Risk and ReturnSuppose your great grand-parents had invested

on your behalf at the end of 1925. How would that $100 have grown if it were placed in one of these

following investments?

Small stocksStandard

and Poor’s 500

World Portfolio

Corporate Bonds

Treasury Bills

Historical Returns• Historical returns is the realized return of a stock.

Here we assume that all dividends:

Immediately reinvested

Used to purchase additional shares of the same stock.

Realized Yield = Dividend Yield + Capital Gain Yield

Year End S&P 500 Index

Dividends Paid*

S&P 500 Realized Return

GM Realized Return

3-Month T-Bill Return

1995 615.93

1996 740.74 16.61 23.0% 8.6% 5.1%

1997 970.43 17.2 33.4% 19.6% 5.2%

1998 1229.23 18.5 28.6% 21.3% 4.9%

1999 1469.25 18.1 21.0% 25.1% 4.8%

2000 1320.28 15.7 -9.1% -27.8% 6.0%

2001 1148.08 15.2 -11.9% -1.0% 3.3%

2002 879.82 14.53 -22.1% -20.8% 1.6%

2003 1111.92 20.8 28.7% 52.9% 1.0%

2004 1211.92 20.98 10.9% -21.5% 1.4%

REALIZED RETURN FOR THE S&P 500, GM and TREASURY BILLS, 1996 - 2004

*Total dividends paid by the 500 stocks in the portfolio, based on the number of shares of each stock in the index, adjusted until the end of the year, assuming they were reinvested when paid.

Source: Standard & Poor’s, GM and Global Financial Data

Volatility Vs Excess Return(Based on 1926 – 2004)

Investment Return Volatility ( Standard Deviation)

Excess Return (Average Return in Excess of Treasury Bills)

Small stocks 42.75% 18.24%

S & P 500 20.36% 8.45%

Corporate Bonds 7.17% 2.65%

Treasury Bills 3.18% 0.00%

Note the positive relationship : The investments with higher volatility have rewarded investors with higher average returns proving the fact that Investors are risk averse requiring a premium to compensate for the extraRisk they are taking on.

0% 40%20% 30%10%

0%

25%

20%

15%

10%

5%Treasury

BillsCorporate

Bonds

World Stocks

S&P 500

Mid-Cap Stocks

Small Stocks

Historical Volatility (Standard deviation)

His

toric

al A

vera

ge R

etur

n

Classification of Risks

• Usually, stock prices and dividends fluctuate

due to two types of news:

Firm specific news / independent risks

Market wide news/ systematic risks

• The volatility will decline until only the

systematic risk, which affects all firms remain.

Relationship between Diversification and Risk

1 5 10 15

No of Securities

Market Risk

Unique Risk

Risk

Diversification of risk

• Diversification eliminates unique risk but does

not eliminate systematic risk.

a. Because investors can eliminate unsystematic

risk, they do not require a risk premium.

b. Because investors cannot eliminate systematic

risk, they must be compensated for holding it.

Diversifiable Vs Systematic Risk Which of the following risks of a stock are likely to be

firm-specific, diversifiable risks and which are likely to

be systematic risks? Which risks will affect the risk

premium that investors will demand?

1. The risk that the CEO retires?

2. The risk that oil prices rise, increasing production cost?

3. The risk that a product design is faulty?

4. The risk that there is an economic slowdown?

You are a risk averse investor who is considering

investing in one of the two economies. The expected

return and the volatility of all stocks in both economies

is the same. In the first economy, all stocks move

together – in good times all prices rise together and in

bad times they all fall together. In the second economy,

stock returns are independent – one stock increasing in

price has no effect on the prices of other stocks. Which

economy would you choose to invest in?

Estimating the Expected Return

Estimating the expected return from an

investment requires two steps:

1. Measuring the systematic risk of the

investment.

2. Determining the risk premium required to

compensate for that amount of systematic

risk.

Measuring Systematic risk

How can we capture the systematic risk

component of a stock’s volatility?

o The risk premium of a security is determined

by its systematic risk and does not depend

upon its diversifiable risk.

o The risk premium for diversifiable risk is zero.

Measuring Systematic Risk

The systematic risk of a security is measured by its

Beta (β).

The Beta(β) of a security is the sensitivity of the

security’s return to the return of the overall

market.

Estimating Beta

Suppose the market portfolio excess return tends to increase by 47% when the economy is strong and decline by 25% when the economy is weak.

(a) What is the beta of a type S firm(having only

systematic risks) whose excess return is 40%

on average when the economy is strong and

–20% when the economy is weak?

(b) What is the beta of a firm which bears only

firm specific risk?

Estimating the risk Premium

Beta measures the amplification of systematic

risk compared to the market as a whole and

investors will require risk premium to make

such an investment.

Market Risk Premium = E[Rmkt] – r f

Estimating a Traded Security’s Expected Return from its Beta(β)

To compensate investors for the time value of their money as well as the systematic risk they are taking in investing in Security s, the expected return will be:

E[R] = Risk free Interest rate + Market risk Premium

Rp = Rf + βp (Rmkt – Rf)

Expected Returns and Beta(β)

Suppose the risk-free rate is 5% and the

economy is equally likely to be strong or weak.

Verify the above mentioned equation with

specific reference to Beta(β) for the firm which

was exposed to systematic risk as mentioned in

the above problem.

Problem based on Beta(β)Suppose the market portfolio is equally likely to increase by 30% or decrease by 10%.

1.Calculate the beta of a firm that goes up on an average by 43% when the market goes up and goes down by 17% when the market goes down.

2.Calculate the beta of a firm that goes up on an average by 18% when the market goes up and goes down by 22% when the market goes down.

3.Calculate the beta of a firm that is expected to go up by 4% independently of the market.

Risk and Cost of Capital

• A firm’s cost of capital for an investment or

project is the expected return its investors

could earn on their securities with the same

risk and maturity and the risk being the

systematic risk.

• So the expected return on a security is also the

cost of capital of a project.

Computing cost of capital Suppose that in the coming year, you expect Microsoft stock to have a volatility of 23% and a beta of 1.28 and McDonald’s stock to have a volatility of 37% and a beta of 0.99.

1.Which stock carries more total risk?

2. Which has more systematic risk?

3.If the risk free interest rate is 4% and the market’s expected return is 10%, estimate the cost of capital for a project with the same beta as McDonald’s stock and also with Microsoft stock. Which project has a higher cost of capital?

Determining the cost of capital

Suppose the market risk premium is 6.5% and

the risk-free interest rate is 5%. Calculate the

cost of capital of a project related to the

following companies:

a.Intel Corporation stock (β of 2.17)

b.Pfizer Inc. (β of 0.54)

c.Procter and Gamble (β of 0.19)

An Efficient Portfolio and a Market Portfolio

An efficient portfolio is a portfolio that

contains only systematic risk and cannot be

diversified further.

The market portfolio is a portfolio that

contains all shares of all stocks and securities

in the market.