Principles of Finance with Excel (Основы финансов c Excel)
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PFE, Chapter 17, Efficiency page 20
Tri-Continental Corporation—A Closed-End Fund
Figure 17.3. Tri-Continental Corporation is a closed-end fund whose shares are registered on
the New York Stock Exchange. On 23 November 2001, Tri-Continental’s assets—the market
value of the shares contained in its portfolio—totaled $3,207,840,000.
Since the fund has 131,077,105 shares, this works out to a net asset value (NAV) per share of:
3, 207,840,000
$22.89
131,077,105
NAV ==.
However, on the same date, the fund’s shares sold for $20.33, a discount of 11.18%. The Tri-
Continental discount is pervasive. In the last 10 years it has averaged 14.57%.
PFE, Chapter 17, Efficiency page 21
Summing up additivity
As long as market participants can freely arbitrage, we expect value additivity to hold:
The value of a basket of goods or financial assets should equal the sum of the values of the
components. Arbitrage in this case means the ability of market participants to create and sell
their own bundles of goods or assets, or to break up existing bundles and sell the components.
This is true whether we’re discussing the cost of a bag of apples in the Asheville farmers’ market
or the price of an open-end mutual fund. But there are also situations, like a closed end fund,
where arbitrage is difficult. For these cases, like the closed-end funds discussed above, we
would not expect value additivity to hold.
We’re not quite done with additivity: In the next section we discuss an interesting case
where value additivity was clearly violated, but where—eventually—market prices came to
reflect value additivity.
17.3. Additivity is not always instantaneous: The case of Palm and 3Com
During the 1990s, 3Com developed the Palm Pilot, a handheld personal information
manager which became a raging success. In March 2000, 3Com sold 5.7% of its Palm
subsidiary to the public. After this “equity carveout” there were separate stock market listings
for Palm (still 94.3% owned by 3Com) and for the parent company 3Com. On March 3, 2000,
the closing stock price for Palm was $80.25 per share and the closing stock price for 3Com was
$83.06 per share. As you’ll see this situation represents an interesting violation of the principle
of value additivity.
PFE, Chapter 17, Efficiency page 22
In the spreadsheet below we calculate the market value of Palm (cell B5) and of 3Com
(cell B10).
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ABC
Palm
Price per share 80.25
Number of shares outstanding 562,258,065
Market value 45,121,209,716 <-- =B4*B3
3Com
Price per share 83.06
Number of shares outstanding 349,354,000
Market value 29,017,343,240 <-- =B9*B8
Value of Palm stock held by 3Com (94.3%) 42,549,300,762 <-- =94.3%*B5
Value of non-Palm 3Com activities -13,531,957,522 <-- =B10-B12
3COM AND PALM
This spreadsheet reflects market prices on
3 March 2000, the day after the issue of 5.7%
of Palm stock held by 3Com
If you look at these numbers you’ll see a startling failure of value additivity:
•
3Com owns most of Palm, but Palm’s value is bigger than 3Com’s! To be more precise:
The 94.3% of Palm stock still owned by 3Com is worth $42.5 billion (cell B12), but all of
3Com is worth only $29.0 billion (cell B10).
•
Using these numbers, the market seems to value all of the non-Palm activities of 3Com at
a negative $13.5 billion!!!! The only way this would be possible is if these activities
were big money losers (which wasn’t the case).
Why did additivity fail in this big way? Why didn’t market participants arbitrage the
3Com and Palm stock prices so that additivity would be restored (below we explain how such an
arbitrage would work)? One possible reason is that markets are (temporarily) relatively stupid:
The enthusiasm for the initial public offering (IPO) of Palm at the beginning of March 2000 was
so overwhelming that investors (temporarily, as you’ll see below) forgot that 3Com still owned
PFE, Chapter 17, Efficiency page 23
most of Palm. So they mispriced the relative values of Palm and 3Com, producing the weird
case shown above. If they had thought a bit, they would have realized that a share of 3Com
should be worth at least 1.52 times the price of a share of Palm:
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ABC
Minimum logical value of 3Com shares, compared to Palm
Number of shares of Palm held by 3Com 530,209,355 <-- =94.3%*B4
Number of 3Com shares 349,354,000
Number of Palm shares per 3Com share 1.52 <-- =B17/B18
Actually, if they knew how to read a balance sheet, they would conclude that the price of a 3Com
share should be even more. In 3Com’s last quarterly statement, just one week before the Palm
IPO, its balance sheet showed almost $3 billion in cash and short-term investments. Assuming
that these items were not needed for production of 3Com’s products, they are worth $8.53 per
3Com share:
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ABC
On 25feb00, from 3Com's balance sheet
Cash and equivalents 1,812,503,000
Short-term investments 1,166,026,000
2,978,529,000 <-- =B24+B23
Cash and investments per 3Com share 8.53 <-- =B25/B9
So the minimum value for a 3Com share should have been:
3 1.52* $8.53Com share price Palm share price≥+
PFE, Chapter 17, Efficiency page 24
Short-selling as a way of correcting market mispricing
Short-selling is a technique of borrowing a stock, selling it, and repaying it later.
