Chapter 5 Risk & Return

Chapter 5: Objectives Inflation and rates of return How to measure risk (variance, standard deviation, beta) How to reduce risk (diversification) How to price risk (security market line, Capital Asset Pricing Model)

Inflation, Rates of Return, and the Fisher Effect Interest Rates

Conceptually: Nominal risk-free Interest Rate k rf = Real risk-free Interest Rate k* + Inflation- risk premium IRP Mathematically: (1 + k rf ) = (1 + k*) (1 + IRP) This is known as the “Fisher Effect” Interest Rates

Suppose the real rate is 3%, and the nominal rate is 8%. What is the inflation rate premium? (1 + krf) = (1 + k*) (1 + IRP) (1.08) = (1.03) (1 + IRP) (1 + IRP) = (1.0485), so IRP = 4.85% Interest Rates

For a Treasury security, what is the required rate of return? Since Treasuries are essentially free of default risk, the rate of return on a Treasury security is considered the “risk-free” rate of return. Required rate of return = Risk-free return

For a corporate stock or bond, what is the required rate of return? How large of a risk premium should we require to buy a corporate security? Required rate of return = += += += + Risk-free returnRiskpremium

Returns Expected Return - the return that an investor expects to earn on an asset, given its price, growth potential, etc. Required Return - the return that an investor requires on an asset given its risk and market interest rates.

Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession.20 4% -10% Normal.50 10% 14% Boom.30 14% 30% For each firm, the expected return on the stock is just a weighted average:

State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession.20 4% -10% Normal.50 10% 14% Boom.30 14% 30% For each firm, the expected return on the stock is just a weighted average: k = P(k1)*k1 + P(k2)*k P(kn)*kn Expected Return

State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession.20 4% -10% Normal.50 10% 14% Boom.30 14% 30% k = P(k1)*k1 + P(k2)*k P(kn)*kn k (OU) =.2 (4%) +.5 (10%) +.3 (14%) = 10%

Expected Return State of Probability Return Economy (P) Orl. Utility Orl. Tech Recession.20 4% -10% Normal.50 10% 14% Boom.30 14% 30% k = P(k1)*k1 + P(k2)*k P(kn)*kn k (OI) =.2 (-10%)+.5 (14%) +.3 (30%) = 14%

Based only on your expected return calculations, which stock would you prefer?

RISK? Have you considered

What is Risk? The possibility that an actual return will differ from our expected return. Uncertainty in the distribution of possible outcomes.

What is Risk? Uncertainty in the distribution of possible outcomes.

What is Risk? Uncertainty in the distribution of possible outcomes. Company A return

What is Risk? Uncertainty in the distribution of possible outcomes. return Company B Company A return

How do We Measure Risk? To get a general idea of a stock’s price variability, we could look at the stock’s price range over the past year. 52 weeks Yld Vol Net Hi Lo Sym Div % PE 100s Hi Lo Close Chg IBM MSFT …

How do We Measure Risk? A more scientific approach is to examine the stock’s standard deviation of returns. Standard deviation is a measure of the dispersion of possible outcomes. The greater the standard deviation, the greater the uncertainty, and, therefore, the greater the risk.

Standard Deviation = (k i - k) 2 P(k i )  n i=1 

Orlando Utility, Inc. ( 4% - 10%) 2 (.2) = 7.2 (10% - 10%) 2 (.5) = 0 (14% - 10%) 2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 = 3.46% Orlando Utility, Inc. ( 4% - 10%) 2 (.2) = 7.2 (10% - 10%) 2 (.5) = 0 (14% - 10%) 2 (.3) = 4.8 Variance = 12 Stand. dev. = 12 = 3.46% = (k i - k) 2 P(k i )  n i=1 

Orlando Technology, Inc. (-10% - 14%) 2 (.2) = (14% - 14%) 2 (.5) = 0 (30% - 14%) 2 (.3) = 76.8 Variance = 192 Stand. dev. = 192 = = (k i - k) 2 P(k i )  n i=1 

Orlando Technology, Inc. (-10% - 14%) 2 (.2) = (14% - 14%) 2 (.5) = 0 (30% - 14%) 2 (.3) = 76.8 Variance = 192 Stand. dev. = 192 = 13.86% = (k i - k) 2 P(k i )  n i=1 

Which stock would you prefer? How would you decide?

Orlando Orlando Utility Technology Expected Return 10% 14% Standard Deviation 3.46% 13.86% Summary

It depends on your tolerance for risk! Remember, there’s a tradeoff between risk and return. Return Risk