8/14/09 Final Exam Page 1 of 23
MS&E 247S
Instructor: Yee-Tien Fu
International Investments
Friday 8/14/09 7-10 pm
Summer 2009
Final Examination
In Class, Open Book, Open Notes, Dictionary, Calculators OK
Levich: Chapters 11-17 and Handouts 17 and 20
The Stanford University Honor Code
The Honor Code is an undertaking of the students, individually and collectively,
that they will not give or receive unpermitted aid in examinations…
that they will do their share and take an active part in seeing to it that others as well as
themselves uphold the spirit and letter of the Honor Code.
I acknowledge and accept the Honor Code.
Name _____________________________ (Signed) _____________________________
Student ID _________________________
Undergraduate / Graduate
Major _____________________________
Summer 2009 Visiting Student?
Yes
No
E-Mail at Stanford and at home institution (optional)
________________________________ _________________________________
Please answer 8 questions (out of ten) professionally within the allocated time.
Please write your answers directly on the question paper in the spaces provided.
Any More Fun Books to Read this summer?
A review of a New York Times Bestseller
“Four hundred years ago, Francis Bacon warned that our minds are wired to deceive us. "Beware the fallacies into
which undisciplined thinkers most easily fall--they are the real distorting prisms of human nature." Chief among
them: "Assuming more order than exists in chaotic nature." Now consider the typical stock market report: "Today
investors bid shares down out of concern over …." Sigh. We're still doing it.
Our brains are wired for narrative, not statistical uncertainty. And so we tell ourselves simple stories to explain
complex thing we don't--and, most importantly, can't--know. The truth is that we have no idea why stock markets go
up or down on any given day, and whatever reason we give is sure to be grossly simplified, if not flat out wrong.
Nassim Nicholas Taleb first made this argument in Fooled by Randomness, an engaging look at the history and
reasons for our predilection for self-deception when it comes to statistics. Now, in The Black Swan: the Impact of
the Highly Improbable, he focuses on that most dismal of sciences, predicting the future. Forecasting is not just at
the heart of Wall Street, but it’s something each of us does every time we make an insurance payment or strap on a
seat belt. … ….
Chris Andersonl
Editor-in-chief, Wired Magazine
MS&E247s International Investments
8/14/09 Final Exam Page 2 of 23
Question I (25 points - Swaps)
1. Suppose Sony has an opportunity to issue $100,000,000 of 5-year dollar bonds. Nomura
and Goldman Sachs will handle the bond issue for a fee of 1.875%. The investment banks
have told Sony that the bonds will be priced at par if they carry a coupon of 8.5%. As the
swap trader for Tokyo Big Bank, you have been quoting the following rates on 5-year swaps:
U.S. dollars:
Japanese yen:
8.00% bid and 8.10% offered against the 6-month dollar LIBOR
4.50% bid and 4.60% offered against the 6-month dollar LIBOR
Sony would like to do the dollar bond issue, but it prefers to have fixed-rate yen debt. If
Tokyo Big gets the proceeds of the dollar bond issue, giving Sony an equivalent amount of
yen, and Tokyo Big agrees to make the dollar interest payments associated with Sony’s
dollar bonds, what yen interest payments should Tokyo Big charge Sony? What is Sony’s
all-in cost in yen? The current spot exchange rate is ¥98.50/$.
Please show clearly all your calculations.
Hint:
The first thing to determine is the dollar proceeds of the bond issue. Because it is priced
at par, Sony will receive 1.875% less than the $100 million provided by investors:
$100,000,000 × (1 – 0.01875) = $98,125,000
This amount will be given to Tokyo Big Bank in exchange for an equal amount of yen:
$98,125,000 × ¥98.50/$ = ¥9,665,312,500
To determine the interest payments, we must examine what Tokyo Big Bank is quoting.
When Tokyo Big Bank does a 5-year swap and pays $100 million of principal, it expects to
pay interest at 8% or 4% semi-annually. Sony wants it to pay the interest on its outstanding
bond, which has a semi-annual coupon of 8.5%. Thus, there is an extra $0.25 million of
interest every half year for 5 years. This amount is given in the column labeled extra dollar
interest.
The yen principal that is associated with $100 million at the current exchange rate of
¥98.50/$ is
$100,000,000 × ¥98.50/$ = ¥9,850,000,000
Tokyo big bank would normally receive interest on this amount at 4.6% from Sony, which
would be ¥226.55 million every half year, but we must increase the yen interest to reflect the
increase in dollar interest that Tokyo Big Bank is paying. In the absence of spot interest
rates for each maturity, we can take the present value of the extra dollar interest at 8%. This
amount is $2.03 million. The yen value of this dollar amount at the current exchange rate is
¥199.03 million. The sequence of 10 semi-annual payments that is equivalent to ¥199.03
million is ¥22.59 million. We must add this interest to the ¥226.55 million to get the full
interest that Sony will pay. Thus, Sony receives ¥9,665,312,500 in the beginning of the
swap, pays semi-annual interest of ¥249.14 million for 5 years, and pays the principal
amount of ¥9,850,000,000 in year 5. The all-in-cost of this yen loan is 5.57%. Notice that
5.57% is only 92 basis points above the all-in cost of the quoted yen interest rate in the
swap, whereas the original dollar bond is 101 basis points above the all-in cost of the quoted
dollar interest rate.
