Chapter 7 – Risk, Return and the Security Market Line  Learning Objectives  Calculate Profit and Returns  Convert Holding Period Returns (HPR) to APR  Appreciate historical returns  Calculate standard deviations and variances  Calculate standard deviations with future data  Understand risk and return tradeoff  Interpret risk and return tradeoff  Discover how to remove some risk  Understand diversification  Explain systematic and unsystematic risk  Understand Beta and what it measures

Returns  Calculating a return  Dollar Return  Ending Value + Distributions – Original Cost  Example 7.1, Bought Trading Card for $50 and sold it for $55, Dollar Return (Profit) $5  Percentage Return  [(Ending Value + Distributions) / Original Cost] – 1  Example 7.1, [$55 +$0 / $50] - 1 = 10%  Calculating a return with distributions  Example 7.1, Stock with dividend  [($ $0.90) / $42.00] – 1 = 16%

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) 1/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

Risk as Uncertainty  Risk is the uncertainty in the outcome of an event (potential good and bad outcomes)  An event where the outcome is known before the event is free of uncertainty or risk-free  Trading Card could go down in value over time  Bought at $50 but sell at $41.50  Return = [($ $50.00) / $50.00] -1 = -17%  Holding period return loss of -17% (bad outcome)

Historical Returns  Year by Year Returns (See Table 7.1)  Four different investments  3-Month Treasury Bill  Long-Term Government Bonds  Large Company Stocks  Small Company Stocks  What do we notice?  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

Measuring Risk Using Variance  Measure of the swing from year to year: Variance (σ 2 )  Greater the variance the greater the potential outcomes  Standard Deviation (σ) = Variance 1/2 [(σ 2 ) 1/2 ]

Historical Returns and Variances  Four Financial Instruments  Highest Return and Highest Variance – Small Stocks  Lowest Return and Lowest Variance – U.S. Treasury Bill  See Figure 7.3 page 196  Linear relationship of risk and return  The greater the return the greater the variance  Relationship of risk and return

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  Example 7.3, Expected Return on a bond

Example 7.3  States of the Economy (World)  Four potential economic states  Each has positive probability  Bond has different “outcome” in each state  Expected return is weighed average  15% x 2% + 45% x 5% + 30% x 8% + 10% x 10%  On average we expect 5.95% return  Variance uses same probabilities of the states of the economy

Risk and Return Tradeoff  Objective: Maximize Return and Minimize Risk  Must tradeoff increases in 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

Diversification – Eliminating Risk  Don’t put all your eggs in one basket  Spread out your investment over a series of investments  If a “bad outcome” should hit one investment a “good outcome” in another investment could offset the bad outcome  Combining Zig and Zag  When one is up the other down  Consistent return from period to period  Spreading investment lowers risk

When Diversification Works  Co-movement of stock returns  Correlation Coefficient  Covariance of two assets divided by their standard deviations (equation 7.10)  Positive Correlation  No benefit if perfectly positively correlated  Example Peat and Repeat Companies  Negative Correlation  Eliminate all risk if perfectly negatively correlated  Example Zig and Zag Companies

Systematic and Unsystematic Risk  Systematic Risk – risk you cannot avoid  Unsystematic Risk – risk you can avoid  Adding more and more stocks  As you add more stocks to portfolio you reduce more of the unsystematic or firm-specific risk  Marginal decline in elimination  Around 25 to 30 stocks can eliminate nearly all unsystematic risk  Variance or Standard Deviation is measure of both systematic and unsystematic risk

Beta – Measure of Risk in a Portfolio  Using Beta for finding the risk of a portfolio  In a well diversified portfolio only systematic risk remains  Systematic risk of portfolio is weighted betas  Example 7.4 (Henry and Rosie’s Betas)  Henry average risk and beta is 1.0  0.25 x x x x 1.4  Rosie is slightly conservative (investments) and beta is 0.94  0.35 x x x x 1.4

Using Beta  Beta Facts  Beta of zero means no risk (i.e. T-Bill)  Beta of 1 means average risk (same as market risk)  Beta < 1, risk lower than market  Beta > 1, risk greater than market  Expected Return and Beta use asset weights in portfolio for portfolio e(r) and β  Expected Return = Σ w i x return i  Beta = Σ w i x β i

Using Beta  Beta also determines expected return of individual asset  Known, risk-free rate  Estimate, expected return on market  Each asset’s expected return function of its risk as measured by beta and the risk-reward tradeoff (slope of SML)

Company: A Portfolio of Projects  All companies are a portfolio of individual projects (or products and services)  Concept of portfolio helps explain  Viewing each project or product with different level of risk (project β) and contribution (expected return)  Different project or product combinations can lower overall risk of the firm  Projects plotting above the SML (buy)  Projects plotting below the SML (sell)

Risk and Return in a Portfolio that is Not Well Diversified  George Jetson investing choice  Only four assets in portfolio (equally weighted)  Expected return = 9.35%  Standard Deviation = 4.29%  Weighted average standard deviations of four assets = 4.4%  Little benefit from diversification  Portfolio needs more assets for benefits of diversification

Security Market Line  Assumptions  #1 – There is a reward for waiting  #2 – The greater the risk the greater the expected reward  #3 – There is a constant tradeoff between risk and reward  E(return) = risk-free rate + slope (level of risk)  Trick is to find the level of risk for an investment and the reward for risk

CAPM  Capital Asset Pricing Model (CAPM)  Expected return of an asset is a function of  The time value of money  Reward for taking on risk  Amount of risk  Security Market Line is application of CAPM  All firms plot on SML (ex-ante)  Firms above the line are under priced  Firms below the line are over priced  Security Market Line estimates expected returns

Applications of SML  Two assets on the SML (two points)  Find slope (reward for risk)  Find intercept (risk-free rate)  Equation of the line in general form  Assets plotting off the line  Find the “expected return” for the level of risk  If the anticipated return is greater than the expected return for that level of risk (asset plots above the line), buy asset  If return less, plots below the line, sell asset

Homework  Problem 6 –Returns  Problem 12 – Variance and Standard Deviation  Problem 15 – Portfolio Expected Return  Problem 16 – Portfolio Expected Variance and Standard Deviation  Problem 24 – SML application  Problem 30 – SML application  Problem 32 – Combining Assets