1 chapter 1 brief history of risk and return ayşe yüce – ryerson university copyright © 2012...

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Chapter 1Brief History of Risk and Return

Ayşe Yüce – Ryerson UniversityAyşe Yüce – Ryerson University Copyright © 2012 McGraw-Hill RyersonCopyright © 2012 McGraw-Hill Ryerson

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To become a wise investor (maybe even one with too much money), you need to know:

1. How to calculate the return on an investment using different methods.

2. The historical returns on various important types of investments.

3. The historical risk on various important types of investments.

4. The relationship between risk and return.


Learning ObjectivesLearning Objectives

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You can retire with One Million Dollars (or more).

How? Suppose: You invest $300 per month. Your investments earn 9% per year. You decide to take advantage of deferring taxes on your

investments.

It will take you about 36.25 years. Hmm. Too long.

Example I: Example I: Who Wants To Be A Millionaire?Who Wants To Be A Millionaire?


44Ayşe Yüce – Ryerson UniversityAyşe Yüce – Ryerson University Copyright © 2012 McGraw-Hill RyersonCopyright © 2012 McGraw-Hill Ryerson

Example II:Example II:Who Wants To Be A Millionaire?Who Wants To Be A Millionaire?Instead, suppose:

•You invest $500 per month.•Your investments earn 12% per year• you decide to take advantage of deferring taxes on your investments

It will take you 25.5 years.

Realistic?•$250 is about the size of a new car payment, and perhaps your employer will kick in $250 per month•Over the last 84 years, the S&P 500 Index return was about 12%

Try this calculator: cgi.money.cnn.com/tools/millionaire/millionaire.html

http://cgi.money.cnn.com/tools/millionaire/millionaire.html

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Our goal in this chapter is to see what financial market history can tell us about risk and return.

There are two key observations: First, there is a substantial reward, on average, for bearing

risk. Second, greater risks accompany greater returns.

These observations are important investment guidelines.


A Brief History of Risk And A Brief History of Risk And ReturnReturn

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Total dollar return is the return on an investment measured in dollars, accounting for all interim cash flows and capital gains or losses.

Example:


Dollar ReturnsDollar Returns

Loss) (or Gain Capital Income Dividend Stock a on Return Dollar Total

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Total percent return is the return on an investment measured as a percentage of the original investment.

The total percent return is the return for each dollar invested.

Example, you buy a share of stock:

Percent ReturnsPercent Returns


)Investment Beginning (i.e., PriceStock Beginning

Stock aon Return Dollar Total Return Percent

or

PriceStock Beginning

Loss)(or Gain Capital Income DividendStock aon Return Percent


Example: Calculating Total Dollar Example: Calculating Total Dollar And Total Percent ReturnsAnd Total Percent Returns

Suppose you invested $1,400 in a stock with a share price of $35. After one year, the stock price per share is $49. Also, for each share, you received a $1.40 dividend.

What was your total dollar return?$1,400 / $35 = 40 sharesCapital gain: 40 shares times $14 = $560Dividends: 40 shares times $1.40 = $56Total Dollar Return is $560 + $56 = $616

What was your total percent return?Dividend yield = $1.40 / $35 = 4%Capital gain yield = ($49 – $35) / $35 = 40%Total percentage return = 4% + 40% = 44%

Note that $616 divided by $1,400 is 44%.


Annualizing Returns, IAnnualizing Returns, I

You buy 200 shares of Lowe’s Companies, Inc. at $18 per share. Three months later, you sell these shares for $19 per share. You received no dividends. What is your return? What is your annualized return?

Return: (Pt+1 – Pt) / Pt = ($19 - $18) / $18 = .0556 = 5.56%

Effective Annual Return (EAR): The return on an investment expressed on an “annualized” basis.

Key Question: What is the number of holding periods in a year?

This return is known as the holding period percentage return.


Annualizing Returns, IIAnnualizing Returns, II

1 + EAR = (1 + holding period percentage return)m

m = the number of holding periods in a year.

In this example, m = 4 (12 months / 3 months). Therefore:

1 + EAR = (1 + .0556)4 = 1.2416.

So, EAR = .2416 or 24.16%.


