RISK AND RATES OF RETURN

• Risk


  The probability of not receiving the expected return from an investment
• Risk


  • Implies a degree of uncertainty
  • Measured by variability in returns - the greater the potential variability of returns, the riskier an investment
• Risk-free investment


  A one-year BSP Treasury bill that provides a "guaranteed" rate of return
• Risky investment


  The annual returns on shares of a stock (or some other variable investment instrument) are inherently riskier - the return may be much less than expected or, in the worst-case scenario, even less than the initial investment
• Types of Risk


  • Credit risk (default risk)
  • Foreign exchange risk (currency risk)
  • Interest rate risk
  • Market risk
  • Industry risk
  • Political risk
• Rate of return


  The amount received on an investment from holding that investment for a period of time relative to the amount of the initial investment
• Calculating Rate of Return

  1. Cash payments received (such as dividends or interest)

  2. Plus: the change in market price appreciation or loss in price

  3. Total

  4. Divided by: the beginning price of the security
• Under rational market conditions, those investments with greater expected risk should provide HIGHER expected rate of return than investments with lower risk
• BSP T-bills (Phil govt securities that mature in less than one year)


  Very safe securities, no default risk, prices relatively stable, offer the most conservative rate of return
• Phil govt bonds and corporate bonds


  Have longer maturity periods than T-bills, prices fluctuate as interest rates vary, inverse relationship between bond prices and interest rates, govt bonds have no risk of default but corporate bonds do have default risk, over time bond rates of return are higher than T-bills, corporate bonds have slightly higher returns than government bonds
• Stocks


  Provide investments signifying an ownership position ("equity") in a corporation, stock investor has a direct share in the risks of the enterprise, on average stock returns are significantly higher than the safe rates of return from T-bills or bonds, returns on common stocks are higher than return on preferred stocks
• Shareholder wealth


  The market value of a company's common stock (a.k.a. market capitalization); calculated as the no. of common shares outstanding times the market price per share
• Shareholder wealth maximization (SWM)

  The maximization of shareholders' purchasing power, in an efficient market SWM is the maximization of the current share price multiplied by the no. of shares outstanding, from a financial perspective SWM is assumed to be the major goal of a firm
• Certainty equivalent (CE)


  A concept that describes the amount of cash an investor would have to be indifferent between the payoff and a given gamble, the smallest certain payoff an investor would accept in exchange for a risky cash flow, a CE factor is used to convert a projected cash flow into a certain cash flow
• Certainty Equivalent and Attitudes Toward Risk

  • When CE is less than expected value - risk aversion is present
  • When CE is equal to expected value - risk indifference is present
  • When CE is greater than expected value - risk preference is present
• Risk aversion


  An investor's dislike of risk and need for a higher rate of return as an inducement to take on riskier investments, most investors are risk averse and seek higher returns for increasing risks
• The actual return on an investment classified as less risky could outperform the actual return on a risky investment, risk increases with time - there is greater certainty/variability in forecasting for distant years
• Probability distribution


  A set of possible values that a random variable (i.e. an investment) can take and the likelihood that each will occur
• Descriptive statistical measures in a probability distribution

  • Expected return
  • Standard deviation
  • Coefficient of variation
• Expected return


  The weighted average of the possible returns where the weights represent the probabilities of occurrence, a measure of central tendency of a probability distribution
• Standard deviation


  A statistical measure showing the variation or dispersion around the expected (most likely) return on an investment, the higher the standard deviation, the greater the variability of returns and the greater the total risk
• Coefficient of Variation (CV)

  Provides a measure of RELATIVE risk, calculated by dividing the standard deviation by the mean of expected return, a higher CV indicates higher RELATIVE risk
• Portfolio


  A mix of two or more assets, may include any combination of cash, bonds, stocks, mutual funds, or other investments, the purpose is to minimize risk
• Covariance


  Shows the way two different assets in a portfolio are expected to vary together - the way returns move relative to one another - rather than independently
• Covariance


  A statistical measure showing the degree to which two random variables (such as two investment returns in a portfolio) move together
• Variance


  Measures how a single random variable moves with itself
• Covariance


  Measures how one random variable moves with another random variable
• Covariance


  • The expected returns on a stock and a put option on the stock move in opposite directions and will have a NEGATIVE covariance
  • The expected returns for two stocks in the same industry most likely would move in the same direction and have a POSITIVE covariance
  • The expected return of a stock paired with a riskless Treasury security would have a ZERO covariance because the riskless asset's returns do not move, regardless of changes in the stock's returns
• As the number of assets in a portfolio grows, the covariance between various securities that have been paired becomes more important
• The more different the movement between assets, the less portfolio risk
• Correlation


  Measures the strength of the linear relationship between two random variables
• Correlation has no units
• The correlation coefficient always lies in a range from -1.0 to +1.0
• Positive correlation


  Securities move in the SAME direction
• +1.0 correlation


  Random variables have perfect positive correlation, a movement in one security results in an EXACT measurable positive movement in the other
• Negative correlation


  Securities move in the opposite direction
• • 1.0 correlation


  Random variables have perfect negative correlation, a movement in one security results in an EXACT MEASURABLE NEGATIVE movement in the other
• 0 correlation


  No linear relationship between the variables, indicating that prediction of Expected Return of Asset 1 cannot be made on the basis of Expected Return of Asset 2, using linear methods
• Risk-adverse investors generally would want to DIVERSIFY holdings to include securities that have LESS-THAN-PERFECT POSITIVE CORRELATION
• The standard deviation of the portfolio is LARGEST when the correlation coefficient is +1, declines when it is 0, and declines further when it is -1