. 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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