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Interest Rates & the pricing of financial assets

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Jed Dean

on 7 April 2013

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Transcript of Interest Rates & the pricing of financial assets

Compounding Interest Rates & TVM Compounding Interest Rates Term Structure of
Interest Rates Net Interest Income & the pricing of financial assets How IR Influence Derivatives Annual Semi-annual Quarterly Equivalent Rate Continuous What ?
Interest is compounded constantly using infinitesimally small amounts of time

Why for derivatives?
A more uniform measure
Continuous returns are time consistent & can be easily added
The product of continuous returns are normal if the returns themselves are normal, not true if non-continuous Can be used to:
Take compounding into account to find the ACTUAL rate realized from an interest rate quoted annually

Compare rates of return with different compounding periods Treasury Rates LIBID LIBOR The rate of interest at which banks are prepared to make a large wholesale deposit with other banks

Calculated for 15 different maturities and for 10 different currencies.

Calculation based upon submissions from LIBOR contributor banks, which are then averaged under a "trimmed mean" methodology

It is widely used as a reference rate for many financial products & instruments, from auto loans to derivatives The rate large banks will accept deposits from other banks.

Calculated through a survey of London banks to determine the interest rate which they are willing to borrow large Euro-currency deposits.

There is a small spread between the quoted LIBID and LIBOR rates (with LIBOR higher than LIBID) Repurchase (Repo) Rates Types of Interest Rates Treasury Rates
Repo Rates
Zero Rates Bond
Applications Zero Rates The rate of interest earned on an investment that begins today and lasts for 'n' years, with a unique payment at the end of the last year.
Used in conjunction with zero coupon bonds Bond Price &
Yield Par Yield Forward Rates Definition Valuation & Formulas Forward Rate Agreements Bootstrap Method Duration Modified Duration Convexity L
N The amount charged, expressed as a percentage of principal, by a lender to a borrower for the use of assets.

Typically noted on an annual basis, known as the annual percentage rate (APR).

1$ Today > 1$ Tomorrow M-Periods r= interest rate
n= number of years r= interest rate
n= number of years
m= number of periods (within a year) Rates that an investor earns on Treasury
Bills and Treasury Bonds.

Typically considered "risk-free" (academia)

Not used as rf by derivatives traders

Artificially low from tax & regulation issues

LIBOR rates, a more realistic measure A rate applicable to a financial transaction that will take place in the future. As we have the equation for bond prices, we can try to figure out how it reacts in response to yield. helps in understanding the market expectation (yield curve) Forward rates are higher than expected future zero rates

Investors prefer to invest in short-term maturities, preserving their liquidity

Theory is consistent with the empirical result that yield curves tend to be upward sloping more often than downward sloping. Liquidity Preference Theory Short, medium, and long term rates are determined independently from each other

Institutional lenders prefer maturities in the ranges in which they operate

For Example:
Commercial banks = Short - medium terms because of nature of deposits
Insurance companies = longer terms because of their long
term liabilities Market Segmentation Theory Forward rates are equal to expected future zero rates

Expected one-period rate of return is the same regardless of maturity

For Example:
Two 1 year maturities = one 2 year maturity Expectations Theory Relationship between yield and maturity differing only in length of time to maturity Due to the special structure of the price of the bond, when the yield changes by 10% or more, 2 bonds with the same duration will behave very differently (yellow area)

The change of yield will even
change the speed of the changing of
duration. Example: Above, we can see 2 bonds with the same duration can greatly diverge in price as the yields grow. convexity fills in this short fall of duration as a measure of volatility. Duration assumes only one cmpdg period per year. For multiple periods we can use Modified Duration

Also a sensitivity measure for bond prices The OTC agreement of interest rate applied in borrowing or lending between two parties in a specified future period of time. The value of an FRA: Bootstrapping is a method used to compute interest rates for zero-coupon securities greater than one year, allowing one to artificially create the Yield Curve the method is based on this formula: spot zero rate, n years spot zero rate n-1 years forward rate from n-1
to n years Repo Agreement Financial institution that owns securities agrees to sell them today and buy them back in the future

Overnight repos are most common

Securities sold are often Treasuries, prior to credit crisis CDOs were
often used Example: Collateral Value = $100
Proceeds from sale = $98
Repurchase price = $100

Haircut = $2 Calculated from the difference between the SELL price and the REPURCHASE price
Collateralized Lending
Overnight or Term
Low Risk compounding interest rate forward rate zero rate bootstrap method calculation of bond prices (changing daily) pricing of all other derivative Loan rates > deposit rates

Mis-match between maturities
Can lead to liquidity problems for lender
Creates interest rate risk
Managed by using derivatives, Interest rate swaps Changing the formula to: Bond Yield:
The single discount rate that, when applied to all cash flows, gives a bond price equal to its market price. Bond prices:
Can be calculated (theoretically) by taking the PV of all cash flows
A different zero rate should be used for
each cash flow Treasury zero rates Maturity
2.0 Zero rate %
6.8 2-year Treasury bond
Principle: $100
Coupon: 6% per annum
Semi-annual compounding Bond Yield: y=6.76% The coupon rate that causes the bond price to equal its par/principal value c=6.87% per annum (semiannual) or
c=6.76% with continuous compounding A measure of how long on average (weighted) the bond holder must wait before receiving cash payments Zero coupon bond (n years) has a duration equal to 'n' years A coupon bond of (n years) has a duration < n years Bond
Price Dur. yield curve forward rate
agreement Always implied between two consecutive spot zero rates Where:
P= Principal
Rk= Agreed FRA interest rate
Rf= Forward LIBOR T1-T2, determined at T0
Rm= Actual LIBOR observed at T1 Is it over yet?!? NOPE!
Q&A! HULT Jed Dean
R. Ty Brown
Anastasia Oleneva
Imam Santoso
Edoardo Felici
Weiliang Zhang Team 8
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