Deck 12: The Extended Cost-Of-Carry Model

Question 1

COMIND index is computed by averaging commodity prices.Compute the six-month forward price for this index if the spot price is 1,000 and the continuously compounded annual rates for various costs and benefits are 5 percent for the interest rate,2 percent for the dividend yield,3 percent for the storage cost,and 1 percent for the convenience yield.

A) $1,021.05
B) $1,025.32
C) $1,030.45
D) $1,040.81
E) None of these answers are correct.

Answer 1

B

Question 2

Which of the following statements about a stock index is INCORRECT?

A) A stock index is a hypothetical portfolio formed according to some criteria or rules.
B) A stock index can be sold short.
C) A stock index gives a quick sense of the performances of the market or a sector of the economy.
D) A stock index provides a benchmark against which performance of fund managers are measured.
E) A stock index can be used for creation of derivative products.

Answer 2

B

Question 3

Which of the following statements is INCORRECT about exchange-traded funds (ETFs)?

A) ETFs are securities giving the holder fractional ownership rights over a basket of securities.
B) ETFs trade on exchanges continuously during trading hours.
C) ETF trades require brokerage commissions.
D) ETF shares cannot be shorted.
E) Arbitrage helps to ensure that an ETF's price will not move too far from its net asset value.

Answer 3

D

Question 4

BUG's stock price S is $50 today.It pays a dividend of $0.25 after two months and $0.30 after five months.If the continuously compounded interest rate is 4 percent per year,then the forward price of a six-month forward contract on BUG is:

A) $49.75
B) $50
C) $50.46
D) $50.76
E) None of these answers are correct.

Question 5

A trader can borrow money at 6 percent and lend money at 5 percent,where the interest rates are continuously compounded annual rates.A brokerage commission of 0.5 percent of the stock price is charged today but the broker waives transactions costs on the maturity date.If BUG's stock price S is $50 today,then the seven-month forward price on BUG's stock should lie between:

A) $51.22 and $52.04
B) $51.47 and $51.78
C) $51.22 and $52.54
D) $51.22 and $51.47
E) None of these answers are correct.

Question 6

Consider the "SINDY index" obtained by averaging stock prices and a synthetic index "SINDY spot" that replicates its performance.SINDY's current level I is 11,000 and the synthetic index's price S is $11,000.Stocks constituting SINDY spot paid $200 of dividends last year and are expected to pay the same this year.Let the continuously compounded interest rate r be 5 percent per year.If the six-month forward price on a newly written forward contract on SINDY is being quoted in the market for 11,200,then the arbitrage profit that you can make today by trading one contract as well as other securities is:

A) 0
B) $5
C) $17
D) $23
E) None of these answers are correct.

Question 7

Consider the "SINDY index" obtained by averaging stock prices and a synthetic index "SINDY spot" that replicates its performance.SINDY's current level I is 11,000 and the synthetic index's price S is $11,000.Stocks constituting SINDY spot paid $200 in dividends last year and are expected to pay the same this year.Let the continuously compounded interest rate r be 5 percent per year.Then the six-month forward price on a newly written forward contract on SINDY is:

A) $10,981
B) $11,176
C) $11,201
D) $11,276
E) None of these answers are correct.

Question 8

The following is NOT an implication of the cost-of-carry relation for valuing a stock index futures contract:

A) the futures price depends directly upon the level of the stock market index
B) if the stocks in the index increase the level of dividend payments over the life of the futures contract,the futures price will fall,with everything else constant
C) if the level of interest rates increases,the futures price will increase,with everything else constant
D) if the level of interest rates increases,the futures price will decrease,with everything else constant
E) None of these answers are correct.

Question 9

The spot exchange rate is $0.56 per Brazilian real in American terms.Assume interest rates are continuously compounded.A US dollar invested in Treasury bonds grows to $1.0101 after ninety days.A real invested in risk-free Brazilian government Treasury securities grows to 1.0113 reals at the end of the same time period.A broker offers to trade a ninety-day forward contract to buy or sell 1 million reals at the exchange rate of $0.55 per real.The arbitrage profit that you can make today by trading one forward and other securities is approximately equal to:

A) $7,550
B) $9,242
C) $10,546
D) $17,630
E) None of these answers are correct.

