Homework Assignment #1:Answer Key

to 1 , because arbitragers may wait to save some of their gunpowder till period two.
Hence, 1= − 1
1
+ 1
1
,whichimplies 1 = − 1 + 1 .
(b) If arbitragers had access to unlimited funds what will 2 equal?
brief answer If 2 −→ ∞ then arbitragers will offset all noise trader risk and we have
1 = 2 =
(c) Suppose that the supply function of funds to investors is given by
" µ1 2
2 = 1 + #
1 − 1
(1)
1 1 1
(1) = 1 0 ≥ 1 00 ≤ 0
where 1 is the amount invested by arbitragers in period 1, and 0 measures the sensitivity
of 2 to the term in the brackets. If 2 = 1 what happens to 2 ? What happens
if 2 1 ? Explain why this could be important.
brief answer If 2 = 1 then we have 2 = 1 h³ ´ i
1
1
+
1 − 1
1
=⇒ 2 = 1 ,that
is if there is no change in price then funds available are the same. If prices fall,
however, then clearly 2 1 . How much this falls depends on the size of 0 ,the
more sensitive is supply to recent returns the greater the fall. This could be important
because it makes traders reluctant to fully commit to arbitrage possibilities. A shortterm
fluctuation could wipe them out. This makes noise trader sentiment more
important. If fund supply is very sensitive then arbitragers may even have to sell out
in period two, which would move prices even farther from V.
(d) What does 0 0 imply about the nature of arbitrage? Explain. If 0 is larger are
arbitragers more likely to succeed or more likely to fail in offsetting noise traders signals
in period 2?
brief answer When we have PBA then agency intrudes into the arbitrage process. This
means that arbitragers must take into account the possibility that they will lose funds
at the most opportune times for investment. This makes them less willing to commit
their funds and makes it less likely that noise traders are offset.
4