Chapter 5 Risk Return Chapter 5

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

Interest Rates Conceptually: Nominal risk-free Interest Rate = Real risk-free Interest Rate krf k* + Inflationrisk premium IRP Mathematically: (1 + krf) = (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. 0485), so IRP = 4. 85%

For a Treasury security, what is the required rate of return? Required rate of return = Risk-free 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.

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

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:

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: k = P(k 1)*k 1 + P(k 2)*k 2 +. . . + P(kn)*kn

Expected Return State of Probability Economy (P) Recession. 20 Normal. 50 Boom. 30 Return Orl. Utility Orl. Tech 4% -10% 14% 30% k = P(k 1)*k 1 + P(k 2)*k 2 +. . . + P(kn)*kn k (OU) =. 2 (4%) +. 5 (10%) +. 3 (14%) = 10%

Expected Return State of Probability Economy (P) Recession. 20 Normal. 50 Boom. 30 Return Orl. Utility Orl. Tech 4% -10% 14% 30% k = P(k 1)*k 1 + P(k 2)*k 2 +. . . + P(kn)*kn k (OI) =. 2 (-10%)+. 5 (14%) +. 3 (30%) = 14%

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

Have you considered RISK?

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. Company A Company B 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 100 s Hi Lo Close Chg 134 80 IBM. 52. 5 21 143402 98 95 9549 -3 115 40 MSFT … 29 558918 55 52 5194 -475

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

Standard Deviation s= S P(ki) n i=1 (ki - 2 k)

s= n S (ki - 2 k) P(ki) 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%

s= n S (ki - 2 k) P(ki) i=1 Orlando Technology, Inc. (-10% - 14%)2 (. 2) = 115. 2 (14% - 14%)2 (. 5) = 0 (30% - 14%)2 (. 3) = 76. 8 Variance = 192

Which stock would you prefer? How would you decide?

Summary Orlando Technology Expected Return 14% Orlando Utility 10%

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