Question 1

The market segmentation and preferred habitat theories of term structure

Accepted Answer

Market segmentation theory suggests that investors and borrowers prefer specific maturities and are not willing to depart from them regardless of yield, while preferred habitat theory acknowledges this preference but also recognizes that investors may be willing to extend or shorten their maturities if the yield is attractive enough. Market segmentation theory is now rare, and preferred habitat theory is widely accepted.

Question 2

Forward rates ____________ future short rates because ___________.

Accepted Answer

Forward rates differ from future short rates because they are imperfect forecasts. While forward rates are estimated based on market expectations, they do not always accurately predict future interest rates. Future short rates, on the other hand, are extracted from yields to maturity and are a more reliable indication of what rates are likely to be in the future.

Question 3

Statistical estimation of the yield curve contains apparent pricing error.These error terms are probably a result of

Accepted Answer

All the mentioned factors, including tax effects, call provisions, and out-of-date price quotes, can contribute to apparent pricing errors in the statistical estimation of the yield curve.

Question 4

Investors can use publicly available financial date to determine which of the following?
I.the shape of the yield curve
II.future short-term rates
III.the direction the S&P/TSX composite index is heading
IV.the actions to be taken by the Bank of Canada

Accepted Answer

The answer of Investors can use publicly available financial date...

Question 5

The concepts of spot and forward rates are most closely associated with which one of the following explanations of the term structure of interest rates.

Accepted Answer

The Expectations Hypothesis is the theory that the shape of the yield curve depends on investors' expectations of future interest rates. The spot rate is the current interest rate for a specific maturity, while the forward rate is the expected future interest rate for a specific maturity. This theory suggests that the forward rate can be calculated using the spot rate and investors' expectations of future spot rates.

Question 6

Interest rates might decline

Accepted Answer

Interest rates might decline if real interest rates or the inflation rate are expected to decline, as both factors contribute to the overall level of interest rates.

Question 7

The yield curve

Accepted Answer

The yield curve is a graphical representation of the term structure of interest rates (A), and it is often depicted for government bonds like Canada bonds to maintain a constant risk profile across different maturities (B).

Question 8

The most recently issued Treasury securities are called

Accepted Answer

The most recently issued Treasury securities are referred to as "on the run" securities. These securities are generally considered to be more liquid and have tighter bid-ask spreads than older, "off the run" securities.

Question 9

An upward sloping yield curve

Accepted Answer

An upward sloping yield curve indicates that interest rates are expected to increase in the future. It also incorporates a liquidity premium, which compensates investors for holding longer-term bonds that are less liquid than shorter-term bonds. The curve can also reflect the confounding of the liquidity premium with interest rate expectations. Therefore, all of these statements are true for an upward sloping yield curve.

Question 10

Given the yield on a 3 year zero-coupon bond is 7.2% and forward rates of 6.1% in year 1 and 6.9% in year 2,what must be the forward rate in year 3?

Accepted Answer

To answer this question, we can use the formula for calculating forward rates:

(1 + y)^n = (1 + f1)^1 x (1 + f2)^2 x (1 + f3)^3

where:
y = Yield to maturity
f1, f2, f3 = Forward rates for year 1, year 2, and year 3.

Substituting the given values, we get:

(1 + 0.072)^3 = (1 + 0.061)^1 x (1 + 0.069)^2 x (1 + f3)^3

Solving for f3, we get:

f3 = (1 + 0.072)^3 / [(1 + 0.061)^1 x (1 + 0.069)^2]^(1/3) - 1

f3 = 0.086 or 8.6%

Therefore, the answer is B) 8.6%.

Question 11

If you have just purchased a 4-year zero coupon bond,what would be the expected rate of return on your investment in the first year if the implied forward rates stay the same? (Par value of the bond = $1,000)

Accepted Answer

A zero coupon bond does not pay interest, but it is purchased at a discount and pays its par value at maturity. The expected rate of return on a zero coupon bond can be calculated using the formula:
(Par value/Purchase price)^(1/years to maturity) - 1

For a 4-year zero coupon bond, the purchase price would be:
Purchase price = Par value / (1 + implied rate)^4

Since the implied forward rates stay the same, the rate used to calculate the purchase price would be the current 4-year implied forward rate.
If we assume the current 4-year implied forward rate is 3%, we can calculate the purchase price as follows:
Purchase price = $1,000 / (1 + 0.03)^4 = $822.70

Then, the expected rate of return in the first year can be calculated as:
($1,000 / $822.70)^(1/4) - 1 = 0.0275 or 2.75%

Therefore, the best choice is B, with an expected rate of return of 3%, which is the closest to the calculated rate using the formula above.

