Question 1

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the par coupon on a 4-year coupon bond selling at par?

Accepted Answer

The par coupon on a 4-year coupon bond selling at par can be found by setting up the equation for the bond's price equal to its par value (usually 100). The price of a coupon bond is the present value of its coupons plus the present value of its face value. Given the prices of zero-coupon bonds, we can infer the discount rates for each year. The bond selling at par means its price is 100. The equation considering annual coupons C and the discount factors derived from the zero-coupon bonds is:$$100 = \frac{C}{1.048} + \frac{C}{1.107} + \frac{C}{1.175} + \frac{C + 100}{1.270}$$Solving for C gives a coupon rate close to 6.06%, which means the bond's annual coupon is 6.06% of its face value.

Question 2

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the continuously compounded 3-year zero yield?

Accepted Answer

The continuously compounded 3-year zero yield is the yield to maturity on a 3-year zero coupon bond. The price of a zero coupon bond is equal to the present value of its future cash flows, which in this case is the face value of the bond. The present value of a future cash flow is equal to the cash flow divided by the discount factor, which is equal to e^(-rt), where r is the continuously compounded interest rate and t is the time in years. In this case, the face value of the bond is 100, the price of the bond is 85.16, and the time to maturity is 3 years. Therefore, the continuously compounded 3-year zero yield is:r = -ln(85.16/100)/3 = 0.0535 = 5.35%

Question 3

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 78.81.What is the 1-year implied forward rate from year 3 to year 4?

Accepted Answer

The forward rate can be calculated using the formula: (P3/P4)^(1/n) - 1, where P3 is the price of the 3-year bond, P4 is the price of the 4-year bond, and n is the number of years between the bonds. Plugging in the values: (85.16/78.81)^(1/1) - 1 = 6.7%.

Question 4

What is the pure yield curve and why is it common to present coupon-based yield curves in practice?

Accepted Answer

The answer of What is the pure yield curve and...

Question 5

The price of a 6-month T-bill is 96.73.You wish to enter into a repurchase agreement that provides for your purchase of a $100,000 bond in 10 days at a price of 97.02.What is the implied 10 day repo rate in this transaction?

Accepted Answer

The implied repo rate is calculated as [(97.02 - 96.73) / 96.73] * (360/10) = 0.30%.

Question 6

A 4-year bond with a price of 100.696 exists.The duration on the bond is 3.674.If the yield rises from 5.8% to 6.2%,what is the new bond price as estimated by the duration?

Accepted Answer

Using the duration formula, we can calculate the approximate percentage change in bond price:
Duration = (1/Price) * (dPrice/dYield)
3.674 = (1/100.696) * (dPrice/0.058)
dPrice = 2.018

To estimate the new bond price, we can use the formula:
New Price = Old Price * (1 - Duration * ΔYield)
New Price = 100.696 * (1 - 3.674 * (0.062 - 0.058))
New Price = $99.30

Question 7

You wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days.The price of a 150-day zero coupon bond is 0.9823 and the price of 310-day zero coupon bond is 0.9634.What are the transactions used to create this instrument?

Accepted Answer

CTo create a synthetic forward rate agreement that locks in a return between 150 and 310 days, you would need to lend (sell) the 150-day bond and borrow (buy) more of the 310-day bond to cover the longer period. The correct transactions are those that involve lending the shorter duration bond and borrowing the longer duration bond to capitalize on the interest rate differences over the specified period. Option A and C correctly represent these actions, with slight variations in the amounts to adjust for the price differences between the two bonds.

Question 8

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 79.81.What is the yield to maturity (effective annual yield)on the 4-year bond?

Accepted Answer

To calculate the yield to maturity (YTM) of the 4-year bond, we need to use the formula:

Current price = Face value / (1 + YTM)^n

where n is the number of years to maturity.

For the 3-year bond:

85.16 = Face value / (1 + YTM)^3

Solving for the face value, we get:

Face value = 85.16 x (1 + YTM)^3

For the 4-year bond:

79.81 = Face value / (1 + YTM)^4

Substituting the face value from the previous equation, we get:

79.81 = 85.16 x (1 + YTM)^3 / (1 + YTM)^4

Simplifying the equation:

79.81 = 85.16 / (1 + YTM)

(1 + YTM) = 85.16 / 79.81

(1 + YTM) = 1.0674

YTM = 0.0674

Effective annual yield = (1 + YTM)^4 - 1

= (1.0674)^4 - 1

= 0.058 or 5.8%

Therefore, the answer is C, 5.8%.

