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| | Fixed
Income,
& Fixed
Income Derivatives,
& Fixed
Income Risk Management Last revised:
March 02, 2002
New, this month:
Table of Contents for this page:
Ask Dr. Risk! TM | Derivatives
DictionaryTM | Derivatives
DigestTM |
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Ask Dr. Risk
Dr. Risk
promises you at least a brief response to your
important question, as soon as he has a free
moment. A question of sufficiently general interest to make it into the 'Zine,
tends to generate a more comprehensive response. All questions and answers
become the property of The William Margrabe Group, Inc
8/28/00
Can ... (8/28/00)
Dear Dr. Risk –
Do
you have any thoughts about options on Mortgage backed securities. There is
little written up on the topic, and the link between implied volatility and
prepay modeling? –
Michel
Dear Michel –
. – Dr.
Risk
TOP
8/28/00
Can you ever have too much money? Yes, because ... (8/28/00)
Dear Dr. Risk
– after the electronic payment system develop, how can it affect the transaction demand for money, under the Baumol model? –
Stephen
Dear Stephen – Baumol's
model of optimal cash balance allows us to answer in the affirmative that
eternal question, "Can you ever have too much money?" Of course, by
money we mean the paper and metal stuff that you use to make transactions, not
the store of wealth.
Baumol's model is a
relatively straightforward application of the classic economic order quantity (EOQ)
model, which academics proposed years ago for determining optimal inventory.
Here, we're talking about the optimal inventory of cash, hence the obvious
application. The idea is that cash is a useful commodity, but using it has a
couple of costs. As your holdings of cash increase, one cost increases, but the
other decreases. The optimal cash withdrawal is at the minimum level of total
costs.
One cost is the
interest opportunity cost during the period between visits to the bank for cash.
You go to the bank and get C dollars, which you spend at a uniform rate, until
you run out of cash and go to the bank, again. Your
average balance is half the amount of cash you withdraw, C/2. The rate of
interest you could earn on money kept in the bank is r. Thus, your annual
interest opportunity cost for withdrawing cash to walk around with and
make transactions is Cr/2.
Your other cost is the direct cost, each time you
withdraw money. That could include a $2.00 fee for using the ATM, as well as
your opportunity cost for your 15 minutes walking to the ATM, at a $20/hour
value of your time. Let $b denote the sum of ATM fees, value of time spent going
to and using the ATM, etc. You spend cash at the rate $S per year. The
number of visits per year is n = S/C. The direct cost per year is bn = bS/C.
Total cost, the sum of those two costs, is a
function of the cash withdrawal
TC(C) = Cr/2 + bS/C.
TC is at its minimum when its slope is zero. Using little differential calculus,
that's where
dTC/dC = r/2 - bS/C2 = 0
C2 = 2bS/r.
C = Ö(2bS/r)
If you don't like using calculus, build a spreadsheet and see how TC changes as
you increase C.
Now, we can answer your question. The use of the
electronic payments will clearly reduce annual cash payments. To find the impact
of a decline in S, you could use more calculus or build another spreadsheet.
dC/dS = (2b/r) / [2Ö(2bS/r)]
= b / rC.
Hence, the elasticity of cash balance to a change in cash spending is
(S/C) dC/dS = 2bS / 2rC2 = 1/2.
Thus, a small percentage change in cash spending will lead to half as large a
percentage change in cash balances.
Holding total spending constant, and assuming
that spending is either through ePayments or cash, we have the impact of a
dollar increase in ePayments:
dC = dC/dS dS = –dC/dS d(ePayments).
