考試時間：13：30 - 15：00

以英文出題之題目可以中文回答

Everyone has to do your best to pass this course.

# China Real GDP Growth

1992 - 2017 | Quarterly

| % | CEIC

The Gross Domestic Product (GDP) in China expanded 6.8 % YoY in Sep 2017, following a growth of 6.9 % in the previous quarter. Real GDP Growth YoY data in China is updated quarterly, available from Mar 1992 to Sep 2017, with an average rate of 9.4 %. The data reached an all-time high of 15.3 % in Mar 1993 and a record low of 6.4 % in Mar 2009. CEIC calculates Real GDP Growth from quarterly Real GDP Index. The National Bureau of Statistics provides Real GDP Index, at previous year prices.

In the latest reports, Nominal GDP of China reached 3,176.1 USD bn in Sep 2017. Its GDP deflator (implicit price deflator) increased 4.1 % in Sep 2017. GDP Per Capita in China reached 8,127.5 USD in Dec 2016. Its Gross Savings Rate was measured at 46.4 % in Dec 2016.

https://www.ceicdata.com/en/indicator/china/real-gdp-growth

# Steve Jobs's Top 10 Rules For Success

# Beware False Signals From the P/E Ratio

The price-to-earnings (P/E) ratio is a fairly simple tool for assessing company value. Judging by how often the P/E ratio gets touted—by Wall Street analysts, the financial media and colleagues at the office water cooler—it's tempting to think it's a foolproof tool for making wise stock investment choices. Think again—the P/E ratio is not always reliable. There are plenty of reasons to be wary of P/E-based stock valuations. (See also: *Financial Ratios*.)

## Calculating the P/E Ratio: A Quick Review

On the surface, calculating price to earnings is fairly straightforward. The first step in generating a P/E ratio is to calculate earnings per share (EPS). Typically, EPS equals the company's after-tax profits divided by the number of shares in issue.

EPS = Post-Tax Profits / Number of Shares

From the EPS, we can calculate the P/E ratio. The P/E ratio equals the company's current market share price divided by the earnings per share for the previous year.

P/E = Share Price / EPS

The P/E ratio is supposed to tell investors how many years' worth of current earnings a company will need to produce in order to arrive at its current market share value. So, let's say the imaginary company Widget Corp. earned $1 per share over the past year and it's trading at $10.00 per share. The P/E ratio would be $10/$1 = 10. What this tells us is that the market prices it at 10 times earnings. Or in other words, for every share purchased, it will take 10 years of cumulative earnings to equate to the current share price. Naturally, investors want to be able to buy more earnings for every dollar they pay, so the lower the P/E ratio, the less expensive the stock.

The ratio sounds simple enough, but let's look at some of the dangers associated with taking P/E ratios at face value.

The first part of the P/E equation—price—is straightforward. We can be fairly confident what the market price is. On the other hand, coming up with an appropriate earnings number can be tricky. You have to make a lot of decisions how to define earnings.

## What's In Those Earnings?

For starters, earnings aren't always clear cut. Earnings can be affected by unusual gains or losses which sometimes obscure the true nature of the earnings metric. What's more, reported earnings can be manipulated by company management to meet earnings expectations, while creative accounting choices—shifting depreciation policies or adding or subtracting non-recurring gains and expenses—can make bottom line earnings numbers bigger and, in turn, P/E ratios, smaller and the stock appear less expensive. Investors need to be wary of how companies arrive at their reported EPS numbers. Appropriate adjustments often have to be done in order to obtain a more accurate measure of earnings than what is reported on the balance sheet.

## Trailing or Forward Earnings?

Then there is the matter of whether to use trailing earnings or forward earnings figures.

Located right in the company's latest published income statement, historic earnings are easy to find. Unfortunately, they are not much use for investors, since they say very little about what earnings are in store for the year and years ahead. It's the company's future earnings that investors are interested in most since as they reflect a stock's future prospects.

Forward earnings (also called future earnings) are based on the opinions of Wall Street analysts. Analysts, if anything, typically tend to be overoptimistic in their assumptions and educated guesses. At the end of the day, forward earnings suffer the problem of being a lot more useful than historic earnings but prone to inaccuracies.

## What About Growth?

The biggest limitation of the P/E ratio: It tells investors next to nothing about the company's EPS growth prospects. If the company is growing quickly, you will be comfortable buying it even it had a high P/E ratio, knowing that growth in EPS will bring the P/E back down to a lower level. If it isn't growing quickly, you might shop around for a stock with a lower P/E ratio. It is often difficult to tell if a high P/E multiple is the result of expected growth or if the stock is simply overvalued.

