Sample R.P. Yield Curve, True Scaling Source: Bloomberg, LP
Sample U.S. Yield Curve, True Scaling Source: Bloomberg, LP
Sample Australian Yield Curve, True Scaling Source: Bloomberg, LP
Sample Brazilian Yield Curve, True Scaling Source: Bloomberg, LP
Sample Indonesian Yield Curve, True Scaling Source: Bloomberg, LP
Sample Japanese Yield Curve, True Scaling Source: Bloomberg, LP
Sample LIBOR Yield Curve, True Scaling Source: Bloomberg, LP
Sample Malaysian Yield Curve, True Scaling Source: Bloomberg, LP
Sample Thailand Yield Curve, True Scaling Source: Bloomberg, LP
Sample U. K. Yield Curve, True Scaling Source: Bloomberg, LP
Nominal/market interest rate
= real rate of return + risk premium + inflation expectation
Given a table of spot rates, forward rates may be estimated n by: (1 [R + ] n) fn =
[(1+Rn-1)n-1 ]
THEORIES AFFECTING THE TERM STRUCTURE OF RATES (lifted from Levi) •
Liquidity premium theory – Ist < Ilt as LT risks are higher
•
Expectations theory – Ilt are the average of Ist. Dictates the slope of the yield curve
•
Segmentation (hedging) theory – yield curve is composed of somewhat independent maturity segments
Benchmark rates normally used: 91-day t-bills, LIBOR, SIBOR, PHIBOR, MRR, etc. LIBOR – London Inter-bank Offer Rate - rate in which London banks borrow among themselves
SIMPLE INTEREST I = Interest Income P = Principal r = Interest Rate or the price charged for the use of money (usually represented on a per annum basis) T = Time; which is usually represented as a fraction of a standard period, usually one year, and represented in no. of days The day count basis used can be either a) Actual / 360
money market
b) Actual / 365
bond basis
c) 30 / 360
TIME VALUE OF MONEY - The peso on hand now is worth more than a peso a year from now - This is bec. the peso on hand can be invested to earn interest income over the future period - this is the time value of money and it represents the opportunity cost of not having use of the money now. If we use the Money Market basis for day count, then I = Prt / 360 M or Maturity Value; M=P+I = P + Prt / 360 M = P ( 1 + rt/360)
COMPOUNDING P = Principal p = no. of compounding periods per year n = no. of periods of the investment r = Interest Rate T = no. of days per period Mx ; Maturity Value at end of period x such that M1 = maturity value at end of period 1 M2 = maturity value at end of period 2
M1 = P (1 + rt/360) butsincet/360=1/p
t
p 30
monthly
90
quarterly
4
180
semi annual
2
360
annual
12
1
M1 = P (1 + r/p) M2 = P (1 + r/p)
but since M1 = P (1 + r/p)
M2 = P (1 + r/p)(1 + r/p) M3 = M2 (1 + r/p)
but since M2 = P (1 + r/p)(1+r/p)
M3 = P (1 + r/p)(1+ r/p) (1+r/p) M4 = M3 (1 + r/p)
but since M2 = P (1 + r/p)(1+r/p)(1+r/p)
M4 = P (1 + r/p)(1+ r/p) (1+r/p)(1+r/p) simplifying:
M4 = P (1+ r/4)4 or Mn
for quarterly compounding within 1 year
= P (1+ r/p)n X p
or from: FV = P (1 + r) t generic annual compounding formula becomes: FV = P (1 + r/p) n X p
The maturity value Mn is also called the
Future value or FV of the investment. The Principal P is also called the
Present value or PV of the investment.
Mn = P (1+ r/p)n X p FV = PV (1+ r/p)n X p where: n is the number of years p is the number of compounding periods within the year
rearranging: PRESENT VALUE
PV =
FV (1 + i)n
or
PV =
FV __________________
( 1 + r/p)n X p - is the formula used to price future cash flows - the rate, r is also known as the yield to maturity (YTM) or the discount factor (DF) - where p = no. of periods per year n = no. of periods of the investment - this formula is the building block for deriving the formula to price a bond