So, every dollar increase in ePayments leads to a decrease in the size of the
cash withdrawal of b / rC, and a decrease in the average cash balance of half
that. – Dr. Risk
TOP
Looking
for LIBOR in All the Wrong Places (7/28/00)
Dear Dr. Risk
– I am trying to find out the US$ Libor rates
for the period of one week at
the beginning of each year from 1983 through to 1993. Please please help as I
have tried everywhere –
Gerry
Dear Gerry – While
I'm sure you know what you want, Dr. Risk doesn't. For example, there are five
one-week periods at the start of every year that include the January 1 -
Monday-Friday, Tuesday-Monday, etc. Do you want the week that includes Jan. 1,
which may include the end of the previous year? Do you need to include the turn
of the year? With the first business day?. Which one do you want, or don't you
care? Please give us some context. What are you trying to accomplish? –
Dr. Risk
Dear Dr. Risk
– I am purely trying to indicate to a client
that the LIBOR rate for one year
in 1983 was x% at the beginning of the year. For example a rate for the
1st
or 2nd of the year would be superb. I just need an indication of roughly
what the rate was. I have found in Bloomberg the rates from 1984 but not
before. I just need 1983 for my client.
– Gerry
Dear Gerry – An
interviewer once asked John Wayne what was the most important quality he looked
for in a woman. His reponse: "She's got to BE there."
Sounds
as though that's all you need from your LIBOR data: They’ve
gotta BE there. Nothing complicated, but apparently not trivial to deliver.
You
might try the famous Federal Reserve Statistical Release H.15: http://www.bog.frb.fed.us/releases/H15/data.htm.
It has historical data. I don’t know how far it goes back. However, it
wouldn’t amaze me to hear that your other source got its data from this
source, and they both begin with 1984.
You’re
with [a top ten investment bank], right? Surely, someone in your company has a
contract with DataStream or DRI.
This gives them access to LIBOR data. You'll have to see where the series starts.
– Dr. Risk
Option-adjusted
Spread versus Photo Spread (7/28/00)
Dear Dr. Risk
– Could you
explain me please what is option-adjusted spread? What's difference with just
spread for convertible bonds?
– Jine
Dear Jine –
The option-adjusted spread (OAS) is a tool for allowing an analyst to compare
the relative values of related bonds, some with and some without embedded call
options.
We'll get to the convertible bond in a
minute, but the discussion will be easier if we start talking about the
"ordinary bond", without the option to convert to shares. The ordinary
bond has a par value, coupon rate, payment frequency, maturity date, and current
market price. Dr. Risk assumes that you know how to compute the yield on the
ordinary bond. However, we'll review this computation for some readers who
aren't so familiar with this process. The bond's yield – or yield to
maturity – is the bond's "internal rate of return", which may
ring some bells for readers with a economic background. That is, the yield is the
discount rate that solves the equation that has the underlying bond’s market
value on the left side and the bond-pricing, present-value formula on the right
side.
Now, suppose you have a callable bond,
with the same terms as the ordinary bond, plus the call terms. (It's a little
easier to talk about callables, first.) You could compute a yield to maturity
via the standard formula for the callable bond, using the ordinary bond's par
value, coupon rate, payment frequency, and maturity date, but callable bond's
current market value on the left side. The callable bond's market price is lower
than the ordinary bond's, because the callable bond is the ordinary bond minus a
valuable call option. With a lower price, you’ll get a higher yield. Thus, the
callable bond will have a positive yield spread over the ordinary bond. You
might interpret the positive yield spread as compensation for the possibility
that the issuer will call the bond away, before the investor can capture its
value.
Now, let's see how someone might
use the OAS to compare the ordinary and callable bonds. Suppose one company has
issued a bunch of bonds at various maturities, and only one of them is callable.
An investor wants to know if the callable bond's relative value makes it
attractive to buy. If you graph yield versus maturity for all the company's
bonds, all the bonds will probably line up fairly neatly along a relatively
smooth curve – except for the callable bond. That yield sticks out above the
smooth yield curve like a huge, hideous zit on the sticks out from the smooth
curve of silky, milky skin on a Playboy Playmate of the Month's butt. Not
good! A naive investor might want to buy the bond, because it's yield is so
large, compared to similar bonds with nearby maturities.
