Reading 43: Portfolio Risk and Return (P.1)


  1. Calculate and interpret major return measures and describe their appropriate uses
  • Holding period return (HPR)

  • Average returns
  • The arithmetic mean return is the simple average of a series of periodic returns.
  • The geometric mean return is a compound annual rate.

  • The money-weighted rate of return is the internal rate of return on a portfolio based on all of its cash inflows and outflows.
  • Other return measures
  • Gross return: refers to the total return on a security portfolio before deducting fees for the management and administration of the investment account.
  • Net return: refers to the return after these fees have been deducted.
  • Pretax nominal return: return prior to paying taxes. Dividend income, interest income, short-term capital gains and long-term capital gains may be taxed at different rates.
  • Real return: is nominal return adjusted for inflation.

Ex: Nominal return: 7%, inflation: 2%. ⇒ Approximately: 7-2 = 5%, real return: 1,07/1,02 = 4.9%

  • A leveraged return: return to an investor that is a multiple of the return on the underlying asset. Equal (% of gains or losses on investment)/ cash investment.

2. Describe characteristics of the major asset that investors consider in forming portfolios

  • Asset classes with the greatest average returns also have the highest standard deviations (risk) of returns.
  • Liquidity is an additional characteristic to consider when choosing investments because liquidity effect the price and expected return of a securities.
  • US, small-cap stocks ⇒ greatest average returns & greatest risk over period. Treasury bill ⇒ lowest (return & risk).


3. Calculate and interpret the mean, variance and covariance (correlation) of asset returns based on historical data.

  • Variance (Standard deviation) of return for an Individual security

Where: N (n): total number period

x, the mean or expected return

  • Covariance and correlation of returns for two securities: Measures the extent to which 2 variables move together over time.
  • Positive covariance ⇒ the variables (rates of return on 2 stocks) tend to move together.
  • Negative covariance ⇒ 2 variables tend to move in opposite directions.
  • Zero covariance ⇒ no linear relationship. Knowing 1 tells nothing about 2.
  • Focus on the calculation of the covariance between 2 asset’s returns using Historical data.