[Answer to Question I, 25 points]
8/14/09 Final Exam Page 3 of 23
Answer: Please fill in the blanks in the following exhibit and provides the analysis in the space
provided. Note that the all-in cost is also known as the swap rate.
Sony's Dollar Bond Issue and Cash Flows in the Swap into Yen with Tokyo Big Bank
(All cash flows are in millions of dollars or yen)
Dollar Bond Issue
Year
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
AIC
Annual AIC
98.13
-4.25
-4.25
-4.25
-4.25
-4.25
-4.25
-4.25
-4.25
-4.25
-104.25
4.49%
9.17%
Swap Receipts (+) and Payment (-)
with Tokyo Big Bank
notional $
dollars
notional ¥
-100.00
-98.13
9,850.00
4.00
4.25
-226.55
4.00
4.25
-226.55
4.00
4.25
-226.55
4.00
4.25
-226.55
4.00
4.25
-226.55
4.00
4.25
-226.55
4.00
4.25
-226.55
4.00
4.25
-226.55
4.00
4.25
-226.55
104.00
104.25
-10,076.55
4.00%
4.49%
2.30%
8.16%
9.17%
4.65%
extra
dollar
interest
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
0.25
extra
yen
interest
22.59
22.59
22.59
22.59
22.59
22.59
22.59
22.59
22.59
22.59
Note: The present value at 4.00% of the 10 extra interest payment of $0.25 million is $2.03 million.
This is equivalent to 199.73 million yen at the current exchange rate.
The present value at 2.30% of 10 extra interest payment of 22.59 million yen is 199.73 million yen.
The annual AIC calculations compound the semi-annual rates, e.g. (1.0449^2) = 1.0917.
Effective
yen
cash flows
9,665.31
-249.14
-249.14
-249.14
-249.14
-249.14
-249.14
-249.14
-249.14
-249.14
-10,099.14
2.75%
5.57%
MS&E247s International Investments
8/14/09 Final Exam Page 4 of 23
Question II (25 points – Swaps)
Suppose a life insurance company issued $100 million of five-year Guaranteed
Investment Contracts (GICs) that commit it to pay a fixed rate of 9% semi-annually.
Suppose the company is able to invest $100 million in a five-year semi-annual
floating rate instrument yielding 6-month LIBOR plus 100 b.p. [1 b.p. = (1/100) x 1%]
a.
Describe the interest exposure by the insurance company. At what point
would the company not be able to earn enough on the floating rate
instrument to pay for its fixed obligations?
b.
Suppose there is available in the market a 5-year fixed-floating interest rate
swap with a notional amount of $ 100-million with the following terms:
-
receive fixed 8.5% every six months
pay 6-month LIBOR
How can the insurance company use this swap to hedge its interest rate
exposure?
c.
Calculate the spread the company would lock in if it chooses to enter the
swap agreement.
[Answer to Question II, 25 points]
MS&E247s International Investments
8/14/09 Final Exam Page 5 of 23
Question III (25 points – Synthetic interest rate futures)
a.
(10 points) Refer to the schematic diagram below, derive step-by-step the formula for the
synthetic interest rate futures of the foreign currency, for the period [t1, t2], in terms of the
parameters shown in the schematic diagram.
b.
(15 points) How do you arbitrage if the synthetic interest rate futures price is higher than that
of the outright interest rate futures? Please show all steps.
Hint (ii):
[Answer to Question III, 25 points]
MS&E247s International Investments
8/14/09 Final Exam Page 7 of 23
Question IV (25 points – Foreign Currency Futures and Options)
4. On April 28, 1995, the Paine Webber Group introduced a new type of security on the NYSE:
U.S. dollar increase warrants on the yen. At exercise, each warrant entitled the holder to an
amount of U.S. dollars calculated as
Greater of (i) 0 and (ii) $100 – [$100 × ¥83.65/$ / Spot rate)]
The “spot rate” in the formula refers to the yen/dollar rate on any day during the exercise period,
which extended until April 28, 1996. The 1-year forward rate on April 28 was ¥79.72/$, and the
spot rate was ¥83.65/$.
a. What view on the future yen/dollar rate do investors in this security hold?
b. This security was issued at a price of $5.50. To see whether the security is fairly priced,
which option prices would you want to examine?
[Answer to Question IV, 25 points]
a. What view on the future yen/dollar rate do investors in this security hold?