$1 Investment in Canadian S&P/TSX $1 Investment in Canadian S&P/TSX IndexIndex


A $1 Investment in Different Types of Portfolios, A $1 Investment in Different Types of Portfolios, 1926-20091926-2009


Financial Market HistoryFinancial Market History


The Historical Record: Total Returns on Large-The Historical Record: Total Returns on Large-Company StocksCompany Stocks


The Historical Record: Total Returns on Small-The Historical Record: Total Returns on Small-Company StocksCompany Stocks


The Historical Record: Total Returns on Long-term The Historical Record: Total Returns on Long-term U.S. BondsU.S. Bonds


The Historical Record: Total Returns on U.S. T-billsThe Historical Record: Total Returns on U.S. T-bills


The Historical Record: InflationThe Historical Record: Inflation


Historical Average ReturnsHistorical Average Returns A useful number to help us summarize historical financial data

is the simple, or arithmetic average.

Using the data in Table 1.1, if you add up the returns for large-company stocks from 1926 through 2009, you get about 987 percent.

Because there are 84 returns, the average return is about 11.75%. How do you use this number?

If you are making a guess about the size of the return for a year selected at random, your best guess is 11.75%.

The formula for the historical average return is:

n

returnyearly Return AverageHistorical

n

1i


Average Annual Returns for Average Annual Returns for Five Portfolios and InflationFive Portfolios and Inflation


Average Annual Risk Premiums Average Annual Risk Premiums for Five Portfoliosfor Five Portfolios


Average Returns: The First Average Returns: The First Lesson Lesson

Risk-free rate: The rate of return on a riskless, i.e., certain investment.

Risk premium: The extra return on a risky asset over the risk-free rate; i.e., the reward for bearing risk.

The First Lesson: There is a reward, on average, for bearing risk.

By looking at Table 1.3, we can see the risk premium earned by large-company stocks was 7.9%! Is 7.9% a good estimate of future risk premium? The opinion of 226 financial economists: 7.0%. Any estimate involves assumptions about the future risk

environment and the risk aversion of future investors.


World Stock Market World Stock Market CapitalizationCapitalization

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International Equity Risk International Equity Risk PremiumsPremiums


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Why Does a Risk Premium Why Does a Risk Premium Exist?Exist?

Modern investment theory centers on this question.

Therefore, we will examine this question many times in the chapters ahead.

We can examine part of this question, however, by looking at the dispersion, or spread, of historical returns.

We use two statistical concepts to study this dispersion, or variability: variance and standard deviation.

The Second Lesson: The greater the potential reward, the greater the risk.


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The Bear Growled and Investors The Bear Growled and Investors HowledHowled


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Return Variability: The Statistical Return Variability: The Statistical ToolsTools

VAR(R) σ SD(R)

The formula for return variance is ("n" is the number of returns):

Sometimes, it is useful to use the standard deviation, which is related to variance like this:

1N

RR σ VAR(R)

N

1i

2

i2


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Return Variability Review and Return Variability Review and ConceptsConcepts

Variance is a common measure of return dispersion. Sometimes, return dispersion is also call variability.

Standard deviation is the square root of the variance.Sometimes the square root is called volatility. Standard Deviation is handy because it is in the same "units" as the average.

Normal distribution: A symmetric, bell-shaped frequency distribution that can be described with only an average and a standard deviation.

Does a normal distribution describe asset returns?


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Frequency Distribution of Returns Frequency Distribution of Returns on Common Stocks, 1926-2009on Common Stocks, 1926-2009


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Example: Calculating Historical Example: Calculating Historical Variance and Standard DeviationVariance and Standard DeviationLet’s use data from Table 1.1 for Large-Company Stocks.

The spreadsheet below shows us how to calculate the average, the variance, and the standard deviation (the long way…).

(1) (2) (3) (4) (5)Average Difference: Squared:

Year Return Return: (2) - (3) (4) x (4)1926 11.14 11.48 -0.34 0.121927 37.13 11.48 25.65 657.921928 43.31 11.48 31.83 1013.151929 -8.91 11.48 -20.39 415.751930 -25.26 11.48 -36.74 1349.83

Sum: 57.41 Sum: 3436.77

Average: 11.48 Variance: 859.19

29.31Standard Deviation:


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Historical Returns, Standard Deviations, Historical Returns, Standard Deviations, and Frequency Distributions: 1926-2009and Frequency Distributions: 1926-2009


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The Normal Distribution and Large The Normal Distribution and Large Company Stock ReturnsCompany Stock Returns


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Returns on Some Returns on Some ““Non-NormalNon-Normal”” DaysDays


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Arithmetic Averages versus Arithmetic Averages versus Geometric AveragesGeometric Averages

The arithmetic average return answers the question: “What was your return in an average year over a particular period?”

The geometric average return answers the question: “What was your average compound return per year over a particular period?”

When should you use the arithmetic average and when should you use the geometric average?

