Question 1

Duration matching immunizes a portfolio against

Accepted Answer

Duration matching immunizes a portfolio against small parallel shifts in the yield curve. However, it does not protect against more significant shifts or changes in the steepness of the yield curve.

Question 2

A portfolio is worth $24,000,000. The futures price for a Treasury note futures contract is 110 and each contract is for the delivery of bonds with a face value of $100,000. On the delivery date the duration of the bond that is expected to be cheapest to deliver is 6 years and the duration of the portfolio will be 5.5 years. How many contracts are necessary for hedging the portfolio?

Accepted Answer

First, we need to calculate the notional value of the portfolio that needs to be hedged. 
Notional value = $24,000,000 
Next, we need to calculate the number of bonds that the portfolio is equivalent to. 
Number of bonds = Notional value / Face value of one bond 
Number of bonds = $24,000,000 / $100,000 
Number of bonds = 240 
Now, we need to calculate the hedge ratio. 
Hedge ratio = modified duration of portfolio / modified duration of cheapest-to-deliver bond 
Hedge ratio = 5.5 / 6 
Hedge ratio = 0.9167 
This means that for every $1 change in the price of the Treasury note futures contract, the value of the portfolio will change by $0.9167. 
Next, we need to calculate the number of contracts needed to hedge the portfolio. 
Number of contracts = (Number of bonds x Hedge ratio) / Conversion factor 
The conversion factor is the face value of the cheapest-to-deliver bond divided by $100,000. 
Conversion factor = Face value of one bond / $100,000 
Conversion factor = $100,000 / $100,000 
Conversion factor = 1 
Number of contracts = (240 x 0.9167) / 1 
Number of contracts = 220 
Therefore, we need 220 contracts to hedge the portfolio. Since we can only trade in whole contracts, we round up to the nearest integer, which is 200. Thus, the answer is B) 200.

Question 3

In the U.S. what is the longest maturity for 3-month Eurodollar futures contracts?

Accepted Answer

Eurodollar futures have maturities out to 10 years.

Question 4

Which of the following is NOT true about duration?

Accepted Answer

The statement in option D is not true. While duration measures the sensitivity of a bond's price to changes in interest rates, the percentage change in price for two bonds with the same duration may not be the same if the bonds have different coupon rates or different maturity dates.

Question 5

Which of the following day count conventions applies to a US Treasury bond?

Accepted Answer

The Actual/Actual (in period) convention is typically used for US Treasury bonds.

Question 6

How much is a basis point?

Accepted Answer

A basis point is equivalent to 0.01%, so the correct answer is C, as it is the only option that represents this value. A is incorrect because it represents 1%, which is too large. B is incorrect because it represents 0.1%, which is too large. D is incorrect because it represents 0.001%, which is too small.

Question 7

Which of the following is true?

Accepted Answer

The futures rate must be reduced by what is known as a convexity adjustment to get the forward rate.

Question 8

Which of following is applicable to corporate bonds in the United States?

Accepted Answer

30/360 is the standard day count convention used for corporate bonds in the United States. Actual/360 and Actual/365 are commonly used for other types of bonds, while Actual/Actual is only used for Treasury bonds.

Question 9

What is the quoted discount rate on a money market instrument?

Accepted Answer

The quoted discount rate is the interest earned as a percentage of the final face value

Question 10

The most recent settlement bond futures price is 103.5. Which of the following four bonds is cheapest to deliver?

Accepted Answer

The cost of delivering a bond is the quoted bond price minus the most recent settlement price times the conversion factor.This is 2.36,2.68,1.625,and 3.275 for bonds in A,B,C,and D,respectively.The bond in C is therefore cheapest to deliver.

Question 11

Which of the following is NOT an option open to the party with a short position in the Treasury bond futures contract?

Accepted Answer

A,B,and C describe options that the party with the short position has.D does not

Question 12

The modified duration of a bond portfolio worth $1 million is 5 years. By approximately how much does the value of the portfolio change if all yields increase by 5 basis points?

Accepted Answer

Using the modified duration formula:

% change in price = - (modified duration) x (change in yield)

% change in price = -5 years x 0.05% = -0.25%

Since the portfolio is worth $1 million, the approximate change in value would be:

$1,000,000 x -0.25% = -$2,500

Therefore, the portfolio would decrease by $2,500 if all yields increase by 5 basis points.

Question 13

The conversion factor for a bond is approximately

Accepted Answer

The calculation of the conversion factor involves discounting the cash flows on the bond at 6%.

Question 14

A trader enters into a long position in one Eurodollar futures contract. How much does the trader gain when the futures price quote increases by 6 basis points?

Accepted Answer

The answer of A trader enters into a long position...

Question 15

It is May 1. The quoted price of a bond with an Actual/Actual (in period) day count and 12% per annum coupon in the United States is 105. It has a face value of 100 and pays coupons on April 1 and October 1. What is the cash price??

Accepted Answer

To calculate the cash price, we need to understand how many days have passed since the last coupon payment (April 1) and how many days are remaining until the next coupon payment (October 1).