Answer: The investor gets the greater of (i) 0 and (ii) $100 – [$100 × ¥83.65/$ / S(¥/$)]. If
the yen remains unchanged at ¥83.65/$, the payoff is zero. If the yen strengthens, the ratio
of ¥83.65/$ / S(¥/$) > 1, and you would be subtracting an amount greater than $100, so the
payoff would be zero. As the yen weakens, the payoff increases to a maximum of $100.
Thus, the investor must think that the yen is going to weaken.
b. This security was issued at a price of $5.50. To see whether the security is fairly
priced, which option prices would you want to examine?
Answer: While the payoff on the security is non-linear in the yen-dollar exchange rate, it is
linear in the dollar-yen exchange rate. The payoff is zero at exchange rates above 1 /
(¥83.65/$) = $0.0119546/¥ and it increases linearly along a forty-five degree angle at
exchange rates below $0.0119546/¥ until the payoff is $100 at an exchange rate of zero.
This payoff is identical to the payoff on a yen put with a strike price of $0.0119546/¥ for an
amount of yen equal to $100 × ¥83.65/$ = ¥8,365. Thus, you should examine the price of a
yen put for this amount against dollars to determine if $5.50 is the correct price for the
security.
8/14/09 Final Exam Page 9 of 23
MS&E247s International Investments
Question V (25 points – Real Options—Copano project revisited in the deflation era)
Suppose that a commodity chemical company titled Copano is considering investing in a
new plant. The project will cost $60 million immediately for permits and preparation, which
will take a year. At the end of that year, the firm could invest $400 million to complete the
design phase. Managers believe that once the design phase is over, the firm has a twoyear window during which it can invest the $800 million needed to build the plant. Since
the project involves a phased investment, it can be treated as a compound option: A $60
million investment creates the right to invest $400 million in one year, and exercise of the
option creates the right to invest $800 million to purchase a new asset, namely the plant.
The possible plant values may be constructed by a multiplicative factor of 1.1 when market
flourishes and a multiplicative factor of (1/1.1) when market turns sour.
a. Draw Copano’s event tree. The possible plant value starts at 1,000 millions.
b. With risk-free interest rate being 8%, replicate each call option with borrowing (B) and
asset / plant purchase (M), and draw the Copano decision tree in the deflation era. Clearly
indicate your decisions on the decision tree.
Hint (i) event tree:
1,331.00
1,210.00
1,100
1,000
1,100
1,000
909.0909
909.0909
826.4463
751.3148
Hint (ii): Construct the synthetic call equations for t=3: (please check for accuracy prior to
accepting the hint)
531.00
410.00
1,100
300
1,000
200
909.0909
109.0909
26.4463
0
M (1,331) – (1 + .08) (B) = 531
M (1,100) – (1 + .08) (B) = 300
•
•
M=1, B=740.740
1 * 1,210 – 740.74 = 469.26 => replace 410
M (1,100) – (1 + .08) (B) = 300
M (909.0909) – (1 + .08) (B) = 109.0909
MS&E247s International Investments
•
•
M = 1, B=740.740
•
M = 0.69, B = 480
1 * 1,000 – 740.74 = 259.26 => replace 200
M (909.0909) – (1 + .08) (B) = 109.0909
M (751.3148) – (1 + .08) (B) = 0
0.69 * 826.4463 – 480 = 91.43 => replace 26.4463
[Answer to Question V, 25 points]
8/14/09 Final Exam Page 10 of 23
MS&E247s International Investments
8/14/09 Final Exam Page 11 of 23
Question VI (25 points – Put-Call-Forward Parity)
a. Derive the Put-Call-Forward Parity with diagrams and equations.
b. How do you take advantage of the arbitrage opportunity if you find that the actual price
of the put option is above the theoretical price determined using the parity condition?
c. What are the four exact steps to arbitrage if you find that the actual price of the put
option is below the theoretical price determined using the parity condition? Please use the
following key words: put option, call option, futures, zero-coupon bonds.
MS&E247s International Investments
8/14/09 Final Exam Page 12 of 23
Question VII (25 points – Foreign Currency Options)
7. Assume that today is September 12. You have been asked to help a British client who is
scheduled to pay €1,500,000 on December 12, 91 days in the future. Assume that your client
can borrow and lend pounds at 5% p.a.
a. Describe the nature of your client’s transaction exchange risk.
b. What is the option cost for a December maturity and a strike price of £0.72/€ to hedge the
transaction? The option premiums per 100 euros are £1.70 for calls and £2.40 for puts.
c. What is the maximum pound cost your client will experience in December?
d. Determine the value of the spot rate (£/€) in December that makes your client indifferent ex
post to having done the option transaction or a forward hedge if the forward rate for delivery
on December 11 is £0.70/€.
Hint:
[Answer to Question VII, 25 points]
a. Describe the nature of your client’s transaction exchange risk.