A P/E ratio, even one calculated using a forward earnings estimate, doesn't always tell you whether or not the P/E is appropriate to the company's forecasted growth rate. So, to address this limitation, we turn to another ratio, the PEG ratio:

PEG = PE/forecast EPS growth rate over the next 12 months

In a nutshell, the lower the PEG ratio, the better. A PEG of 1 suggests that the P/E is in line with growth; below 1 implies that you are buying EPS growth for relatively little; a PEG greater than 1 could mean the stock is overpriced. However, even when the P/E ratio is standardized for growth, you are basing your investment decision on outside estimates, which may be wrong. (See also: *PEG Ratio Nails Down Value Stocks*.)

## What About Debt?

Finally, there's the tricky issue of a company's debt load. The P/E ratio does nothing to factor in the amount of debt that a company carries on its balance sheet. Debt levels have an impact on financial performance and valuation, yet the P/E doesn't allow investors to make apples-to-apples comparisons between debt-free firms and those bogged down with outstanding loans and liabilities.

One way to address this limitation is to consider a company's enterprise value or EV in place of its Price (P).

(simplified) EV = Market Capitalization + Net Debt

Let's say the Widget Corp., with a market share price of $10 per share, also carried the equivalent of $3 per share of net debt on its balance sheet. The company, then, would have total enterprise value of $13 per share. If Widget Corp. produced EPS this year of $1, its P/E ratio would be 10. But more sophisticated investors would perform the calculation with enterprise value in the numerator and EBITDA in the denominator.

## The Bottom Line

Sure, the P/E ratio is popular and easy to calculate. But it has big shortcomings that investors need to consider when using it to assess stock values. Use it carefully. No single ratio can tell you all you need to know about a stock. Be sure to use a variety of ratios to get a fuller picture of financial performance and stock valuation.

Read more: Beware False Signals From The P/E Ratio

# Beware False Signals From the P/E Ratio

Read more: Beware False Signals From The P/E

The price-to-earnings (P/E) ratio is a fairly simple tool for assessing company value. Judging by how often the P/E ratio gets touted—by Wall Street analysts, the financial media and colleagues at the office water cooler—it's tempting to think it's a foolproof tool for making wise stock investment choices. Think again—the P/E ratio is not always reliable. There are plenty of reasons to be wary of P/E-based stock valuations. (See also: *Financial Ratios*.)

## Calculating the P/E Ratio: A Quick Review

On the surface, calculating price to earnings is fairly straightforward. The first step in generating a P/E ratio is to calculate earnings per share (EPS). Typically, EPS equals the company's after-tax profits divided by the number of shares in issue.

EPS = Post-Tax Profits / Number of Shares

From the EPS, we can calculate the P/E ratio. The P/E ratio equals the company's current market share price divided by the earnings per share for the previous year.

P/E = Share Price / EPS

The P/E ratio is supposed to tell investors how many years' worth of current earnings a company will need to produce in order to arrive at its current market share value. So, let's say the imaginary company Widget Corp. earned $1 per share over the past year and it's trading at $10.00 per share. The P/E ratio would be $10/$1 = 10. What this tells us is that the market prices it at 10 times earnings. Or in other words, for every share purchased, it will take 10 years of cumulative earnings to equate to the current share price. Naturally, investors want to be able to buy more earnings for every dollar they pay, so the lower the P/E ratio, the less expensive the stock.

The ratio sounds simple enough, but let's look at some of the dangers associated with taking P/E ratios at face value.

The first part of the P/E equation—price—is straightforward. We can be fairly confident what the market price is. On the other hand, coming up with an appropriate earnings number can be tricky. You have to make a lot of decisions how to define earnings.

## What's In Those Earnings?

For starters, earnings aren't always clear cut. Earnings can be affected by unusual gains or losses which sometimes obscure the true nature of the earnings metric. What's more, reported earnings can be manipulated by company management to meet earnings expectations, while creative accounting choices—shifting depreciation policies or adding or subtracting non-recurring gains and expenses—can make bottom line earnings numbers bigger and, in turn, P/E ratios, smaller and the stock appear less expensive. Investors need to be wary of how companies arrive at their reported EPS numbers. Appropriate adjustments often have to be done in order to obtain a more accurate measure of earnings than what is reported on the balance sheet.

## Trailing or Forward Earnings?

Then there is the matter of whether to use trailing earnings or forward earnings figures.

