11-1 lecture 11 introduction to risk, return, and the opportunity cost of capital

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Lecture 11

Introduction to Risk, Return, and the Opportunity Cost of Capital

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Risk and Return

Risk and Return are related.

How?

This chapter will focus on risk and return and their relationship to the opportunity cost of capital.

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Equity Rates of Return: A Review

Capital Gain + Dividend Initial Share PricePercentage Return =

Capital GainInitial Share PriceCapital Gain Yield =

Dividend Initial Share PriceDividend Yield =

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Rates of Return: ExampleExample: You purchase shares of GE stock at $15.13 on December 31, 2009. You sell them exactly one year later for $18.29. During this time GE paid $.46 in dividends per share. Ignoring transaction costs, what is your rate of return, dividend yield and capital gain yield?

$18.29 $15.13 $.46

$15.1323.93%Percentage Return

$18.29 $15.13$15.13 20.89%Capital Gain Yield

$.46Dividend Yield = 3.04%

$15.13

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Real Rates of Return

1 + nominal rate of return1 + inflation rate1 real rate of return =

Example: Suppose inflation from December 2009 to December 2010 was 1.5%. What was GE stock’s real rate of return, if its nominal rate of return

was 23.93%?

Recall the relationship between real rates and nominal rates:

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Capital Market History:Market Indexes

• Market Index - Measure of the investment performance of the

overall market.

• Dow Jones Industrial Average (The Dow)

• Standard & Poor’s Composite Index (S&P 500)

Other Market Indexes?

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Total Returns for Different Asset Classes

The Value of an Investment of $1 in 1900

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What Drives the Difference in Total Returns?

Maturity Premium: Extra average return from investing in long- versus short-term Treasury securities.

Risk Premium: Expected return in excess of risk-free return as compensation for risk.

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Risk Premium: ExampleInterest Rate on Normal Risk

Expected Market Return = +Treasury Bills Premium

1981: 21.6% = 14% + 7.6%

2008: 9.8% = 2.2% + 7.6%

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Returns and Risk

How are the expected returns and the risk of a security related?

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Measuring Risk

Variance: Average value of squared deviations from mean. A measure of volatility.

Standard Deviation: Square root of variance. Also a measure of volatility.

What is risk?

How can it be measured?

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Variance and Standard Deviation: Example

Coin Toss Game: calculating variance and standard deviation

(assume a mean of 10)

(1) (2) (3)

Percent Rate of Return Deviation from Mean Squared Deviation

+ 40 + 30 900

+ 10 0 0

+ 10 0 0

- 20 - 30 900

Variance = average of squared deviations = 1800 / 4 = 450

Standard deviation = square of root variance = 450 = 21.2%

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Histogram of Returns

What is the relationship between the volatility of these securities and their expected returns?

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Historical Risk(1900-2010)

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Risk and DiversificationDiversification

Strategy designed to reduce risk by spreading a portfolio across many investments.

Unique Risk:Risk factors affecting only that firm. Also called “diversifiable risk.”

Market Risk:Economy-wide sources of risk that affect the overall stock market. Also called “systematic risk.”

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Diversification: Building a Portfolio

fraction of portfolio rate of returnPortfolio Rate of Return = x

in first asset on first asset

fraction of portfolio rate of return+ x

in second asset on second asset

A portfolio’s rate of return is the weighted sum of each asset’s rate of return.

Two Asset Case:

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Building a Portfolio: ExampleConsider the following portfolio:

Stock Weight Rate of Return

IBM

Starbucks

Walmart

What is the portfolio rate of return?

50%IBMw

25%SBUXw

25%Ww

Portfolio Rate of Return =

(50% 8.3%) 25% 12.5% 25% 4.7%

8.45%

IBM IBM SBUX SBUX W Ww r w r w r

8.3%IBMr

12.5%SBUXr

4.7%Wr

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Do stock prices move together?

What effect does diversification have on a portfolio’s total risk, unique risk and market risk?

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Risk and Diversification

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Thinking About Risk

Message 1• Some Risks Look Big and Dangerous but Really Are

Diversifiable

Message 2• Market Risks Are Macro Risks

Message 3• Risk Can Be Measured