Chapter 5 Risk and Return  Returns  Dollar and Percentage  Holding Period Returns  Converting to Annual Returns  Historical Returns  Risk using Variance or Standard Deviation  Risk as Uncertainty  Returns in an Uncertain World  Risk and Return Tradeoff

Returns  Calculating a return  Dollar Return  Ending Value + Distributions – Original Cost  Example 5.1, Bought Trading Card for $5.00 and sold it for $6.25, Dollar Return (Profit) $1.25  Percentage Return  [(Ending Value + Distributions) / Original Cost] – 1  Example 5.1, $1.25 / $5.00 = 25%  Calculating a return with distributions  Example 5.2, Stock with dividend

Holding Period Returns  Holding Period Returns (HRP)  The return for the length of time that investment is held  Not consistent with interest rates from Chapter 4  Need to convert to annual basis for comparison  Annualized return = (1 + HRP) n – 1  Warning on extrapolation of holding period returns for less than a year  Compounding requires each additional investment period with same holding period return

Historical Returns  Year by Year Returns  Four different investments  3-Month Treasury  Long-Term Government Bonds  Large Company Stocks  Small Company Stocks  Large Swings from year to year  Most consistent performer, 3-Month Treasury  Relationship of average return and standard deviation – first look at risk and return tradeoff

Risk Using Variance or Standard Deviations  Measure of the swing from year to year: Variance or Standard Deviation  Greater the variance or standard deviation the greater the potential outcomes  Standard Deviation (σ) = Variance 1/2 (σ 2 )  Normal Distribution helps explain probability of a potential outcome

Risk as Uncertainty  Risk is the uncertainty in the outcome of an event  An event where the outcome is known before the event is free of uncertainty or risk-free  Example of a horse race  Before the race, all horses entered in the race have a chance to win  However, some have a better chance to win than others  Standard Deviation will be one measure of risk

Returns in an Uncertain World  Investments or bets are made prior to the event  Need to calculate the expected outcome of the event  Need the list of all potential outcomes  Need the chance of each potential outcome  Expected Return = Σ outcome i x probability i  Payoff or return for investment is the outcome

Returns in an Uncertain World  Variance or Standard Deviation in Uncertain World  Need the probabilities of all outcomes  Need the expected outcome  Σ(outcome i – expected outcome) x probability i  Example 5.3 – Expected Return of Long Bond  Four potential outcome (states of the world)  Probability of each outcome known (or estimated)  Calculate expected return of 6.35%  Calculate variance of % or standard deviation of %

Risk and Return Tradeoff  Objective: Maximize Return and Minimize Risk  Must tradeoff increases risk and return with decreasing risk and return  Investment Rule #1 – Two assets with same expected return, pick one with lower risk  Investment Rule #2 – Two assets with the same risk, pick one with higher return  What to do when one investment has both higher return and more risk versus another asset?  Must look to individual choice

Problems  Problem 5 – Holding Period and Annual Return  Problem 8 – Comparing Returns  Problem 9 – Historical Return Averaging  Problem 11– Standard Deviations  Problem 13 – Expected Return  Problem 14 – Variance and Standard Deviation of Expected Return