Located right in the company's latest published income statement, historic earnings are easy to find. Unfortunately, they are not much use for investors, since they say very little about what earnings are in store for the year and years ahead. It's the company's future earnings that investors are interested in most since as they reflect a stock's future prospects.

Forward earnings (also called future earnings) are based on the opinions of Wall Street analysts. Analysts, if anything, typically tend to be overoptimistic in their assumptions and educated guesses. At the end of the day, forward earnings suffer the problem of being a lot more useful than historic earnings but prone to inaccuracies.

## What About Growth?

The biggest limitation of the P/E ratio: It tells investors next to nothing about the company's EPS growth prospects. If the company is growing quickly, you will be comfortable buying it even it had a high P/E ratio, knowing that growth in EPS will bring the P/E back down to a lower level. If it isn't growing quickly, you might shop around for a stock with a lower P/E ratio. It is often difficult to tell if a high P/E multiple is the result of expected growth or if the stock is simply overvalued.

A P/E ratio, even one calculated using a forward earnings estimate, doesn't always tell you whether or not the P/E is appropriate to the company's forecasted growth rate. So, to address this limitation, we turn to another ratio, the PEG ratio:

PEG = PE/forecast EPS growth rate over the next 12 months

In a nutshell, the lower the PEG ratio, the better. A PEG of 1 suggests that the P/E is in line with growth; below 1 implies that you are buying EPS growth for relatively little; a PEG greater than 1 could mean the stock is overpriced. However, even when the P/E ratio is standardized for growth, you are basing your investment decision on outside estimates, which may be wrong. (See also: *PEG Ratio Nails Down Value Stocks*.)

## What About Debt?

Finally, there's the tricky issue of a company's debt load. The P/E ratio does nothing to factor in the amount of debt that a company carries on its balance sheet. Debt levels have an impact on financial performance and valuation, yet the P/E doesn't allow investors to make apples-to-apples comparisons between debt-free firms and those bogged down with outstanding loans and liabilities.

One way to address this limitation is to consider a company's enterprise value or EV in place of its Price (P).

(simplified) EV = Market Capitalization + Net Debt

Let's say the Widget Corp., with a market share price of $10 per share, also carried the equivalent of $3 per share of net debt on its balance sheet. The company, then, would have total enterprise value of $13 per share. If Widget Corp. produced EPS this year of $1, its P/E ratio would be 10. But more sophisticated investors would perform the calculation with enterprise value in the numerator and EBITDA in the denominator.

## The Bottom Line

Sure, the P/E ratio is popular and easy to calculate. But it has big shortcomings that investors need to consider when using it to assess stock values. Use it carefully. No single ratio can tell you all you need to know about a stock. Be sure to use a variety of ratios to get a fuller picture of financial performance and stock valuation.

Read more: Beware False Signals From The P/E Ratio https:

2. International Financial Management Supplement-How To Find PE And PEG Ratios.pdf

3. Introduction to Modern Portfolio Theory.pdf

4. Risk managements in financial markets-Basic concepts (Dr. Chao in NHU).pptx

# The Amazon Effect On The U.S. Economy

Amazon.com Inc. (AMZNAMZNAmazon.com Inc 1,137.29+0.94%) is everywhere. By disrupting the way people shop, Amazon has created economic ripple effects that go far beyond the customer’s wallet to directly and indirectly impact economic activity, whether that impact is inflation, jobs or investment.

## The Wallet Opener

Amazon started with books and then added pretty much everything you can think of, from engagement rings to coffins, for sale on their site. Add the convenience of having it delivered promptly to your doorstep, and customers have rewarded Amazon with open wallets, so much so that North American electronics and general merchandise sales for the company have grown from a mere 2% of total general merchandise retail sales (GAFO) in 2006 to more than 60% in 2016. Similarly over the past 10 years, this category of Amazon sales has increased from a little over 7% of e-commerce retail sales to more than 66%. And the growth is accelerating. Last year alone, this segment saw a 28% jump in sales compared to 2015.

If you consider a more macro picture, consumers spending more is a good sign because it contributes to the GDP. Having said that, in no way is consumer spending on Amazon significant enough yet to tip the GDP scale. But it could be in future.

## The Inflation Killer

Amazon has disrupted traditional retail and accelerated the demise of struggling players. Without storefronts the company’s overhead costs are significantly lower than other retailers giving them an edge to undercut on prices and operate on wafer thin profit margins.

