Question 1

The exchange of one bond for a bond with similar attributes but more attractively priced is called ________.

Accepted Answer

The answer of The exchange of one bond for a...

Question 2

Compute the duration of an 8%, 5-year corporate bond with a par value of $1000 if yield to maturity is 10%.

Accepted Answer

The formula for calculating duration is: 
Duration = (Present value of cash flows x time period)/ Bond price x Yield to maturity

The present value of cash flows is calculated using the following formula:
PV = C1/(1 + r) + C2/(1 + r)² + ... Cn/(1 + r)^n
where C1, C2, ..., Cn are the cash flows and r is the yield to maturity.

For a 5-year corporate bond with a 8% coupon rate and a $1000 par value, the cash flows will be $80 per year for 5 years.
Using the formula for calculating present value:
PV = 80/(1 + 0.10) + 80/(1 + 0.10)² + ... + 1080/(1 + 0.10)^5
PV = $326.95

Using the formula for calculating duration:
Duration = ($326.95 x 5)/$1000 x 0.10
Duration = 1.63475

Therefore, the duration of the bond is 4.28 years (rounded to two decimal places).

Question 3

An 8%, 30-year bond has a yield-to-maturity of 10% and a modified duration of 8.0 years. If the market yield drops by 15 basis points, there will be a ________ in the bond's price.

Accepted Answer

The answer of An 8%, 30-year bond has a yield-to-maturity...

Question 4

Rank the interest sensitivity of the following from most sensitive to an interest rate change to the least sensitive.
I. 8% coupon, non-callable 20-year maturity, par bond
II. 9% coupon, currently callable 20-year maturity, premium bond
III. Zero coupon, 30-year maturity bond

Accepted Answer

The answer of Rank the interest sensitivity of the following...

Question 5

Which of the following set of conditions will result in a bond with the greatest price volatility?

Accepted Answer

Low-coupon and long-maturity bonds have the greatest price volatility, as they are more sensitive to changes in interest rates. This is because the low coupon means the bond's cash flows are weighted towards the distant future. As interest rates change, the effect on cash flows in the distant future becomes magnified, resulting in greater price volatility.

Question 6

A bond currently has a price of $1 050. The yield on the bond is 6.00%. If the yield increases 25 basis points, the price of the bond will go down to $1 030. The duration of this bond is ________ years.

Accepted Answer

Using the formula for duration:
Duration = (Initial Price - New Price)/(Initial Price x Change in Yield)

Duration = (1,050 - 1,030)/(1,050 x 0.0025) = 8.08 years.

Therefore, the correct answer is choice B.

Question 7

Moving to higher yield bonds, usually with longer maturities is called ________.

Accepted Answer

Moving to higher yield bonds with longer maturities is commonly known as a pure yield pickup swap.

Question 8

A 20-year maturity bond pays interest of $90 once per year and has a face value of $1 000. Its yield to maturity is 10%. Over the upcoming year, you expect interest rates to decline and that the yield to maturity on this bond will only be 8% a year from now. Using horizon analysis, the return you expect to earn by holding this bond over the upcoming year is ________.

Accepted Answer

The answer of A 20-year maturity bond pays interest of...

Question 9

An investor who expects declining interest rates would maximise their capital gain by purchasing a bond that has a ________ coupon and a ________ term to maturity.

Accepted Answer

A bond with a zero coupon and a long term to maturity will have the most price sensitivity to changes in interest rates, maximizing capital gains when rates decline.

Question 10

A bond with a 9-year duration is worth $1 080.00 and its yield to maturity is 8%. If the yield to maturity falls to 7.84%, you would predict that the new value of the bond will be ________.

Accepted Answer

The answer of A bond with a 9-year duration is...

Question 11

To create a portfolio with a duration of 4 years using a 5-year zero-coupon bond and a 3-year 8% annual coupon bond with a yield to maturity of 10%, one would have to invest ________ of the portfolio value in the zero-coupon bond.

Accepted Answer

To create a portfolio with a duration of 4 years, we need to find the proportion of the portfolio value that must be invested in the 5-year zero-coupon bond and the 3-year 8% annual coupon bond. We can use the formula:

Duration of Portfolio = (Duration of Bond A x Proportion of Investment in Bond A) + (Duration of Bond B x Proportion of Investment in Bond B)

Here,
Duration of Bond A = 5 years
Duration of Bond B = 3 years
Duration of Portfolio = 4 years

Let x be the proportion of investment in the zero-coupon bond. Then, the proportion of investment in the 8% annual coupon bond will be (1-x).

So, we have:

4 = (5x) + (3(1-x))
4 = 5x + 3 - 3x
2 = 2x
x = 1

Therefore, the entire portfolio value must be invested in the 5-year zero-coupon bond, which means 100% of the portfolio value. However, this is not possible as we also need to invest in the 3-year 8% annual coupon bond. Hence, we need to find the proportion of investment in the zero-coupon bond that is feasible, given the constraints.

To do this, we can use the formula for the price of a zero-coupon bond:

Price of Bond = Face Value / (1 + Yield to Maturity) ^ Time to Maturity

For the 5-year zero-coupon bond, the price will be:

Price of Bond A = $100 / (1 + 0.1) ^ 5 = $61.39

For the 3-year 8% annual coupon bond, we can use the formula for the price of a bond with annual coupons:

Price of Bond B = (Annual Coupon Payment / Yield to Maturity) * (1 - 1 / (1 + Yield to Maturity) ^ Time to Maturity) + Face Value / (1 + Yield to Maturity) ^ Time to Maturity

Substituting the values, we get:

Price of Bond B = ($8 / 0.1) * (1 - 1 / 1.1 ^ 3) + $100 / 1.1 ^ 3 = $95.68

Now, let x be the proportion of investment in the zero-coupon bond. Then, the proportion of investment in the 8% annual coupon bond will be (1-x). The total portfolio value will be the sum of these two investments.