Question 9

A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan.If settled at the time of borrowing,what amount would the borrower pay or receive on a $500,000 loan if the prevailing 6-month interest rate is 2.9%?

Accepted Answer

To calculate the settlement amount on a Forward Rate Agreement, we need to find the difference between the agreed interest rate and the prevailing interest rate, and then multiply it by the loan principal and the number of days in the loan period.

In this case, the loan principal is $500,000, the number of days in the loan period is 182 (assuming a 6-month period of 182.5 days), and the difference between the agreed interest rate of 3.1% and the prevailing interest rate of 2.9% is 0.2%.

So, the settlement amount would be:
($500,000 x 0.2% x 182)/365 = $972 (rounded to the nearest dollar)

Since the prevailing interest rate is lower than the agreed interest rate, the borrower would need to make a payment of $972 to compensate the lender for the difference in interest rates. Thus, the correct answer is C.

Question 10

The annual coupon rate on a 1-year treasury bond is 5.5%.The coupon on a 2-year treasury bond is 5.8%.What is the implied YTM on a hypothetical 2-year zero coupon treasury bond?

Accepted Answer

The implied yield to maturity (YTM) on a 2-year zero coupon bond can be calculated using the bootstrapping method, which involves using the yields of shorter-term bonds to derive the yield of a longer-term bond. Given the annual coupon rates and assuming a face value of $100 for simplicity, the calculation would involve solving for the YTM that equates the present value of the bond's cash flows to its price. Since the bond is a zero-coupon bond, its cash flows consist only of the face value at maturity. The calculation involves finding the rate that equalizes the present value of the $100 to be received in two years with the current prices of the 1-year and 2-year coupon bonds, taking into account the given coupon rates. The correct answer, 5.81%, reflects the compounded effect of the given yields over the two years, indicating a slightly higher yield expectation for the zero-coupon bond compared to the coupon bonds, which is typical due to the zero-coupon bond's higher interest rate risk and delayed cash flow.

Question 11

Compute the conversion factor on a semi-annual 6.8% coupon bond,which matures in exactly 5 $ \frac{1}{2} $ years.

Accepted Answer

The correct answer is A.The conversion factor for a semi-annual 6.8% coupon bond that matures in exactly 5 1/2 years is 1.037. This is because the conversion factor is calculated as (1 + (coupon rate / 2)) ^ (number of years * 2), which in this case is (1 + (0.068 / 2)) ^ (5.5 * 2) = 1.037.

Question 12

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 78.81.What is the yield to maturity (effective annual yield)on the 3-year bond?

Accepted Answer

The answer of The price of a 3-year zero coupon...

Question 13

Explain the expectations hypothesis and its ability to accurately forecast interest rates.

Accepted Answer

The answer of Explain the expectations hypothesis and its ability...

Question 14

The annual coupon rate on a 1-year treasury bond is 5.5%.The coupon on a 2-year treasury bond is 5.8%.What is the continuously compounded yield on a 2-year zero coupon bond?

Accepted Answer

We can use the formula for the pricing of a coupon bond to find the yield on the zero coupon bond. Let F be the face value of the bond and r be the continuously compounded yield on the 2-year zero coupon bond. Then we have:

F = (5.5/100)F/(1+r) + (F + (5.8/100)F)/(1+r)^2

Simplifying this equation, we get:

1 + r = [(100 + 5.8)/100]/[(100 + 5.5)/100]^2

1 + r = 1.058/1.055^2

1 + r = 1.056492

r = 5.6492%

Therefore, the answer is B) 5.65%.

Question 15

Given a 3-year,8.0% annual coupon bond with a par value of $1,000,what is the bond's Macaulay duration if the yield to maturity is 9.5%?

Accepted Answer

The Macaulay duration of a bond is a measure of its price sensitivity to changes in interest rates. It is calculated as the weighted average of the times to maturity of the bond's cash flows, with the weights being the present values of the cash flows.In this case, the bond has a par value of $1,000, an 8.0% annual coupon rate, and a 3-year maturity. The yield to maturity is 9.5%.The present value of the bond's cash flows can be calculated as follows:PV = $1,000 / (1 + 0.095)^3 + $80 / (1 + 0.095) + $80 / (1 + 0.095)^2 + $80 / (1 + 0.095)^3= $1,000 / 1.2882 + $80 / 1.095 + $80 / 1.1941 + $80 / 1.2983= $776.92 + $73.03 + $67.01 + $61.67= $978.63The Macaulay duration of the bond can be calculated as follows:MD = (PV1 * T1 + PV2 * T2 + PV3 * T3 + PV4 * T4) / PV= ($776.92 * 3 + $73.03 * 2 + $67.01 * 1 + $61.67 * 0) / $978.63= $2.779Therefore, the bond's Macaulay duration is 2.779 years.

