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Chapter 2

# FIN 501 Chapter Notes - Chapter 2: Toronto Stock Exchange, Squared Deviations From The Mean, Standard Deviation

by OC10512

This

**preview**shows pages 1-2. to view the full**6 pages of the document.**Chapter 2: Diversification and Asset Allocation

Diversification is important because portfolios with many investments usually produce a more consistent and

stable total return than portfolios with just one investment

When you own many stocks, even if some of them decline in price, others are likely to increase in price (or stay

at the same price)

We assume that investors prefer more return to less return and second, we assume that investors prefer less risk

to more risk

2.1 Expected Returns and Variances:

Expected Return: average return on a risky asset expected in the future

- Two states of economy = means that there are two possible outcomes

- Expected Return on a security or other asset = the sum of the possible returns multiplied by

their probabilities

- Risk Premium = Expected Return – Risk-free Rate

= E ( –

- Using our projected returns, we can calculate the projected or expected risk premium as the

difference between the expected return on a risky investment and the certain return on a risk-free

investment

Calculating the Variance: first determine the squared deviations from the expected return. We then

simply multiply each possible squared deviation by its probability. Next we add these up, and the result

is the variance

- In chapter 1, we estimated the average return and the variance based on historical events and on

some actual events

- Here, we have projected future returns and their associated probabilities, so this information with

which we must work

2.2 Portfolios:

Portfolios: group of assets such as stocks and bonds held by an investor

Investors tend to own more than just a single stock, bond, or other asset

Portfolio return and portfolio risk are of obvious relevance

Portfolio Weights: percentage of a portfolio’s total value invested in a particular asset

- There are many equivalent ways of describing a portfolio

- The most convenient approach is to list the percentages of the total portfolio’s value that are

invested in each portfolio asset [call these percentages the portfolio weights]

- Ex: if we have $50 in one asset and $150 in another, then out total portfolio is worth $200. The

percentage of our portfolio in the first asset is $50/$200 = 0.25. The percentage in the second asset

is $150/$200 = 0.75. The weights sum up to 1.00 since all of our money is invested somewhere.

Portfolio Expected Returns:

- This method of calculating the expected return on a portfolio works no matter how many assets

there are in the portfolio

- Suppose we had n assets in our portfolio, where n is any number at all. If we let stand for the

percentage of our money in Asset i, then the expected return is:

- The expected return on a portfolio is a straightforward combination of the expected returns on the

assets in that portfolio

Portfolio Variance:

- Note that the return is the same no matter if a recession or a boom occurs

- This portfolio has a zero variance and no risk!

Only pages 1-2 are available for preview. Some parts have been intentionally blurred.

- This is a nice bit of a financial alchemy. We take 2 risky assets and by mixing them just right, we

create a riskless portfolio.

- Ex: Suppose putting 2/11 (18%) in Net-cap and the other 9/11 (82%) in J-mart (page 41)

2.3 Diversification and Portfolio Risk:

The Effect of Diversification: Another Lesson from Market History

- Copp and Cleary (see figure 2.1) examined diversification characteristics of the Canadian

portfolios by forming portfolios of 222 randomly chosen Canadian stocks

- Table 2.7: Portfolio Standard Deviation = illustrates their results of standard deviation of monthly

portfolio returns

- In column 3 of Table 2.7 (page 43) we see that the standard deviation for a “portfolio” of one

security is 13.47%. If you randomly select a stock listen on the Toronto Stock Exchange and put

all your money into it, your standard deviation of return would typically have been about 13% per

month

- Obviously, such a strategy has significant risk! If you were to randomly select 2 securities and put

half your money in each, your average standard deviation would have been 11%

- The important thing to notice in Table 2.7 is that the standard deviation declines as the number of

securities is increased

- The nearby Investment Updates box offers further historical perspective on the need for

diversification [Figure 2.1: Portfolio Diversification page 44]

The Principle of Diversification:

- Figure 2.1: plotted the standard deviation of the return vs. the number of stocks in the portfolio

- The benefit in terms of risk reduction from adding securities drops off as we add more and more

- By the time we have 10 securities, most of the diversification effect is already realized, and by the

time we get to 20 or so, there is little remaining benefit

- In other words, the benefit of further diversification increases at a decreasing rate, so the “law of

diminishing returns” applies here as it does in so many other places

- Investors should be thinking of terms of 30 or 50 randomly chosen stocks when they are building a

diversified portfolio

- Figure 2.1 illustrates 2 key points: page 44

1. Some of the riskiness associated with individual assets can be eliminated by forming

portfolios- the process of spreading an investment across assets (and thereby forming a

portfolio) is called diversification.

The principle of diversification = spreading an investment across a number of

assets will eliminate some, but not all, of the risk

Risk that can be eliminated by diversification are called “diversifiable” risks

2. There is a minimum level of risk that cannot be eliminated by simply diversifying. This

minimum level is labeled “non-diversifiable risk” in Figure 2.1. Taken together, these 2

points are another important lesson from financial market history: Diversification reduces

risk, but only up to a point.

2.4 Correlation and Diversification:

Why Diversification Works:

- Why diversification reduces portfolio risk as measured by the portfolio standard deviation is

important and worth exploring in some detail

- The key concept is correlation: the tendency of the returns on two assets to move together

- If the return on two assets tend to move up and down together, we say they are positively

correlated

- If they tend to move in opposite directions, we say they are negatively correlated

- If there is no particular relationship between the two assets, we say they are uncorrelated

- The correlation coefficient, which is used to measure correlation, ranges from -1 to +1, and we

will denote the correlation between the returns on two assets, say A and B, as Corr( )

- The Greek letter (rho) is often used to designate correlation as well

- A correlation of +1 indicates that the 2 assets have a perfect positive correlation

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