Bonds Flashcards
What are bonds?
Bonds are issued by governments and corporations to raise money from investors in exchange of a promise to future payments.
What are the operations with bonds?
Buy the financial asset (investment operation) and short-sell the financial asset (financing operations).
What is short-selling?
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.
When does an agent short-sell?
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.
When is there an arbitrage opportunity?
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.
What is an arbitrage strategy?
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.
What is the law of one price?
The law of one price says that two different portfolios/assets that have the same payoff scheme need to have the same price today.
What is the primary and the secondary market?
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.
How is the coupon rate expressed?
APR
Who is the borrower and the lender?
The issuer is the borrower and the holder of the bond is the lender.
What is the coupon’s formula?
C = (Coupon Rate * Face Value)/Nº of coupon payments a year
How do we price bonds?
Through the present value of all future cash-flows.
P0 = C1/(1 + y) + C2/(1 + y)^2 + (CT + FV) / (1 + y)^T
What is the relationship between the bond’s price and the discount rate?
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)
Where do accrued interests matter?
In the secondary market.
What is the accrued interests formula?
Accrued Interest = C * Days since last coupon payment/Days separating coupon payments
What rate do we use to compute the price of a bond?
YTM
What rate do we use to compute the value of a bond?
Spot rates
What does it mean to assume the financial markets are normal?
Financial assets are traded with NPV=0 so the bond’s price and its value are the same, so there are no arbitrage opportunities.
What are spot rates?
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.
Why do spot rates change overtime?
Market conditions
What is the YTM?
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.
When can we use the YTM?
The YTM can only be used in a specific point in time and for only one bond.
What does the YTM assume?
The YTM assume the bond’s cash-flows are reinvested at the same rate as the YTM until the maturity date.
When can we find the YTM?
We can only find the YTM if we have the price.
How can we find the YTM with excel?
IRR() (the bond’s price need to be negative)
What is the relationship between spot rated and the YTM?
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).
What does it mean if a bond is being traded at premium and what does it imply?
Premium: P0 > FV which implies YTM < coupon rate
What does it mean if a bond is issued at par?
Par: P0 = FV which implies YTM = coupon rate
What does it mean if a bond is issued at discount?
Discount: P0 < FV which implies YTM > coupon rate
Why is it indifferent if you buy a bond at premium or discount?
If you demand a YTM higher than the coupon rate (what the bond pays you) the price will decrease.
What is the holding period return?
HPRt/t+1 = ((Pt+1 - P1) + Cft+1)/Pt
What are the 3 methods to find spot rates?
1) Zero-coupon bonds
2) Bootstrap
3) Forward rates
How do we find the spot rate with zero-coupon bonds?
In zero-coupon bonds the spot rate is the same as the YTM, assuming normal markets.
How is the investor compensated in zero-coupon bonds?
The price is lower than the face value.
What are the conditions to use bootstrap?
It can’t be a zero-coupon bond, we need to know the price and n-1 spot rates.
What are forward rates?
Rates that are acquired today but will be used in the future.
What is the formula for forward rates and spot rates?
(1 + 0r3)^3 = (1 + 0r2)^2 * (1 + 2f3)
(1 + 0r3)^3 = (1 + 0r1) * (1 + 1f2) * (1 + 2f3)
What is the yield curve?
A graph of spot rates.
What is the liquidity preference theory?
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.
What is the expectation theory?
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.
What is the probability of default?
The likelihood that a borrower will fail to pay.
What can be used to measure the probability of default?
Credit rating
What is the effect of time on bond prices?
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.
What is the duration?
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.
How is duration related to the coupon rate?
Everything else constant, duration is inversely related with bond’s coupon rate.
What is the duration’s formula?
Duration = (1* C1/(1 + YTM) + 2 * C2/(1 + YTM)^2 + … + T * (CT + FV)/(1 + YTM)^T))/P0
What is the modified duration?
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.
What is the modified duration formula?
D/(1 + YTM)
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).
True
True or false: A bond is traded at discount if its price is below its face value.
True
True or false: The YTM of a bond is always closest to the highest spot rate that the bond uses.
False
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.
False
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.
False
True or false: A bond’s YTM can be used to find the price of this bond, for this specific point in time.
True
True or false: A bond’s YTM can be used to find the value of this bond, for this specific point in time.
False
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.
False
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.
True
True or false: A bond’s YTM is the return achieved from the bond since the point that it was issued until maturity.
False
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).
True
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
True
True or false: According to the Expected Theory, E1[0r1] should be equal to 1f2.
True
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.
True
True or false: When you can explain the yield curve with the Liquidity Preference Theory you can
also explain it with the Expectation Theory.
True
True or false: . Everything else constant, buying a bond traded at discount is a better choice than buying a bond traded at premium.
False
True or false: If all spot rates suddenly increase by 1 percentage point, the bond’s price decreases
approximately by its duration in percentage.
True
True or false: A decreasing yield curve can be explained by the liquidity preference theory.
False
True or false: Spot rates can be used to find the price of any bond with the same type of risk.
False
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.
False
True or false: Spot rates can be applied to any bond with the same type of risk.
True
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.
False
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.
True
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.
True
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.
True
True or false: The expectation theory states that if 0r1 is higher than E1[0r1] the yield curve should be increasing
False
True or false: . The Liquidity Preference Theory can only be applied to increasing yield curves.
True
True or false: When all spot rates suddenly decrease by 1 percentage point the bond’s price decreases by approximately the duration in percentage (%).
False
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.
False
True or false: The Law of One Price states that two portfolios that have the same future payoff scheme have the same price (today).
True
how do you calculate E1(0r1)?
(1 + 0r2)^2 = (1 + 0r1) * (1 + E1(0r1))
when should you short-sell?
when value is greater than price
how do you calculate the change in price using the duration?
-(D/(1 + YTM)) * change in r