Question 16

You wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days.The price of a 150-day zero coupon bond is 0.9823 and the price of 310-day zero coupon bond is 0.9634.What is the approximate yield on the synthetic FRA?

Accepted Answer

The yield on the synthetic forward rate agreement (FRA) can be calculated using the prices of the zero-coupon bonds for the respective periods. The formula to approximate the yield is:$$ \text{Yield} = \left( \frac{\text{Price of shorter-term bond}}{\text{Price of longer-term bond}} - 1 \right) \times \frac{360}{\text{Days between the two periods}} $$Given:- Price of 150-day bond = 0.9823- Price of 310-day bond = 0.9634- Days between the two periods = 310 - 150 = 160 days$$ \text{Yield} = \left( \frac{0.9823}{0.9634} - 1 \right) \times \frac{360}{160} \approx 2.0\% $$Therefore, the approximate yield on the synthetic FRA is 2.0%.

Question 17

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the implied 2-year forward rate between years 2 and 4?

Accepted Answer

The answer of The prices of 1,2,3,and 4-year zero coupon...

Question 18

The conversion factor on a deliverable bond is 1.03 and the bond price is 100.50.The observed futures price is 97.5 and the YTM is 5.8%.What is invoice less market price on the security?

Accepted Answer

The answer of The conversion factor on a deliverable bond...

Question 19

A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan.If settled in arrears,what amount would the borrower pay or receive on an $800,000 loan if the prevailing 6-month interest rate is 3.6%?

Accepted Answer

The answer of A Forward Rate Agreement contains an agreed...

Question 20

Two months from today you plan to borrow $3 million for 6 months at LIBOR.You hedge your interest rate risk with a euro dollar futures contract priced at 93.6.If settled in arrears,what is your payment if the 6-month LIBOR is 2.5% in two months?

Accepted Answer

The payment can be calculated by understanding the mechanics of a Eurodollar futures contract and the relationship with LIBOR. The Eurodollar futures price is quoted as 100 minus the interest rate, so a price of 93.6 implies an interest rate of 6.4% (100 - 93.6). If the 6-month LIBOR rate in two months is 2.5%, the change in interest rate from the futures contract price is 6.4% - 2.5% = 3.9%. The payment is calculated on the basis of $1 million per basis point (0.01%) for a 6-month period. Therefore, the payment is 3.9% (or 390 basis points) times $1 million, which equals $3.9 million for a full year. However, since the loan is for 6 months, the amount is halved, resulting in $1.95 million. The futures contract is for $3 million, so the calculation is based on this amount, leading to a payment of $10,500 (3.9% of $3 million for 6 months).

Quiz 7: Interest Rate Forwards and Futures

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the par coupon on a 4-year coupon bond selling at par?

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the continuously compounded 3-year zero yield?

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 78.81.What is the 1-year implied forward rate from year 3 to year 4?

What is the pure yield curve and why is it common to present coupon-based yield curves in practice?

The price of a 6-month T-bill is 96.73.You wish to enter into a repurchase agreement that provides for your purchase of a $100,000 bond in 10 days at a price of 97.02.What is the implied 10 day repo rate in this transaction?

A 4-year bond with a price of 100.696 exists.The duration on the bond is 3.674.If the yield rises from 5.8% to 6.2%,what is the new bond price as estimated by the duration?

You wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days.The price of a 150-day zero coupon bond is 0.9823 and the price of 310-day zero coupon bond is 0.9634.What are the transactions used to create this instrument?

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 79.81.What is the yield to maturity (effective annual yield) on the 4-year bond?

A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan.If settled at the time of borrowing,what amount would the borrower pay or receive on a $500,000 loan if the prevailing 6-month interest rate is 2.9%?

The annual coupon rate on a 1-year treasury bond is 5.5%.The coupon on a 2-year treasury bond is 5.8%.What is the implied YTM on a hypothetical 2-year zero coupon treasury bond?

Compute the conversion factor on a semi-annual 6.8% coupon bond,which matures in exactly 5 $\frac{1}{2}$ years.

