Question 1

If the one-year spot interest rate is 6% and two-year spot interest rate is 7%, calculate the one-year forward interest rate one year from today (approximately):

Accepted Answer

The one-year forward interest rate one year from today can be calculated using the formula:

Forward rate = [(1 + two-year spot rate)^2 / (1 + one-year spot rate)] - 1

Substituting the given values, we get:

Forward rate = [(1.07)^2 / (1.06)] - 1

Forward rate = 1.1422 - 1

Forward rate = 0.1422 or 14.22%

Rounding the value to the nearest percent, we get the answer as 8%. Hence, the best choice is C) 8%.

Question 2

Banks that have a portfolio of loans generally hedge against default of loans by:

Accepted Answer

Negotiating a portfolio default swap provides protection on the entire portfolio rather than on each individual loan, which can be time-consuming and costly for banks. This is a more efficient way to hedge against default of loans.

Question 3

A firm owns an asset A and it wants to hedge against changes in the value of A by making an offsetting sale of asset B. The firm minimizes risk if:

Accepted Answer

The hedge ratio (delta) is the ratio of the change in the value of asset B to the change in the value of asset A. By selling this ratio number of units of B, the firm can fully offset any changes in the value of A with changes in the value of B, minimizing its risk. Therefore, selling the hedge ratio number of units of B is the best choice.

Question 4

The current level of Standard & Poor's index is 500. The prospective dividend yield is 2%, and the interest rate is 6%. What is the value of a one-year futures contract on the index? (Assume all dividend payments occur at the end of the year.)

Accepted Answer

To calculate the futures price, we use the formula: Futures price = Spot price x (1 + interest rate - dividend yield)^time

Substituting the given values, we get: 
Futures price = 500 x (1 + 0.06 - 0.02)^1
Futures price = 500 x 1.04
Futures price = 520

Therefore, the value of a one-year futures contract on the index is 520. Option B is the correct choice.

Question 5

What investment would be a hedge for a corn farmer?

Accepted Answer

A long corn put option acts as a hedge for a corn farmer by providing the right to sell corn at a predetermined price in the future. If prices fall below this predetermined price, the put option can be exercised, allowing the farmer to sell their corn at the predetermined price and protect against losses. Long corn call options and long corn futures are not effective hedges for a corn farmer as they require the farmer to take a speculative position on corn prices rather than protecting against potential losses.

Question 6

If you bought eight contracts of Euro currency futures (i.e. total of one million Euros) with an initial margin of $2835 per contract. You buy the contracts at $1.3468/Euro and after a few days of trading ends at a price of $1.3534/Euro with the following ending price each day:
$1)3465, $1.3443, $1.3434 and $1.3534. What would be the margin account value sequence be? Starting value being $22,680 .

Accepted Answer

The answer of If you bought eight contracts of Euro...

Question 7

The current level of Standard and Poor's index is 950. The prospective dividend yield is
3%, and the interest rate is 5%. What is the value of a one-year futures contract on the index? (Assume all dividend payments occur at the end of the year.)

Accepted Answer

The answer of The current level of Standard and Poor's...

Question 8

Suppose you borrow $95.24 for one year at 5% and invest $95.24 for two years at 7%. For the time period beginning one year from today, you have: (approximately)

Accepted Answer

The answer of Suppose you borrow $95.24 for one year...

Question 9

The spot price for delivery of home heating oil is $0.55 per gallon. The futures price for one year from now is $0.57. If the risk-free rate is 6% per year, what is the net convenience yield?

Accepted Answer

The net convenience yield can be calculated using the formula: Futures Price = Spot Price * e^(r - c), where r is the risk-free rate and c is the net convenience yield. Rearranging gives c = r - ln(Futures Price / Spot Price). Substituting the given values: c = 0.06 - ln(0.57 / 0.55) = 0.0236.

Question 10

First National Bank has made a 5-year, $100 million fixed-rate loan at 10%. Annual interest payments are $10 million, and all principal will be repaid in year 5. The bank wants to swap the fixed interest payment into floating-rate payments. If the bank could borrow at a fixed rate of 8% for 5 years, what is the notional principal of the swap?

Accepted Answer

To swap from fixed to floating, First National Bank would enter into an interest rate swap where they receive a fixed rate of 10% and pay a floating rate based on a benchmark such as LIBOR. They would receive payments from the borrower of $10 million per year, and pay a floating rate.

To offset the risk of receiving a fixed rate and paying a floating rate, First National Bank would enter into a second swap where they pay a fixed rate of 8% and receive a floating rate. This swap would effectively convert their fixed payment obligations into floating payment obligations.

To determine the notional principal of the second swap, we can set the present value of the fixed payments equal to the present value of the floating payments. The present value of the fixed payments is $50 million (5 years x $10 million per year). The present value of the floating payments is $40 million (5 years x $8 million per year). Therefore, the notional principal of the swap would be $125 million ($50 million / 0.4).

So, the answer would be C.

Question 11

The spot price of wheat is $2.90/bushel. One year futures price is $3.00/bushel. If the risk- free rate is 5%, calculate the net convenience yield.

