Bonds

Question 1

What are bonds?

Answer 1

Bonds are issued by governments and corporations to raise money from investors in exchange of a promise to future payments.

Question 2

What are the operations with bonds?

Answer 2

Buy the financial asset (investment operation) and short-sell the financial asset (financing operations).

Question 3

What is short-selling?

Answer 3

Short-selling means selling something you don’t have, so you borrow sell and receive money all at time zero. You have the obligation of paying who lent you money in all future periods.

Question 4

When does an agent short-sell?

Answer 4

An agent short-sells when they think stocks are going down. If the bet is price, the agent will then be able to buy for a lower price.

Question 5

When is there an arbitrage opportunity?

Answer 5

An arbitrage opportunity happens when an investor can set up an arbitrage strategy , the price from the market is different than the bod’s value.

Question 6

What is an arbitrage strategy?

Answer 6

An arbitrage strategy always has two sides: financing (where the money comes from) and the investing side (what you do with the money). It needs to yield payofft»0 with at least one positive payoff, without any kind of risk (investor can’t use their own money). It appears from misspricing in the financial market.

Question 7

What is the law of one price?

Answer 7

The law of one price says that two different portfolios/assets that have the same payoff scheme need to have the same price today.

Question 8

What is the primary and the secondary market?

Answer 8

In the primary market bons are issued, sold by governments and corporations to investors. In the secondary market bonds are traded among investors after the issue.

Question 9

How is the coupon rate expressed?

Answer 9

APR

Question 10

Who is the borrower and the lender?

Answer 10

The issuer is the borrower and the holder of the bond is the lender.

Question 11

What is the coupon’s formula?

Answer 11

C = (Coupon Rate * Face Value)/Nº of coupon payments a year

Question 12

How do we price bonds?

Answer 12

Through the present value of all future cash-flows.
P0 = C1/(1 + y) + C2/(1 + y)^2 + (CT + FV) / (1 + y)^T

Question 13

What is the relationship between the bond’s price and the discount rate?

Answer 13

Convex. If the probability to not receive face value decreases, you increase the discount rate (as you’re closer to maturity date you increase by less)

Question 14

Where do accrued interests matter?

Answer 14

In the secondary market.

Question 15

What is the accrued interests formula?

Answer 15

Accrued Interest = C * Days since last coupon payment/Days separating coupon payments

Question 16

What rate do we use to compute the price of a bond?

Answer 16

YTM

Question 17

What rate do we use to compute the value of a bond?

Answer 17

Spot rates

Question 18

What does it mean to assume the financial markets are normal?

Answer 18

Financial assets are traded with NPV=0 so the bond’s price and its value are the same, so there are no arbitrage opportunities.

Question 19

What are spot rates?

Answer 19

Spot rates are a set of discount rates applicable today and for different maturities. We use them to get the bond’s value. Spot rates allow you to value bonds with the same risk in a specific point in time.

Question 20

Why do spot rates change overtime?

Answer 20

Market conditions

Question 21

What is the YTM?

Answer 21

A YTM is a discount rate that sets the present value of the promised payments equal to the current market price of the bond. It is the return you earn as an investor from holding the bond from the moment you buy it until maturity.

Question 22

When can we use the YTM?

Answer 22

The YTM can only be used in a specific point in time and for only one bond.

Question 23

What does the YTM assume?

Answer 23

The YTM assume the bond’s cash-flows are reinvested at the same rate as the YTM until the maturity date.

Question 24

When can we find the YTM?

Answer 24

We can only find the YTM if we have the price.

Question 25

How can we find the YTM with excel?

Answer 25

IRR() (the bond's price need to be negative)

Question 26

What is the relationship between spot rated and the YTM?

Answer 26

The YTM is a non-linear average of the spot rates that the bond uses (higher than the lowest and lower to the highest) The YTM is relatively closer to the last spot rate that the bond uses (the one with the highest weight).

Question 27

What does it mean if a bond is being traded at premium and what does it imply?