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 78.81.What is the yield to maturity (effective annual yield) on the 3-year bond?

Explain the expectations hypothesis and its ability to accurately forecast interest rates.

The annual coupon rate on a 1-year treasury bond is 5.5%.The coupon on a 2-year treasury bond is 5.8%.What is the continuously compounded yield on a 2-year zero coupon bond?

Given a 3-year,8.0% annual coupon bond with a par value of $1,000,what is the bond's Macaulay duration if the yield to maturity is 9.5%?

You wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days.The price of a 150-day zero coupon bond is 0.9823 and the price of 310-day zero coupon bond is 0.9634.What is the approximate yield on the synthetic FRA?

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the implied 2-year forward rate between years 2 and 4?

The conversion factor on a deliverable bond is 1.03 and the bond price is 100.50.The observed futures price is 97.5 and the YTM is 5.8%.What is invoice less market price on the security?

A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan.If settled in arrears,what amount would the borrower pay or receive on an $800,000 loan if the prevailing 6-month interest rate is 3.6%?

Two months from today you plan to borrow $3 million for 6 months at LIBOR.You hedge your interest rate risk with a euro dollar futures contract priced at 93.6.If settled in arrears,what is your payment if the 6-month LIBOR is 2.5% in two months?

Quiz 7: Interest Rate Forwards and Futures

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the par coupon on a 4-year coupon bond selling at par?

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the continuously compounded 3-year zero yield?

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 78.81.What is the 1-year implied forward rate from year 3 to year 4?

What is the pure yield curve and why is it common to present coupon-based yield curves in practice?

The price of a 6-month T-bill is 96.73.You wish to enter into a repurchase agreement that provides for your purchase of a $100,000 bond in 10 days at a price of 97.02.What is the implied 10 day repo rate in this transaction?

A 4-year bond with a price of 100.696 exists.The duration on the bond is 3.674.If the yield rises from 5.8% to 6.2%,what is the new bond price as estimated by the duration?

You wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days.The price of a 150-day zero coupon bond is 0.9823 and the price of 310-day zero coupon bond is 0.9634.What are the transactions used to create this instrument?

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 79.81.What is the yield to maturity (effective annual yield) on the 4-year bond?

A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan.If settled at the time of borrowing,what amount would the borrower pay or receive on a $500,000 loan if the prevailing 6-month interest rate is 2.9%?

The annual coupon rate on a 1-year treasury bond is 5.5%.The coupon on a 2-year treasury bond is 5.8%.What is the implied YTM on a hypothetical 2-year zero coupon treasury bond?

Compute the conversion factor on a semi-annual 6.8% coupon bond,which matures in exactly 5 12 \frac{1}{2} 21​ years.

The price of a 3-year zero coupon government bond is 85.16.The price of a similar 4-year bond is 78.81.What is the yield to maturity (effective annual yield) on the 3-year bond?

Explain the expectations hypothesis and its ability to accurately forecast interest rates.

The annual coupon rate on a 1-year treasury bond is 5.5%.The coupon on a 2-year treasury bond is 5.8%.What is the continuously compounded yield on a 2-year zero coupon bond?

Given a 3-year,8.0% annual coupon bond with a par value of $1,000,what is the bond's Macaulay duration if the yield to maturity is 9.5%?

You wish to create a synthetic forward rate agreement in which you would lock in a return between 150 and 310 days.The price of a 150-day zero coupon bond is 0.9823 and the price of 310-day zero coupon bond is 0.9634.What is the approximate yield on the synthetic FRA?

The prices of 1,2,3,and 4-year zero coupon government bonds are 95.42,90.36,85.16,and 78.81,respectively.What is the implied 2-year forward rate between years 2 and 4?

The conversion factor on a deliverable bond is 1.03 and the bond price is 100.50.The observed futures price is 97.5 and the YTM is 5.8%.What is invoice less market price on the security?

A Forward Rate Agreement contains an agreed interest rate of 3.1% on a 6-month loan.If settled in arrears,what amount would the borrower pay or receive on an $800,000 loan if the prevailing 6-month interest rate is 3.6%?

Two months from today you plan to borrow $3 million for 6 months at LIBOR.You hedge your interest rate risk with a euro dollar futures contract priced at 93.6.If settled in arrears,what is your payment if the 6-month LIBOR is 2.5% in two months?

Compute the conversion factor on a semi-annual 6.8% coupon bond,which matures in exactly 5 $\frac{1}{2}$ years.