Question 12

The pure yield curve can be estimated

Accepted Answer

The pure yield curve represents the theoretical yield curve assuming no liquidity or credit risk. It can be estimated by using zero-coupon bonds as they do not have any coupon payments and therefore, the yield represents only the pure yield for that maturity. Coupon bonds can also be used to estimate the pure yield curve if each coupon is treated as a separate "zero." This is because each coupon represents a separate cash flow and can be discounted separately to arrive at the pure yield for that maturity. Therefore, option E is the best choice as it includes both of these methods. Corporate bonds with different risk ratings and estimating liquidity premiums for different maturities are not directly related to estimating the pure yield curve.

Question 13

The "break-even" interest rate for year n that equates the return on an n-period zero-coupon bond to that of an n-1-period zero-coupon bond rolled over into a one-year bond in year n is defined as

Accepted Answer

The break-even interest rate is essentially the forward rate between two periods, which is represented by choice A. The short rate refers to the rate for a single period, and the yield to maturity and discount rate are broader concepts that do not specifically apply to the comparison of two specific bond periods.

Question 14

Consider two annual coupon bonds,each with two years to maturity.Bond A has a 7% coupon and a price of $1,000.62.Bond B has a 10% coupon and sells for $1,055.12.Find the two one-period forward rates that must hold for these bonds.

Accepted Answer

The answer of Consider two annual coupon bonds,each with two...

Question 15

Assuming the forecasts implicit in a yield curve come to pass,an inverted yield curve would be most favorable for

Accepted Answer

The answer of Assuming the forecasts implicit in a yield...

Question 16

An inverted yield curve is one

Accepted Answer

An inverted yield curve is one in which longer-term bonds have lower yields than shorter-term bonds, causing the curve to slope downward. This is often seen as a sign of an impending recession in the economy.

Question 17

When computing yield to maturity,the implicit reinvestment assumption is that the interest payments are reinvested at the:

Accepted Answer

The answer of When computing yield to maturity,the implicit reinvestment...

Question 18

Which one of the following statements is true?

Accepted Answer

The segmentation hypothesis suggests that the market for bonds is segmented based on maturity, meaning borrowers and lenders have preferences for certain maturities, leading to different interest rates across segments.

Question 19

The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000. $$\begin{array} { | l | l | } 
\hline \text { Maturity (Years) } & \text { Price } \
\hline 1 & \$ 925.16 \
\hline 2 & \$ 862.57 \
\hline 3 & \$ 788.66 \
\hline 4 & \$ 711.00 \
\hline
\end{array}$$
What is,according to the expectations theory,the expected forward rate in the third year?

Accepted Answer

The expected forward rate can be calculated using the formula: $(1 + f_{2,3})^1 = \frac{(1 + y_3)^3}{(1 + y_2)^2}$, where $y_n$ is the yield for n years. Calculate $y_2$ and $y_3$ from the given prices, then solve for $f_{2,3}$.

Question 20

The following is a list of prices for zero coupon bonds with different maturities and par value of $1,000. $$\begin{array} { | l | l | } 
\hline \text { Maturity (Years) } & \text { Price } \
\hline 1 & \$ 925.16 \
\hline 2 & \$ 862.57 \
\hline 3 & \$ 788.66 \
\hline 4 & \$ 711.00 \
\hline
\end{array}$$
What is the price of a 4-year maturity bond with a 10% coupon rate paid annually? (Par value = $1,000)

Accepted Answer

The price of a bond is the present value of its future cash flows, which include the annual coupon payments and the par value at maturity. The 4-year zero-coupon bond's yield can be used to discount these cash flows. The yield is calculated as $(1000/711)^{1/4} - 1$. Using this yield, the present value of the 4 annual $100 coupon payments and the $1,000 par value is $1,035.66.

Quiz 13: Equity Valuation