Investments, tenth edition

    5.   Assets with guaranteed nominal interest rates are risky in real terms because the future inflation 

rate is uncertain.  

    6.   Historical rates of return over the 20th century in developed capital markets suggest the U.S. 

history of stock returns is not an outlier compared to other countries.  

    7.   Investments in risky portfolios  do not  become safer in the long run. On the contrary, the longer 

a risky investment is held, the greater the risk. The basis of the argument that stocks are safe in 

the long run is the fact that the probability of a shortfall becomes smaller. However, probability 

of shortfall is a poor measure of the safety of an investment. It ignores the magnitude of possible 

losses.  

    8.   Historical returns on stocks exhibit more frequent large negative deviations from the mean 

than would be predicted from a normal distribution. The lower partial standard deviation 

(LPSD), the skew, and kurtosis of the actual distribution quantify the deviation from nor-

mality. The LPSD, instead of the standard deviation, is sometimes used by practitioners as a 

measure of risk.  

    9.   Widely used measures of tail risk are value at risk (VaR) and expected shortfall or, equivalently, 

conditional tail expectations. VaR measures the loss that will be exceeded with a specified prob-

ability such as 5%. The VaR does not add new information when returns are normally distrib-

uted. When negative deviations from the average are larger and more frequent than the normal 

distribution, the 5% VaR will be more than 1.65 standard deviations below the average return. 

Expected shortfall (ES) measures the expected rate of return conditional on the portfolio falling 

below a certain value. Thus, 1% ES is the expected return of all possible outcomes in the bottom 

1% of the distribution.    

 Related Web sites 

for this chapter are 

available at   www.

mhhe.com/bkm   

   nominal  interest  rate  

  real  interest  rate  

  effective annual rate (EAR)  

  annual percentage rate (APR)  

  dividend  yield  

  risk-free  rate  

  risk  premium  

  excess  return  

  risk  aversion  

  normal  distribution  

  event  tree  

  skew  

  kurtosis  

  value at risk (VaR)  

  expected  shortfall  (ES)  

  conditional  tail  expectation 

(CTE)  

  lower  partial  standard 

deviation (LPSD)  

  Sortino  ratio  

  lognormal  distribution