Risk and Rates of Return
CHAPTER 8
The Risk Return Trade-off
◦ The slope of the line indicates how much additional return an
investor requires to take on additional risk
◦ A steeper line suggests that the investor is risk averse and will have
a preference for lower risk investments
◦ An investor’s willingness to take on risk varies with time
◦ Movement from riskier investments towards safer investments is
called flight to quality
◦ Risk: The chance that some unfavorable event will occur.
◦ An asset’s risk can be analyzed in two ways 1) on a stand-alone
basis where the asset is considered by itself and 2) on a portfolio
basis where the asset is held as one of a number of assets in a
portfolio
◦ Stand-alone Risk: The risk an investor would face if he or she held
only one asset.
Measures of Stand-Alone Risk
1.
Probability distributions
2.
Expected rates of return
3.
Historical or past realized rates of return
4.
Standard Deviation
5.
Coefficient of Variation
6.
Sharpe Ratio
Probability Distributions and Expected Returns
Probability Distribution of Rates of Return
Measuring Stand-Alone Risk: The Standard Deviation
Calculating Standard Deviation
Using Historical Data to Measure Risk
Stand-Alone Risk= Standard Deviation
Other Measures of Stand-Alone Risk
Risk Aversion and Required Returns
◦ Risk averse investors dislike risk and require higher rates of return
as an inducement to buy riskier securities
◦ The average investor is risk averse
◦ The higher a security's risk the higher its required rate of return
and if this situation does not hold, prices will change to bring
about the required condition.
◦ The difference between the expected rate of return on a given
risky asset and that on a less risky asset is called risk premium (RP)
Risk Return Tradeoff
Risk in a Portfolio Context
Capital Asset Pricing Model (CAPM): A model based on the proposition that any
stock’s required rate of return is equal to the risk-free rate of return plus a risk
premium that reflects only the risk that remains after diversification.
The risk of a stock held in a portfolio is typically lower than when it is held alone.
Because investors dislike risk and because risk can be reduced by holding
portfolios most stocks are held in portfolios. Therefore, the risk and return of an
individual stock should be analyzed in terms of how the security affects the risk
and return of the portfolio in which it is held.
Expected Return on a Portfolio
The expected return on a portfolio is the weighted average of the expected returns of individual
stocks in the portfolio.
Portfolio Risk
Portfolio Risk
The portfolios risk is generally smaller than the average of the stocks’ standard deviation
because diversification lowers portfolio risk
The tendency of two variables to move together is called correlation
Correlation coefficient is a measure of the degree of relationship between two variables
r = −1
◦ 2 stocks can be combined to form a riskless portfolio: σp = 0.
r = +1
◦ Risk is not “reduced”
◦ σp is just the weighted average of the 2 stocks’ standard deviations.
−1 < r < +1
◦ Risk is reduced but not eliminated.
On average the portfolio risk decreases as the number of stocks in the portfolio
increase. If we added enough partially corelated stocks, could we completely eliminate
risk?
Types of Risk
The Beta Coefficient
Portfolio Beta
Security Market Line (SML)
Security Market Line (SML)
Change in Inflation
Change in Risk Aversion