8
Suppose you could freely short-sell Palm stock. Then you could make money from the above
situation by shorting Palm stock and buying 3Com stock. We’ll explain the arbitrage technique
in a second, but the logic is: Palm stock is overpriced (relative to 3Com stock) and 3Com stock
is underpriced (relative to Palm stock); so you should buy the cheap stock (3Com) and sell the
overpriced stock (Palm).
The arbitrage with which an investor could profit from the market mis-pricing is as
follows:
o Borrow a share of Palm stock and sell it. Selling borrowed stock is called short
selling. In the example below, an arbitrageur short sells one share of Palm for
$80.25.
o Buy the equivalent value of 3Com stock. At the time of the arbitrage we explore
below, 3Com was selling for $83.06 per share. The arbitrageur—having just
shorted Palm for $80.25, spends this money to buy 0.966 shares of 3Com
(0.966*$83.06 = $80.25).
If you’re right about the mispricing of the Palm versus 3Com shares, you should make
money under any price scenario. In the example below the arbitrageur shorted 1 share of Palm
on March 3 and used the proceeds to buy 0.966 shares of 3Com. Suppose that the arbitrageur
undid his position on March 10 (meaning: he bought one share of Palm and sold 0.966 shares of
8
The actual procedures for implementing a short sale are not simple. A well-written academic survey is a recent
paper by Gene D’Avolio, “The Market for Borrowing Stock,” unpublished working paper, Harvard University
Economics Dept.
PFE, Chapter 17, Efficiency page 25
3Com). If on 10 March the prices of Palm and 3Com were in line with her additive valuation,
then the arbitrageur would make money. In the example below, the share price of Palm on 10
March is $99 and the share price of 3Com is $159.01. As you can see, the arbitrageur makes
$60.01:
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ABC
March 3, 2000--short-sell 1 Palm share
and buy $80.25/$83.06 = 0.9662 3Com shares
Cash flow 0.00 <-- =80.25-0.9662*83.06
March 10, 2000--buy 1 Palm share
and sell $80.25/$83.06 = 0.9662 3Com shares
Suppose Palm price is 99.00
Logical
minimum
3Com price
159.01 <-- =1.52*B6+8.53
Profit 60.01 <-- =B7-B6
3COM AND PALM: ARBITRAGING THE MISPRICING
If you play with the spreadsheet, you’ll see that as long as you’re right about the price
relation between Palm and 3Com, you’ll make money—whether the price of Palm goes up (as in
the previous example) or down. For example, suppose that shares of Palm go down in price, and
that they sell for $60 on the 10 March:
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ABC
March 3, 2000--short-sell 1 Palm share
and buy $80.25/$83.06 = 0.9662 3Com shares
Cash flow 0.00 <-- =80.25-0.9662*83.06
March 10, 2000--buy 1 Palm share
and sell $80.25/$83.06 = 0.9662 3Com shares
Suppose Palm price is 60.00
Logical
minimum
3Com price
99.73 <-- =1.52*B6+8.53
Profit 39.73 <-- =B7-B6
3COM AND PALM: ARBITRAGING THE MISPRICING
As you can see from this arbitrage example, short-selling is essential to making the prices
“behave” in an additive way. Since short-selling involves selling borrowed stock, one
PFE, Chapter 17, Efficiency page 26
explanation of the lack of additivity in 3Com-Palm prices is that initially there were just too few
Palm shares around for arbitrageurs to sell.
What happened later?
The graph below shows the relation between Palm’s stock price and 3Com’s (column C
of the spreadsheet calculates the ratio
3'
'
Com s stock price
Palm s stock price
). As you can see, the ratio climbed
in the days following the Palm IPO, reaching the 1.52 point on 9 May 2000. From then on until
the end of July 2000, the ratio remained above this ratio—presumably the word had gotten out
and enough investors understood the intricacies the 3Com-Palm relationship to force the prices
into an appropriate pattern.
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ABCD E FGH I J KLM
Palm 3Com
Date Close Close 3Com/Palm
2-Mar-00 95.063 81.813 0.861 <-- =C9/B9
3-Mar-00 80.250 83.063 1.035
6-Mar-00 63.125 69.563 1.102
7-Mar-00 66.875 72.250 1.080
8-Mar-00 64.750 70.438 1.088
9-Mar-00 69.375 68.063 0.981
10-Mar-00 70.000 68.938 0.985
13-Mar-00 64.313 64.313 1.000
14-Mar-00 57.750 54.813 0.949
15-Mar-00 55.750 61.063 1.095
16-Mar-00 55.563 64.500 1.161
17-Mar-00 55.250 68.000 1.231
20-Mar-00 55.250 68.563 1.241
21-Mar-00 48.375 64.109 1.325
22-Mar-00 51.563 63.875 1.239
23-Mar-00 58.188 69.688 1.198
24-Mar-00 57.000 67.000 1.175
27-Mar-00 55.375 67.188 1.213
28-Mar-00 54.813 67.625 1.234
29-Mar-00 49.688 63.188 1.272
30-Mar-00 46.500 58.813 1.265
31-Mar-00 44.875 55.625 1.240
3-Apr-00 40.313 49.750 1.234
4-Apr-00 38.250 44.563 1.165
on 27 July 2000
Daily data, 2 March 2000 - 24 December 2001
PRICE TO PALM'S STOCK PRICE
CALCULATING THE RATIO OF 3COM'S STOCK
Note that remaining Palm stock was distributed to shareholders
3Com Stock Price versus Palm's Price
The data is for the ratio: 3Com/Palm
0.00
0.50
1.00
1.50
2.00
2.50
3.00
2-Mar-00
15-May-00
27-Jul-00
9-Oct-00
20-Dec-00
7-Mar-01
18-May-01
1-Aug-01
18-Oct-01
On 28 July 2000, the ratio dropped precipitously, from 1.815 to 0.347. What happened?
