E
XAMPLE
D
ISCUSSED
IN
C
LASS
ON
J
ANUARY
6, 2011
G
IVEN
:
Denoting the present value at t=0 of $1 to be received at t=n as
DF
n
(discount factor for n
periods), we are given that
DF
7
= 0.495 and that
DF
15
= 0.5. We are also given that we have
$10,000 available to lend or borrow.
Q
UESTIONS
:
(1) Work out
r
7
, the risk free rate in the markets for investment with a term to maturity of 7
years;
(2) Work out
r
15
, the risk free rate in the markets for investment with a term to maturity of 15
years;
(3) Find out if there are arbitrage opportunities here, and if there are, construct an arbitrage table
to show what action you will take to exploit them with what cash flow consequences;
(4) Assuming that the interest rates remain unchanged, work out how many roundtrips it will
take for you to reach $100,000 starting with $10,000.
A
NSWERS
:
(1)
≡
+
DF7 11 r77
+
=
1 r77 1DF7
,
+ =
1 r7 1DF717
=
.
10 49517
= 1.105676, or
r
7
= 10.5676%.
(2)
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 Winter '08
 LI,C.
 Arbitrage, Net Present Value, Equals sign, Riskfree interest rate, Rational pricing

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