A-27
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Securities Markets
1. When investment banks underwrite IPOs, they typically sell stock for 5–10 percent
more than they pay for it. When they underwrite new stock for companies that are al-
ready public, the typical markup is 3 percent. What explains this difference?
ANSWER: The process of underwriting an IPO (initial public offering) is quite costly
for the investment bank since it has to prepare registration statements, comply with
regulatory requirements, and compile and disseminate information on the company
issuing the stock. This often takes the form of “road shows” in which investment
bankers meet with representatives from mutual funds, pension funds, and insurance
companies to convince these institutional savers that they should purchase stock of-
fered in the IPO. Also, investment banks put their reputation on the line when they un-
derwrite stock for a company that issues stock for the first time. In contrast, when
investment banks underwrite stock for companies that are already public, those com-
panies have a reputation of their own in the form of past stock prices. The benefit
provided by the underwriting investment bank in the form of reputation and reduction
of adverse selection is lower than for an IPO, justifying the lower markup.
2. As in Section 5.4, assume that bonds pay a real return of 2 percent. Stocks pay 22
percent half the time and –6 percent half the time. Suppose you initially have wealth
of $100, and let Xbe your wealth after 1 year. What fraction of your wealth should you
hold in stock under each of the following assumptions?
a. You want to maximize the average value of X.
ANSWER: Expected real return of stocks = 0.5(0.22) + 0.5(–0.06) = 0.08 (8%). Your
average wealth Xif you hold 100 percent of your wealth in stocks will be $108. Your
average wealth Xafter 1 year if you hold 100 percent of your wealth in bonds will
only be $102. Holding 100 percent of your wealth in stock will maximize your aver-
age wealth.
b. You want to maximize the value of Xwhen the return on stocks is –6 percent.
ANSWER: If you hold 100 percent of your wealth in stocks and the bad outcome (a
negative 6 percent real return) materializes, then your wealth will decline by 6 percent
to $94. In this situation you should hold all your wealth in bonds. This guarantees a
value of Xat $102. Holding any percentage of your wealth in stock will reduce the
value of Xbelow $102.
A-28 CHAPTER 5 Securities Markets
c. You want to be certain that Xis at least $100 (that is, you don’t lose any of your
initial wealth). Subject to that constraint, you maximize the average value of X.
ANSWER: The share of stock as a percentage of your wealth is s. You want to make
sure that even when the bad outcome occurs, your stock-holding will not reduce your
wealth below $100. You can use the equation below to solve for the share of stock
(s) that will guarantee to keep your wealth intact at $100 even when the bad outcome
occurs:
s$94 + (1 – s)$102 = $100
Solving for s, 1/4 = 0.25 = 25%.
Or you can write the equation in terms of the return on wealth, picking sso that the
return on wealth is 0 percent in the case of the bad (low return) outcome:
s(–6%) + (1 −s)2% = 0%
Again, s= 1/4 = 0.25 = 25%.
You maximize the average value of Xwithout incurring any losses if you hold 25 percent
of your wealth in stock and 75 percent of your wealth in bonds. Increasing the amount
of stocks held will reduce your wealth below $100 when the bad outcome occurs.
3. Suppose two people are the same age and have the same level of wealth. One has
a high-paying job and the other has a low-paying job. Who should hold a higher frac-
tion of his or her wealth in stock? Explain.
ANSWER: The person with the low-paying job is in much the same position as a re-
tiree. Earning a low income is as much a barrier to falling back on future earnings as
