the payoff you

 

receive from your portfolio?

 

1)

 

2)

 

3)

 

4)

 


 

$14.50

 

-$11.50

 

$7.50

 

-$3.00

 


 

TestId: 2001

 

Question 16)

 

The table below gives the implied volatilities of European options on a stock with strike

 

price of $30 and expirations ranging from 1 month to 6 months. What would be the most

 

reasonable implied volatility to use to price a put option with a strike price of $30 that has 2

 

months until expiration?

 

Time to Expiration

 

1 month

 

3 months

 

6 months

 

1)

 

2)

 

3)

 

4)

 


 

40.5%

 

45.5%

 

46.5%

 

43.0%

 


 

Implied Volatility

 

41%

 

45%

 

48%

 


 

TestId: 2001

 

Question 17)

 

The 2-year zero rate is 2.8%. The forward rate for a deposit to be made in 6 months and paid back in 2

 

years (1.5 years after the deposit is made) is 2.5%. What is the 6-month zero rate? All rates in this

 

problem are continuously compounded rates.

 

1)

 

2)

 

3)

 

4)

 


 

3.70%

 

2.65%

 

3.10%

 

4.81%

 


 

TestId: 2001

 

Question 18)

 

You own a portfolio of European options on non-dividend-paying stocks with a total

 

theta of -1,212,939 (theta is calculated as a rate per year). If, in one day, the prices

 

and volatilities of all stocks underlying the options in your portfolio are the same as

 

they are today, and the risk-free rate has not changed, what is the approximate profit

 

or loss you will earn on your portfolio? Positive values represent a gain and negative

 

values represent a loss. When answering this question you should consider the

 

passage of time with respect to the number of trading days (not calendar days) per

 

year.

 

1)

 

2)

 

3)

 

4)

 


 

$1,212,939.00

 

$391.22

 

-$395,931.58

 

-$4,813.25

 


 

TestId: 2001

 

Question 19)

 

I own a bond portfolio that consists of 2 different bond positions. I own $22 million worth of

 

bond A, which has a duration of 12.4 years. I own $18 million of bond B, which has a duration of

 

8.9 years. If the yield on my portfolio increases by 0.08%, approximately how much will the

 

value of my bond portfolio change?

 

1)

 

2)

 

3)

 

4)

 


 

-$32,000

 

-$340,800

 

-$346,400

 

$340,800

 


 

TestId: 2001

 

Question 20)

 

The price of a non-dividend paying stock is $53.25. The 6-month

 

continuously compounded zero rate is 1.5%. The 6-month forward price

 

on the stock is $53.28. Which of the following is true?

 

1) A risk-free profit can be made by buying the stock and taking a

 

short forward position.

 

2) A risk-free profit can be made by taking a short forward position

 

and a short position in the stock.

 

3) A risk-free profit can be made by taking a long forward position

 

and shorting the stock.

 

4) The forward price is correct and thus no risk-free profit can be

 

made.

 


 

TestId: 2001

 

Question 21)

 

You are using a 2-step binomial tree to price a 2-month American put option with a

 

strike price of $24 on stock currently worth $22. The tree used to price the option is

 

shown below. The value indicated at each node is the stock price. The risk-free rate is

 

5%. The risk-neutral probability of an up move is 51.09%. Calculate the price of the

 

option at the initial node.

 

25.42

 

23.65

 

22

 


 

22

 

20.47

 

19.04

 


 

1)

 

2)

 

3)

 

4)

 


 

$2.16

 

$1.92

 

$2.21

 

$4.18

 


 

TestId: 2001

 

Question 22)

 

The 1-year futures price for a futures contract on non-dividend-paying stock XYZ is $32.05. The riskfree rate for all maturities is 10%. The price of a 6-month European put option on a 12-month

 

futures contract with strike price of $30 is $2.45. To be clear, this problem refers to a put option

 

written on a futures contract. The expiration of the put option is in 6 months. The delivery date of

 

the futures contract is in 12 months, or 6 months after the time the put option expires. What is the

 

price of a 6-month European call option written on the same futures contract?

 

1)

 

2)

 

3)

 

4)

 


 

$2.91

 

$4.40

 

$7.33

 

$3.84

 


 

TestId: 2001

 

Question 23)

 

Which of the following is TRUE regarding the implied volatilities of European options written on a

 

non-dividend-paying stock.

 

1) For options with the same expiration date, the implied volatility of a call with a strike that is

 

$5 above the current stock price must be the same as the implied volatility of a put with a

 

strike price that is $5 below the current stock price.

 

2) No-arbitrage conditions guarantee that the implied volatility of a call and the implied

 

volatility of a put with the same strike and expiration must be the same.

 

3) The implied volatility of all options with the same strike price must be the same, even for

 

options with different expiration dates. If this is not the case then there is an arbitrage

 

opportunity.

 

4) The implied volatility of all options with the same expiration date must be the same, even

 

for options with different strikes. If this is not the case then there is an arbitrage

 

opportunity.

 


 

TestId: 2001

 

Question 24)

 

A firm will need to purchase machinery from a European manufacturer in August and will have to pay for

 

the machinery in Euros. To hedge its exposure to the Euro, the firm takes a long position in September

 

Euro futures contracts at a futures price of $1.13. In August, the firm closes out its futures position at a

 

futures price of $1.21. The firm then buys Euros in the spot market for $1.20 so that it can pay the

 

European manufacturer for the machinery. What is the effective exchange rate the firm paid to buy the

 

Euros?

 

1)

 

2)

 

3)

 

4)

 


 

$1.13

 

$1.12

 

$1.21

 

$1.20

 


 

TestId: 2001

 

Question 25)

 

Which of the following most accurately describes an asset backed security (ABS)?

 

1) A short position in a basket of stocks that is intended to hedge against downside risk in

 

the market.

 

2) A set of assets packaged into a company called a special purpose vehicle (SPV) that sells

 

different securities, known as tranches, whose cash flows are determined by the cash

 

flows of the assets owned by the SPV.

 

3) A portfolio of options that is designed to give exposure only to volatility.

 

4) An insurance contract that also has positive exposure to the stock market.

 


 

 

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