A more sophisticated investor
will compute the callable bond's option-adjusted market price by estimating the
value of the option and adding it to the callable bond’s market price. Then he
will use the option-adjusted market price to compute the bond's option-adjusted
yield, using the standard formula for yield. Ordinarily, the option-adjusted
yield lines up better with the other yields on the ordinary bonds.
If
the option-adjusted yield is above the nearby points on the curve, then it has a
positive option-adjusted spread. An investor might conclude that this indicates
that the callable bond is a good buy.
Now
let's consider the convertible bond. It's an
ordinary bond, plus a valuable option to exchange the bond for shares.
Obviously, the convertible bond price will exceed the ordinary bond price. The
higher price leads to a lower yield. This bond will have a "negative spread
over the ordinary bond". Does that mean that the
convertible bond is a definite "sell"? No. You might interpret the
negative yield spread as compensation for the possibility that the investor will
convert the bond into shares, when they're more valuable than the bond. In this
case, you could subtract the value of the conversion option from the convertible
bond's market price to get the option-adjusted price. Then, use this price to
compute option-adjusted yield. The option-adjusted spread is the yield on the
convertible bond, minus the yield of the ordinary bond with the same maturity as
the convertible bond. If the spread is positive, you might think that the
convertible bond is a "buy".
The
basic idea of the OAS makes sense. Would Dr. Risk rely on a small discrepancy in
OAS to make an investment decision?
No. It can be misleading and lead to an unwarranted decision. In that sense
computing OAS is like air-brushing the centerfold photo to remove the zit from
the Playmate’s butt. – Dr.
Risk
Links Links
related to fixed income are below. Links related to other financial topics are here.
Derivatives
DictionaryTM Terms
and definitions relating to fixed income are below. The main Derivatives DictionaryTM
is here.
- 8/28/00
BEARs
- Bonds Earning Accrued Returns (q.v.).
- 8/28/00
Bonds Earning Accrued Returns
- Definition: Private-label equivalents
of stripped Treasurys that predated Treasury STRIPS (q.v.) by about
five years.
-
benchmark
instrument
- Definition: The note or bond that is
the standard of comparison for pricing similar bonds in related markets.
For the USD markets, the on-the-run (q.v.) U.S. Treasury notes and
bonds are the benchmark instruments.
Application: "The ten-year swap coupon is 40 bps over the
on-the-run ten-year Treasury."
-
callable
bond
- Definition: A bond that the issuer
can repurchase from the owner, according to a schedule of dates and
repurchase (call) prices. A bond with an embedded call option.
-
convertible
bond
- Definition: A bond that the issuer
can exchange for something else – ordinarily, common shares of the
corporation that issues both the shares and the bond – according to a
schedule of dates and conversion rates. A bond with an embedded option to
exchange the bond for something else.
- 8/28/00
corporate settlement
- Definition: The regular way to settle
a trade involving shares or corporate bonds. Exchange of cash for bonds on
the third business day after the trade date (T+3).
Comment: Before the SEC required settlement by T+3, corporate
settlement was by the fifth day after the trade (T+5). The SEC is pushing
the stock market to move toward next-day settlement (on T+1).
- 8/28/00
next-day settlement
- Definition: Exchange of cash for
bonds on the business day immediately following the trade date.
Comment: The regular way to settle for Treasury instruments.
-
off-the-run
- Definition: Seasoned, not newly
issued or created. Possibly with a coupon that is far from the going rate
in the market at that time.
Application: "The on-the-run ten-year Treasury is yielding
6.375%."
Comment: The off-the-run notes and bonds tend to be less liquid than
similar on-the-run (q.v.) instruments. Consequently, they trade at
slightly lower prices and higher yields. With off-market coupons either
higher or lower, the tax bite isn't exactly the same for off-the-run and
on-the-run instruments. This implies that a yield curve that reflects both
on-the-run and off-the-run instruments is a "fruit salad".
-
on-the-run
- Definition: Newly issued or created,
with price near par, hence with a coupon that is the going rate in the
market at that time.
Application: "The on-the-run ten-year Treasury is yielding
6.375%."