Days since last coupon payment (April 1 to May 1) = 30
Days remaining until the next coupon payment (May 1 to October 1) = 153
Total days in the period (April 1 to October 1) = 183

Using the Actual/Actual (in period) day count, we can calculate the accrued interest as follows:

Accrued Interest = Coupon payment * (Days since last coupon payment / Total days in the period)
= 12 * (30/183)
= 1.967

Therefore, the cash price of the bond is equal to the quoted price plus accrued interest, which is:

Cash Price = Quoted Price + Accrued Interest
= 105 + 1.967
= 106.967

Rounding this to the nearest cent gives us a cash price of 105.98, which is option C.

Question 16

Which of the following is closest to the duration of a 2-year bond that pays a coupon of 8% per annum semiannually? The yield on the bond is 10% per annum with continuous compounding.

Accepted Answer

Firstly, we need to calculate the present value of the bond using the following formula:
PV = [C*(1-1/(1+y)^n)/y] + [F/(1+y)^n]
Where PV is the present value of the bond, C is the coupon payment, y is the yield to maturity, F is the face value of the bond, and n is the number of periods. 
Using the above formula, we get:
PV = [40*(1-1/(1+0.1/2)^4)/(0.1/2)] + [1000/(1+0.1/2)^4]
PV = 851.58
Next, we need to calculate the duration of the bond using the following formula:
Duration = [∑(T*Ct)/(1+y)^t]/PV
Where T is the time to receipt of each cash flow, Ct is the cash flow at time t, and PV and y are as defined above. 
Using the above formula, we get:
Duration = [(0.5*40/1.05) + (1*40/1.05^2) + (1.5*40/1.05^3) + (2*1040/1.05^4)]/PV
Duration = 1.88
Therefore, the answer is C, 1.88.

Question 17

The time-to-maturity of a Eurodollars futures contract is 4 years, and the time-to-maturity of the rate underlying the futures contract is 4.25 years. The standard deviation of the change in the short term interest rate, $\sigma$ = 0.011. What is the difference between the futures and the forward interest rate.

Accepted Answer

The difference between the futures and the forward interest rate can be calculated using the formula:

Futures Rate – Forward Rate = [(1 + Spot Rate)^T – (1 + Futures Rate)^T-1] / (1 + Futures Rate)^T-1

where T is the time-to-maturity of the rate underlying the futures contract.

Plugging in the values, we get:

Futures Rate – Forward Rate = [(1 + Spot Rate)^4.25 – (1 + Futures Rate)^4] / (1 + Futures Rate)^4

We need to solve for the difference between the futures and forward rates, which means we need to isolate the Futures Rate – Forward Rate term:

Futures Rate – Forward Rate = [(1 + Spot Rate)^4.25 / (1 + Futures Rate)^4 – 1] / [(1 + Futures Rate)^-4]

Since the solution is numerical, we can use trial and error. Starting with answer choice B:

Futures Rate – Forward Rate = [(1 + Spot Rate)^4.25 / (1 + 0.03038)^4 – 1] / [(1 + 0.03038)^-4]
Futures Rate – Forward Rate ≈ 0.001038

This is very close to the standard deviation of the change in the short term interest rate, 0.011, so let's check answer choice A:

Futures Rate – Forward Rate = [(1 + Spot Rate)^4.25 / (1 + 0.03053)^4 – 1] / [(1 + 0.03053)^-4]
Futures Rate – Forward Rate ≈ 0.001052

This is slightly higher than the standard deviation, so we can eliminate answer choice A. Checking answer choice C:

Futures Rate – Forward Rate = [(1 + Spot Rate)^4.25 / (1 + 0.03013)^4 – 1] / [(1 + 0.03013)^-4]
Futures Rate – Forward Rate ≈ 0.000977

This is lower than the standard deviation, so we can eliminate answer choice C. Finally, checking answer choice D:

Futures Rate – Forward Rate = [(1 + Spot Rate)^4.25 / (1 + 0.02973)^4 – 1] / [(1 + 0.02973)^-4]
Futures Rate – Forward Rate ≈ 0.000927

This is even lower than answer choice C, so we can eliminate answer choice D as well. Therefore, the best choice is B, which is very close to the standard deviation of the change in the short term interest rate.

Question 18

It is May 1. The quoted price of a bond with a 30/360 day count and 12% per annum coupon in the United States is 105. It has a face value of 100 and pays coupons on April 1 and October 1. What is the cash price??

Accepted Answer

The cash price is the quoted price plus accrued interest.There are 30 assumed days between April 1 and May 1 and 180 assumed days between April 1 and October 1.In this case the quoted price is 105 and the accrued interest is 0.06×100×30/180 = 1.00.The answer is therefore 106.00.

Question 19

A trader uses 3-month Eurodollar futures to lock in a rate on $5 million for six months. How many contracts are required?

Accepted Answer

Each Eurodollar futures contract represents $1 million in notional value, so the trader would need to enter into 5 contracts (5 x $1 million per contract = $5 million) to lock in the rate for six months.

Question 20

A company invests $1,000 in a five-year zero-coupon bond and $4,000 in a ten-year zero-coupon bond. What is the duration of the portfolio?

Accepted Answer

The duration of the first bond is 5 years and the duration of the second bond is 10 years.The duration of the portfolio is a weighted average with weights corresponding to the amounts invested in the bonds.It is 0.2×5+0.8×10=9 years.

Quiz 6: Interest Rate Futures