429 Midterm Solution Fal 2007
TVM - compensation for delaying consumption
Risk - compensation for taking on risk as we al prefer les risk to more (risk aversion)
Bond valuation does not require forecasting of the cashflow or growth so there is only discount rate risk.
The axes are T (x-axis) and yield (y-axis).
If only liquidity mat ers, the curve must be upwardly sloping and probably linear (though not neces arily)
If there is weak demand for short term bonds, we would see an upward hook on the left-most side of the curve (Nike).
If future growth expectations are strong, the curve rises and increasingly so in the future.
The yield is somewhere between the spot rates as it is a measure of average return but should tend to the longest rate
because the face value comes at the end.
If the coupon rate is high, the yield moves away from the longest rate, al else equal.
However, we need spot rates because arbitrage is defined by discount factors. It refers to the value of a dol ar in at
a particular time, not the average return over a period.
Replication has the advantage that you need only have matching cashflows.
You do NOT need to know whether the
prices are cor ect. So long as you can match the cashflows, no arbitrage wil require prices to equate. The market need
not be ef icient.
The bonds, then, need to be of the same risk clas and must deliver cashflows in similar periods. General y, there must
be as many bonds as there are cashflows in order to replicate. Any two of these is fine
Treasuries should be at the bot om with bil s, notes, then bonds (left to right).
Bil s should be one year or les and so should commercial paper.
In order bot om to top are agency debt, Fed funds, Libor, then Corporates
LIBOR and FF should be on the y-axis
2,000 mil ion
Let's start first by finding the value of the deposits.
Face * C/2
Face * (1+C/2)
PV(D) = C/2*Face*df(0.5) + (1+C/2)*Face*df(1)
= Face * 0.0294
+ Face *
= Face * 1.0194
Now the MD:
MD(D) = Weights * t * (1/(1+y/2) =
So far so good, now how about the lent money?
Since we think interest rates wil fal and since our lending is an as et,
we would like to maximize our MD (rates fal , the money you have lent wil be worth more when it's paid back because
interest rates wil be lower). Hence the MD is quite simply:
MD(L) = T * (1/(1+y/2)
When interest rates increase
0.10% we have:
Change in Deposits = - MD(D) * PV *
Change in Lending = - MD(L) * PV *
Your deposits appreciate but so does the lending so your equity value increases by