That makes some economy watchers nervous about Amazon’s deflationary impact. Ideally, low unemployment is accompanied by wage growth, which in turn fuels inflation as companies pass on the cost to consumers. This is the logic of the Phillip’s Curve, but Amazon has disrupted that as well.

Higher competition and lower prices limit the companies’ ability to pass on any wage increases to consumers. Those worries were recently echoed in the wake of the Whole Foods acquisition where remarks by Chicago Federal Reserve President Charles Evans were construed in that context.

“We know that technology is disruptive. It’s changing a number of business models that used to be very successful, and you have to wonder if certain economic actors can continue to maintain their price margins, or if they are under threat from additional competition,” Evans said according to Bloomberg. “And that could be an undercurrent for holding back inflation.”

## The Employer

In its latest annual report Amazon lists its total number of employees at 341,400. This includes both full-time and part-time employees. For a company this size that number is low but expected because Amazon does not have a significant storefront presence like Wal-Mart Stores Inc. (WMTWMTWal-Mart Stores Inc99.62+10.90%) which employs 2.3 million people worldwide.

Amazon also engages third party contractors/companies for tasks like deliveries.

Those people go door to door dropping off Amazon packages but are not employees for the company. Does that matter? Yes and no.

In a way, these are jobs that are that people are doing, therefore, some credit could go to Amazon for job creation. On the other hand hiring contractual workers helps the company keep its costs in check. Amazon has in the past been sued by contingent workers claiming they received less than minimum wage, meanwhile there were others that criticized the company for harsh working conditions.

Another angle of the jobs conversation is how many jobs Amazon is eliminating. Considering the company is hurting other retailers, forcing them to shutter stores and cut back on costs, any job gains at Amazon may not in fact mean anything. Though the actual extent of job loss is hard to determine according to research by the Institute of Local Self-Reliance (ILSR), in 2015 Amazon’s impact on jobs in the U.S. was a net loss estimated at 148,774 jobs. Another estimate by American Booksellers Association (ABA) and Civic Economics pegged net job loss at 222,000 for 2015. This gap could increase further with automation.

Amazon’s quest for innovation and technology to achieve operational efficiency has people worried about elimination of jobs. Those worries are not far-fetched considering that the company is testing its Amazon Go store in Seattle.

## The Facilitator

Amazon’s logistics infrastructure doesn’t just help it ship to consumers all across the globe, it also aids another group of people: small businesses. Listing their products on Amazon helps them increase their customer reach and the delivery essentially becomes Amazon’s headache.

“More than 100,000 entrepreneurs achieved over $100,000 in sales selling on Amazon in 2016,” the company said in a press release earlier this year.

As small businesses thrive, it will lead to further job creation and spending. Amazon says that 600,000 jobs were created outside of the company as a result of the Amazon Marketplace for small businesses and entrepreneurs.

## The Tax Payer

Income Tax: Does Amazon pay tax? Yes. Is it a lot? No. Principally, President Trump’s claim about Amazon not paying any tax is wrong, however, a 2016 analysis by the New York Times and S&P Global Market Intelligence reveals that from 2007 to 2015, Amazon paid taxes at an average rate of 13%, nearly half of the 26.9% average for the S&P 500 companies. But it wasn’t alone. Other tech giants like Facebook, Alphabet and Apple also had an average tax rate significantly lower than the average.

Sales Tax: Not having a physical presence or employees in certain states also saved Amazon sales tax. Sales tax is a complicated subject with rates and rules varying across states. The most simple explanation in this context is that tax laws in many states need the physical presence of an online retailer in the state in order to collect sales tax. Therefore by not having its own warehouses or employees in certain states, Amazon saved on tax.

This however, wasn’t a problem specific to Amazon as this applied to any online retailer shipping goods across stateliness. The National Conference of State Legislatures in its most recent estimate pegs the 2015 tax revenue loss due to this peculiarity at $25 billion. Amazon acknowledged this issue in its annual reports, and over a period of time it started collecting sales tax on all goods that were sold in or delivered to states that have such a tax. Five states: Alaska, Delaware, Oregon, New Hampshire and Montana do not impose a sales tax.

The sales tax issue gets even more complicated when it pertains to third party sellers.

## The Investment

Amazon is in the race to become the first trillion dollar company by market cap. This year it hit many milestones including crossing the $1,000 mark for its share price. A recent jump in shares briefly crowned CEO Jeff Bezos, who owns 17% in the company, as the richest man in the world.

The run for Amazon shares has been phenomenal for many years. The company made its stock market debut 20 years ago and $100 invested then would have turned close to a spectacular $63,000. (See also: *If You Had Invested Right After Amazon's IPO*.)