Answer 27

Premium: P0 > FV which implies YTM < coupon rate

Question 28

What does it mean if a bond is issued at par?

Answer 28

Par: P0 = FV which implies YTM = coupon rate

Question 28

What does it mean if a bond is issued at discount?

Answer 28

Discount: P0 < FV which implies YTM > coupon rate

Question 29

Why is it indifferent if you buy a bond at premium or discount?

Answer 29

If you demand a YTM higher than the coupon rate (what the bond pays you) the price will decrease.

Question 30

What is the holding period return?

Answer 30

HPRt/t+1 = ((Pt+1 - P1) + Cft+1)/Pt

Question 31

What are the 3 methods to find spot rates?

Answer 31

1) Zero-coupon bonds 2) Bootstrap 3) Forward rates

Question 32

How do we find the spot rate with zero-coupon bonds?

Answer 32

In zero-coupon bonds the spot rate is the same as the YTM, assuming normal markets.

Question 33

How is the investor compensated in zero-coupon bonds?

Answer 33

The price is lower than the face value.

Question 34

What are the conditions to use bootstrap?

Answer 34

It can't be a zero-coupon bond, we need to know the price and n-1 spot rates.

Question 35

What are forward rates?

Answer 35

Rates that are acquired today but will be used in the future.

Question 36

What is the formula for forward rates and spot rates?

Answer 36

(1 + 0r3)^3 = (1 + 0r2)^2 * (1 + 2f3) (1 + 0r3)^3 = (1 + 0r1) * (1 + 1f2) * (1 + 2f3)

Question 37

What is the yield curve?

Answer 37

A graph of spot rates.

Question 38

What is the liquidity preference theory?

Answer 38

Liquidity Preference Theory can only explain yield curves (or segments of the yield curve) that have an upward slope. The theory suggests that investors like to hold cash (liquidity) hence the higher the bond’s maturity the higher the return that they demand.

Question 39

What is the expectation theory?

Answer 39

Expectation Theory: Investors make expectations regarding the future. If those expectations make investors believe that spot rates are going to be higher (lower) in the future than what they are today, the yield curve today will present an upwards (downwards) slope. This theory can explain segments of the yield curve that have upwards (downwards) slope.

Question 40

What is the probability of default?

Answer 40

The likelihood that a borrower will fail to pay.

Question 41

What can be used to measure the probability of default?

Answer 41

Credit rating

Question 42

What is the effect of time on bond prices?

Answer 42

Between coupon payments, the prices of all bonds rise as the remaining cash flows become closer. When the bond is issued at premium, the price drop when a coupon is paid is larger than the price increase between coupons. The prices of all bonds approach the bond's face value when the bonds mature.

Question 43

What is the duration?

Answer 43

A bond's duration measures the sensitivity of a bond's price to changes in interest rates. The duration tells us the average maturity of the bond's payments.

Question 44

How is duration related to the coupon rate?

Answer 44

Everything else constant, duration is inversely related with bond's coupon rate.

Question 45

What is the duration's formula?

Answer 45

Duration = (1* C1/(1 + YTM) + 2 * C2/(1 + YTM)^2 + ... + T * (CT + FV)/(1 + YTM)^T))/P0

Question 46

What is the modified duration?

Answer 46

The modified duration tells us the change in value of a bond due to a change in interest rates. If a bond has a higher modified duration it's more sensitive.

Question 47

What is the modified duration formula?

Answer 47

D/(1 + YTM)

Question 48

True or false: The higher the time left-to-maturity of a bond the more that bond’s price is sensitive to changes in interest rates (spot rates).

Answer 48

True

Question 49

True or false: A bond is traded at discount if its price is below its face value.

Answer 49

True

Question 50

True or false: The YTM of a bond is always closest to the highest spot rate that the bond uses.

Answer 50

False

Question 51

True or false: If the YTM drops the bond’s issuer (company or government that created the bond) will save money in interest (coupon) payments.

Answer 51

False

Question 52

True or false: A bond's YTM can be used to find the value of any bond with the same risk, in that specific point in time.