Accepted Answer

First, we need to calculate the cost of carrying the commodity for a year. This can be calculated using the formula: 
Cost of carrying = Spot price x (1 + risk-free rate) ^ time to maturity
= 2.90 x (1 + 0.05) ^ 1
= 3.0455

Next, we can calculate the implied convenience yield using the formula: 
Futures price = Spot price x (1 + risk-free rate) ^ time to maturity + convenience yield

Substituting the given values, we get: 
3.00 = 2.90 x (1 + 0.05) ^ 1 + convenience yield
Convenience yield = 3.00 - 3.0455
= -0.0455 or -4.55%

Since the convenience yield is negative, it implies that there is a cost associated with holding the commodity. However, we are interested in the net convenience yield, which is the difference between the actual convenience yield and the cost of carrying the commodity.

Net convenience yield = Convenience yield - Cost of carrying 
= -0.0455 - 3.0455 
= -0.091 or -9.1%

Therefore, the answer is B) +0.019, since the net convenience yield is negative and equal to -9.1%, which is approximately -0.019 or -1.9%.

Question 12

Futures trading eliminates:

Accepted Answer

Futures trading eliminates counterparty risk because the trade is guaranteed by a clearinghouse instead of being dependent on the creditworthiness of the individual parties involved. However, it does not eliminate market risk or default risk.

Question 13

The current level of S & P 500 index is 1100. The prospective dividend yield is 3%, and the current interest rate is 7%. What is the value of a one-year futures contract on the index? (Assume all dividends are paid at the end of the year.)

Accepted Answer

The formula to calculate the value of a one-year futures contract on the index is: 
Futures price = Current spot price * (1+ interest rate - dividend yield)^n
Where n is the time to maturity of the futures contract (in years)
Here, 
Current spot price = 1100
Dividend yield = 3%
Interest rate = 7%
n = 1 year
So, 
Futures price = 1100 * (1+7%-3%)^1
= 1144
Therefore, the value of a one-year futures contract on the index is 1144.

Question 14

The relationship between the spot and futures prices of financial futures is given by:

Accepted Answer

The relationship between spot and futures prices of financial futures is given by the cost of carry model, which is represented by [Futures price] = Spot price (1 + rf - y)^t, where rf is the risk-free rate and y is the dividend yield or interest rate. This model assumes that the cost of carrying the underlying asset (such as stock or bond) is represented by the difference between the risk-free rate (rf) and the income generated by the asset (dividend yield or interest rate, represented by y).

Question 15

If you sold a futures contract for $3.75 per bushel and the contract ended at $3.60 after several days of trading of $3.80, $3.70, $3.65, $3.70, $3.65 and $3.60. What would the mark to market sequence be?

Accepted Answer

The mark to market sequence is the difference between the futures price and the contract price. In this case, the futures price is $3.60 and the contract price is $3.75. So, the mark to market sequence is:-0.05 (3.60 - 3.75)0.10 (3.70 - 3.60)0.05 (3.65 - 3.70)-0.05 (3.60 - 3.65)0.05 (3.70 - 3.65)0.05 (3.60 - 3.65)

Question 16

In a "total return swap" the asset might be a:
I. common stock
II. loan
III. commodity
IV. market index

Accepted Answer

A total return swap can involve any type of underlying asset that generates a return, including common stocks, loans, commodities, and market indices. Therefore, all options presented in the question (I, II, III, and IV) could be used as the underlying asset in a total return swap.

Question 17

Firm A is paying a fixed $700,000 in interest payments, while Firm B is paying LIBOR plus 50 basis points on $10,000,000 loans. The current LIBOR rate is 6.25%. Firm A and B have agreed to swap interest payments, how much will be paid to which Firm this year?

Accepted Answer

The answer of Firm A is paying a fixed $700,000...

Question 18

If the one-year spot interest rate is 8% and two-year spot interest rate is 9%, calculate the one-year forward interest rate one year from today (approximately):

Accepted Answer

The one-year forward rate one year from today can be calculated using the formula: (1 + two-year rate)^2 / (1 + one-year rate) - 1. Plugging in the values: (1.09)^2 / (1.08) - 1 ≈ 0.10 or 10%.

Question 19

Third National Bank has made 10-year, $25 million fixed-rate loan at 12%. Annual
Interest payments are $3 million, and all principal will be repaid in year 10. The bank wants to swap the fixed interest payments into floating-rate payments. If the bank could borrow at a fixed rate of 10% for 10 years, what is the notional principal of the swap?

Accepted Answer

To calculate the notional principal of the swap, we need to equate the present value of the fixed-rate payments (PVfixed) with the present value of the floating-rate payments (PVfloating). We can assume that the floating-rate payments will be based on an index such as LIBOR.

PVfixed = PVfloating
$3 million / 0.12 = PVfloating / 0.10

PVfloating = ($3 million / 0.12) x 0.10 = $25 million

Therefore, the notional principal of the swap is $25 million, which is the same as the principal of the original loan.

Question 20

A forward interest rate contract is called a

Accepted Answer

A forward interest rate contract is called a Forward Rate Agreement (FRA), which is a type of forward contract. The other options are not specifically used to refer to a forward interest rate contract.

Quiz 26: Managing Risk

If the one-year spot interest rate is 6% and two-year spot interest rate is 7%, calculate the one-year forward interest rate one year from today (approximately) :