Risk and Return
This chapter focuses on the fundamentals of risk and return—beginning with simple definitions of total and
expected return, risk neutral, risk averse, and risk seeking. The discussion then moves to risk measurement by
focusing on a single asset and measuring risk with statistics associated with a probability distribution—
namely, mean, standard deviation, and coefficient of variation. To demonstrate that insights about risk for a
single asset do not necessarily carry through to a collection of assets, the discussion broadens to risk and
return for a portfolio. Diversification is introduced through examination of risk for a portfolio of positively
correlated, negatively correlated, and uncorrelated assets. The key takeaway is that the volatility (risk) of a
portfolio will be less than a weighted average of the volatilities of the assets in the portfolio as long as the
correlation is less than 1.0. The potential for risk-reduction through international diversification is offered as an
intuitive example. These ideas are used to motivate the Capital Asset Pricing Model (CAPM). Diversifiable
and nondiversifiable risk are distinguished, with the key idea that the market only rewards bearing
nondiversifiable risk because firm-specific risk can so easily be eliminated through diversification. Then, the
CAPM equation and its pictorial representation (Security Market Line or SML) are introduced to show the
link between return and nondiversifiable risk. The chapter concludes by illustrating the impact of changes in
inflation expectations and investor risk aversion on the SML.
Suggested Answer to Opener-in-Review
You learned Bill Miller’s investment performance ranged from the very bottom to the very top of his
profession, thereby suggesting his fund took more risk than other mutual funds. The table below shows the
2009 to 2012 annual returns for Miller’s Opportunity fund and the S&P 500 index.
Year Opportunity Fund S&P 500
2009 76.0% 26.5%
2010 16.6% 15.1%
2011 –34.9% 2.11%
2012 39.6% 16.0%
Calculate average annual return for the Opportunity fund and S&P 500. Which performed better over this
period? If you had invested $1,000 in each fund January 1, 2009, how much money would you have had at
the end of 2012? Calculate the standard deviations of returns for the two funds. Which was more volatile?
Average annual return on Opportunity = (76.0% + 16.6% − 34.9% + 39.6%) 4 = 97.30% 4 = 24.33%.
Average annual return on S & P 500 = (26.5% + 15.1% + 2.11% + 16.0%) 4 = 59.71% 4 = 14.93%.
The Opportunity Fund performed better. A $1,000 investment in Opportunity January 1, 2009 would have
, where rj is return in year j (running to year n) and is average return over n years.