Question 1

If the nominal interest rate per year is 10% and the inflation rate is 4%, what is the real rate of interest?
A) 10%
B) 4%
C) 5.8%
D) None of the above

Accepted Answer

The real rate of interest is calculated as nominal interest rate minus inflation rate, which in this case is 10%-4% = 6%. Therefore, the real rate of interest is 6%, not 10% or 4%.

Question 2

The yield to maturity on a bond is really its internal rate of return.

Accepted Answer

The yield to maturity (YTM) is the interest rate that equates the present value of future cash flows from a bond to its current market price. This calculation is very similar to determining the internal rate of return (IRR) on an investment. Therefore, YTM is commonly referred to as the bond's internal rate of return.

Question 3

Volatility of a bond is given by: 
I. Duration/ (1 + yield)
II. Slope of the curve relating the bond price to the interest rate
III. Yield to maturity
A) I only
B) II only
C) III only
D) I and II only

Accepted Answer

I is the formula for modified duration, which is a measure of a bond's sensitivity to changes in interest rates. A higher modified duration indicates greater price volatility in response to changes in interest rates.

II is the slope of the curve relating the bond price to the interest rate, which is another measure of a bond's sensitivity to changes in interest rates. A steeper slope indicates greater price volatility in response to changes in interest rates.

III is the yield to maturity, which is the total return anticipated on a bond if held until it matures. While yield to maturity is important in determining a bond's value, it does not directly measure the bond's price volatility in response to changes in interest rates.

Question 4

The duration of a zero coupon bond is the same as its maturity.

Accepted Answer

The duration of a zero coupon bond is equal to its maturity because there are no periodic coupon payments to affect the bond's sensitivity to interest rate changes over time.

Question 5

Which of the following statements is true?
I. The spot interest rate is a weighted average of yields to maturity
II. Yield to maturity is the weighted average of spot interest rates and estimated forward rates
III. The yield to maturity is always higher than the spot rates
A) I only
B) II only
C) III only
D) I and III only

Accepted Answer

Yield to maturity is the single discount rate that makes the present value of a bond's payments equal to its price, and it is NOT a weighted average of spot rates. On the contrary, yield to maturity is the weighted average of spot interest rates and estimated forward rates, and it can be influenced by various factors such as coupon payments, time to maturity, and default risk. Moreover, yield to maturity may be higher or lower than the spot rates depending on the shape of the yield curve and the bond's characteristics. Therefore, statement I and III are incorrect, and statement II is correct.

Question 6

If the 4-year spot rate is 7% and the 3-year spot rate is 6%, what is the one-year forward rate of interest three years from now?
A) 10.0%
B) 6.5%
C) 9.6%
D) None of the above

Accepted Answer

The answer of If the 4-year spot rate is 7%...

Question 7

Mr. X invests $1000 at 10% nominal rate for one year. If the inflation rate is 4%, what is the real value of the investment at the end of one year?
A) $1100
B) $1000
C) $1058
D) None of the above

Accepted Answer

Nominal rate is 10%, so the investment will be worth $1100 at the end of one year. However, inflation at 4% reduces the real value of the investment to $1058. This is calculated as follows:
Real Value = Nominal Value/(1+Inflation Rate)
Real Value = $1000/(1+0.04)
Real Value = $1058

Question 8

A forward rate prevailing from period three through to period four can be: 
I. readily observed in the market place
II. extracted from spot interest rate with 3 and 4 years to maturity
III. extracted from 1 and 2 year spot interest rates
A) I only
B) II only
C) III only
D) I and III only

Accepted Answer

Forward rates cannot be readily observed in the market place, but can be extracted from spot interest rates. Specifically, the forward rate between periods three and four can be extracted from the three-year spot rate (period one to three) and the four-year spot rate (period one to four). Therefore, only statement II is correct. Statement III is incorrect because it refers to 1 and 2 year spot rates, which are not relevant to calculating the forward rate between periods three and four.

Question 9

The term structure of interest rates can be described as the:
A) Relationship between the spot interest rates and the bond prices
B) Relationship between spot interest rates and stock prices
C) Relationship between spot interest rates and maturity of a bond
D) None of the above

Accepted Answer

The term structure of interest rates is the relationship between spot (current) interest rates and the maturity of a bond. It shows how interest rates vary across different maturities, such as short-term, intermediate-term, and long-term bonds.

Question 10

How can one invest today at the 2-year forward rate of interest?
I. By buying a 2-year bond and selling a 1-year bond with the same coupon
II. By buying a 1-year bond and selling a 2-year bond with the same coupon
III. By buying a 1-year bond and then after a year reinvesting in a further 1-year bond
A) I only
B) II only
C) III only
D) II and III only

Accepted Answer

Buying a 2-year bond and selling a 1-year bond with the same coupon is a strategy known as a forward rate agreement (FRA), which allows an investor to lock in a future interest rate. Option II involves buying a 1-year bond and selling a 2-year bond with the same coupon, which does not provide an investment at the 2-year forward rate of interest. Option III involves reinvesting after one year, which does not allow an investor to lock in the 2-year forward rate of interest. Therefore, the best choice is Option I only.

Question 11

Which bond is more sensitive to an interest rate change of 0.75%?
Bond A: YTM = 4.00%, Maturity = 8 years, Coupon = 6% or $60, Par Value = $1,000
Bond B: YTM = 3.50%, Maturity = 5 years, Coupon = 7% or $70, Par Value = $1,000
A) A
B) B
C) Both the same
D) Cannot be determined

Accepted Answer

Bond A has a longer maturity and a lower YTM than Bond B, which makes it more sensitive to changes in interest rates. Additionally, the coupon rate of Bond A is lower than its YTM, indicating that it was issued at a premium, making it even more sensitive to interest rate changes. Therefore, Bond A is more sensitive to an interest rate change of 0.75%.