Answer: Your client is scheduled to pay €1,500,000 in 91 days. If no hedging is done, and the euro
strengthens in value relative to the pound, the client will lose money. The amount of the loss could
be substantial if a major strengthening occurs.
b. What is the option cost for a December maturity and a strike price of £0.72/€ to hedge the
transaction? The option premiums per 100 euros are £1.70 for calls and £2.40 for puts.
Answer: To hedge foreign currency costs with an option, you must purchase a call option that gives
you the right to buy euros. This puts a ceiling on your costs. The cost of the option would be £1.70
per 100 euro, or
(1.70/100) x 1,500,000 = 25,500
c. What is the maximum pound cost your client will experience in December?
Answer: If the exchange rate is greater than £0.72/€ in December, your client will be able to buy
euros at that value. If the future spot exchange rate is lower than £0.72/€, the client will buy euros
at the future spot exchange rate. In either case, if they hedge with the option contract, they will have
higher costs. The future value of £25,500 at 5% for 91 days is
25,500 x [1 + (5/100) x (91/365)] = 25,817.88
Thus, the minimum net cost that the client will face is
[0.72 x 1,500,000] + 25,817.88 = 1,105,817.88
MS&E247s International Investments
8/14/09 Final Exam Page 13 of 23
d. Determine the value of the spot rate (£/€) in December that makes your client indifferent ex
post to having done the option transaction or a forward hedge if the forward rate for delivery
on December 11 is £0.70/€.
Answer: If the client does the forward hedge, their cost will be
[0.70 x 1,500,000] = 1,050,000
If the client does the option hedge and does not have to exercise the option, they will buy the euros
in 91 days, and their cost will be
S(t+89) x 1,500,000 +25,817.88
If this option cost is to equal the forward cost, we know
S(t+89) x 1,500,000 + 25,817.88 = 1,050,000.
Solving this equation gives S(t+89) = 0.6828
8/14/09 Final Exam Page 14 of 23
MS&E247s International Investments
Question VIII (25 points –What a pleasant surprise in dismal days!)
Read the following Bloomberg article about unexpected excellent financial performance of Google during the aftermath of
the subprime mortgage crisis. Then answer the questions that follow.
Google Earnings Gave Options
Traders a 17,530% Gain (Update1)
By Michael Patterson and Jeff Kearns
April 18 (Bloomberg) -- Options traders who predicted
Google Inc. would beat estimates earned as much as
17,530 percent on their investments today, the mostprofitable bet among all U.S. equity derivatives.
Contracts giving the right to buy Google shares for
$530 before the close of trading today jumped as high
as $17.63 from their 10-cent closing price yesterday.
That gain almost matched the 18,760 percent advance
in the Dow Jones Industrial Average since the
beginning of 1900, according to Bloomberg data.
``Today in Google you see the power of leverage in
options, especially going into earnings,'' said Peter
Bottini, executive vice president of trading at
OptionsXpress Holdings Inc., a Chicago-based online
brokerage. ``We were swamped with customers who
were calling in at the open of the market.''
Google shares climbed 20 percent, the most since its
initial public offering in 2004, to $539.41 after the
owner of the most popular Internet search engine
beat the average analyst profit estimate by 7.1
percent. Google had dropped 35 percent this year on
concern the U.S. economic slump would hurt spending
on online advertising.
Google call-option volume jumped to 311,139
contracts, the most since January 2006. Those
contracts outnumbered trading in bearish bets, or
puts, by 1.6-to-1. Call options give the right to buy a
security for a certain amount, called the strike price,
by a given date. Puts convey the right to sell.
`Playing Google'
``We expect our more active customers to come out
of the woodwork and start playing Google again,''
Bottini said.
Today's share surge was more than triple what the
options market was expecting as of yesterday, based
on prices paid for April contracts with a strike price
closest to yesterday's closing share price, Bloomberg
data show.
Google closed yesterday at $449.54. At the same
time, the price of $450 straddles, which combine a put
and a call at that strike price, was $30. That indicates
traders expected a move of at least that amount, or
6.7 percent, in order to break even on the position.
``The market viewed this as a long shot, but not an
impossibility,'' said Chris Jacobson, a senior options
strategist at Susquehanna Financial Group in Bala
Cynwyd, Pennsylvania.
Google contracts were the fifth-most traded among
U.S. stock options in the first quarter, according to
Chicago-based Options Clearing Corp., which settles
all trading of exchange-listed contracts. There were
7.69 million Google options traded during the first
three months of the year.
a. (5 points) Was the market efficient? Comment.
b. (5 points) Where did the magic power of leverage come from? Compare fairly your return on
shares investments and on the out-of-the-money call options investments made one day before
the financial report release.
c. (5 points) Will you be able to generalize this model as a rare event probability mingled with
extremely high payoffs and hence producing attractive expected payoffs? How is this model
applicable in investments? On what circumstances? Elaborate.
d. (5 points) What’s important about the call to put ratio, 1.6-to-1 in the above case? What signal
does the ratio carry?
e. (5 points) How could somebody forecast in an educated way that Google would have such a
wonderful performance in economic downturn but some couldn’t? How do you make sure that
you are among the educated ones?
