There are several different investment options. These include the S&P 500, small stocks, world portfolios, corporate bonds, and treasury bills. The S&P consists of 500 stocks which represent leaders in different industries and are the largest firms in terms of market capitalization. Small stocks are a portfolio of stocks of US firms whose market values are in the bottom 10% of all stocks traded on the NYSE. The world portfolio consists of international stocks from all of the world's major stock markets in North America, Europe, and Asia. Corporate bonds are a portfolio of long term AAA rated US corporate bonds with 20 year maturities. Treasury bills are investments in 3 month US treasury bills which are continually reinvested as they mature. Stocks have long been known to be riskier investments than bonds, but as a result, stocks earn higher average annual returns. This higher average return is compensation to investors for their riskier investments. It is important to note that investors are averse to risk when it comes to investments.

Historical Risks and Returns of Stocks

The realized return for an individual investment is the total return that occurs over a particular time period. The realized return from an investment in stock from T to T+1 is:

Rt+1 = (Div t+1 / Pt) + (Pt+1 - Pt) / Pt which is also the Dividend Yield + Capital Gain Yield

The annual realized return is:

1+Rannual = (1+R1)(1+R2)(1+Rn)

In any given year we only observe one actual realized return from all of the possible returns that could have been realized. We can observe realized returns over many years.

The average annual return of an investment is simply the average of the realized returns for each year.The average return provides an estimate of the return we should expect in any given year - the expected return.

Average Annual Return = 1/T (R1+R2+....+RT)

To calculate the variability of returns, we calculate the standard deviation of the distribution of realized returns. The standard deviation is the square root of the variance of the distribution of realized returns.Variance measures the variability in returns by taking teh differences of the returns from the average return and squaring those differences. The standard deviation indicates the tendency of the historical returns to be different from their average and how far from the average they tend to be. It captures an investor's intuition of risk.

The standard deviation plays a role in describing a normal distribution which is a symmetric probability distribution that is completely characterized by its average and standard deviation. About two thirds of all possible outcomes fall within one standard deviation above or below the average and about 95% of all possible outcomes fall within two standard deviations above and below the average. The 95% confidence interval is calculated as follows:

Average +/- (2 * SD)

The Historical Tradeoff Between Risk and Return

Investments with higher volatility have rewarded investors with higher average returns. Because investors are averse to risk, these risky investments must offer higher average returns as compensation. Investments with higher volatility should have a higher risk premium and therefore higher returns. However, there is no clear relationship between volatility and returns for individual stocks. The following do hold true however:

There is a relationship between size and risk: on average larger stocks have lower volatility than smaller stocks

Even the largest stocks are typically more volatile than a portfolio of large stocks

All individual stocks have lower returns and/or higher risk than portfolios

While the volatility seems to be a reasonable measure of risk when evaluating a large portfolio, the volatility of an individual security doesn't explain the size of its average return.

Common Versus Independent Risk

Common risk is risk that is linked across outcomes. Independent risk is risks that bear no relation to each other. This means that knowing the outcome of one event provides no information about another outcome. Independent risks can be eliminated in a portfolio through diversification... the averaging out of risks in a large portfolio.

Diversification in Stock Portfolios

The risk of any given portfolio depends upon whether the individual risks within it are common or independent. As mentioned previously, independent risks can be diversified while common risks cannot.

Stock prices and dividends are impacted by two types of news: Company/Industry specific news or Market wide news. Fluctuations of a stock's return as a result of company/industry specific news are independent risks. This means that they are unrelated across stocks. Independent risks are also known as unsystematic risk.When many stocks make up a portfolio, the unsystematic risks of each individual stock will average out and be eliminated through diversification. Fluctuations of a stock's return that are due to market wide news are common risk. All stocks are affected by this news. Common risk is also referred to as systematic risk. Since systematic risk affects all firms, it cannot be eliminated through diversification. When firms carry both types of risk, only the unsystematic risk will be eliminated by diversification when we combine many firms into a portfolio. The volatility will therefore decline until only the systematic risk remains.Because of this, the volatility of a portfolio is lower than the volatility of the individual stocks in the portfolio.

The risk premium of a stock is not affected by its diversifiable, unsystematic risk. Therefore, the risk premium for diversifiable risk is zero. Investors are not compensated for holding unsystematic risk. Investors are compensated for holding systematic risk however. Systematic risk can only be eliminated by sacrificing expected returns and investing in other securities. The risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk. Because of this, a stock's volatility (measures total risk) is not useful in determining the risk premium that investors will earn.