Comment: The on-the-run notes and bonds tend to be more liquid than
similar off-the-run (q.v.) instruments. Consequently, they trade at
slightly higher prices and lower yields than off-the-run counterparts. The
tax bite for on- and off-the-run instruments differs too. This implies
that a yield curve that reflects both on-the-run and off-the-run
instruments is a "fruit salad".
-
OAS
- Option-adjusted spread (q.v.).
-
option-adjusted
spread (OAS)
- Definition: The spread of a bond's
yield (q.v.) over its benchmark bond, after adjusting for any
embedded options. The adjustment consists typically of valuing the
embedded options, adjusting the market price for the bond, then computing
the yield the regular way .
Application: A tool for allowing an analyst to compare the relative
values of related bonds, with and without embedded call options.
- 8/28/00
recons
- Definition: Reconstitutions of STRIPS
(q.v.) into U.S. Treasury bonds.
Comment: This is how Joseph Jett created $350 million of bogus
P&L at Kidder, Peabody in the early 1990s.
- 8/28/00
regular-way settlement
- Definition: The ordinary timing for
exchanging cash for bonds in a particular market.
Application: Regular-way settlement is on the next business day (on
T+1) in the market for Treasuries, skip-day (q.v., on T+2) in the
market for for swaps and CDs, and in three business days for shares and
corporate bonds.
- 8/28/00
same-day settlement
- Definition: Exchange of money for
bonds on the same day as the transaction.
Comment: This is not ordinary, and works better for trades executed
earlier in the day.
- 8/28/00
skip-day settlement
- Definition: Exchange of cash for
bonds on the second business day after the trade date.
Comment: The regular way to settle for swaps and CDs, and a common
way to settle Treasury transactions that occur late in the day.
- 8/28/00
Separately Traded Registered Interest and Principal Securities
(STRIPS)
- Definition: Zero coupon bonds that
the U.S. Treasury made possible, beginning in 1985. The owner of a bond
wires it to an account at the New York Fed via FedWire. The Fed assigns a
separate ID number to the final principal payment and each of the coupon
payments, then wires the components back to their owner.
Application: If the parts of a bond are worth sufficiently more
than the whole, a bond arbitrageur may find it worthwhile to buy a bond,
strip it, and sell the STRIPS. If the parts are worth sufficiently less
than the whole, the bond arb may buy the pieces, ship them to the Fed to
reconstitute the bond, and sell the bond.
Comment: Joseph Jett's first job at Kidder, Peabody was trading
STRIPS. Eventually, during the early 1990s, he created some $350 million
of bogus P&L doing forward recons (q.v.).
Source: Jett, Joseph (with Sabra Chartrand). Black
and White on Wall Street. New York: William Morrow, 1999.
- spot
date
- Definition: The conventional
settlement date for a spot transaction in the fixed income market. In the
USD fixed income market, the spot date is two business days after the
transaction date.
- 8/28/00
STRIPS
- Separately Traded Registered Interest and
Principal Securities (q.v.).
8/28/00 "Bondholders
Risk Losing Their Status As Shareholders' Interest Comes First." Wall
Street Journal
(2000 August 14) By John Parry and Jennifer Ablan.
"Debt downgrades loom for a lot of seemingly successful U.S. companies.
The culprit? Corporate share buybacks. These buybacks impair the corporation's
credit worthiness, because they remove assets (cash) from the corporation,
reducing the collateral for the debt. For example, in April 2000, after Ford's
board approved a plan that would distribute as much as $10 billion in cash to
shareholders, Moody's cut its rating of Ford Motor Credit Co. debt from A1 to
A2.
If you think of shares as call options on the corporation's assets, the
effect is easy to understand. The bondholders own the assets, but are short a
call. A dollar dividend or buyback reduces assets by a dollar, and shares and
bonds each by less than a dollar. However, the shareholders get the entire
dollar that leaves the corporation, so they're better off. The bondholders are
worse off.
Top
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