After markets closed on July 27, 3Com distributed all remaining Palm shares to its
PFE, Chapter 17, Efficiency page 27
shareholders. There was no longer any compelling reason for 3Com’s share price to be related
to Palm’s. As you can see in the graph above, since then the ratio of the prices has been all over
the place.
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ABC D E FG
Date Palm 3Com
Ratio of
3Com/Palm
17-Jul-00 39.500 66.813 1.691
18-Jul-00 37.313 64.063 1.717
19-Jul-00 34.875 62.750 1.799
20-Jul-00 36.750 66.625 1.813
21-Jul-00 38.313 68.000 1.775
24-Jul-00 36.625 66.188 1.807
25-Jul-00 36.563 67.938 1.858
26-Jul-00 36.688 67.875 1.850
27-Jul-00 35.563 64.563 1.815 <-- =C107/B107
28-Jul-00 37.250 12.938 0.347 <-- =C108/B108
31-Jul-00 39.000 13.563 0.348
1-Aug-00 39.375 13.688 0.348
2-Aug-00 39.125 14.438 0.369
CALCULATING THE RATIO OF 3COM'S STOCK
PRICE TO PALM'S STOCK PRICE
Daily data, 2 March 2000 - 24 December 2001
Note that remaining Palm stock was distributed to shareholders
on 27 July 2000
Palm's stock
p
rice
3Com's stock
price
3Com sells for
1.815 times Palm
What happened on 27 July 2000?
On 27 July 2000 (the divestiture of all Palm stock by 3Com), the price of 3Com dropped
precipitously. By that date investors—well informed about the coming divestiture of Palm—
realized that the divestiture of the stock by 3Com would lower 3Com’s value. And so it did:
PFE, Chapter 17, Efficiency page 28
Palm and 3Com--Stock Prices
2 March 2000 - 24 December 2001
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
2-Mar-00
15-May-00
27-Jul-00
9-Oct-00
20-Dec-00
7-Mar-01
18-May-01
1-Aug-01
18-Oct-01
Palm
3Com
Palm and 3Com—what’s the point?
Additivity is a basic efficiency feature of financial markets. As in the case of closed-end
funds, it may not hold where the structural features of the funds make arbitrage difficult, or—as
in the case of Palm and 3Com—it may take some time for markets to figure out what’s
happening and to initiate the arbitrage which will lead to additivity. Difficulties in short-selling
can lead to failure of additivity.
17.4. Efficient Markets Principle 3: Cheap information is worthless
Financial markets are awash in information, and it is important for you to have some
opinions about how this information affects market prices. In this section we discuss three
hypotheses that relate to how information is incorporated into financial markets. The finance
PFE, Chapter 17, Efficiency page 29
jargon for these hypotheses is: Weak-form efficiency, semi-strong form efficiency, and strong-
form efficiency.
In one form or another all three of these hypotheses state that information is important
and that cheap and easily-accessible information is likely to be worthless. The cheaper and more
easily-accessible the information, the less it’s worth.
Read the previous paragraph again. It sounds contradictory!
• Information is important? This seems obvious. Whether it’s the cost of a bank loan or
information about whether Upward Slopes Ski Site is making money—the more
informed you are about a financial asset, the more you should be able to judge its worth.
• Cheap and easily-accessible information is likely to be worthless? If it’s so important,
why isn’t it worth anything? The reason is that many people think that it’s important, and
so they’re all trying to figure out what the information is and how it affects the value of
the asset. With so much energy expended on finding out the effect of the information and
with the information so cheap, you’re likely to find that the whole price impact of the
information has already been extracted and is already reflected in the market price.
Weak-form efficiency: almost always true
The hypothesis of weak-form efficiency says that you cannot predict the future price of a
financial asset by carefully examining the asset’s past prices and its current price. Since
everyone has easy and cheap access to the past prices of IBM stock, there’s nothing left to be
learned from these prices—all possible information contained in these prices is already
incorporated in the current market price of IBM. Everyone knows past prices, and therefore, if
you could make a profitable prediction based on a stock’s price history, so could everyone else.