Question 10

Today's spot exchange rate S_A is $1.30 per euro in American terms.The continuously compounded annual risk-free interest rates are r = 4 percent in the United States (domestic)and r_E = 3 percent in the Eurozone.Then a trader using the cost-of-carry model will quote the six-month forward rate in American terms as:

A) $1.2107
B) $1.3005
C) $1.3065
D) $1.3508
E) None of these answers are correct.

Question 11

Some index funds modify the index matching strategy to boost performance.Such strategies do NOT include the following:

A) investing dividend income to buy stocks in the same proportion as in the index as soon as they arrive
B) buying futures instead of stocks when futures are cheaper
C) picking up extra income by lending securities
D) temporarily holding a bit more of a thinly traded stock than is called for in a benchmark
E) buying stocks being added to an index in advance of the effective date of those changes

Question 12

BUG's stock price S is $50 today.It pays a dividend of $0.25 after two months and $0.30 after five months.The continuously compounded interest rate is 4 percent per year.Transactions costs are $0.10 per stock traded,a $0.25 one-time fee for trading forward contracts,and no charges for trading bonds.If the six-month forward price is $51,the arbitrage profit that you can make today by trading one forward contract and other securities is:

A) 0
B) $0.18
C) $0.41
D) $0.53
E) None of these answers are correct.

Question 13

BUG's stock price S is $50 today.It pays a dividend of $0.25 after two months and $0.30 after five months.The continuously compounded interest rate is 4 percent per year.If the six-month forward price is $51,the arbitrage profit that you can make today by trading one forward contract and other securities is:

A) 0
B) $0.18
C) $0.41
D) $0.53
E) None of these answers are correct.

Question 14

BUG's stock price S is $50 today.It pays a dividend of $0.25 after two months.If the continuously compounded interest rate is 4 percent per year,then the six-month forward price on BUG stock is:

A) $49.75
B) $50
C) $50.45
D) $50.76
E) None of these answers are correct.

Question 15

Which of the following statements is INCORRECT?

A) A stock market index is a hypothetical portfolio formed according to some criteria or rules.
B) Most indexes,unlike total return indexes,make no adjustment for regular cash dividends.
C) Total return indexes assume that all disbursements from the company including regular dividends get reinvested in the hypothetical index portfolio.
D) The cost-of-carry model that has a total return index as the underlying requires dividend adjustments.
E) The cost-of-carry model that uses indexes like the Dow Jones Industrial Average and the Standard and Poor's 500 index requires dividend adjustments.

Question 16

Assume that interest rates are constant.Given a risk-free rate of 6 percent,a dividend yield of 2 percent,and index level of 1,100,then the stock market index futures price with delivery in 3 months is:

A) 1,000.01
B) 1,111.06
C) 1,040.00
D) 10,000.10
E) None of these answers are correct.

Question 17

Turkish interest rates are 4 percent per annum,while US interest rates are at 5 percent per annum.The spot exchange rate is 1.75 Turkish lira per US dollar,while the six-month forward price is 1.70 lira per US dollar.The arbitrage profit that you can generate today by trading one six-month forward contract and other securities is:

A) $0.057
B) $0.137
C) $0.374
D) $0.574
E) None of these answers are correct.

Question 18

In a simple cost-of-carry model with dollar dividends,we:

A) lower the stock price by the present value of all future dividends
B) lower the stock price by the present value of all future dividends paid over the forward's life
C) lower the stock price by more than the amount of the dividends due to taxes and transactions costs
D) lower the stock price by less than the amount of the dividends due to the signaling effect of dividends
E) adjust the quantity of shares held for dividends and not the stock price

Question 19

Alloyum costs $0.10 per month to store (which is paid up front)but gives a convenience yield of $0.12 per month (which is received on the maturity date).If Alloyum's spot price S is $200 per ounce and the continuously compounded interest rate r is 5 percent per year,then the six-month forward price is:

A) $204.96
B) $210.03
C) $205.05
D) $224.93
E) None of these answers are correct.

Question 20

When the forward price is less than the expected future spot price,we say that the:

A) market is in backwardation
B) market is in contango
C) market is in normal backwardation
D) net hedging hypothesis is in effect
E) None of these answers are correct.