. Investment returns

. Risk

. Expected rate of return and standard deviation

. Diversification

. Beta coefficient - market risk

. Return on a portfolio and portfolio beta

. Relationship between risk and rates of return

## . Investment returns

Dollar return vs. rate of return

If you invested $1,000 and received $1,100 in return, then

your dollar return = 1,100 - 1,000 = $100 and

your rate of return = (1,100 - 1,000) / 1,000 = 10%

. Risk

The chance that some unfavorable event will occur

Stand-alone risk vs. market risk

Stand-alone risk: risk of holding one asset measured by standard deviation and its systematic risk is measured by beta.

Market risk: risk of holding a well-diversified portfolio is also measured by standard deviation and its systematic by beta

## . Expected rate of return and standard deviation

Probability distribution: a list of possible outcomes with a probability assigned to each outcome

Expected rate of return: the rate of return expected to be realized

Variance and standard deviation: statistical measures of variability (risk)

Coefficient of variation (CV) = standard deviation / expected rate of return,

which measures the risk per unit of expected return

Using historical data to estimate average return and standard deviation

Stock returns: expected vs. realized

Expected return

Use Excel to calculate mean and standard deviation with historical data

Risk premium: the difference between the expected/required rate of return on a

given security and that on a risk-free asset

## . Diversification

As you increase the number of securities in your portfolio, the portfolio total risk decreases

Total risk = firm’s specific risk + market risk

Total risk = diversifiable risk + nondiversifiable risk

Total risk = unsystematice risk + systematic risk

## . Beta coefficient - market risk

Sensitivity of an asset (or a portfolio) with respect to the market or the extent to which a given stock’s returns move up and down with the stock market

Plot historical returns for a firm along with the market returns (S&P 500 index, for example) and estimate the best-fit line. The estimated slope of the line is the estimated beta coefficient of the stock, or the market risk of the stock.

## Return on a portfolio and portfolio beta

Expected return on a portfolio: the weighted average of the expected returns on the assets held in the portfolio

For example, the expected rate of return on stock A is 10% and the expected rate

of return on stock B is 14%. If you invest 40% of your money in stock A and 60%

of your money in stock B to form your portfolio then the expected rate of return

on your portfolio will be 12.4% = (0.4)*10% + (0.6)*14%*

Portfolio beta: weighted average of individual securities’ betas in the portfolio

For example, if the beta for stock A is 0.8 and the beta for stock B is 1.2, with the

weights given above, the beta for your portfolio is 1.04 = (0.4)*0.8 + (0.6)*1.2

## . Relationship between risk and rates of return

Required rate of return: the minimum rate of return necessary to attract an investor to purchase or hold a security

Market risk premium: the additional return over the risk-free rate needed to compensate investors for assuming an average amount (market) of risk

For example, if the required rate of return on the market is 11% and the risk-free

rate is 5% then the market risk premium will be 6%

Risk premium for a stock: the additional return over the risk-free rate needed to compensate investors for assuming the risk of that stock

For example, if the required rate of return on a stock is 15% and the risk-free rare

is 5% then the risk premium for that stock will be 10%

## Capital Asset Pricing Model (CAPM)

Ri = Rf + Beta*Market Risk Premium

where Ri is the required rate of return on stock i; Rf is the risk-free rate;

Security market line (SML): a line that shows the relationship between the required return of an asset and the market risk

Overvalued vs. undervalued securities

If the actual return lies above the SML, the security is undervalued

If the actual return lies below the SML, the security is overvalued

Example: a stock has a beta of 0.8 and an expected rate of return of 11%. The

expected rate of return on the market is 12% and the risk-free rate is 4%. Should

you buy the stock?

Answer: required rate of return for the stock (using CAPM) is

4% + (12% - 4%)*(0.8) = 10.4% < 11% (expected rate of return)

The stock is under-valued

The impact of inflation: a parallel shift in SML

Change in risk aversion: the slope of SML gets steeper

Change in beta: changes the required rate of return

The CAPM is a single variable model and multivariable models are proposed by some researchers with the statement that they give better estimates of risk and risk premium and therefore better required return estimates.

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