Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

AFM 273 > Chapter 6 > Flashcards

Chapter 6 Flashcards

Excl. 6.5

1
Q

What is a bond?

A

Its a security sold by governments and corporations:

The purpose of a bond is to help raise money from investors in exchange for promised future payments.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

What is a bond indenture?

A

A bond indenture is the terms and conditions of a bond.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

What does a bond indenture include?

A
  • It indicates the amounts and dates of all promised payments that need to be made.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

When is the payment date?

A

These are when the payments should be made all the way until the final repayment date.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is the final repayment date called?

A

The maturity date

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What is the term of the bond?

A

Its the time up until the maturity date for a bond

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is one type of payment bonds make? (interest payments)

A

Coupons (payments)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

What are coupon payments?

A

These are the promised interest payments of the bond

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

How do we know how much the coupon payments will be?

A

The bond indenture will specify the amount each coupon payment will make all the way until the maturity date of the bond.

An example is that the coupons might be paid semiannually

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

What is the face value

A

Its the principal (amount) that would be repaid at the maturity of the bond.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

What is the coupon rate?

A

Its how we determine the amount of each coupon payment.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

Who sets the coupon rate?

A

This rate is set by the issuer and is stated in the bond indenture.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

How to calculate the coupon payment?

A

CPN = Coupon rate * Face value / (# of coupon payments per year)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

What is the simplest type of bond?

A

Zero-coupon bond

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What is a characteristic that zero-coupon bonds have that other bonds might not have?

A

-They do make any coupon payments.

  • The only ‘cash payment’ the investors recieve is the face value of the bond on the maturity date.
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

What is an example of a zero-coupon bond?

A

Treasury bills

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

What is a treasury bill?

A

Its a government of Canada bond that matures in one year.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

How does a bond trade at?

A
  • Zero- coupon bonds trade at a discount (a price lower than the face value)
  • Also called a pure discount bond
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

What/s another form of payment for a zero-coupon bond?

A

When bonds trade at a discount you are still compensated with the difference between the price and the face value as the price is always less.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

What is IRR?

A

Its the rate of return an investment is expected to make.

It shows how much you’ll earn from an investment overtime, expressed as a percentage.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

What is the IRR of a zero-coupon bond?

A

Its the rate of return that investors will earn on their money when they buy the bond at the current price and hold it to maturity.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What do we call the IRR of an investment?

A

Yield to maturity

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What is the YTM (or the yield to maturity)?

A

The YTM of a bond is the discount rate that sets the present value of the promised bond payments equal to the current market price of the bond

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

What is the YTM of a zero coupon bonds?

A

Its the return you will earn as an investor from holding the bond to maturity and receiving the promised face value payments

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

If the YTM for a bond is 3.5%, what does the YTM mean (3.5%)?

A

This means that investing in this bond and holding it to maturity is like earning 3.5% interest on your initial investment.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

If the YTM is 3.5%, what does the law of one price say?

A

Law of one price: It says that if two things are the same (like two risk-free investments), they should cost the same or give the same return (interest rate).

Since this bond is risk-free and gives a 3.5% return, other one-year, risk-free investments (like government bonds) must also give 3.5%.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

How to calculate the YTM?

A

YTM = (FV/P) ^1/n -1

28
Q

What is the spot rate of interest?

A
  • This is the interest rate you need to look at today if you want to figure out the value of money you’ll get at a specific future time.
  • It’s kind of like the interest rate for a particular time period (like one year, two years, etc.).
29
Q

What does the law of one price talk about for zero-coupon bond’s (spot rate of interest and the YTM)?

A
  • The Law of One Price in this context means that, for risk-free investments like a zero-coupon bond, the spot rate of interest (the interest rate for a specific period) must be the same as the bond’s yield to maturity (YTM).
30
Q

What is the relationship between a risk-free rate and the Yield to maturity? (for zero-coupon bonds)

A
  • The risk-free rate and the YTM is the same.
  • Financial professionals use the term spot rate of interest and YTM to refer to the same thing when they’re talking about zero-coupon bonds that are risk-free (safe bonds). In other words, the interest rate for a zero-coupon bond over a certain period is the same as its YTM
31
Q

What is the zero-coupon yield curve?

A

Its when we plot the risk-free interest rates for different maturities that corresponds to the yields of risk-free zero coupon bonds

32
Q

What are ‘coupon bonds’?

A

These are bonds that pay regular coupon interest payments up to maturity, they also pay out the face value at maturity.

33
Q

How to calculate the price of a bond using the YTM?

A

P = PV(Annuity (general) for the coupon bond) + PV(face value)

C1 = Coupon bond (face value * rate) /2

34
Q

Can we calculate the YTM using the Price equation when calculating the PV of a coupon bond (using the YTM)?

A
  • There is no simple formula to solve for YTM.
  • Use rate on excel
35
Q

When we calculate the YTM using the formula what kind of rate do we find?