MS&E247s International Investments
[Answer to Question VIII, 25 points]
8/14/09 Final Exam Page 15 of 23
第 1 頁，共 1 頁
Bloomberg Printer-Friendly Page
Google Earnings Gave Options Traders a 17,530% Gain (Update1)
By Michael Patterson and Jeff Kearns
April 18 (Bloomberg) -- Options traders who predicted Google Inc. would beat estimates earned as much as
17,530 percent on their investments today, the most-profitable bet among all U.S. equity derivatives.
Contracts giving the right to buy Google shares for $530 before the close of trading today jumped as high as
$17.63 from their 10-cent closing price yesterday. That gain almost matched the 18,760 percent advance in
the Dow Jones Industrial Average since the beginning of 1900, according to Bloomberg data.
``Today in Google you see the power of leverage in options, especially going into earnings,'' said Peter
Bottini, executive vice president of trading at OptionsXpress Holdings Inc., a Chicago-based online
brokerage. ``We were swamped with customers who were calling in at the open of the market.''
Google shares climbed 20 percent, the most since its initial public offering in 2004, to $539.41 after the
owner of the most popular Internet search engine beat the average analyst profit estimate by 7.1 percent.
Google had dropped 35 percent this year on concern the U.S. economic slump would hurt spending on online
advertising.
Google call-option volume jumped to 311,139 contracts, the most since January 2006. Those contracts
outnumbered trading in bearish bets, or puts, by 1.6-to-1. Call options give the right to buy a security for a
certain amount, called the strike price, by a given date. Puts convey the right to sell.
`Playing Google'
``We expect our more active customers to come out of the woodwork and start playing Google again,''
Bottini said.
Today's share surge was more than triple what the options market was expecting as of yesterday, based on
prices paid for April contracts with a strike price closest to yesterday's closing share price, Bloomberg data
show.
Google closed yesterday at $449.54. At the same time, the price of $450 straddles, which combine a put and
a call at that strike price, was $30. That indicates traders expected a move of at least that amount, or 6.7
percent, in order to break even on the position.
``The market viewed this as a long shot, but not an impossibility,'' said Chris Jacobson, a senior options
strategist at Susquehanna Financial Group in Bala Cynwyd, Pennsylvania.
Google contracts were the fifth-most traded among U.S. stock options in the first quarter, according to
Chicago-based Options Clearing Corp., which settles all trading of exchange-listed contracts. There were 7.69
million Google options traded during the first three months of the year.
To contact the reporters on this story: Michael Patterson in New York at [email protected];
Jeff Kearns in New York at [email protected].
Last Updated: April 18, 2008 17:06 EDT
Terms of Service | Privacy Policy | Trademarks
http://www.bloomberg.com/apps/news?pid=20670001&refer=&sid=aiQY8LDduXjA
2008/6/22
Counting the clicks, and the money, at Google - Print Version - International He... 第 1 頁，共 3 頁
Counting the clicks, and the money, at Google
By Miguel Helft
Monday, June 2, 2008
MOUNTAIN VIEW, California: If Google were the U.S. government, the data that streams into
Nicholas Fox's laptop every day would be classified as top secret.
Fox is among a small group of Google employees who keep a watchful eye on the vital signs of one of
the most successful and profitable businesses on the Internet. The number of searches and clicks, the
rate at which users click on ads, the revenue all this generates - everything is tracked hour by hour,
then compared with the data from a week earlier, then charted.
"You can see very, very quickly if anything is amiss," said Fox, the director of business product
management at Google.
Fox and his "ads quality" team can also quickly see whether something is working particularly well. His
group's mission, to constantly fine-tune Google's ad delivery system, has one overriding objective:
show users only the ads they are most likely to be interested in and click on.
Google runs a complex auction-based system that determines which ads will appear where, and in
what order. Every time the team alters the formulas that select and rank ads, Fox can run a test and
quickly see the effect of the changes on users, advertisers and Google's revenue - which, in this year's
first quarter, came in at the rate of more than $2 million an hour.
The job has given Fox, a soft-spoken 29-year-old with an obvious affinity for nuance and numbers, a
detailed understanding of the complex dynamics at work inside Google's ad-driven economic engine.
Fox, who graduated from Harvard with a degree in economics and spent two years at McKinsey &
Co., the management consulting firm, before joining Google in 2003, also helped organize its
"Revenue Force." This select group of company engineers, sales and finance people, product
managers and statisticians is charged with keeping top executives apprised of the forces that make
Google tick.
Google reveals little of these forces to the outside world. Even on Wall Street, many experts describe
Google as a giant black box that they struggle to comprehend. In recent months, for instance, analysts
and investors grew increasingly worried about reports of a decline in clicks on Google ads in the
United States, which they interpreted as a sign that Google's business could be suffering from the
economic slowdown. But inside Google, Fox and others were growing confident that the company
would do just fine.
