Investments, tenth edition

  SOLUTIONS TO CONCEPT CHECKS  

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  5

   CASUAL OBSERVATION AND  

formal research 

both suggest that investment risk is as impor-

tant to investors as expected return. While we 

have theories about the relationship between 

risk and expected return that would prevail 

in rational capital markets, there is no theory 

about the levels of risk we should find in the 

marketplace. We can at best estimate the level 

of risk likely to confront investors from his-

torical experience. 

 This situation is to be expected because 

prices of investment assets fluctuate in response 

to news about the fortunes of corporations, as 

well as to macroeconomic developments. There 

is no theory about the frequency and impor-

tance of such events; hence we cannot deter-

mine a “natural” level of risk. 

 Compounding this difficulty is the fact that 

neither expected returns nor risk are directly 

observable. We observe only  realized  rates of 

return. Hence, to make forecasts about future 

expected returns and risk, we must learn how 

to “forecast” their past values, that is, the 

expected returns and risk that investors actu-

ally anticipated, from historical data. (There 

is an old saying that forecasting the future 

is even more difficult than forecasting the 

past.) Moreover, in learning from a historical 

record we face what has become known as 

the “black swan” problem.  

1

   No matter how 

long a historical record, there is never a guar-

antee that it exhibits the worst (and best) 

that nature can throw at us in the future. This 

problem is particularly daunting when con-

sidering the risk of long-run investments. In 

this chapter, we present the essential tools for 

estimating expected returns and risk from the 

historical record and consider implications for 

future investments.

  

 We begin with interest rates and invest-

ments in safe assets and examine the history 

of risk-free investments in the U.S over the last 

86 years. Moving to risky assets, we begin with 

scenario analysis of risky investments and the 

data inputs necessary to conduct it. With this 

in mind, we develop statistical tools needed 

to make inferences from historical time series 

of portfolio returns. We present a global 

view of the history of stock and bond returns 

worldwide. We end with implications of the 

historical record for future investments and 

risk measures commonly used in the industry.