Answer 52

False

Question 53

True or false: A bond's YTM can be used to find the price of this bond, for this specific point in time.

Answer 53

True

Question 54

True or false: A bond's YTM can be used to find the value of this bond, for this specific point in time.

Answer 54

False

Question 55

True or false: A bond's YTM is directly proportional to the price. This means that the higher the bond’s YTM the higher is its price.

Answer 55

False

Question 56

True or false: A bond's YTM is a proxy of the return that the investor will achieve from the point that the investor purchased the bond, assuming that the bond is kept until maturity.

Answer 56

True

Question 57

True or false: A bond's YTM is the return achieved from the bond since the point that it was issued until maturity.

Answer 57

False

Question 58

True or false: A bond's YTM is is inversely related with its price (everything else constant, the higher the bond’s YTM the lower will be the price).

Answer 58

True

Question 59

True or false: A bond's YTM is the discount rate that makes the present value of all the future cash-flows equal the bond’s price

Answer 59

True

Question 60

True or false: According to the Expected Theory, E1[0r1] should be equal to 1f2.

Answer 60

True

Question 61

True or false: . According to the Liquidity Preference Theory, the higher the maturity of a bond’s payment the higher the return demanded by investors.

Answer 61

True

Question 62

True or false: When you can explain the yield curve with the Liquidity Preference Theory you can also explain it with the Expectation Theory.

Answer 62

True

Question 63

True or false: . Everything else constant, buying a bond traded at discount is a better choice than buying a bond traded at premium.

Answer 63

False

Question 64

True or false: If all spot rates suddenly increase by 1 percentage point, the bond’s price decreases approximately by its duration in percentage.

Answer 64

True

Question 65

True or false: A decreasing yield curve can be explained by the liquidity preference theory.

Answer 65

False

Question 66

True or false: Spot rates can be used to find the price of any bond with the same type of risk.

Answer 66

False

Question 67

True or false: Spot rates determine the interval for a bond’s YTM, assuming efficient markets. This means that, under efficient markets, a bond’s YTM is always higher than lowest spot rate, and lower than the last spot rate that the bond uses.

Answer 67

False

Question 68

True or false: Spot rates can be applied to any bond with the same type of risk.

Answer 68

True

Question 69

True or false: When the coupon rate of a bond is greater than the current YTM, the bond’s price is below its face value.

Answer 69

False

Question 70

True or false: The Expectation Theory states that when the expected one-year spot rate for next year is lower than the current one-year spot rate, the yield curve should start with a negative slope.

Answer 70

True

Question 71

True or false: Assume efficient markets and that you have available zero-coupon bonds for any desired maturity, and the same level of risk. The graph of the YTM of those zero-coupon bonds creates the yield curve for that level of risk.

Answer 71

True

Question 72

True or false: The YTM at time “t” is the return that the investor expects to get if she buys the bond at time “t” and keeps it until maturity.

Answer 72

True

Question 73

True or false: The expectation theory states that if 0r1 is higher than E1[0r1] the yield curve should be increasing

Answer 73

False

Question 74

True or false: . The Liquidity Preference Theory can only be applied to increasing yield curves.

Answer 74

True

Question 75

True or false: When all spot rates suddenly decrease by 1 percentage point the bond’s price decreases by approximately the duration in percentage (%).

Answer 75

False

Question 76

True or false: Consider a bond with 2 or more future payments. The YTM of that bond is equal to the weighted average of the spot rates that the bond uses.

Answer 76

False

Question 77

True or false: The Law of One Price states that two portfolios that have the same future payoff scheme have the same price (today).

Answer 77

True

Question 78

how do you calculate E1(0r1)?

Answer 78

(1 + 0r2)^2 = (1 + 0r1) * (1 + E1(0r1))

Question 79

when should you short-sell?

Answer 79

when value is greater than price

Question 80

how do you calculate the change in price using the duration?

Answer 80

-(D/(1 + YTM)) * change in r