## Chapter 10 - Risk and Return In Capital Markets

A First Look at Risk and Return

There are several different investment options. These include the S&P 500, small stocks, world portfolios, corporate bonds, and treasury bills. The S&P consists of 500 stocks which represent leaders in different industries and are the largest firms in terms of market capitalization. Small stocks are a portfolio of stocks of US firms whose market values are in the bottom 10% of all stocks traded on the NYSE. The world portfolio consists of international stocks from all of the world's major stock markets in North America, Europe, and Asia. Corporate bonds are a portfolio of long term AAA rated US corporate bonds with 20 year maturities. Treasury bills are investments in 3 month US treasury bills which are continually reinvested as they mature. Stocks have long been known to be riskier investments than bonds, but as a result, stocks earn higher average annual returns. This higher average return is compensation to investors for their riskier investments. It is important to note that investors are averse to risk when it comes to investments.

Historical Risks and Returns of Stocks

The

realized returnfor an individual investment is the total return that occurs over a particular time period. The realized return from an investment in stock from T to T+1 is:Rt+1 = (Div t+1 / Pt) + (Pt+1 - Pt) / Ptwhich is also theDividend Yield + Capital Gain YieldThe annual realized return is:

1+Rannual = (1+R1)(1+R2)(1+Rn)In any given year we only observe one actual realized return from all of the possible returns that could have been realized. We can observe realized returns over many years.

The

average annual returnof an investment is simply the average of the realized returns for each year.The average return provides an estimate of the return we should expect in any given year - the expected return.Average Annual Return = 1/T (R1+R2+....+RT)To calculate the variability of returns, we calculate the standard deviation of the distribution of realized returns. The

standard deviationis the square root of the variance of the distribution of realized returns.Variancemeasures the variability in returns by taking teh differences of the returns from the average return and squaring those differences. The standard deviation indicates the tendency of the historical returns to be different from their average and how far from the average they tend to be. It captures an investor's intuition of risk.The standard deviation plays a role in describing a

normal distributionwhich is a symmetric probability distribution that is completely characterized by its average and standard deviation. About two thirds of all possible outcomes fall within one standard deviation above or below the average and about 95% of all possible outcomes fall within two standard deviations above and below the average. The95% confidence intervalis calculated as follows:Average +/- (2 * SD)The Historical Tradeoff Between Risk and Return

Investments with higher volatility have rewarded investors with higher average returns. Because investors are averse to risk, these risky investments must offer higher average returns as compensation. Investments with higher volatility should have a higher risk premium and therefore higher returns. However, there is no clear relationship between volatility and returns for individual stocks. The following do hold true however:

While the volatility seems to be a reasonable measure of risk when evaluating a large portfolio, the volatility of an individual security doesn't explain the size of its average return.

Common Versus Independent Risk

Common riskis risk that is linked across outcomes.Independent riskis risks that bear no relation to each other. This means that knowing the outcome of one event provides no information about another outcome. Independent risks can be eliminated in a portfolio throughdiversification... the averaging out of risks in a large portfolio.Diversification in Stock Portfolios

The risk of any given portfolio depends upon whether the individual risks within it are common or independent. As mentioned previously, independent risks can be diversified while common risks cannot.

Stock prices and dividends are impacted by two types of news: Company/Industry specific news or Market wide news. Fluctuations of a stock's return as a result of company/industry specific news are independent risks. This means that they are unrelated across stocks. Independent risks are also known as

unsystematic risk.When many stocks make up a portfolio, the unsystematic risks of each individual stock will average out and be eliminated through diversification. Fluctuations of a stock's return that are due to market wide news are common risk. All stocks are affected by this news. Common risk is also referred to assystematic risk.Since systematic risk affects all firms, it cannot be eliminated through diversification.When firms carry both types of risk, only the unsystematic risk will be eliminated by diversification when we combine many firms into a portfolio. The volatility will therefore decline until only the systematic risk remains.Because of this, the volatility of a portfolio is lower than the volatility of the individual stocks in the portfolio.The risk premium of a stock is not affected by its diversifiable, unsystematic risk. Therefore, the risk premium for diversifiable risk is zero. Investors are not compensated for holding unsystematic risk. Investors are compensated for holding systematic risk however. Systematic risk can only be eliminated by sacrificing expected returns and investing in other securities. The risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk. Because of this, a stock's volatility (measures total risk) is not useful in determining the risk premium that investors will earn.