please answer 8 questions (out of ten) professionally ......interest that sony will pay. thus, sony...

8/14/09 Final Exam of 23

MS&E 247S International Investments Summer 2009 Instructor: Yee-Tien Fu Friday 8/14/09 7-10 pm 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 _________________________ Major _____________________________

Undergraduate / Graduate 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 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: 8.00% bid and 8.10% offered against the 6-month dollar LIBOR Japanese yen: 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 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

extra extra Effective dollar yen yen

Year notional $ dollars notional ¥ interest interest cash flows0 98.13 -100.00 -98.13 9,850.00 9,665.31

0.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.141 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14

1.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.142 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14

2.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.143 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14

3.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.144 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.14

4.5 -4.25 4.00 4.25 -226.55 0.25 22.59 -249.145 -104.25 104.00 104.25 -10,076.55 0.25 22.59 -10,099.14

AIC 4.49% 4.00% 4.49% 2.30% 2.75%Annual AIC 9.17% 8.16% 9.17% 4.65% 5.57%

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.

Swap Receipts (+) and Payment (-)with Tokyo Big Bank

(All cash flows are in millions of dollars or yen)

Dollar Bond Issue

MS&E247s International Investments

8/14/09 Final Exam 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]

Ted

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credit: Fouad Zakharia


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]

Ted

註解

credit: Yu Chiu



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.



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 two-year 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 1,100

1,000 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



• M = 1, B=740.740

• 1 * 1,000 – 740.74 = 259.26 => replace 200 M (909.0909) – (1 + .08) (B) = 109.0909 MM ((775511..33114488)) –– ((11 ++ ..0088)) ((BB)) == 00

• M = 0.69, B = 480 0.69 * 826.4463 – 480 = 91.43 => replace 26.4463 [Answer to Question V, 25 points]

Ted

註解

credit: Alexandros Trimis

Ted

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credit: Yuxin Chuah



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.

Ted

註解

credit: Chengwu Shao



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



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

Ted

註解

credit: Chengwu Shao



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 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.

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?



[Answer to Question VIII, 25 points]

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

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Chapter 12 Currency and Interest Rate Options

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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.

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A good investor has to pay attention to corporate governance and strength/weakness. Google is a technology firm and hence its technological superiority is the key concern. See the New York Times / International Herald Tribune article.

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, co-founder 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



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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





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 AUGUST 11, 2009. Economists Call for Bernanke to Stay, Say Recession Is Over . 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.

Many of the economists said there is little to be gained by changing the Fed chairman, especially considering the massive task at hand for the central bank as the economy emerges from the recession.

"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 policy-making tool, the federal-funds rate, isn't likely to change at this meeting or any time soon.



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.

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.

f. (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]



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:



[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.

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

-124,250

1.7010 1.6612

Expected Exchange rate

$ gain/ loss 65,750

40,500

-50,000 Put option

futures



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/￡

Ted

註解

credit: Yuxin Chuah



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]

Ted

註解

credit: Yuxin Chuah

please answer 8 questions (out of ten) professionally ......interest that sony will pay. thus, sony...

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