Question 12

In the US, most bonds make coupon payments annually.

Accepted Answer

The answer of In the US, most bonds make coupon...

Question 13

If the 3-year spot rate is 10.5% and the 2-year spot rate is 10%, what is the one-year forward rate of interest two years from now?
A) 3.7%
B) 9.5%
C) 11.5%
D) None of the above

Accepted Answer

The formula for calculating the one-year forward rate of interest two years from now is:
[(1 + 3-year spot rate)^3 / (1 + 2-year spot rate)^2] - 1 = one-year forward rate two years from now
Plugging in the given values, we get:
[(1.105)^3 / (1.1)^2] - 1 = 0.115 or 11.5%
Therefore, the answer is C.

Question 14

The longer a bond's duration greater is its volatility.

Accepted Answer

A bond's duration measures its sensitivity to changes in interest rates. The longer the duration, the more sensitive the bond's price is to interest rate movements, which can lead to increased volatility.

Question 15

Interest represented by "r2" is:
A) Spot rate on a one-year investment (APR)
B) Spot rate on a two-year investment (APR)
C) Expected spot rate 2 years from today
D) Expected spot rate one year from today

Accepted Answer

"r2" represents the spot rate on a two-year investment (APR).

Question 16

If the 5-year spot rate is 10% and the 4-year spot rate is 9%, what is the one-year forward rate of interest four years from now?
A) 14.1%
B) 9.5%
C) 1.0%
D) 11.0%

Accepted Answer

The answer of If the 5-year spot rate is 10%...

Question 17

If a bond's volatility is 5% and the interest rate changes by 0.5% (points) then the price of the bond:
A) changes by 5%
B) changes by 2.5%
C) changes by 7.5%
D) none of the above

Accepted Answer

The price of the bond will change by 2.5%. This can be calculated by multiplying the bond's volatility (5%) by the change in interest rate (0.5%) which equals 0.025 or 2.5%.

Question 18

What forward rate is embedded in a two year zero coupon bonds with a yield to maturity Of 6% and a three year zero coupon bond and a yield to maturity of 6.5%? Assume both bonds are currently priced at par.
A) 5.50%
B) 6.00%
C) 6.50%
D) 7.50%

Accepted Answer

The answer of What forward rate is embedded in a...

Question 19

The expectations hypothesis states that the forward interest rate is the: 
I. expected future spot rate
II. always greater than the spot rate
III. yield to maturity
A) I only
B) II only
C) III only
D) II and III only

Accepted Answer

The expectations hypothesis states that the forward interest rate is equal to the expected future spot rate. Therefore, the correct option is I only. Option II is false as the forward interest rate can be either greater or less than the spot rate depending on market expectations. Option III is not always true as the forward rate can differ from the yield to maturity if there is a variance in expectations regarding future interest rates.

Question 20

The duration of any bond is the same as its maturity.

Accepted Answer

Duration measures the sensitivity of a bond's price to changes in interest rates and is typically shorter than the bond's maturity, except for zero-coupon bonds where they are the same.

Quiz 3: Valuing Bonds

If the nominal interest rate per year is 10% and the inflation rate is 4%, what is the real rate of interest?

The yield to maturity on a bond is really its internal rate of return.

Volatility of a bond is given by: I. Duration/ (1 + yield) II. Slope of the curve relating the bond price to the interest rate III. Yield to maturity

The duration of a zero coupon bond is the same as its maturity.

Which of the following statements is true? I. The spot interest rate is a weighted average of yields to maturity II. Yield to maturity is the weighted average of spot interest rates and estimated forward rates III. The yield to maturity is always higher than the spot rates

If the 4-year spot rate is 7% and the 3-year spot rate is 6%, what is the one-year forward rate of interest three years from now?

Mr. X invests $1000 at 10% nominal rate for one year. If the inflation rate is 4%, what is the real value of the investment at the end of one year?

A forward rate prevailing from period three through to period four can be: I. readily observed in the market place II. extracted from spot interest rate with 3 and 4 years to maturity III. extracted from 1 and 2 year spot interest rates

The term structure of interest rates can be described as the:

Which bond is more sensitive to an interest rate change of 0.75%? Bond A: YTM = 4.00%, Maturity = 8 years, Coupon = 6% or $60, Par Value = $1,000 Bond B: YTM = 3.50%, Maturity = 5 years, Coupon = 7% or $70, Par Value = $1,000

In the US, most bonds make coupon payments annually.

If the 3-year spot rate is 10.5% and the 2-year spot rate is 10%, what is the one-year forward rate of interest two years from now?

The longer a bond's duration greater is its volatility.

Interest represented by "r2" is:

If the 5-year spot rate is 10% and the 4-year spot rate is 9%, what is the one-year forward rate of interest four years from now?

If a bond's volatility is 5% and the interest rate changes by 0.5% (points) then the price of the bond:

What forward rate is embedded in a two year zero coupon bonds with a yield to maturity Of 6% and a three year zero coupon bond and a yield to maturity of 6.5%? Assume both bonds are currently priced at par.

The expectations hypothesis states that the forward interest rate is the: I. expected future spot rate II. always greater than the spot rate III. yield to maturity

The duration of any bond is the same as its maturity.