A

We find the effective rate for each coupon interval (e.g if its a coupon of every 6 months the rate for each 6 months)

To get the annual YTM, you multiply that rate by the number of coupon periods in a year (e.g., if there are 2 coupon payments in a year, multiply by 2)

-When you adjust it to an APR (annual percentage rate), it represents the YTM on an annual basis, with the same compounding interval as the coupon rate

36
Q

How can bonds trade at (coupon bonds)

A

It can trade at a :
- premium
- par
- Discount

37
Q

Can zero-coupon bonds trade at par/premium

A

No they only trade at a discount

38
Q

What does trading at a discount mean?

A

Its when the price is less than the FV

39
Q

What does trading at a premium mean?

A

A price greater than the face value

40
Q

What does trading at par mean?

A

It means trading at a price equal to their face value

41
Q

When a coupon bond trades at a discount, what does the invetsor earn in profit?

A

They earn the return from :
1. The coupon payments
2. They also earn from the difference between the face value and the price as the FV exceeds the price

In this case the the YTM exceeds the coupon rate if the bond trades at a discount

42
Q

When a bond trades at a premium to its face value, what does the investor earn in profit?

A

When the bond trades at a premium:

  • The YTM is less than the coupon rate
  • The investor’s return from the coupon is diminished by receiving a FV less than the Price paid for.
43
Q

When a bond trades at par to its face value, what does the investor earn in profit?

A

The coupon rate is equal to the YTM meaning the investor is not receiving any increase or decrease in their investment.

44
Q

What does issuers of coupon choose what type of coupon rate?

A

They choose a coupon rate that is very close to , par (YTM = Coupon rate)

45
Q

What happens when interest rates in the economy fluctuate?

A

The yield investors demand to invest in bonds will also change.

46
Q

What happens when there is High YTM

A

Lower price bond: When interest rates (or the yield investors expect) go up, bond prices go down because future cash flows (like the $100 face value) are discounted more heavily.

47
Q

What happens where there is Lower YTM?

A

Higher Bond Price: When interest rates go down, bond prices rise because the future cash flows are more valuable

48
Q

When do we usually see the bonds price change

A

When the interst rate changes

49
Q

When do we see the prices change?

A

Its also dependent on the timing of the cash flows

50
Q

What happen if the bond has shorter maturity?

A

If a bond has shorter maturity (it matures soon), it is less sensitive to changes in interest rates. Why? Because you’re getting your money back soon, so changes in interest rates don’t affect it as much

51
Q

What happen if the bond has longer maturity?

A

If a bond has a longer maturity (it matures far in the future), it is more sensitive to interest rate changes. Since you’re waiting longer for your money, changes in interest rates have a bigger impact on its present value

52
Q

How sensitive are bonds with higher or lower coupon rates?

A
  • Bonds with higher coupon rates (paying more interest upfront) are less sensitive to interest rate changes. This is because you’re getting more of your cash flows early, so the bond’s value doesn’t change as much with interest rate movements.
  • Bonds with lower coupon rates are more sensitive because most of the cash flows come later, so changes in interest rates have a bigger effect
53
Q

how sensitive is the bonds price when it comes to duration?

A
  • A bond with high duration is very sensitive to interest rate changes, meaning its price will go up or down a lot if interest rates change.
  • A bond with low duration is less sensitive, meaning its price won’t change as much if interest rates change.
54
Q

How is it possible to replace the cash flows of a coupon using zero-coupon bonds?

A
  1. We can use the law of one price to compute the price of a coupon bond from the prices of zero-coupon bonds
55
Q

For example, we can replicate a three-year, $1000 bond that pays 10% annual coupons using three zero-coupon bonds as follows:

A
  1. Match each coupon payment with a zero-coupon bond with a face value equal to the coupon payment and a term equal to the time remaining to the coupon date.
  2. Also match the final bond payment (final coupon plus return of face value) in three years to a three-year, zero-coupon bond with a corresponding face value of $1100.
  3. Because the coupon bond cash flows are identical to the cash flows of the portfolio of zero-coupon bonds, the Law of One Price states that the price of the portfolio of zero-coupon bonds must be the same as the price of the coupon bond.

(draw it out again)

I

56
Q

How can we calculate the price of a coupon bond using the zero-coupon yields (spot rates of interest)?

A

To find the price (P) of the coupon bond, you calculate the present value of all its future payments (both coupon payments and the face value) using the spot or the zero-coupon bond rates.(YTM)

For the first coupon payment (CPN), you divide it by (1 + r₁). This discounts the coupon payment using the spot rate for the first period (r₁).

For the second coupon payment, you divide it by (1 + r₂)². This discounts the second coupon payment using the spot rate for the second period (r₂).

You continue doing this for each coupon payment, using the appropriate spot rate for each time period.

For the final coupon payment and the face value (FV), you discount both together using the spot rate for the final period (rₙ).

Spot rate = YTM

57
Q

How can we compute the YTM of a zero-coupon bond from the price of its coupon bond?

A

Use the rate function on excel.
Due to the law of one price because of the relationship between the price we can find the YTM.

