This document discusses risk and return in investments over time. It provides historical returns for various investments from 1995-2004 such as the S&P 500, GM stocks, and Treasury bills. It also discusses the relationship between risk and return, showing that higher volatility investments like small stocks have provided higher average returns. Diversification reduces unique "diversifiable" risk but not systematic market risk, which requires a risk premium.
2. Risk and Return
Suppose 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 stocks
Standard
and Poor’s
500
World
Portfolio
Corporate
Bonds
Treasury
Bills
3.
4. 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
5. 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
6. 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 extra
Risk they are taking on.
8. 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.
10. 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.
11. 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?
12. 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?
13. 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.
14. 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.
15. 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.
16. 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?
17. 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
18. 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)
19. 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.
20. 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.
21. 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.
22. 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?
23. 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)
24. 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.
