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**preview**shows pages 1-2. to view the full**8 pages of the document.**CHAPTER 10: Risk and Return in Capital Markets

A First Look at Risk and Return

• S&P/TSX Composite Index – a potfolio ostuted “tadad & Poo’s “&P, of the

largest, most-liquid stocks and income trust units traded on the TSX.

• S&P 500 Index – a portfolio, constructed by S&P, including 90 U.S. stocks up to 1957 and

500 U.S. stocks after that. The firms represented are leaders in their respective

industries and are among the largest firms in terms of market capitalization (share

prices times the number of shares in the hands of shareholders) traded on U.S. markets.

A $100cad initial investment is first converted into U.S. dollars and then invested in the

S&P 500. The value of the investment is converted back into Canadian dollars each

month in order to calculate returns from the perspective of a Canadian investor.

• Long-Term Government of Canada Bonds – these bonds have maturities of approx. 30

years.

• Government of Canada Treasury Bills – short term (maturity of up to 1 year), zero-

coupon debt, issued by the Government of Canada to provide financing for the

government.

• Suppose your great-grandparents invested $100 on your behalf at the beginning of

1956, and they instructed their broker to reinvest any dividend or interest earned in the

account until …

• Investors do not like risk and are averse to fluctuations in the value of their investments

and therefore demand a risk premium to bear it. Because investors can eliminate some

risk by holding large portfolios of stocks, not all risk is entitled to a risk premium.

• Stocks are riskier investments than bonds, but they earn higher average annual returns.

We interpret the higher average return on stocks vs. bonds as compensation to

investors for the greater risk they are taking.

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Historical Risks and Returns of Stocks

Computing Historical Returns

• Realized Return/Total Return – the total return on an investment that occurs over a

particular time period.

• You can compute the total return for any security in the same way by replacing the

dividend payments with any cash flows such as coupon payments paid for bonds.

• Calculating Total Return for ONE PMT – Use the folloig euatio…

• If you hold the stock beyond the date of the first dividend payment, then to compute

your return, you must specify how you invest any dividends you receive. To focus on the

returns of a single security, we assume that all dividends are immediately reinvested

and used to purchase additional shares of the same stock of security.

• Calculating Total Return for MULTIPLE PMT – First, you have to use the total return

equation for each dividend payment/each period. Then once you have the returns for

each payment/period, you must use the following equatio…

• In any given year, we observe only one actual realized return from all of the possible

returns that could have been realized. However, we can observe realized returns over

many years.

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Average Annual Returns

• Average Annual Return (Arithmetic Average) – the average of the realized returns for

each year (the most likely return).

• The compound annual return is a better description of the long-term historical

performance of an investment. It is most often used for comparison purposes.

• The aitheti aeage etu should e used he tig to estiate a iestet’s

expected return over a future horizon based on its past performance.

• Geometric Average: (1) FV = $ [+R+R+R…..] then (2) Answer to the

power of 1/T, then subtract 1.

The Variance and Volatility of Returns

• Variance – a method to measure the variability of returns by taking the differences of

the returns from the average return and squaring those differences.

• Standard Deviation/Volatility – a common method used to measure the risk of a

probability distribution. It is the square root of the variance.

• SD indicates the tendency of the historical returns to be different from their average

and how far from the average they tend to be. SD therefore captures our intuition of

risk: how often we will miss the mark and how far off will we be?

• Calculating Volatility/Variance/SD: (1) find the average annual return, (2) use the

variance estimate equation – break it up and do it one calculation at a time, make sure

the percentages are inputted as decimals OR divide by 10,000! Make sure SD is a %!

Use arithmetic average!

• See page 354 in the textbook to see how to calculate the SD in Excel!

The Normal Distribution

• Normal Distribution – a symmetric probability distribution that is completely

characterized by its average and SD. 95% of all possible outcomes fall within two SD

above and below the average.

• 95% Confidence Interval – a range of values that is likely to include an unknown

parameter. If independent samples are taken repeatedly from the same population,

then the true parameter will lie outside the 95% confidence interval 5% of the time.

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