Additional Topics
Additional items to address:
Holding Period Return
Short Selling with Margin Requirements
Holding Period Return
In general, the holding period return for any financial
instrument can be defined as:
HPR =
(Appreciation in Price + Income Received) / Beginning Price
So Holding Period Return covers any type of value derived
from owning the asset whether reflected as a price increase
or in the form of income paid (such as dividends)
Holding Period Return
Examples:
T-Bill purchased for 9925 and matures for face value of
10,000 at the end of 90 days
HPR for the 90 day period = 75 / 9925 = .7557%
Stock purchased for 100 and grows to 120 after one year,
paying a dividend of 5
HPR for year = (20 + 5) / 100 = 25%
Holding Period Return
We know that the return on financial instruments may not be
certain, especially for equities. In these cases, we may
consider what the Expected HPR is given the returns we
anticipate in different economic scenarios
If there are S possible states of the world at the end of the
measuring period, with state s having probability p(s), and
generating a return of r(s), then
Expected HPR = Σ p(s) r(s)
Holding Period Return
Example: Assume you buy an equity at the beginning of the year for $25
and it pays a dividend of $5 at the end of the year. The following
potential scenarios could play out:
State of the World
Probability
Price at End of Year
Large Growth
.20
$40
Moderate Growth
.50
$30
Moderate
Recession
.30
$20
What is the Expected Holding Period Return?
Holding Period Return
Under Large Growth scenario, HPR = (15 + 5) / 25 = 80%
Under Moderate Growth scenario, HPR = (5 + 5) / 25 = 40%
Under Moderate Recession scenario, HPR = (-5 + 5) / 25 =
0%
Expected HPR = .20(80%) + .50(40%) + .30(0%)
= 16% + 20% = 36%
Short Selling and Margin
In the previous class we talked about how it was possible to
perform a short sale on a financial instrument by
borrowing it from the inventory of a dealer and selling it to
a third party
The hope is that the instrument declines in price and you can
re-supply it to the dealer buy purchasing in the open
market at the lower price and make a profit
Clearly, the dealer is taking some sort of credit risk when he
allows you to borrow the instrument, so he sets up some
requirements to protect his interest
Short Selling and Margin
Initial Margin = Amount required to initiate the trade
= Amount generated from sale of borrowed assets PLUS
an additional amount to cover the risk that the price of the
stock may increase
The additional amount is usually a function of the initial value
of the trade
So if you short sell n shares of a stock valued at time zero at
S0, and the initial margin requirement is u, then the initial
value of the sale is n S0, and the additional initial margin =
u n S0
Short Selling and Margin
To minimize the credit risk, the dealer will always require that
the “investor’s equity position” be at least a fraction v of
the market value of the assets (v < u )
This is called the
maintenance margin requirement
“Investor’s Equity Position” - recall that on a balance sheet, a person’s
“equity” or “surplus” is the difference between the assets they own and
the liabilities they have promised to fulfill
Short Selling and Margin
Note that Investor’s Equity
= Investor’s Asset – Investor’s Liability
= (Gain from short sale + additional initial margin)
- Current Market Price of Stock
= n S0 + u n S0 - n S1
So dealer requires that
n S0 + u n S0 - n S1 > v n S1
Short Selling and Margin
Example: Sell Short 100 shares of stock at current price of $65, initial
margin requirement = 50%, maintenance margin requirement of 30%
So investor sells the 100 shares and receives $6500, plus must also keep
an additional $3250 on deposit. Total initial asset = $9750
Maintenance Margin = 30% * 100 * Current Market Price
Stock price goes to $70:
Investor’s Equity = n S0 + u n S0 - n S1 = $6500 + $3250 - $7000 = $2750
Maintenance Margin = 30% * 100 * 70 = $2100
Since Equity > Maintenance Margin, then no adjustments needed
Short Selling and Margin
Stock price goes to $80:
Investor’s Equity = n S0 + u n S0 - n S1 = $6500 + $3250 - $8000 = $1750
Maintenance Margin = 30% * 100 * 80 = $2400
Since Equity < Maintenance Margin, so an adjustment needed via a
margin call
Dealer may require that the full initial additional margin of $3250 is
re-established
Short Selling and Margin
At what exact price would a margin call be initiated?
Where n S0 + u n S0 - n S1 = v n S1
Solving for S1:
S1 = (n S0 + u n S0 ) / (n + v n)
In our example: S1 = ($6500 + $3250 ) / (100 + .3(100))
= $9750 / 130
= $75