When we find the YTM is a weighted average of the spot rates (the zero-coupon bond yields) for 1, 2, and 3 years. These spot rates are:

1-year spot rate: 3.5%
2-year spot rate: 4.0%
3-year spot rate: 4.5%

Since the bond pays most of its value in the third year (the face value of $1,000), the YTM is closest to the 3-year spot rate (4.5%). This means that the timing of cash flows is important: the later payments (which include the face value) carry more weight when calculating the YTM.

58
Q

What are corporate bonds?

A

These are bonds where the issuer might default (may not back the full amount promised) in the bond indenture

59
Q

What is another term for risk of default?

A

Credit risk of a bond
- Bond’s cash flows are not known with certainty

60
Q

How does credit risk of default affect bond price and yields?

A

Due to that the fact that cash flows promised by the bond are the most that bondholders can hope to recieve.:

61
Q

What does an investor do when they buy a bond that has credit risk?

A

If a bond has credit risk the investor tries to pay less for the bond.

Lower Price:

If a bond has credit risk, investors worry they might not receive all the promised payments (due to the issuer defaulting on some payments).

Because of this risk, investors pay less for the bond than they would for a bond that has no credit risk (a default-free bond).
Paying less for the bond means you’re getting it at a discount compared to a bond with no risk.

Higher Yield:

Even though investors pay less for the bond, the promised payments (coupons and face value) stay the same.
Since YTM is calculated using the promised payments and the price paid, when the price is lower but the promised payments stay the same, the YTM goes up.
The higher YTM reflects the extra return investors demand for taking on the credit risk. Investors expect a higher return because there’s a chance they won’t get all their money.

62
Q

What happens when there is no risk of default?

A

The no risk of default means that the bond issuer is guaranteed to make all promised payments:

  • They will recieve all coupon payments.
  • Investors would not demand a higher yield to compensate for the risk
  • If there are two bonds that offer the same cash flows and the same level of risk (due to the law of one price) they should have the same price : The Law of One Price says that two investments that offer the same cash flows and have the same level of risk should have the same price
63
Q

What if there is a chance of default?

A

lets say:
- Investors believe that Loblaw will default with certainty at the end of the one year and will be able to pay 90% of its outstanding obligation even though it promise to pay 1000 at year end:

Due to the fact that bondholders know they will recieve 900. Investors can predict the price of the bond using the amount that they will recieve.

This $900 payment is certain and considered risk-free because investors know Loblaw will definitely pay that amount, even though it’s less than the original promise. We can calculae the price of the bond using the PV:

P = 900/(1+YTM)

Due to the idea of default it lowers the cash flows investors expect to recieve and the price they are wlling to pay

64
Q

If a bond has certainty of default how can they calculate the YTM? (Based on the promised payment)

A

When computing the YTM, we use the promised (what they expect to get) rather than the actual cash flow , using the

YTM = (FV/P) - 1

  • This means that the YTM of the bond is 15.58%. However, this is based on the promised cash flow of $1,000, not the actual expected cash flow of $900.
  • Even though the YTM is 15.58%, investors know they will only receive $900. So the expected return is lower because the actual cash flow is less than the promised amount.
65
Q

How can we compute the expected return?

A

Expected return = Expected cash flow/P -1

(this is the expected return that is based on the actual expected cash flow and not what was promised)

66
Q

what if there was a risk of default (somewhere in between certainty of default and no default)?

Example: To illustrate, again consider the one-year, $1000, zero-coupon bond issued by Loblaw. This time, assume that the bond payoffs are uncertain. In particular, there is a 50% chance that the bond will repay its face value in full and a 50% chance that the bond will default, and you will receive $900

A
  1. In this scenario you would multiply the (0.51000) + (0.5900) = 950 the average essentially. (this would give us our expected cash flow)
  2. To determine the price of the bond:
  • We use the cost of capital here as the rate as it represents the return investors expect based on the risk they are taking:

Cost of capital = Risk free rate + risk premium (The risk premium is an extra return that investors demand to compensate for the extra risk they are taking)

  1. Price is = Expected cash flow/(1+ cost of capital)
    - Investors are willing to pay 903.50 today for 950 in the future
  2. How can we calculate the bond’s YTM? (based on the promsied cash flow)

1000/903.50 -1= 10.63%

So, the YTM for this bond is 10.63%, meaning that if Loblaw pays the full $1,000, the return to the investor will be 10.63%.

  1. How can we calculae the expected return knowing theres a 50% chance Loblaw will default and pay 900?
  • Step 4: Expected Return
    In this step, we calculate the expected return for the bond, considering that there’s a 50% chance Loblaw will default and pay only $900.

What We Know:
The YTM of 10.63% assumes that Loblaw will pay the full $1,000. But investors know that there’s a 50% chance that they will only get $900 if Loblaw defaults.
The expected return considers both possible outcomes—either getting $1,000 or $900.
Expected Return Calculation:
If Loblaw pays $1,000 (no default), the return is 10.63%.
If Loblaw pays $900 (default), the return is negative because investors will get less than they paid: 900/903.50 -1 = -0.43%

Expected return = 0.50(10.63%) + 0.50%(-0.43) = 5.1%

So, the expected return is 5.1%, which is exactly the same as the cost of capital (the return investors expect given the risk involved).

AFM 273 (5 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions