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outflow Price at sale
Purchase Note: Dividend payment amounts
“ Cash flow known may vary from quarter to quarter.
with 100%

FIGURE 2.10 Cash flows of a typical equity.

We need to think not only about probabilities related to the nature and
size of future dividends, but also about what to assume for the end price of
an equity purchase. At least among the so-called blue chip (stocks of strong
and well-established companies with reputations for paying dividends over
a variety of market cycles) equities, investors tend to rest pretty comfortably
with the assumption that regular and timely dividend payments will be made
(just as with the debt instruments issued by blue chip corporations).
How can an investor attempt to divine an end price of an equity? There
are formulas available to assist with answering this question, one of which
is called the expected growth in dividends formula. As the name implies, a
forecast of future dividends is required, and such a forecast typically is made
with consideration of expectations of future earnings.
The expected growth in dividends approach to divining a future price
for an equity is expressed as

Expected future price per share
Expected dividend1s2 per share
Cost of equity 1 % 2 Expected growth rate of dividend1s2 1 % 2

While this formula may provide some rudimentary guidance on future
price behavior, it falls short of the world of bonds where at least a final matu-
rity price is prespecified.
Perhaps because of the more open-ended matter of determining what an
equity™s price ought to be, there tends to be less of a focus on using quanti-

Cash Flows

tative valuation methods with equities in favor of more qualitative measures.7
For example, some equity analysts assign great value to determining an
equity™s book value and then forecasting an appropriate multiple for that
book value. Book value is defined as the current value of assets on a com-
pany™s balance sheet according to its accounting conventions, and the term
“multiple” is simply a reference to how many times higher the book value
could trade as an actual market price. For an equity with a $10 per share
book value that an analyst believes should trade at a multiple of eight within
the span of a year, the forecast is for a market value of $80 per share. The
decision to assign a multiple of 8 instead of 4 or 20 may stem from any-
thing ranging from an analyst™s gut feeling to an extensive analysis of a com-
pany™s overall standing relative to peer groups. Other valuation methods
might include analysis of an equity™s price relative to its earnings outlook,
or even technical analysis, which involves charting an equity™s past price
behavior to extrapolate what future price patterns may actually look like.
Investors typically buy bonds for different reasons than why they buy
equities. For example, an investor who is predisposed to a Treasury bond is
likely to be someone who wants the predictability and safety that the
Treasury bond represents. An investor who is predisposed to the equity of
a given issuer (as opposed to the debt of that issuer) is likely to be someone
who is comfortable with the risk and uncertainty of what its price will be
in two years™ time or even two months™ time.
There are some pretty clear expectations about price patterns and
behavior of bonds; in the equity arena, price boundaries are less well delin-
eated. As two significant implications of this observation, equities tend to
experience much greater price action (or volatility) relative to bonds, and
the less constrained (and greater potential) for experiencing upside perfor-
mance would be more likely linked with equities as opposed to bonds (at
least as long as the longer-run economic backdrop is such that the underly-
ing economy itself is growing). Both of these expectations hold up rather well
on a historical basis.

I do not mean to detract from the rigor of analysis that often accompanies a
qualitative approach. The point is simply that a key forecast (or set of forecasts) is
required (often pertaining to the expected behavior of future dividends and/or
earnings), and this, by definition, requires cash flow assumptions to be made. This
forecasting requirement is in contrast to the cash flow profile of a Treasury note
where all expected distributions are known at time of purchase.



Currencies are considerably simpler than either equities or bonds when it
comes to spot pricing. From a cash flow perspective, there is a cash outflow
when a currency is purchased and a cash inflow when a currency is sold.
There are no intervening cash flows. As with equities, there are no maturity
dates, yet since there is typically one currency per country, shaping a view
on a currency™s prospects could well become much more involved than what
is required for developing an outlook for a single company (as with fore-
casting future dividends). Chapter 3 explores important credit quality con-
siderations for currencies.

In summary, the spot price of an asset is nothing more than what the mar-
ket says the price should be. There may very well be a difference between
the market™s price and our own views on an asset™s true value. The fact that
fixed income securities have an end price that is known at the time of pur-
chase greatly facilitates the matter of arriving at an appropriate spot price
of bonds. By contrast, the lack of a certain future value of an equity or
unhedged currency gives rise to the use of various qualitative methods. For
currencies, these methods may involve models centered on interest rate par-
ity or purchasing power parity theories. In the case of equities these meth-
ods may involve models centered on forecasts of future dividends or earnings
or even technical analysis.