First, we need to learn how to calculate a geometric average.


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Example: Calculating a Geometric Example: Calculating a Geometric Average ReturnAverage Return

Let’s use the large-company stock data from Table 1.1.

The spreadsheet below shows us how to calculate the geometric average return.

Percent One Plus CompoundedYear Return Return Return:1926 11.14 1.1114 1.11141927 37.13 1.3713 1.52411928 43.31 1.4331 2.18411929 -8.91 0.9109 1.98951930 -25.26 0.7474 1.4870

1.0826

8.26%

(1.4870)^(1/5):

Geometric Average Return:


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Arithmetic Averages versus Arithmetic Averages versus Geometric AveragesGeometric Averages

The arithmetic average tells you what you earned in a typical year.

The geometric average tells you what you actually earned per year on average, compounded annually.

When we talk about average returns, we generally are talking about arithmetic average returns.

For the purpose of forecasting future returns: The arithmetic average is probably "too high" for long forecasts. The geometric average is probably "too low" for short forecasts.


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Geometric versus Arithmetic Geometric versus Arithmetic AveragesAverages


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Risk and ReturnRisk and Return

The risk-free rate represents compensation for just waiting.

Therefore, this is often called the time value of money.

First Lesson: If we are willing to bear risk, then we can expect to earn a risk premium, at least on average.

Second Lesson: Further, the more risk we are willing to bear, the greater the expected risk premium.


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Historical Risk and Return Historical Risk and Return Trade-OffTrade-Off


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Dollar-Weighted Average Dollar-Weighted Average Returns, IReturns, I

There is a hidden assumption we make when we calculate arithmetic returns and geometric returns.

The hidden assumption is that we assume that the investor makes only an initial investment.

Clearly, many investors make deposits or withdrawals through time.

How do we calculate returns in these cases?


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Dollar-Weighted Average Dollar-Weighted Average Returns, IIReturns, II If you only make an initial investment at the start of year one:

The arithmetic average return is 2.50%. The geometric average return is 2.23%.

Suppose you makes a $1,000 initial investment and a $4,000 additional investment at the beginning of year two. At the end of year one, the initial investment grows to $1,100. At the start of year two, your account has $5,100. At the end of year two, your account balance is $4,845. You have invested $5,000, but your account value is only $4,845.

So, the (positive) arithmetic and geometric returns are not correct.


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Dollar-Weighted Average Returns Dollar-Weighted Average Returns and IRRand IRR


The US stock market in 2000s was one of the worst decades ever in investment history, investors were better off investing in anything else, including bonds and gold.

Many investors were lured to the stock market by the bull market in 1980s through the 1990s with over 17% average returns.

For investors counting on stocks for retirement plans, the most recent decade means many have fallen behind retirement goals.

Decline in dividends presented another hurdle for stock market, playing an important role in helping achieve a 9.5% average annual return since 1926 with a yield of 4%.

43Ayşe Yüce Copyright © 2012 McGraw-Hill Ryerson

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A Look AheadA Look AheadThis textbook focuses exclusively on financial assets:

stocks, bonds, options, and futures.

You will learn how to value different assets and make informed, intelligent decisions about the associated risks.

You will also learn about different trading mechanisms and the way that different markets function.


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Useful Internet SitesUseful Internet Sites cgi.money.cnn.com/tools/millionaire/millionaire.html

(millionaire link)

finance.yahoo.com (reference for a terrific financial web site)

www.globalfinancialdata.com (reference for historical financial market data—not free)

www.robertniles.com/stats (reference for easy to read statistics review)

www.tsx.com (reference for the Toronto Stock Exchange) www.osc.gov.on.ca (reference for the Ontario Securities

Commission)


http://cgi.money.cnn.com/tools/millionaire/millionaire.html

http://finance.yahoo.com/

http://www.globalfinancialdata.com/

http://www.robertniles.com/stats

http://www.tsx.com/

http://www.osc.gov.on.ca/

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ReturnsDollar ReturnsPercentage Returns

The Historical RecordA First LookA Longer Range LookA Closer Look

Average Returns: The First LessonCalculating Average ReturnsAverage Returns: The Historical RecordRisk Premiums


Chapter Review Chapter Review

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Chapter ReviewChapter ReviewReturn Variability: The Second Lesson

Frequency Distributions and VariabilityThe Historical Variance and Standard DeviationThe Historical RecordNormal DistributionThe Second Lesson

Arithmetic Returns versus Geometric Returns

The Risk-Return Trade-Off


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