In the past 10 years, the stock has given a whopping 1180% return, as of August 17, 2017, while the 5 year return was nearly 300%. The S&P 500 meanwhile returned only 68% over the 10 year period. Imagine the wealth that was created by Amazon's stock return and the potential economic activities it could finance in the future.

## The Investor

Amazon isn’t just a bumper investment for those who go in at the right time, it is a big investor itself. As of 2016 year-end, the company held a portfolio of $19.6 billion in cash equivalents and marketable debt securities. It also had $467 million worth of equity investments or equity warrants in public and private companies.

# Why Stock Investors Shouldn't Sell Now

Investors should remain invested in equities and not get scared into selling by pullbacks in the market, according to strategists at Morgan Stanley

(MSMSMorgan Stanley48.63+1.10%), as quoted by Bloomberg. In a detailed report of more than 40 pages, Morgan Stanley acknowledges that "most major asset classes look rich versus history," but they add that "equities can still get richer into end-of-cycle," per Bloomberg.

Three factors typically send economies into recession and stock markets tumbling, Morgan Stanley says: excessive tightening of credit by central banks, large increases in debt, and extreme optimism among investors that former Federal Reserve Chairman Alan Greenspan once dubbed "irrational exuberance." Morgan Stanley does not see any of these three factors in place right now, Bloomberg says.

## How Long Can the Bulls Run?

Joseph Zidle of Bernstein Portfolio Advisors LLC, recently among the most bullish strategists, now expects excessive tightening by the Fed to be an inevitable recessionary trigger, though he adds that the bull market may have many more months left to run. Meanwhile, another prominent strategist, Jonathan Golub of Credit Suisse Group (CS

), expects the S&P 500 Index (SPX) to reach 2,875 in 2018, an advance of nearly 12% from its opening on November 15. (For more, see also:*Get Ready For The Coming Bear Market and Recession*.)

Strategists at Charles Schwab Corp. (SCHWSCHWCharles Schwab Corp44.73+0.43%) remain bullish on equities, for a variety of reasons. Among these: December historically sees gains, including the so-called Santa Claus rally; all major world economies continue to grow; corporate profits are still rising; and the markets are habitually shrugging off political risks. (For more, see also: *Charles Schwab Upbeat as Impact Conference Kicks Off*.)

Investors should be on the lookout for three leading indicators of a downturn in the economy and in equities, Morgan Stanley says. First, when the currencies of emerging market countries and key commodities peak in value versus the U.S. dollar, the S&P 500 tends to reach its own peak about seven to 10 months later. Second, credit spreads, or the difference in yield on U.S. Treasury debt and lower-quality bonds with similar maturities issued by corporate borrowers, tend to bottom out about four months before the U.S. stock market peaks. Third, declining measures of economic activity, such as manufacturing surveys, orders for durable goods, and average weekly hours worked, tend to precede an equity market peak by four to six months.

## Actions to Take Now

Morgan Stanley suggests keeping some cash at the ready as a prudent measure right now. They also recommend that cautious investors shift their equity holdings into call options on the S&P 500 as a way to participate in further upside while capping the downside. They also recommend using a bear put spread options strategy on high yield debt as a hedge, Bloomberg indicates. (For more, see also: *Stock Investors' Handbook for a Bear Market*.)

## The Economics of Scarcity

Meanwhile, publicly-traded stocks are becoming an increasingly scarce commodity, driving equity prices upward for this reason alone, the Financial Times reports. Share repurchases by U.S. corporations since the financial crisis have added up to a staggering figure of nearly $5 trillion, per the FT. According to research by S&P Global, the number of shares outstanding from S&P 500 companies is about the same as it was a decade ago, even as the index has almost doubled in value.

Another factor driving scarcity is the growth of passive investing in index funds and ETFs, the FT adds, citing analysis by Christopher Harvey at Wells Fargo & Co. (WFCWFCWells Fargo & Co54.24+0.92%). As these funds grow in size, they need to buy more of the equities in the market indexes that they track, removing yet more shares from general circulation. This only adds to the scarcity of equity shares in the open market, propping up their prices. Harvey sees a parallel with quantitative easing by central banks, which took government bonds out of the open market, thereby boosting their prices. (For more, see also: *The Incredible Shrinking Stock Market*.)