& futures

A forward is one small step away from spot. As the term implies, a forward
is an agreement to exchange a financial asset for cash at some point in the

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future”at some point beyond the time frame implied by the asset™s typical
settlement conventions.
In the spot market, a typical settlement period for a Treasury bill is one
business day. A settlement for the same day that the trade is agreed on is
called a same-day settlement or cash settlement. Any settlement agreement
that extends beyond one business day is a forward settlement. If the num-
ber of days happens to be three, then in the vernacular of the bond markets
this is referred to as corporate settlement. It takes this name because cor-
porate bonds settle differently from Treasury instruments; they generally set-
tle over three days instead of just one. If the future settlement date happens
to be something other than cash, next day, or corporate, then it has no spe-
cial name ” it is simply referred to as being a forward settlement transac-
tion of so many days from the trade date. The trade date is when a price,
product, and quantity are agreed on, and the settlement date is when the
product is exchanged for cash (or some other agreed-on exchange).
For a settlement date that goes beyond the day-to-day convention of the
respective asset class, the spot price needs to be adjusted. To better under-
stand why, let us consider a more extreme case where a settlement does not
occur for one year.
Assume we desire to buy 10 ounces of gold for $400 per ounce, but we
do not want to take physical delivery of the gold for one year. Perhaps we
do not have the cash on hand today but anticipate having it in one year.
Further, perhaps we believe that when we do have the cash in one year, the
spot price of gold will be appreciably above $400 per ounce.
The person who is selling us those 10 ounces of gold may not like
the fact that she has committed to selling something so far into the future
for no up-front payment. Indeed, if our seller had received $4,000 under
a regular settlement, then that $4,000 could have been invested in a one-
year Treasury bill. But there is no $4,000 to invest over the one-year
period because no exchange has taken place yet. This absence of an
immediate payment represents an opportunity cost to our seller.
Therefore, our seller is going to ask us to commit to a forward price of
something above $400/ounce. How much above? Whatever the differ-
ence is between the total spot price of the gold and the opportunity cost
of not having that total spot value over the course of one year. If the
cost of money for one year were 5 percent, then the opportunity cost
for our gold seller is $200:

$200 $4,200 $4,000.
$4,200 $4,000 (1 5% 365/365).
$4,000 10 $400/ounce.


If the forward date were six months (183 days) instead of one year, then
the opportunity cost for our gold seller would be $100:

$100 $4,100 $4,000.
$4,100 $4,000 (1 5% 183/365).

Thus, the gold seller probably would want to sell the 10 ounces of gold
for a total of $4,200 for a one-year settlement agreement and for $4,100
for a six-month settlement agreement.
The formula for a forward in the simple case of gold can be written as:

S 11

where S spot
R opportunity cost
T time

Now that we have reviewed the basic concepts underlying forwards, it is an
easy matter to tie in the role of futures. Just like forwards, futures represent
a vehicle for making a commitment today to purchase or sell something at
a later date. The biggest difference between a forward and a future is how
the cash flows work. With a forward agreement to buy 100 ounces of gold,
for example, no cash is exchanged for the physical gold until the expiration
day of the forward contract. With a futures contract on gold, it works a lit-
tle differently.
Assume that the price of gold with a one-year futures contract is $440
an ounce and that an investor chooses to go long (purchase) a gold futures
contract with the one-year futures price at that level. That future price of
$440 becomes a line in the sand; it is the benchmark against which daily
price changes in the value of gold will be measured over an entire year. At
the end of one year, the investor can take delivery of the gold underlying the
futures contract for $440 an ounce. However, it is important to note what
happens between the time the futures contract is obtained and when it
expires a year later.
Let us say that the futures contract is obtained on a Monday with gold
at $440 an ounce. On Tuesday, the very next day, say the gold market closes
at $441 an ounce. This additional $1 value of gold ($441 versus $440) goes

Cash Flows

into a special account of the investor (usually called a margin account8) that
typically is maintained at the exchange (such as the Chicago Mercantile
Exchange) where the futures contract was transacted. If she wanted to, our
gold futures investor could immediately unwind (offset with an opposite
trade) her futures contract (by selling the same contract) and instantly make
a $1 profit. However, if our investor is a purchaser of gold and truly believes
that a future price of $440 will be a bargain in one year™s time, then she could
very well decide to hold the contract to expiration. In this instance the $1
that goes into her account on Tuesday may not be something she considers
to be a profit; rather, she may just consider it to be $1 less she will have to
pay for gold in a year if the price remains at $441 an ounce.
Of course, the likelihood is fairly small that gold will remain at one price
for an entire year. In fact, the gold investor expects that gold will keep climb-
ing in price, though likely with some volatility along the way; the price of
gold probably will not rise every single day, and over the course of a year it
could very well end up lower than $440 an ounce.
Again, at least in the present case with gold, the biggest difference


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