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WHAT IS PRICE RISK?
The uncertainty on bond prices that reflects the uncertainty on future market rates
- r goes up; price goes down : (
- r goes down; price goes up : )
What is Reinvestment risk?
After receiving the coupon payments, investors may not be able to reinvest the received money at the original yield to maturity
- r goes up; price goes down : (
- higher yield : )
- r goes down; price goes up : )
- lower yield : (
Describe the Inverse relation between bond price and interest rate (convexity)
An increase in a bond’s yield to maturity results in a smaller price decline than the price increase associated with a decrease in yield (the convexity)
What is Interest rate sensitivity?
For a small change in interest rate (Delta)r), how much will the bond price change relative to the original bond price (Delta)P/P)
Describe the relation between maturity and interest rate sensitivity. (infer)
The longer the maturity, the higher the interest rate sensitivity.
As maturity increases, interest rate sensitivity increases at a decreasing rate
Describe the relation between coupon rate and interest rate sensitivity (infer)
The larger the coupon rate, the lower the interest rate sensitivity
Describe the relation between yield and interest rate sensitivity. (infer)
The larger the yield, the lower the interest rate sensitivity
What is Macaulay's Duration?
The effective maturity of a bond.
Defined as the weighted average of the time at which payments are received
The weight is proportional to the present value of each payment relative to the bond price
Interest rate sensitivity is proportional to duration and not to maturity
What are the properties of duration?
Duration is equal to maturity for zero coupon bonds but shorter than maturity for all other bonds
The duration of a perpetuity is (1 + y) / y
The duration of a bond portfolio is the weighted average duration of its component bonds, with the weights proportional to the values of the component bonds
Describe Immunization: As the market rate goes up..
The price of a bond will drop (a loss) (Price risk)
The return at which an investor reinvests the received coupon payments will rise (a gain) (Reinvestment risk)
If an investor’s holding period of the bond is the same as the bond’s duration, then the ____and the ____will cancel out
Interest rate fluctuations will have no effect on the investor’s return
What is Immunization Extension?
By matching the durations of assets and liabilities, a fund/portfolio can immunize itself against interest rate changes
As interest rate increases, both assets and liabilities decrease in their values by the same amount
As interest rate decreases, both assets and liabilities increase in their values
What is Passive Management in Bond Portfolio?
- Still need continual rebalance
- Large interest rate changes
- Passage of time
- Cost-benefit tradeoff
- Transaction costs vs. Perfect immunization
What is active management in bond portfolis?
- Bond swap
- Based on interest rate predictions
e.g., when we expect the interest rate to go down in the future, should we buy (or sell) bonds with shorter duration or bonds with longer duration?
What is an interest rate swap?
For a certain amount of notional principal, one party exchanges a fixed rate for a variable one, and the other exchanges a variable rate for a fixed one
Notional principal: Used to calculate swap payments only. Not really exchanged
What is a call option?
The right to buy a specified asset at a specified price on or before a specified date
What is a put option?
The right to sell an specified asset at a specified price on or before a specified date
What is in the money?
An immediate exercise will be profitable
What is out the money?
An immediate exercise will not be profitable
What is at the money?
Asset price is equal to the exercise price (S0 = X)
What is an American option?
An option that can be exercised at any time on or before expiration
What is an European option?
An option that can be exercised only on expiration
Of an American and an European option , which is more valuable? Why?
American, it is more flexible.
What rae some of the Put-call parity: limitations?
Applies only to European options
Each position is held until maturity
Assuming that the underlying asset pays no dividend
What makes up a protective put?
asset + put
What makes up a covered call?
what makes up a straddle call?
what makes up a collar
What is a vertical money spread?
Mix of options with different exercise prices.
What is a horizontal /time spread?
Mix of options with different expiration dates.
What is the intrinsic value of an option?
payoff of an option under the current underlying asset price.
What is the time value of an option?
The difference b/w the observed option price and the intrinsic value
How does share price influence option calls and puts respectively?
How does Exercise price influence option calls and puts respectively?
How does stock price volatility influence option calls and puts respectively?
How does time to expiration influence option calls and puts respectively?
How does interest rate influence option calls and puts respectively?
How does Dividend yield influence option calls and puts respectively?
Option Pricing Models
What does the Black-Scholes option pricing model show us?
What option prices should be in equilbrium (the theoretical prices)
The observed option prices may not be the same as the theoretical ones
For a given length of time, we can
always divide it into subperiods in which the underlying asset price either
goes up or goes down. With infinite subperiods, the possible underlying asset
price at the end of the given period follows a lognormal distribution
Building on the law of one price, if we know what the
underlying asset price will likely be, we know what the ________________
option value/price will
In the Black-Scholes formula, we assume that the _________ (the theoretical one) is unknown but other variables are known to solve
- We can also assume that volatility is unknown but other variables and the option
- price (the observed one) are known
- Solve for volatility
If the observed volatility is larger than the implied
volatility, the option is considered as a
Recall the relation between option value and stock price volatility
If observed volatility > implied volatility, theoretical.........
option price > observed option price
What is Hedge Ratio?
The change in the price of an option for a $1 increase in the underlying asset price
Delta c / Delta S for call and Delta p / Delta S for put
Make sure you know this very well
If one option is for one
underlying share, the hedge ratio can be interpreted as:
- The number of shares required to
- hedge against the price risk of one option
- (1 / hedge ratio) would be the
- number of options required to hedge against the price risk of one share of
Macaulays duration is less than modified duration except for:
a. zero coupon bonds
b. premium bonds
c. bonds selling at par value
d. none of the above
Is the decrease in a bonds price corresponding to an increase in its yield to maturity more or less than the price increase resulting from a decrease in yield of equal magnitude?
the increase will be larger than the decrease in price.
rank the interest rate sensitivity of the following pairs of bonds.
(a.) bond A is an 8% coupon, 20 year maturity bond selling at par value.
bond b is an 8% coupon, 20 year maturity bond selling below par value.
(b.)Bond a is a 20 year non callable coupon bond with a coupon rate of 8%
bond b is a 20 year, callable bond with a coupon rate of 9%, also selling at par.
(a) bond b has a higher yield to maturity than bond a since its coupon pmts and maturity are equal to those of a, while its price is lower. Duration of B must be shorter.
(b) bond a has a lower yield and a lower coupon, both of which cause it to have a longer duration than that of bond b. moreover, bond a cannot be called. Therefore, the maturity of bond a is at least as long as bond b.
which of the following statements is false?
a. a short position in a call option will result in a loss if the stock price exceeds the exercise price
b. the value of a long position equals zero or the stock price minus the exercise price.
c. the value of a long position equals zero or the exercise price minus the stock price, whichever is higher.
d. a short position in a call option has a zero value for all stock prices equal to or less than the exercise price.
c is false. it describes the payoff to a put, not an option.
how would you describe passive bond portfolio management?
- control risk
- immunization/cash flow matching
- balance risk and return
how would you describe active bond portfolio management?
trade on interest rate predictions
- trade on markey inefficiencies.
- looking for mispriced bonds.
when we expect the interest rate to go down in the future, should we buy or sell bonds with shorter durations or bonds with longer durations?
buy bonds with longer durations
what is hedge ratio?
the change in price of an option for a $1 increase in the stock price.
modified duration__________ as coupon___________
modified duration__________ as maturity___________
how do you find the maximum possible profit on a put?
if the price goes to zero, what will you make.