Read more: Why Stock Investors Shouldn't Sell Now: Morgan Stanley | Investopedia

國際財務管理期中考試題重點

兩重要參考檔案

國際財務管理教案-財務風險管理概論基礎篇

Chapter 1. Risk Management Concepts

直接從International Financial Management 本網址左下方附件下載

考試日期與時間

11月10日(五) 13：30-15：10

International Financial Management Mid-term Exam Main-points

(The foreign students) has been announced.

Please download the following file below the left bottom.

The questions of Mid-term Exam

Reference files

# How To Find P/E And PEG Ratios

Read more: How To Find P/E And PEG Ratios

When reading about or researching company performance, you will often be reflecting on earnings calculations - but do these numbers make any sense to you? And could you tell the difference between a P/E ratio and a PEG ratio?

The stock price (per share) of a company divided by its most recent 12-month earnings per share is called its price-to-earnings ratio (P/E ratio). If this P/E ratio is then divided by expected earnings growth going forward, the result is called the price/earnings to growth ratio (PEG ratio). A lot of the information out there about how to determine a stock's proper ratios and use them to effectively value a stock discusses metrics like the stock's historic ratios, using them to compare industry ratios, or make statements like "a PEG below 1 is good."

This information isn't wrong, but if you need to understand and find these ratios for yourself, you'll need some extra help. Fortunately, with the aid of a simple hand-held financial calculator, there is a simple mathematical approach to finding rational P/E and PEG ratios.

The best way to understand the significance of the P/E ratio is to turn it upside down. If you divide the earnings by the price (E/P) you get the inverse of the P/E ratio, which is called the earnings yield. The earnings yield tells an investor how much return (on a per-share basis) the stock's shareholders earned over the past 12 months, based on the current share price. Remember that earnings, regardless of whether they are paid out in the form of a dividend or retained by the company for reinvestment into further growth opportunities, still belongs to the shareholders. Shareholders hope that these earnings will grow going forward, but there is no way to perfectly predict what that growth will be.

## Earnings Yield Vs. Bond Yields

Investors have a vast array of investment options at their disposal at all times. For the purposes of this discussion, let's assume that the choice is limited to stocks or bonds. Straight bonds, whether government or corporate, pay a guaranteed fixed rate of return for some period of time, as well as a guaranteed return of the original investment at the end of that fixed period. The earnings yield on a stock is neither guaranteed nor of a definite time period. However, earnings can grow, while bond yields remain fixed. How do you compare the two? What are the key factors to consider?

## Growth Rate, Predictability and Fixed-Income Rates

The key factors you need to consider are: growth rate, earnings predictability and current fixed-income rates. Let's assume you have $10,000 to invest and that United States government Treasury bonds of five-year maturity are yielding 4%. If you invest in these bonds, you can earn interest of $400 per year (4% of $10,000) for a cumulative return of $2,000 over five years. At the end of five years, you get your $10,000 investment back when the bond matures. The cumulative return over the five-year period is 20% ($2,000/$10,000).

## Example - Calculating a Stock's P/E

Now, let's assume that you buy stock in XYZ Corp. for $40 per share, and that XYZ had earnings over the last 12 months of $2 per share. The P/E ratio of XYZ stock is 20 ($40/$2). The earnings yield of XYZ is 5% ($2/$40). Over the next five years, XYZ's earnings are expected to grow by 10% per year. Let's further assume that this earnings growth is 100% predictable. In other words, the earnings are guaranteed to grow by 10% per year - no more, no less. What P/E ratio should XYZ stock have to make it an equal investment opportunity to the five-year Treasury bond yielding 4%?

Using a present value/future value calculator, we can determine a mathematical value for XYZ. To do this, we take the 20% cumulative yield of the bond over the next five years and enter that as the future value (FV). Enter "0" as the present value (PV). Enter "5" as the number of periods (n). Enter 10 as the annual interest rate (i). Now, using a beginning period setting (BGN), calculate payment (PMT). The answer will show as -2.98. Drop the negative to find that the comparable earnings yield should be 2.98%. If we divide 1 by 2.98% (.0298) we find that the P/E should be 33.56. Because current earnings per share are $2, the price of the stock should be $67.12 ($2 x 33.56). The earnings yield is 2.98% ($2/$67.12).

If we invest our $10,000 in XYZ stock at that price we get 149 shares. In year one, earnings per share should increase by 10%, from $2 per share to $2.20 per share. Our return will be approximately $328 (149 shares x $2.20 per share). In year two, the earnings return on our investment will increase by another 10% to approximately $360 per share. Year three will be $396, followed by year four at $436 and finally year five at $480. If you add these together, you get a cumulative earnings return of $2,000 - the same as you would have received from the Treasury bond. The stock owner will receive this $2,000 in the form of dividends or an increase in the stock's value or both. (*Note:* For the sake of simplicity we are ignoring the time value of money considerations of receiving cash flows earlier over the five-year period for the Treasury bond as opposed to the stock.)