"I wouldn't quite go so far as to say we are recession-proof," said Hal Varian, Google's chief
economist. "But we are recession-resistant."
Google's financial results for the first three months of the year surpassed expectations. Still, some
analysts point out that Google's growth is slowing, especially in the United States. The extent to which
that slowdown is the fault of the economy or just the size and maturity of Google's business remains a
matter of debate on Wall Street.
Fox acknowledged that searches and clicks in some areas, including real estate and travel, have
grown more slowly recently. But he noted that there is not an exact correlation between clicks and
revenue: "Clicks are only part of the story."
The idea of linking ads with search results was first developed not by Google but by GoTo9.com,
which later changed its name to Overture Services and then was bought in 2003 by Yahoo. Overture
ranked ads based on how much advertisers were willing to bid for a certain keyword. The higher the
bid, the better the placement.
http://www.iht.com/bin/printfriendly.php?id=13386562
2008/6/22
Counting the clicks, and the money, at Google - Print Version - International He... 第 2 頁，共 3 頁
As Google's engineers developed their own search advertising system, they understood early on that
giving top billing to the highest bidder would have little benefit for Google if that ad did not attract
clicks. That is because advertisers typically pay Google only when a user clicks on their ad. So Google
decided to rank ads based on a combination of bid price and "click-through rate," the frequency with
which users click on a given ad.
Fox's team took things from there and gradually became better at figuring out what ads would click
with users. Yahoo tried to catch up by building a new search advertising system that works more like
Google's. It helped increase revenue, but by Yahoo's own account, Google still earns 60 percent to 70
percent more on average than Yahoo on every search. Microsoft has also lagged, in part because it
lacks enough advertisers. It acknowledged as much with its recent attempt to buy Yahoo.
Fox said Google's ability to constantly fine-tune its operations was intricately linked with its obsession
with measuring just about everything that happened on its system.
The tools to do so, however, were not always there. About four years ago, as revenue was more than
doubling every year and profit was growing even faster, top executives became concerned that
Google's business could be riding a bubble in online advertising.
Traffic was growing rapidly, as was the average price that advertisers were paying for clicks. But Fox
and others realized that measuring the average cost-per-click was not good enough. Google users
might be clicking on more high-priced ads and fewer lower-priced ads. That would cause the average
cost-per-click to rise, but it would say little about the health of the overall system.
So Varian and Diane Tang, principal engineer in the ads quality group, helped devise what they call a
basket of keywords. Much like the consumer price index, a basket of goods and services that
economists use to track inflation, the measure is made up of a broad sample of keywords and is
weighted to make it statistically accurate. This internal benchmark helps Google get a clearer picture
of its performance.
As measurements improved, Fox's team was able to unleash a stream of experiments meant to
optimize the ad system. They evaluated changes to things as diverse as the clickable area and
background color of ads, and the criteria for placing ads above search results, rather than alongside
them.
Over time, the company also looked beyond click-through rates to rank ads. Google now takes into
account the "landing page" that the ad links to, and, for example, gives low grades to pages whose
sole purpose is to show more ads. Soon, the loading speed of a landing page will also be considered,
Mr. Fox said.
These factors contribute to an ad's "quality score." The higher that score, the less the advertiser has to
bid to secure top billing. For example, an advertiser who offers to pay $1 per click to attract those
searching for "vacation rentals in Colorado" may receive more prominent placement than another who
bids $1.50 for the same query but has a lower quality score. An advertiser with a very low quality
score may have to bid so much for placement as to make it uneconomical.
Quality scores work as an incentive to advertisers to improve their ads, which benefits users and, in
turn, benefits Google, Fox said.
Not all advertisers appreciate Google's approach. Many complain that despite efforts by Google to be
more transparent, they remain in the dark about what really goes on inside the company's ad
machine.
"To the extent that Google is a black box, it is not a good thing for advertisers," said Anil Kamath, cofounder and chief technology officer of Efficient Frontier, which runs search advertising campaigns for
marketers. Kamath said Google still offered the most effective system for search marketers, but said
many advertisers complain that the company was, in essence, deciding who can and cannot advertise
on its system.
By the nature of their work, Fox and other members of the Revenue Force have a front-row seat to the
sometimes peculiar relationship between world events and Google's business.
In mid-February, for instance, the group was taken aback when they saw the number of searches drop
unexpectedly. With their antennas keenly tuned to any sign that the economic slowdown could be
http://www.iht.com/bin/printfriendly.php?id=13386562
2008/6/22
Counting the clicks, and the money, at Google - Print Version - International He... 第 3 頁，共 3 頁
hitting Google's business, members of the team rushed to come up with a diagnosis. That meant
poring over statistics, calling field offices and checking data centers worldwide to ensure none were
afflicted by bugs.
