Risk and Rates of Return Stand-alone risk Portfolio risk Risk & return: CAPM / SML

What are Investment Returns Investment returns measure the financial results of an investment. Returns may be historical or prospective (anticipated). Returns can be expressed in: Taka Percentage Terms

Investment returns (Amount received – Amount invested) The rate of return on an investment can be calculated as follows: (Amount received – Amount invested) Return = ________________________ Amount invested For example, if $1,000 is invested and $1,100 is returned after one year, the rate of return for this investment is: ($1,100 - $1,000) / $1,000 = 10%.

Return R = Dt + (Pt - Pt-1 ) Pt-1 Income received on an investment plus any change in market price, usually expressed as a percent of the beginning market price of the investment. Dt + (Pt - Pt-1 ) R = Pt-1

Return Example The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year?

Return Example = 5% R = $1.00 + ($9.50 - $10.00 ) $10.00 The stock price for Stock A was $10 per share 1 year ago. The stock is currently trading at $9.50 per share, and shareholders just received a $1 dividend. What return was earned over the past year? $1.00 + ($9.50 - $10.00 ) = 5% R = $10.00

What is investment risk? Two types of investment risk Stand-alone risk Portfolio risk Investment returns are not known with certainty. Investment risk is related to the probability of earning a low or negative actual return. The greater the chance of lower than expected or negative returns, the riskier the investment.

Investment alternatives Economy Prob. A B C D E Recession 0.1 8.0% -22.0% 28.0% 10.0% -13.0% Below avg 0.2 -2.0% 14.7% -10.0% 1.0% Average 0.4 20.0% 0.0% 7.0% 15.0% Above avg 35.0% 45.0% 29.0% Boom 50.0% -20.0% 30.0% 43.0%

Return: Calculating the expected return for each alternative

Summary of expected returns for all alternatives Exp return B 17.4% E 15.0% D 13.8% A 8.0% C 1.7% B has the highest expected return, and appears to be the best investment alternative, but is it really? Have we failed to account for risk?

How to Determine the Expected Return and Standard Deviation Ki Pi (Ki)(Pi) -.15 .10 -.015 -.03 .20 -.006 .09 .40 .036 .21 .20 .042 .33 .10 .033 Sum 1.00 .090 The expected return, R, for Stock is .09 or 9%

Risk: Calculating the standard deviation for each alternative

Standard deviation calculation

How to Determine the Expected Return and Standard Deviation Ki Pi (Ki)(Pi) (Ki -K)2(Pi) -.15 .10 -.015 .00576 -.03 .20 -.006 .00288 .09 .40 .036 .00000 .21 .20 .042 .00288 .33 .10 .033 .00576 Sum 1.00 .090 .01728

Determining Standard Deviation (Risk Measure) s = S ( Ki - K )2( Pi ) = .01728 s = .1315 or 13.15%

Comments on standard deviation as a measure of risk Standard deviation (σi) measures total, or stand-alone, risk. The larger σi is, the lower the probability that actual returns will be closer to expected returns. Difficult to compare standard deviations, because return has not been accounted for.

Determining Expected Return (Continuous Dist.) K = S ( Ki ) / ( n ) K is the expected return for the asset, Ki is the return for the ith observation, n is the total number of observations.

Determining Standard Deviation (Risk Measure) s = S ( Ki - K )2 ( n )

9.6%, -15.4%, 26.7%, -0.2%, 20.9%, 28.3%, -5.9%, 3.3%, 12.2%, 10.5% Calculate the Expected Return and Standard Deviation

Comparing risk and return Security Expected return Risk, σ A 8.0% 0.0% B 17.4% 20.0% C 1.7% 13.4% D 13.8% 18.8% E 15.0% 15.3%

Coefficient of Variation (CV) A standardized measure of dispersion about the expected value, that shows the risk per unit of return.