What is the P/E if XYZ earnings growth is projected to be 20% per year? The answer would be 44.64 and the price of the stock should be $89.28. The earnings yield would be 2.24%. The earnings on your $10,000 (112 shares) investment would be $269, $323, $387, $464 and $557 for a total of $2,000. It seems intuitive that a stock with earnings growth that is projected to be greater than another's would trade at a higher P/E. Now you see why this is the case from a mathematical perspective.

## The Real World

In the example above, the P/E of XYZ rose from 33.56 to 44.64, when earnings expectations rose from 10 to 20%. What happened to the PEG? At 10%, the PEG would be 3.36 (33.56/10). At 20%, the PEG would be 2.23 (44.64/20). All things being equal then, the PEG of higher growth companies will normally be lower than the PEG of slower growing companies, even though the P/E may be higher.

In real life, earnings are not perfectly predictable, so you must adjust your required earnings yield up from the guaranteed yield of bonds to compensate for that lack of predictability. The amount of that adjustment is purely subjective and fluctuates constantly as economic conditions change. In analyzing a particular stock, you need to consider how predictable that company's earnings growth has been in the past as well as possible interruptions to growth going forward.

In the example above, the price of XYZ stock is $40 per share. The reason it's trading for $40 probably revolves around uncertainties regarding the predictability of that expected earnings growth. As a result, the market, based on the cumulative subjective perspective of thousands of investors, has built in a higher return requirement. If XYZ does indeed experience a 10% earnings growth over the next five years, an investor buying the stock at $40 per share will be well rewarded as the earnings stream on $10,000 (250 shares) will be $500, $550, $605, $665 and $732 for a total of $3,052, rather than $2,000. The possibility of this additional return compensates the investor for the risk that the expected earnings growth rate of 10% may not materialize.

## Summing up

Despite the subjective risk-assessment variables, P/E ratios and PEG ratios do have a mathematical rationale. First, the ratios are based on the earnings yield theory, which is married to current fixed rates of return. As interest rates rise, P/E ratios will tend to fall because they're inverse and the earnings yield (E/P) needs to rise to be competitive. As rates fall, P/E ratios tend to rise on average and earnings yields fall.

## The Bottom Line

Over and above the fixed-income impact, P/E ratios will be higher for stocks with more predictable earnings growth and lower for stocks with less predictable earnings growth. If two stocks have comparable levels of predictability, the P/E will be higher for stocks with higher expected earnings growth and lower for stocks with lower expected earnings growth. PEG ratios for slower-growing companies will normally be higher than for faster-growing companies. Using a basic financial calculator, you can determine what these ratios should be at any given point under any given set of circumstances.

http://www.investopedia.com/articles/fundamental-analysis/09/price-to-earnings-and-growth-ratios.asp#ixzz4wuav0gT1

Compounding is the process of generating more return on an asset's reinvested earnings. To work, it requires two things: the reinvestment of earnings and time. Compound interest can help your initial investment grow exponentially. For younger investors, it is the greatest investing tool possible, and the #1 argument for starting as early as possible. Below we give a couple of examples of compound interest.

Example #1: Apple stock

An investment of $10,000 in the stock of Apple (AAPL) that was made on December 31, 1980 would have grown to $2,709,248 as of the market’s close on February 28, 2017 according to Morningstar’s Advisor Workstation tool. This translates to an annual return of 16.75%, including the reinvestment of all dividends from the stock.

Apple started paying dividends in 2012. Even so, if those dividends hadn’t been reinvested the ending balance of this investment would have been $2,247,949 or 83% of the amount that you would have had by reinvesting.

While Apple of one of the most successful companies, and their stock is a winner year-in and year-out, compound interest also works for index funds, which which are managed to replicate the performance of a major market index such as the S&P 500.

Example #2: Vanguard 500 Index

Another example of the benefits of compounding is the popular Vanguard 500 Index fund (VFINX) held for the 20 years ending February 28, 2017.

A $10,000 investment into the fund made on February 28, 1997 would have grown to a value of $42,650 at the end of the 20-year period. This assumes the reinvestment of all fund distributions for dividends, interest or capital gains back into the fund.

Without reinvesting the distributions, the value of the initial $10,000 investment would have grown to $29,548 or 69% of the amount with reinvestment.