The team eventually determined that Google was suffering from a series of unrelated minor ailments.
The celebrations of Mardi Gras and the Chinese New Year were keeping people away from their
computers, while bad weather had knocked out electricity in parts of China, Varian said.
Other events have given Google unexpected increases in traffic because they kept people at home,
like heavy rains and flooding in England last summer and a transport strike in France last fall.
"Bad weather is good for Google," Varian said, "as long as it is not too bad."
Notes:
Copyright © 2008 The International Herald Tribune | www.iht.com
http://www.iht.com/bin/printfriendly.php?id=13386562
2008/6/22
MS&E247s International Investments
8/14/09 Final Exam Page 16 of 23
Question VIII (25 points – The exiting strategy of the economic stimulus program)
Read the following Wall Street Journal article about the end of recession and exiting strategy. Then answer the
questions that follow.
ECONOMIC FORECASTING
Many of the economists said there is little to be
AUGUST 11, 2009.
gained by changing the Fed chairman, especially
Economists Call for Bernanke to Stay, Say Recession
considering the massive task at hand for the central
Is Over .
bank as the economy emerges from the recession.
By PHIL IZZO
Economists are nearly unanimous that Ben
Bernanke should be reappointed to another term as
Federal Reserve chairman, and they said there is a
71% chance that President Barack Obama will ask
him to stay on, according to a survey.
Meanwhile, the majority of the economists The Wall
Street Journal surveyed during the past few days
said the recession that began in December 2007 is
now over. Battling the downturn defined most of Mr.
Bernanke's term, which began in early 2006 and
expires in January, and economists say his handling
of the crisis has earned him four more years as Fed
chief.
"He deserves a lot of credit for stabilizing the
financial markets," said Joseph Carson of
AllianceBernstein. "Confidence in recovery would be
damaged if he was not reappointed."
The Journal surveyed 52 economists; 47 responded.
After months of uncertainty, economists are finally
seeing a break in the clouds. Forecasts were revised
upward for every period, with 27 economists saying
the recession had ended and 11 seeing a trough this
month or next. Gross domestic product in the third
quarter is now expected to show 2.4% growth at a
seasonally adjusted annual rate amid signs of life in
the manufacturing sector, partly spurred by inventory
adjustments and strong demand for the "cash for
clunkers" car-rebate program.
A better-than-expected employment report for July,
where employers cut 247,000 jobs and the jobless
rate fell for the first time in 15 months, suggests the
worst is over. The unemployment rate is still
expected to rise to 9.9% by December, but
economists forecast that the economy will shed far
fewer jobs over the next 12 months than they had
forecast last month.
"Continuity is critical as we emerge from this crisis.
Otherwise we could slip back in again," said Diane
Swonk of Mesirow Financial. "Bernanke is the best
suited to undo what has been done when the time
comes."
The Fed has taken unprecedented steps in an effort
to avoid another Great Depression, and its exit
strategy remains a key question. Some hints may
emerge as the central bank's August policy meeting
comes to an end Wednesday. The Fed's key policymaking tool, the federal-funds rate, isn't likely to
change at this meeting or any time soon.
8/14/09 Final Exam Page 17 of 23
MS&E247s International Investments
Only six economists expect the Fed to raise the
federal-funds rate, now between 0% and 0.25%, this
year. Most expect an increase at some point in 2010,
but more than a quarter of respondents don't see the
rate moving until 2011 or later.
"The exit strategy will be very, very slow and
cautious," said John Silvia of Wells Fargo. "The Fed
will unwind the balance sheet before they raise the
fed funds rates."
The Fed's balance sheet -- the total value of all its
loans and securities holdings -- had more than
doubled during the course of the crisis to more than
$2 trillion, as lending facilities expanded in an effort
to unfreeze credit markets. But as markets get back
to normal, demand already has begun to wane, and
the balance sheet has started to shrink. Now the
composition of the balance sheet has begun to shift
to Treasurys, mortgage-backed securities and
agency debt as the Fed moves through a $1.75
trillion program announced in March to bring down
long-term interest rates.
The Fed is deciding at this week's meeting whether
to let that program run its course and how best to
communicate its intentions to markets.
f.
Whatever the Fed decides, the economists
expressed some confidence that the central bank will
be dealing with how to manage a recovery, not
another recession. They expect GDP growth to
remain above 2% at an annualized rate through the
first half of next year, and they put the chances at
just 20% of a "double-dip" second downturn before
2010.
But some said a recovery could make Mr.
Bernanke's road to reappointment more rocky. "Once
it is perceived that the economy is on its way to
recovery, it gives Obama the opportunity to put in his
own person," Mr. Silvia said. "It could be like Great
Britain at the end of World War II. 'Thank you for all
the hard work, Mr. Churchill, but we're going to bring
someone else in to handle the next phase.'" Former
president George W. Bush appointed Mr. Bernanke
to succeed the departing Alan Greenspan.