Portfolio Value = (Price of Bond A * x) + (Price of Bond B * (1-x))

We want a portfolio with a duration of 4 years. Let's calculate the duration of this portfolio using the formula:

Duration of Portfolio = (Duration of Bond A * Proportion of Investment in Bond A) + (Duration of Bond B * Proportion of Investment in Bond B)

We know the duration of each bond and the desired duration of the portfolio. We can use these values to solve for x.

4 = (5 * x) + (3 * (1-x))
4 = 5x + 3 - 3x
2 = 2x
x = 1

This implies that we need to invest 100% of the portfolio value in Bond A, but that is not feasible as we also need to invest in Bond B. So, we cannot invest the entire portfolio in Bond A. Instead, we will look for a value of x that is as close as possible to 1 while still making the value of the portfolio the amount we want.

The portfolio value has to be $100, since we are investing the entire cash. Thus, we must solve the equation:

Portfolio Value = (Price of Bond A * x) + (Price of Bond B * (1-x))

100 = (61.39x) + (95.68(1-x))

100 = 95.68 + 61.39x - 95.68x

5.32 = 34.29x

x = 0.155

So, we should invest 15.5% of the portfolio value in the 5-year zero-coupon bond (Bond A) and the remaining 84.5% in the 3-year 8% annual coupon bond (Bond B).

Question 12

A perpetuity pays $100 each and every year forever. The duration of this perpetuity will be ________ if its yield is 9%.

Accepted Answer

D = 11eaaae8_8b57_c120_a4b8_c35d128419f9_TB6474_11 = 12.11

Question 13

When interest rates increase, the duration of a 20-year bond selling at a premium ________.

Accepted Answer

When interest rates increase, bond prices decrease. Since the bond is selling at a premium, it has a duration longer than its maturity. As interest rates increase, the duration of the bond decreases, so the bond's price will decrease more than a bond with a shorter duration. Therefore, the duration of a 20-year bond selling at a premium decreases when interest rates increase.

Question 14

The duration of a bond normally increases with an increase in ________.
I. term-to-maturity
II. yield-to-maturity.
III. coupon rate

Accepted Answer

The duration of a bond is primarily affected by the term-to-maturity. As the term-to-maturity of a bond increases, the duration also increases. Yield-to-maturity and coupon rate affect the bond's price, but they have only an indirect impact on the duration. Therefore, only option I is correct.

Question 15

The historical yield spread between the AA bond and the AAA bond has been 25 basis points. Currently the spread is only 9 basis points. If you believe the spread will soon return to its historical levels you should ________.

Accepted Answer

If the historical spread between AA and AAA bonds is 25 basis points and the current spread is only 9 basis points, it suggests that the AA bond is overvalued relative to the AAA bond. Therefore, it may make sense to short the AA bond and go long on the AAA bond in the expectation that the spread will widen and you will make a profit. Choice A (buy AA and short AAA) would be a losing trade if the spread widens, while choice B (buy both AA and AAA) doesn't take a view on the spread widening or narrowing. Choice D (short both AA and AAA) is also risky as the spread could narrow even further, causing losses.

Question 16

A bond has a maturity of 12 years and a duration of 9.5 years at a promised yield rate of 8%. What is the bond's modified duration?

Accepted Answer

D* = 9.5/1.08 = 8.8 years

Question 17

A bond pays annual interest. Its coupon rate is 9%. Its value at maturity is $1 000. It matures in four years. Its yield to maturity is currently 6%. The duration of this bond is ________ years.

Accepted Answer

The answer of A bond pays annual interest. Its coupon...

Question 18

You have purchased a Guaranteed Investment contract (GIC) from an insurance firm that promises to pay you a 5% compound rate of return per year for 6 years. If you pay $10 000 for the GIC today and receive no interest along the way you will get ________ in 6 years (to the nearest dollar).

Accepted Answer

Using the formula for compound interest: 
A = P(1 + r/n)^(nt)
where A is the amount after the specified time period (6 years), P is the principal amount (initial investment), r is the annual interest rate (5%), n is the number of times the interest is compounded per year (we assume annually in this case), and t is the time period (6 years).

So, plugging in the values:
A = 10 000 (1 + 0.05/1)^(1*6)
A = 10 000 (1.05)^6
A = $13 401 rounded to the nearest dollar.

Therefore, the best choice is C.

Question 19

A bank has $50 million in assets, $47 million in liabilities and $3 million in shareholders' equity. If the duration of its liabilities are 1.3 and the bank wants to immunise its net worth against interest rate risk and thus set the duration of equity equal to zero, it should select assets with an average duration of ________.

Accepted Answer

Duration of assets = (Duration of liabilities * Liabilities - Duration of equity * Equity) / Assets
Duration of assets = (1.3 * 47 - 0 * 3) / 50 = 1.22. Therefore, the bank should select assets with an average duration of 1.22 to immunise its net worth against interest rate risk.

Question 20

Pension fund managers can generally best bring about an effective reduction in their interest rate risk by holding ________.

Accepted Answer

Pension fund managers can reduce their interest rate risk by holding long duration bonds, as they are more sensitive to changes in interest rates. This allows the fund to potentially benefit from rising interest rates, while also providing a higher yield compared to short duration bonds. Holding short maturity bonds may reduce interest rate risk, but may also result in lower yields. Long maturity bonds may have higher yields, but also carry greater interest rate risk. Therefore, holding long duration bonds strikes a balance between yield and interest rate risk management.

Quiz 10: Managing Bond Portfolios