Risk rankings, by coefficient of variation CV A 0.000 B 1.149 C 7.882 D 1.362 E 1.020 C has the highest degree of risk per unit of return. B, despite having the highest standard deviation of returns, has a relatively average CV.

Investor attitude towards risk Risk aversion – assumes investors dislike risk and require higher rates of return to encourage them to hold riskier securities. Risk premium – the difference between the return on a risky asset and less risky asset, which serves as compensation for investors to hold riskier securities.

Portfolio construction: Risk and return Assume a two-stock portfolio is created with $50,000 invested in both HT and Collections. Expected return of a portfolio is a weighted average of each of the component assets of the portfolio. Standard deviation is a little more tricky and requires that a new probability distribution for the portfolio returns be devised.

Calculating portfolio expected return

An alternative method for determining portfolio expected return Economy Prob. B C Port. Recession 0.1 -22.0% 28.0% 3.0% Below avg 0.2 -2.0% 14.7% 6.4% Average 0.4 20.0% 0.0% 10.0% Above avg 35.0% -10.0% 12.5% Boom 50.0% -20.0% 15.0%

Calculating portfolio standard deviation and CV

Comments on portfolio risk measures σp = 3.3% is much lower than the σi of either stock (σB = 20.0%; σC. = 13.4%). σp = 3.3% is lower than the weighted average of B and C’s σ (16.7%). \ Portfolio provides average return of component stocks, but lower than average risk.

Breaking down sources of risk Stand-alone risk = Market risk + Firm-specific risk Market risk – portion of a security’s stand-alone risk that cannot be eliminated through diversification. Measured by beta. Firm-specific risk – portion of a security’s stand-alone risk that can be eliminated through proper diversification.

Illustrating diversification effects of a stock portfolio # Stocks in Portfolio 10 20 30 40 2,000+ Company-Specific Risk Market Risk 20 Stand-Alone Risk, sp sp (%) 35

Total Risk = Systematic Risk + Unsystematic Risk Systematic Risk is the variability of return on stocks or portfolios associated with changes in return on the market as a whole. Unsystematic Risk is the variability of return on stocks or portfolios not explained by general market movements. It is avoidable through diversification.

Total Risk = Systematic Risk + Unsystematic Risk Factors such as changes in nation’s economy, tax reform by the Government, or a change in the world situation. STD DEV OF PORTFOLIO RETURN Unsystematic risk Total Risk Systematic risk NUMBER OF SECURITIES IN THE PORTFOLIO

Total Risk = Systematic Risk + Unsystematic Risk Factors unique to a particular company or industry. For example, the death of a key executive or loss of a governmental defense contract. STD DEV OF PORTFOLIO RETURN Unsystematic risk Total Risk Systematic risk NUMBER OF SECURITIES IN THE PORTFOLIO

Capital Asset Pricing Model (CAPM) CAPM is a model that describes the relationship between risk and expected (required) return; in this model, a security’s expected (required) return is the risk-free rate plus a premium based on the systematic risk of the security.

Capital Asset Pricing Model (CAPM) Model based upon concept that a stock’s required rate of return is equal to the risk-free rate of return plus a risk premium that reflects the riskiness of the stock after diversification.

CAPM Assumptions 1. Capital markets are efficient. 2. Homogeneous investor expectations over a given period. Risk-free asset return is certain 4. Market portfolio contains only systematic risk.

An index of systematic risk. What is Beta? An index of systematic risk. It measures the sensitivity of a stock’s returns to changes in returns on the market portfolio. The beta for a portfolio is simply a weighted average of the individual stock betas in the portfolio.

Beta Measures a stock’s market risk, and shows a stock’s volatility relative to the market. Indicates how risky a stock is if the stock is held in a well-diversified portfolio.

Comments on beta If beta = 1.0, the security is just as risky as the average stock. If beta > 1.0, the security is riskier than average. If beta < 1.0, the security is less risky than average. Most stocks have betas in the range of 0.5 to 1.5.