Presidents appoint Fed chiefs to four-year terms, and
there are no term limits. Mr. Bernanke's term expires
Jan. 31.
Though the economists were overwhelmingly
supportive of Mr. Bernanke, they don't think his
tenure was without mistakes. A slow initial response
to the credit squeeze and the decision to let Lehman
Brothers fail were cited as the biggest errors.
(5 points) Define exit strategy in the context of the article.
g. (5 points) Is the exit strategy a stabilizing intervention? Discuss.
h. (5 points) Is the exit strategy a sterilization intervention? Explain.
i.
(10 points) What kind of exit strategy you will devise now for implementing in (i) six months
from today, and (ii) twelve months from today? How will your strategies affect US interest rate
and US currency value? Can you, the promising future candidate of the Chair of the Federal
Reserve afford be too optimistic? Be overly cautious? Elaborate.
[Answer to Question VIII, 25 points]
MS&E247s International Investments
8/14/09 Final Exam Page 18 of 23
MS&E247s International Investments
8/14/09 Final Exam Page 19 of 23
Question X (25 points – hedging with futures and options)
Palmfue expects to receive royalty payments totaling £6.25 million next month. It is
interested in protecting these receipts against a drop in the value of the pound. It can sell
30-day pound futures at a price of $1.6513 per pound or it can buy pound put options with
a strike price of $1.6612 at a premium of 2.0 cents per pound. The spot price of the pound
is currently $1.6560, and the pound is expected to trade in the range of $1.6250 to
$1.7010. Palmfue's treasurer believes that the most likely price of the pound in 30 days
will be $1.6400.
a. (5 points) How many futures contracts will Palmfue need to protect its receipts? How
many options contracts? Under what condition (if any, you may be creative) would
you recommend Palmfue to hedge 50% of its receipts with futures and the rest with
options?
b. (5 points) Diagram Palmfue's profit and loss associated with the put option position
and the futures position within its range of expected exchange rates. Ignore
transaction costs and margins.
c. (5 points) Calculate what Palmfue would gain or lose on the option and futures
positions within the range of expected future exchange rates and if the pound settled
at its most likely value.
d. (5 points) What is Palmfue's break-even future spot price on the option contract? On
the futures contract?
e. (5 points) Calculate and diagram the corresponding profit and loss and break-even
positions on the futures and options contracts for those who took the other side of
these contracts.
Hint:
MS&E247s International Investments
8/14/09 Final Exam Page 20 of 23
[Answer to Question X, 25 points]
a. Using CME ￡ options, size of ￡62,500,
# of ￡ options = 6,250,000 / 62,500 = 100
Using CME ￡ futures, size of ￡62,500
# of ￡ futures = 6,250,000 / 62,500 = 100
when one wants to diversify the default risk.
b.
$ gain/
loss
65,750
40,500
futures
Expected
Exchange
rate
1.6612
-50,000
-124,250
b. Options
6.25M (1.6612 – 1.6250) = $226,250
Cost = 0.02 x 6.25M = $125,000
Gain at $1.6250/￡ = 226,250 – 125,000 = 101,250
Loss when rate than $1.6612/￡ = -$125,000
c. Futures
Gain at $1.6250/￡ = 6.25M (1.6513 – 1.6250) = $164,375
Loss at $1.7010/￡ = 6.25M (1.6513 – 1.7010) = -$310,625
At most likely value,
Options: 6.25M (1.6612 – 1.6400) = $132,500
1.7010
Put option
MS&E247s International Investments
8/14/09 Final Exam Page 21 of 23
Cost = 0.02 x 6.25M = $125,000
Gain = $132,500 – 125,000 = $7,500
Futures: Gain = 6.25M (1.6513 – 1.6400) = $70,625
d. Options: Gain = 6.25M (1.6612 – x) – 125,000 = 0 => x = $1.6412/￡
Futures: Gain = 6.25M (1.6513 – x) = 0 => x = $1.6513/￡
MS&E247s International Investments
8/14/09 Final Exam Page 23 of 23
Question XI (25 points – hedging contingent litigation)
iNOS computer in the States had a wonderful year selling the world’s lightest cellular phone
airweight. When they celebrate for the success, the general manager iNOS received a lawyer’s
letter, indicating that iNOS’ heat radiating technology infringed the patent of the current market
leader SONi and SONi has filed a lawsuit and asked for a claim of ￥100 billion to resolve the issue.
iNOS’ lawyer said the company may lose the case with a probability of 50%. The CFO was called
in to arrange for the financial hedging of the contingent lawsuit loss. You are hired by the CFO to
list all possible ways of hedging with financial derivatives; and you are asked to provide detailed
discussion of advantages and disadvantages of each alternative. You are also asked to illustrate
with all possible scenarios when the hedge is done with (i) futures, and (ii) options. Please be
quantitative, i.e., providing exact numbers of contracts to purchase in futures and options.
[Answer to Question XI, 25 points]