Question 1

Advantages of cash flow matching and dedicated strategies include ________.
I. once the cash flows are matched there is no need for rebalancing
II. cash flow matching typically earns a higher rate of return than active bond portfolio management
III. financial institution's liabilities often exceed the maturity of available bonds, making cash matching even more desirable

Accepted Answer

The answer of Advantages of cash flow matching and dedicated...

Question 2

A zero coupon bond is selling at a deep discount price of $430.00. It matures in 13 years. If the yield to maturity of the bond is 6.7%, what is the duration of the bond?

Accepted Answer

The answer of A zero coupon bond is selling at...

Question 3

A bond portfolio manager notices a hump in the yield curve at the five-year point. How might a bond manager take advantage of this event?

Accepted Answer

By buying the 5-year bonds and shorting the surrounding maturity bonds, the portfolio manager can take advantage of the hump in the yield curve by earning higher yields on the 5-year bonds while hedging against interest rate changes on the surrounding maturities. This strategy is known as a barbell strategy. Buying the surrounding maturity bonds along with the 5-year bonds (Option B) would result in a less effective yield curve positioning, while shorting both the 5-year bonds and surrounding maturities (Option C) would leave the portfolio exposed to potential losses from a flattening or inversed yield curve.

Question 4

You have a 15 year maturity 4% coupon, 6% yield bond with duration of 10.5 years and a convexity of 128.75. The bond is currently priced at $805.76. If interest rate were to increase 200 basis points your predicted new price for the bond (including convexity) is ________.

Accepted Answer

First, we need to calculate the bond's modified duration:

Modified Duration = Duration / (1 + Yield) = 10.5 / 1.06 = 9.91

Next, we can use the following formula to calculate the approximate percentage change in price:

ΔP/P = -Modified Duration * ΔYield + 0.5 * Convexity * (ΔYield)^2

where ΔYield = 200 basis points = 0.02.

Plugging in the numbers, we get:

ΔP/P = -9.91 * 0.02 + 0.5 * 128.75 * (0.02)^2
ΔP/P = -0.1982 + 0.00026
ΔP/P = -0.19794

So the predicted percentage change in price is -19.794%. To get the new price, we multiply this percentage change by the current price and subtract the result from the current price:

New Price = $805.76 * (1 - 0.19794) = $646.92

However, we need to add the convexity in order to get a more accurate prediction. The convexity adjustment is calculated as follows:

Convexity Adjustment = 0.5 * Convexity * (ΔYield)^2
Convexity Adjustment = 0.5 * 128.75 * (0.02)^2
Convexity Adjustment = 0.0013

Adding this adjustment to the predicted percentage change, we get:

New Price = $805.76 * (1 - 0.19794 + 0.0013) = $666.88

Therefore, the best choice is C, $666.88.

Question 5

You have an investment horizon of 6 years. You choose to hold a bond with a duration of 4 years. Your realised rate of return will be larger than the promised yield on the bond if ________.

Accepted Answer

When interest rates increase, bond prices decrease. This means that if the investor sells the bond before maturity, they can receive a higher price than the price they paid for it. This results in a larger realised rate of return than the promised yield on the bond.

Question 6

If you choose a zero coupon bond with a maturity that matches your investment horizon which of the following statements is/are correct?
I. You will have no interest rate risk on this bond.
II. Absent default, you can be sure you will earn the promised yield rate.
III. The duration of your bond is less than the time to your investment horizon.

Accepted Answer

I is correct because zero coupon bonds have no coupon payments, so there is no interest rate risk associated with changes in interest rates.
II is correct because the yield rate on a zero coupon bond is fixed at the time of purchase and will be paid at maturity, assuming no default.
III is also correct because the duration of a zero coupon bond is always less than its maturity, meaning that the bond's price will be less sensitive to changes in interest rates than a bond with coupon payments. Choosing a zero coupon bond with a maturity that matches your investment horizon can help minimize interest rate risk.

Question 7

Convexity of a bond is ________.

Accepted Answer

Convexity is the rate of change of the price-yield curve divided by bond price. It measures the sensitivity of a bond's price to changes in interest rates and indicates the degree of curvature of the price-yield relationship. A higher convexity indicates a greater price change for a given change in yield, and vice versa. Therefore, B is the correct answer. A is incorrect as horizon analysis is a method used to forecast returns based on an analysis of past market data. C is incorrect as bond duration is a measure of a bond's sensitivity to interest rate changes. D is incorrect as there is a correct answer.

Question 8

Immunisation of coupon paying bonds is not a passive strategy because ________.
I. the portfolio must be rebalanced every time interest rates change
II. the portfolio must be rebalanced over time even if interest rates don't change
III. convexity implies duration based immunisation strategies don't work

Accepted Answer

Immunisation of coupon paying bonds is not a passive strategy because the portfolio must be rebalanced every time interest rates change to maintain the duration and cash flow profile, which is stated in I. Additionally, even if interest rates don't change, the portfolio must still be rebalanced over time due to bond cash flows, as mentioned in II. However, convexity does not imply that duration-based immunisation strategies don't work, so III is incorrect. Therefore, the best choice is B, I and II only.

Question 9

The duration is independent of the coupon rate only for which one of the following?

