MODULE 2.2: Implied Returns and Cash Flow Additivity Flashcards
What is a pure discount bond?
A bond that you can buy at a discount of the face value, and then at the maturity of the bond, you receive back the face value of the bond. There is no additional coupon that is paid during the duration of the bond.
example: you purchase a 30 year maturity bond for 750 and the face value of the bond is $1000. An example of this would be the zero coupon bond
What is an annual coupon bond
similar to a zero coupon bond but you recieve a specific percent of money which is called the coupon rate at specific time periods (annual for this). The coupon rate could be a specific percentage of the par value. When the bond matures, you then also receive the face value of the bond similar to a zero coupon bond.
pure discount bond calculation
can do this on the calculator using the PV / FV / N / i/y / PMT keys
manual formula is FV / (1+r) ^ t = PV
can also just do to the - t or t and not divide
pv = fv(1+r) ^ -t
Cash Flow Additivity principle definition
the PV of any stream of cash flows equals the sum of the PVs of cash flows.
Forward Interest Rates definition with examples
When you don’t have to start making interest payments until a certain period of time. 1y1y = rate for a 1 year loan to be made one year from now.
- Forwared create agreements - businesses lock in future borrowing reates to protect against int rate changes
- construction loans
Forward Currency Exchange Rates Meaning
price of one countrys currency in terms of another countries currency. 1.4 USD/EUR means that one euro is worth 1.4 dollars.
Option Pricing Model definition
option = the right to buy or sell an asset on a future date at a specific price.
Call option:
- stock price = 50
- strike : 55
- expiration 3 months from now
- i have their right to buy this stock at $55, even if the market goes higher. if the price goes to 70, i can either exercise my option and buy it for $55, or sell it at the market price of 70 and make a profit.
- options cost money to buy
put options means they want to sell at a set price. If someone buys a put option
option pricing model formula
- take the number we would be the value at expiration after an up move (60 - 55) (price if the stock increases - call option number) = 5
- divide 5 by the stock increase - stock decrease to get the value of h (5 / (60-42))
- this is the number of shares of hte underlying we would need to buy for each call option we would write - THE HEDGE RATION OF THE OPTION = .278
Annual coupon bond calculation
calculator - same thing as a zero bond calculation on the calculator but we now have an interest payment in the form of the PMT key.
Consider the 10-year, $1,000 par value, 10% coupon, annual-pay bond we examined in an earlier example, when its price was $1,134.20 at a yield to maturity of 8%. What is its yield to maturity if its price decreases to $1,085.00?
- N = 10
- FV = 1000
- PMT = 100
- PV = -1085
- CPT I/Y (because we need to calculate the YIELD to maturity and the price DECREASES so negative )= 8.69%
What is the relationship between bond prices and bond yields? Explain.
Inverse relationship. Bond prices go up, bond yields go down. Bond yields go up , bond prices go down.
The government is borrowing your money, and will pay you interest for it. If interest rates in the economy go up, the new bonds usually give you a better yield. How can old bonds compete? They can lower their prices to stay attractive.
- new bonds offer better int rates
- your existing bond becomes less attractive due to same old rate
- if i want to sell, i need to lower it’s price because everyone wants to sell their current bond and buy the new ones with better int rates
Cash Flow Additivity principle calculation
$100/1.1 + 100/(1.1)^2 + 400/(1.1)^3 + 100/(1.1)^4 = 542.38$
spot rate definition and relation to forward rates
pay interest on a loan today. Any spot rate and forward rates that cover the same time period should have the same cost
spot rate calculation
- Calculate (1 + S₂)² = (1 + S₁)(1 + f₁,₂)
S2 = spot rate 2
S1 = spot rate 1
f = forawd rate
think of 1+S
WE ADD 1 WHENEVER WE’RE WORKING WITH INTEREST RATES
Squaring S2 = S2 represents the two-period spot rate. Squaring accounts for the compound interest effect over the full two periods
Currency Exchange Rate Arbitrage calculation
this is the forward exchange rate that would prevent arbitrage:
Formula:
Forward Exchange Rate = Spot Exchange Rate × (Price Currency Interest Rate / Base Currency Interest Rate)
Step by step:
1. Identify the spot exchange rate between the two currencies
- Determine the interest rate for the price currency (numerator)
- Determine the interest rate for the base currency (denominator)
- Divide the price currency interest rate by the base currency interest rate
- Multiply this ratio by the spot exchange rate
This calculation ensures there’s no opportunity for risk-free profit through currency arbitrage
1. The resulting forward rate balances the interest rate differential between the two currencies, preventing traders from profiting by borrowing in one currency to invest in another.
