Interest rates Flashcards
When asked to find an equivalent rate to a semi annual componding rate to quarterly compounded rate - what do you do?
set the two equal to eachother, R4 can be algebraically solved to find the rate quarterly componded
How do I change a annually compounded rate into a continuously compounded rate?
Rc=m x ln ( 1+ Rm/m)
how do i change a continously compounded rate into annual compound?
RM = m ( e^RC/m -1)
what is a zero rate
rate of interest earned on an investment starting today lasting n years. all interest and principal realised at end. worked out via RC rate - worked as given
bond pricing - assume 6% on a 2-year treasury bond with a principal of 100$ semi annually how would you work out price? (using zero rates as given)
3e0.05x5 +3e^0.058x1 …… = 98.39
Bootstrap method?
method of determining Treasury zero rates from t-bills and other coupon bearing bond prices
Foward rate
interest rates implied by current zero rates for periods of time in the futuree.g 4% in 2 years is roughly the same as 3% in year 1 + 5% in year 2….
same goes for 4.6% for 3 years - same as 3%+5%+5.8%
foward rate equation
RF=(R2T2 -1T1) / T2-T1
what causes the zero rate curve to slope upward?
if R2>R1 e.g rate for t2 is greater than rate for t1, eventually it will plateu
Foward rate Agreements?
OTC agreement ensuring a certain rate will aplly to either borrowing or lendng a certain principal over a certain time
how might FRA work? in regard to x lending to Y at a fixed rate
if x lends to Y x earns L(RK-RM)(T2-T1) such that it makes when the the fixed rate is greater than that the actual libo rate between periods t1 and t2
opposite applies to Y who earns when the actual rate is above the agreed rate
FRA valuations at any given point T
VFRA= L(RK-RF,T)(T2-T1) x e^-R2(t2-t)
where r2 is the coninously componded rate for maturity T2
The value of the contract at a given time depends on the
difference between the fixed rate : (set in the contract)
and the prevailing forward rate (RF calculated at start) at time applied tothe principal for the duration of the loan.
Duration of a bond equation
D = sum ( Ti x (Cie^-yt) / B)
B being the bond price
is the weighted average of the times when payments are
made, with weights given by the shares of each cash flow in
the total value of the bond. The sum of all weights equals 1.
change in yield
