Summary
Summary Formulas
- Institution
- The University Of York (UOY)
This sheet provides all the formulas you need for this module.
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Derivatives Corporate Finance Formulas:• Basis = spot price - futures price
• Basis risk arises because of the uncertainty about the basis when the
hedge is closed out.
Long Hedges for the purchase of an asset:
Short hedges for the sale of an asset:
Optimal Hedge Ratio:
Proportion of the exposure that should optimally be hedged is:
¿ σS
h =ρ
σF
• sS is the standard deviation of the change in the spot price during the
hedging period, DS
• sF is the standard deviation of the change in the futures price during the
hedging period, DF
, • r is the correlation coefficient between DS and DF
Alternative definition of the optimal hedge ratio:
^
^ ^ρ σ S
h=
σ^F
Optimal number of Contracts:
• No adjustment for daily settlement
¿ h¿ Q A
N =
QF
• Tailing adjustment to allow for daily settlement of futures.
^
hV
N ¿= A
VF
Hedging using Index futures:
To hedge the risk in a portfolio, the number of contracts that should be shorted
is:
VA
β
VF
• b is the portfolio’s beta
• VA is the current value of the portfolio.
• VF is the current value of one futures contract
Compounding and measuring interest rates:
• Compounding is the process in which an asset’s earnings are reinvested
go generate additional earnings
, • Suppose an amount A is invested for n years at an annual interest rate of
R. If the rate is compounded m times per annum, the terminal value of
the investment is
( )
mn
R
A 1+
m
• In the limit as we compound more and more frequently, we obtain
continuously compounded interest rates.
• With continuous compounding, an amount A invested for n years at rate
R grows to A e Rn
Conversion formulas:
Suppose Rc is the interest rate with continuous compounding and Rm is the
equivalent rate with compounding m times per annum
mn
R
A(1+ m ) =A e R n c
m
Rm m R
(1+ ) =e c
m
Rm
Rc =mln (1+ )
m
Rc /m
Rm =m(e −1)
Forward rates:
• Forward interest rates are the rates of interest implied by current zero
rates for periods of time in the future
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