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BEYOND THE PAGE
mhhe.com/brealey12eDilution● ● ● ● ●
FINANCE IN PRACTICE
❱ Most warrants give the holder the option to buy stock
in the company. A less common warrant is the put
warrant that allows the holder to sell stock back to the
company.
In April 2006, the Chinese liquor producer
WuLiangYe Corporation issued 313 million put war-
rants on the Shenzhen Stock Exchange. The maturity
date for the warrants was April 2, 2008, and the last
date for trading was March 26, 2008. The exercise price
for the warrants was 5.63 yuan, and the stock price at
the time of issue was 5.03 yuan.
After the warrants were issued, the price of
WuLiangYe stock rose steadily to touch a high of 71.56
yuan in October 2007. By that point there was almost no
chance that the stock price would fall below 5.63 yuan
by April 2008, so the put warrants were almost certain
to expire unexercised. By that stage the Black– Scholes
formula showed that the warrants were effectively
worthless. Yet, as the price of the stock rose, so did that
of the warrants. By June 2007 the warrant price had
reached a high of 8.15 yuan, before falling to one penny
in the last minute of the last trading day.
The WuLiangYe put warrants were not an isolated
case of mispricing. Another 15 Chinese put warrants
were similarly overvalued during this period. So why
didn’t smart investors arbitrage the mispricing by sell-
ing the warrants and buying delta shares of stock? If
short sales of the put warrants had been allowed, this
arbitrage would have been very profitable. However,
in China investors were prohibited by law from short-
selling stocks or warrants. In addition, China limits the
amount by which a share price may change in a single
day to 10%. During the final few days of trading, the
price of WuLiangYe stock was sufficiently high that
the 10% limit meant that the put warrant would inevi-
tably expire worthless. Yet the warrants traded for sig-
nificant amounts of money.
How could the price of an option depart so dramati-
cally from any reasonable estimate of its value? Did the
investors who bought the warrants at 8.15 yuan mis-
takenly believe that they were getting an option to buy
WuLiangYe stock for 5.63 yuan? Perhaps wise inves-
tors, who were unable to sell the warrants short, decided
instead to join the bandwagon by buying the warrants
to resell them later to a greater fool at an even higher
price. If so, the Chinese put–warrant episode is another
example of the bubbles that we discussed in Chapter 13.Source: Wei Xiong and Jialin Yu, “The Chinese Warrants Bubble,” American
Economic Review, 101(6): 2723–2753.The Chinese Warrants Bubble
21-5 Option Values at a Glance
So far our discussion of option values has assumed that investors hold the option until maturity.
That is certainly the case with European options that cannot be exercised before maturity but
may not be the case with American options that can be exercised at any time. Also, when we
valued the Google call, we could ignore dividends, because Google did not pay any. Can the
same valuation methods be extended to American options and to stocks that pay dividends?
Another question concerns dilution. When investors buy and then exercise traded options,
there is no effect on the number of shares issued by the company. But sometimes the com-
pany itself may give options to key employees or sell them to investors. When these options
are exercised, the number of outstanding shares does increase, and therefore the stake of
existing stockholders is diluted. Option valuation models need to be able to cope with the
effect of dilution. The Beyond the Page feature shows how to do this.
In this section we look at how the possibility of early exercise and dividends affect option
value.American Calls—No Dividends Unlike European options, American options can be exercised
anytime. However, we know that in the absence of dividends the value of a call option increases
with time to maturity. So, if you exercised an American call option early, you would needlessly