Deck 4: Pricing Forwards Futures II

Question 1

A commodity has a spot price of $25 and a one-month forward price of $25.02. The one-month risk-free rate is 2% in continuously compounded and annualized terms. Assuming no other costs or benefits of carry on the commodity, what must be the lower bound on the convenience yield that prevents arbitrage?
(a) 0%
(b) 1%
(c) 2%
(d) 3%

Answer 1

B.

Question 2

Backwardation becomes more likely when, ceteris paribus,
(a) The dividend rate declines.
(b) Storage costs increase.
(c) Convenience yields decline.
(d) Interest rates decline.

Answer 2

D.

Question 3

Consider futures on a stock market index. Which of the following scenarios is most likely to increase the futures-spot basis?
(a) Interest rates and dividend yields both decline.
(b) Interest rates decline and dividend yields increase.
(c) Interest rates and dividend yields both increase.
(d) Interest rates increase and dividend yields decline.

Answer 3

D.

Question 4

The risk-free interest rate drops but the futures on a stock market index rises. Which of the following statements is the most accurate?
(a) There are arbitrage profits to be made by going long futures, short spot, and investing.
(b) There are arbitrage profits to be made by going short futures, long spot, and borrowing.
(c) The futures is overvalued but this may or may not mean an arbitrage opportunity is available.
(d) There is not enough information in the question to identify if there is an arbitrage or not.

Question 5

Two stocks, A and B, have expected returns for one year of $- 10 \%$ and $+ 10 \%$ respectively. The stocks have identical prices of $100 each, do not pay dividends, and the one-year risk-free rate of return is 2% in simple terms. The one-year forward prices of the two stocks are:

A) A: 90; B: 110
B) A: 92; B: 112
C) A; 102; B: 102
D) A: 112; B: 112

Question 6

CAP Inc.'s stock is trading at $40. Its beta in the capital asset pricing model (CAPM) is 1.3. The one-year risk-free rate of interest is 2% and the equity premium for one year is assumed to be 6%, both in simple terms. The stock pays no dividends. Use simple interest for compounding. The one-year forward price of CAP's stock is:
(a) $40.80
(b) $42.40
(c) $43.20
(d) $43.92

Question 7

Stock A has a spot price of $50. It is expected to appreciate by 2% over the next quarter. The risk-free rate for the next quarter is 2% in continuously-compounded and annualized terms, and the quarterly continuous dividend payment is also 2% in continuously-compounded and annualized terms. The three-month forward price is
(a) $50.00
(b) $50.25
(c) $50.50
(d) $50.75

Question 8

Stock B is trading at $1100. The risk-free rate is 1% for all maturities and the average dividend on the stock is $10 each quarter-end. What is the six-month forward price of the stock, assuming interest calculations are on a continuously-compounded basis?
(a) $1,050.65
(b) $1,085.49
(c) $1,105.51
(d) $1,125.54

Question 9

If there is a convenience yield, then the following is true of the forward price:
(a) The forward price is higher than it would be if there were no convenience yield.
(b) The bid price may be higher than the ask price on the forward.
(c) The forward price does not depend on the convenience yield.
(d) The forward price is lower than it would be with no convenience yield.

Question 10

If the implied repo rate is lower than the borrowing rate $R _ { b }$ and the lending rate $R _ {\ell }$ for the same maturity, what strategy would you adopt to undertake an arbitrage?

A) Buy the asset spot, sell it forward, lend at rate $R _ {\ell }$ .
B) Buy the asset spot, sell it forward, borrow at rate $R _ { b }$ .
C) Sell the asset spot, buy it forward, lend at rate $R _ {\ell }$ .
D) Sell the asset spot, buy it forward, borrow at rate $R _ { b }$ .

Question 11

Using the spot and forward markets to borrow at the implied repo rate entails
(a) Selling the spot asset and buying it forward.
(b) Buying the spot asset and selling it forward.
(c) Selling the spot today and buying it back at the then-prevailing spot price in the future.
(d) Buying the spot today and selling it at the then-prevailing spot price in the future.

Question 12

The spot price trades at the following bid/ask quote: 100-101 . If the simple interest rate for one year is 2%, which of the following statements is most accurate?
(a) You can execute an arbitrage by buying spot and selling forward.
(b) You can execute an arbitrage by selling spot and buying forward.
(c) You can execute an arbitrage by selling spot, buying forward, and investing the proceeds of the spot sale at 2%.
(d) You cannot execute an arbitrage at these prices.

Question 13

Forward pricing by replication depends on the following assumption:
(a) That the nominal interest rate for the cost of carry is positive.
(b) That long positions are easier to take in the forward contract than in the spot asset.
(c) That the underlying is a traded asset which is storable.
(d) That the spot asset is not a financial security.

Question 14

The spot price trades at a bid/ask quote of 100-101 (you can buy at 101 and sell at 100). The one-year forward trades at 99-101.90 (you can buy forward at 101.90 and sell forward at 99). If the simple interest rate for one year is 2%, which of the following statements is most accurate?
(a) You can execute an arbitrage by buying spot and selling forward.
(b) You can execute an arbitrage by selling spot and buying forward.
(c) You can execute an arbitrage by selling spot, buying forward, and investing the proceeds of the spot sale at 2%.
(d) You cannot execute an arbitrage at these prices.

Question 15

For commodity forwards and futures, which of the following statements is valid?
(a) The presence of a convenience yield means that the market will be in contango.
(b) Convenience yields may lead to the market being in backwardation.
(c) If there are storage costs, the convenience yield is zero-it is no longer convenient to hold the commodity.
(d) As supply becomes plentiful, convenience yields will rise.

Question 16

Which of the following statements about index futures is false?
(a) Index futures are cash-settled.
(b) Index futures track the underlying index.
(c) Index futures are rarely shorted because it is very difficult to borrow all the stocks in the index in the correct proportions in order to effect the short.
(d) Index futures are marked-to-market daily.

Question 17

If the stock market index is at a level of 1,120 and the one-year forward on the index is 1,210, what is the implied repo rate in continuously-compounded terms (assuming zero dividends on the index)?
(a) 5.72%
(b) 6.52%
(c) 7.72%
(d) 8.62%

Question 18

You are long a forward on the S&P 500 index that you entered into two months ago and has a month left to maturity. If the one-month rate of interest increases, then, ceteris paribus,
(a) The value of your forward contract increases.
(b) The value of your forward contract decreases.
(c) The value of your forward contract is unaffected since the delivery price on your contract was already locked in two months ago.
(d) The value of your forward contract is unaffected since the level of the index does not change.

Question 19

The volatility of a stock index falls sharply, the index drops in value, and its expected return increases. Assuming all else (dividend yield, interest rates, etc.) are constant, which of the following is true?
(a) The futures price on the index increases because of the increased expected return on the index.
(b) The futures price decreases because of the drop in the level of the index.
(c) The futures price stays the same because the drop in the level of the index is negated by the increased expected return.
(d) The futures may increase, decrease or stay the same depending on the extent of fall in volatility relative to the increase in expected returns.

Question 20

Commodity forward contracts differ from financial forwards in the following manner:
(a) The underlying asset in a commodity forward is an asset that may be used in production and that gets consumed in the process.
(b) Commodity forwards are always more costly than financial forwards when the spot assets have the same prices.
(c) Commodity forwards have physical delivery whereas financial forwards have cash delivery.
(d) Commodity forwards do not have inconvenience yields whereas financial forwards do.