Accepted Answer

The duration of perpetuities is independent of the coupon rate because perpetuities do not have a maturity date, meaning the cash flows are infinite and the timing of the cash flows does not affect the duration calculation. The duration of discount bonds increases as the coupon rate decreases, while the duration of premium bonds decreases as the coupon rate decreases. Short-term bonds may or may not have a significant duration impact from changes in the coupon rate, depending on how short the term is and how large the coupon rate changes are.

Question 10

What strategy might an insurance company employ to ensure that it will be able to meet the obligations of annuity holders?

Accepted Answer

Cash flow matching is a strategy where an insurance company invests its assets in such a way that it can generate cash flows that match the future obligations of annuity holders. This helps ensure that the company will have sufficient funds to meet the annuity payments as they become due. In other words, the company matches the duration and cash flow patterns of its investments to those of its liabilities. This is considered to be a conservative and effective way to manage the risks associated with annuity obligations. Index tracking, yield pickup swaps, and substitution swaps are not relevant strategies to ensure the company will be able to meet its obligations to annuity holders.

Question 11

Which one of the following statements correctly describes the weights used in the Macaulay duration calculation?
The weight in Year t is equal to ________.

Accepted Answer

The Macaulay duration uses weights that are the percentage of the total present value of the investment received in each year.

Question 12

You have a 25-year maturity 10% coupon, 10% yield bond with duration of 10 years and a convexity of 135.50. If the interest rate were to fall 125 basis points your predicted new price for the bond (including convexity) is ________.

Accepted Answer

The answer of You have a 25-year maturity 10% coupon,...

Question 13

When bonds sell above par, what is the relationship of price sensitivity to rising interest rates?

Accepted Answer

The answer of When bonds sell above par, what is...

Question 14

As compared with equivalent maturity bonds selling at par, deep discount bonds will have ________.

Accepted Answer

Deep discount bonds will have greater price volatility because they are sold at a significantly lower price than their par value, meaning that even small fluctuations in market interest rates can have a larger impact on their price. They may also have longer average maturity and less call protection. However, they may have lower reinvestment risk because the investor receives the full par value at maturity, reducing the need to constantly reinvest coupon payments.

Question 15

If an investment returns a higher percentage of your money back sooner it will ________.

Accepted Answer

When an investment returns a higher percentage of your money back sooner, it means that the investment is more likely to be stable and predictable, resulting in lower price volatility.

Question 16

A 20-year maturity corporate bond has a 6.5% coupon rate (the coupons are paid annually). The bond currently sells for $925.50. A bond market analyst forecasts that in five years, yield rates on these bonds will be at 7.0%. You believe that you will be able to reinvest the coupons earned over the next five years at a 6% rate of return. What is your expected annual compound rate of return if you plan on selling the bond in five years?

Accepted Answer

The answer of A 20-year maturity corporate bond has a...

Question 17

Convexity implies that duration predictions ________.
I. underestimate the % increase in bond price when the yield falls
II. underestimate the % decrease in bond price when the yield rises
III. overestimates the % increase in bond price when the yield falls
IV. overestimates the % decrease in bond price when the yield rises

Accepted Answer

The answer of Convexity implies that duration predictions ________.
I. underestimate...

Question 18

You have an investment that in today's dollars returns 15% of your investment in Year 1, 12% in Year 2, 9% in Year 3 and the remainder in Year 4. What is the duration of this investment?

Accepted Answer

To calculate the duration of the investment, we need to take the weighted average of the time it takes to receive each cash flow. The formula for duration is given by:

Duration = (CF1*1 + CF2*2 + CF3*3 + CF4*n) / (CF1 + CF2 + CF3 + CF4)

Where CF is the cash flow in the respective year and n is the number of years for the final cash flow.

Plugging in the given cash flows, we get:

Duration = (0.15*1 + 0.12*2 + 0.09*3 + x*4) / (0.15 + 0.12 + 0.09 + x)

Simplifying the equation, we get:

Duration = (0.54 + 4x) / (0.36 + x)

We know that the sum of the percentages must be 100%, so the remaining cash flow in Year 4 is:

100% - 15% - 12% - 9% = 64%

Therefore,

x = 0.64

Plugging x back into the duration equation, we get:

Duration = (0.54 + 4(0.64)) / (0.36 + 0.64) = 3.22 years

Question 19

Market economists all predict a rise in interest rates. An astute bond manager wishing to maximise her capital gain might employ which strategy?

Accepted Answer

When interest rates rise, bond prices typically fall. However, the degree to which prices fall depends on the bond's duration. Higher duration bonds (those with longer time to maturity) are more sensitive to interest rate changes and will experience greater price declines than lower duration bonds (those with shorter time to maturity). Therefore, an astute bond manager wishing to maximise her capital gain might switch from high duration to low duration bonds in anticipation of rising interest rates.

Question 20

You have an investment horizon of 6 years. You choose to hold a bond with a duration of 6 years and continue to match your investment horizon and duration throughout your holding period. Your realised rate of return will be the same as the promised yield on the bond if ________.
I. interest rates increase
II. interest rates stay the same
III. interest rates fall

Accepted Answer

When the bond's duration matches the investment horizon, the realized rate of return will equal the promised yield regardless of interest rate changes, as the effects of price changes and reinvestment rate changes offset each other.

Quiz 10: Managing Bond Portfolios