risk either by selling equity or by hedging. Risk management can be It is
only in an imperfect market that risk management matters. In this case,
you useful in an imperfect market. have to think about all the capital
structure issues raised in Chapters 17
26.8, p. 1020 more binomial tree levels, you indeed end up with a
continuous distribution that looks a lot like a bell-shaped curve.) 1017
1018 CHAPTER 26 APPENDIX THE IDEAS BEHIND THE BLACKSCHOLES FORMULA 26.7 THE OPTION HEDGE First, set out your
goal: F
down once, or move down twice. Use the letter u to describe the stock
price multiplier when an up move occurs, and d to describe the stock
price multiplier when a down move occurs. You can represent the stock
price process with a binomial treewhere one br
figured out in quite the same waya particular way to see and explain
finance. Of course, writing it has taken me far longer than I had
anticipated5 years and still counting just for the first edition! But it
will all have been worth it if you have learned
are no easy solutions. It is generally agreed that teaching introductory
finance in a business school is among the most difficult assignments an
instructor can take on. There are different levels of student preparedness,
and there is a large amount of mat
possible to have a security that is an option on an option, but the fact is
that almost all common financial options are such. This is because the
stock on which they are written is itself an option on the underlying firm
value. Thus, CBOE options are ess
MATHEMATICAL AND STATISTICAL BACKGROUND . Finding a
base: 32 = 9 3 = 91/2 xa = b x = b1/a A power of 1/2 is also
equivalent to the square root operation. . Finding an exponent: 32 = 9
2 = ln(9) ln(3) ax = b x = ln(b) ln(a) (Instead of the natural log ln,
share another property: Real-world constraints may prevent us from
doing certain research. In physics, particle colliders have become so
expensive that physicists can no longer study certain particles. In
finance, our financial institutions have come to c
hedge its S&P 500 risk by shorting the stock market. This is cheaply
done by trading S&P 500 futures or forwards. If the firm is worth $100
million and has a beta of 1.5, shorting $150 million in this future should
do the trick. The hedge ratio is really
compute the European Black-Scholes call value: BS(S = $80.50, K =
$100, rF = 1.77%, t = 0.1333, = 30%). The interest rate to maturity is
1.01770.1333 1.00234. Thus, the present value of the strike price is
PV($100) $100/1.00234 $99.767. Next, d1 ln($80.50
Using the computer spreadsheet you created in Question 26.31, graph
the Black-Scholes value as a function of todays stock value for options
with three different volatilities: 20%, 80%, and 160%. That is, repeat
Figure 26.4 for a 3-month option with strike
interest or principal timely and in full. Default risk (or credit premium or
credit risk) The probability of failing to repay either interest or principal
timely and in full. Default risk premium The difference between the
promised rate and the expected r
from Leeson is that becoming notorious is not a bad way to earn large
fees on the after-dinner speaking circuit. Source: BBC. no airline hedged
even 1 full year of jet fuel consumption. They typically hedged only
about 15% of their annual fuel purchases.
outstanding Inventory divided by total sales on credit, times number of
days outstanding. Days of payables outstanding (DPO) Accounts
payable divided by total sales on credit, times number of days
outstanding. Days of receivables outstanding (DRO) See day
different payoff patterns (tables). For example, the owner of a call option
enjoys limited liability and thus can, at most, lose the money paid for the
call. The seller of a put option can lose an unlimited amount. Q 26.2 An
option that is far in-the-mone
temporarily disappeared. Bulldog bonds Foreign bonds in Great Britain.
Bureau of Labor Statistics (BLS) The U.S. government agency that
determines the compositions of a number of prominent stock and bond
indexes and publishes the average Business judgment
dead put, compute the net value of a live put (C0(K) + PV0(K) S0 )
minus that of a dead put cfw_(K S0). It is cfw_C0(K) + PV0(K) S0 cfw_(K
S0). This can be simplified into C0(K) + [PV0(K) K]. This
expression is worth more if the call is worth more (the s
sampled, the size of the pool of alums ends up being the primary
predictor of recruiter opinion in the BW survey. The result is
inevitable: The average recruiter ranks his or her own alma mater
highest (or at least very highly). As a consequence, the corr
Like FannieMae, an agency (corporation) set up by the U.S.
government. It facilitates student loans. B-4 APPENDIX B A SHORT
GLOSSARY OF SOME BONDS AND RATES Savings bonds: Issued
by the U.S. Treasury, savings bonds can only be purchased from, or sold
to,
bonds See treasury inflation protected securities. Credit Default Swap
(CDS) A tradable credit derivative contract that transfers the default risk
from a bond buyer to a bond seller. Credit line A loan provision that, like
instant debt, permits borrowers
a 5% risk-free rate of return, and a standard deviation of return of 20%
on the underlying stock. (a) What is the price of the position if there are
3 months to maturity? (b) What is the price if nothing changed and there
is only 1 month left to maturity?
maturity The time to final payback of principal and interest on a bond.
Bond seniority A bond provision that specifies exactly which
bondholders are paid first in case of bankruptcy and liquidation. Bondwashing A tax arbitrage strategy for bonds in which
higher. Higher input costs may not be detrimentalin fact, some
financially strong firms may even benefit from otherwise adverse
economic price developments if their competitors are forced out of
business. Another hedging consideration is more technical: W
http:/welch.econ.brown.edu/: . I wrote a description of what I think our
profession has accomplished over the last few decades and what
challenges lie ahead. . I described alternative finance degree choices,
such as undergraduate finance education or mast
for a good business school. A good business school is a center of thought
and research. If you expect primarily vocational training from your
business school, your finance education will be a rather unrewarding
experience. Good business schools should pro
companys specific product or service marketing Method of thinking
Methods of this companys practice Concepts of ideas for the next 20
years Implementation of ideas from the last 10 years Knowledge for a
lifetime Knowledge tailored to this years business c
can hedge different The basic idea of risk management through hedging
is simple: The firm reduces a types of risks with many toolsnot just
with derivatives. source of risk that it otherwise faces. The firm has a
number of risk-management tools at its disp
price of $80, a strike price of $75, 3 months to maturity, a 5% risk-free
rate of return, and a standard deviation of return of 20% on the
underlying stock. Check it against the solution in Question 26.12. Q
26.33 Price the earlier call option but with a
first published in 1998. This rankings issue has become one of BWs top
sellers. Unfortunately, the quality of the BW rankings is only mediocre.
Worse, their influence on business education has been both enormous
and negative. The not-so-secret sauce in BW
reorganization A chapter in the current U.S. Federal Bankruptcy Code
that allows for corporate reorganization of a firm in bankruptcy. Chapter
7 liquidation A chapter in the current U.S. Federal Bankruptcy Code that
allows for corporate liquidation of a f