In this and the Apple example, current year taxes would have been due on any fund distributions or stock dividends if the investment was held in a taxable account, but for most investors, these earnings can grow tax-deferred in a retirement account such as a employer-sponsored 401(k).

Starting Early

Another way to look at the power of compounding is to compare how much less initial investment you need if you start early to reach the same goal.

A 25-year-old who wishes to accumulate $1 million by age 60 would need to invest $880.21 each month assuming a constant return of 5%.

A 35-year-old wishing to accumulate $1 million by age 60 would need to invest $1,679.23 each month using the same assumptions.

A 45-year-old would need to invest $3,741.27 each month to accumulate the same $1 million by age 60. That’s almost 4 times the amount that the 25-year old needs. Starting early is especially helpful when saving for retirement, when putting aside a little bit early in your career can reap great benefits.

No one investing strategy or approach fits all. Every investor has different reasons for investing, different goals, different time horizons and varying degrees of comfort with investing. It’s important to define and articulate your own parameters.

## Goals

What are your objectives for the money that you will be investing? Is safety of principal with some level of return sufficient? Are you trying to accumulate money for a longer-term goal such as a college education for your kids or perhaps a comfortable retirement for yourself?

You might even have different investments for different goals. The point is that before you decide to invest any money it is important to understand why you are investing and the end result that you are seeking.

Goals and objectives should not be created in a vacuum. You also need to know your risk tolerance and time horizon as part of the goal-setting process.

## Risk tolerance

Risk can mean a lot of things, but in the context of investing it means the risk of losing money. In other words, the risk that the amount of money invested will decrease in value, possibly to zero.

All investing involves risk in one way or another. Stocks can and often do go down in value over certain periods of time—in 2008, the S&P 500 dropped by 37%. While this decline in the stock market was one of the worst in history, less severe market corrections are not uncommon.

How much of a drop in value for your investments can you stomach? Your risk tolerance will likely be in part a function of when you need the money—known as your time horizon—which is usually a function of age. Someone in their 20s or 30s who is saving for retirement shouldn’t give too much thought to fluctuations in the value—known as the volatility—of their investments.

In contrast, someone in their 60s likely will and should have a lower risk tolerance if for no other reason than they don’t have the time to fully recoup a major loss in the value of their investments.

Your investments should be aligned with the time horizon in which you will need the money, especially if some or all of your investments are targeted for a specific goal.

For example, if you are young parents investing for your newborn’s college education, your long time horizon allows you to take a bit more risk in the initial years. When your kid gets to high school, you might adjust the investment mix to help ensure that you don’t suffer any major losses in the years leading up to the start of college.

## Trading Frequency

How long will you stay in one particular investment? Legendary investor Warren Buffett rarely sells a stock he owns and doesn’t get rattled by market fluctuations. This is generally known as a “buy-and-hold” strategy.

At the other extreme are traders who buy and sell stocks on a daily basis. This is fine for professionals, but rarely a good idea for the average investor.

Nobody is advocating that your need to hold an investment forever, and in fact things change and you should be reviewing your individual holdings periodically to ensure they are still appropriate for your situation.

## Knowledge and comfort

Some investment vehicles require sophisticated knowledge and monitoring, while others are more set-and-forget. Your investment decisions should be based on your comfort level and your willingness to devote time to researching your choices.

An easy route is to choose a variety of low-cost index funds that cover various parts of the markets such as bonds, domestic stocks and foreign stocks. Another alternative to consider are professionally managed vehicles such as target date mutual funds, where the manager allocates portfolio over time. These funds are designed to gradually reduce their exposure to equities as the target date of the fund gets closer

Investors with more knowledge and experience might consider actively managed mutual funds, individual stocks, real estate or other alternative investments.

## Understand what you don’t know

It is important that investors understand what they do and don’t know. They should never be talked into investing in something that they don’t understand or are uncomfortable with.

# What Is Your Risk Tolerance?

# 2017 International Financial Management Course

2. IFM CH04.ppt

3. IFM CH05.ppt

4. IFM CH06.ppt

5. IFM CH07.ppt

6. IFM CH08.ppt

7. IFM course File 002- Financial Risk-Key Fundamentals and case study.pdf

8. Introduction to Modern Portfolio Theory.pdf

9. Risk managements in financial markets-Basic concepts (Dr. Chao in NHU).pptx

10. 國際財務管理-財務風險管理概論(106.10.13).ppt

11. 國際財務管理教案-財務風險管理概論基礎篇.ppt