Risk n Return

1. Risk and Return

2. Risk and Rates of Return
 Stand-Alone Risk
 Portfolio Risk
 Risk and Return: SML
7-2

3. What is investment risk?
 Two types of investment risk
 Stand-alone risk
 Portfolio risk
 Investment risk is related to the probability of earning a low or
negative actual return.
 The greater the chance of lower than expected or negative returns,
the riskier the investment.
7-3

4. Investment Returns
The rate of return on an investment can be calculated as follows:
For example, if $1,000 is invested and $1,100 is returned after one year, the
rate of return for this investment is:
($1,100 – $1,000)/$1,000 = 10%.
7-4
 
Cost
Cost
value
ending
Expected
Return



5. Calculating Standard Deviation
2
Variance
ˆ

 

 
 
N
2
i
i=1
=Standard deviation
(r -r) P
7-5

6. Standard Deviation for Each Investment
7-6
%
0
.
0
)
1
.
0
(
)
5
.
5
5
.
5
(
)
2
.
0
(
)
5
.
5
5
.
5
(
)
4
.
0
(
)
5
.
5
5
.
5
(
)
2
.
0
(
)
5
.
5
5
.
5
(
)
1
.
0
(
)
5
.
5
5
.
5
(
P
)
r̂
r
(
bills
-
T
2
/
1
2
2
2
2
2
bills
-
T
N
1
i
i
2
























 

σHT = 20%
σM = 15.2% σUSR = 18.8%
σColl = 13.2%

7. Comparing Standard Deviations
USR
Prob.
T-bill
HT
0 5.5 9.8 12.4 Rate of Return (%)
7-7

8. Comparing Standard Deviations
USR
Prob.
T-bill
HT
0 5.5 9.8 12.4 Rate of Return (%)
7-8

9. Comments on Standard Deviation as a
Measure of Risk
 Standard deviation (σi) measures total, or stand-alone, risk.
 The larger σi is, the lower the probability that actual returns will be closer to
expected returns.
 Larger σi is associated with a wider probability distribution of returns.

10. Comparing Risk and Return
7-10
Security Expected Return, Risk, 
T-bills 5.5% 0.0%
HT 12.4 20.0
Coll* 1.0 13.2
USR* 9.8 18.8
Market 10.5 15.2
*Seems out of place.
r̂

11. Risk Attitudes
Certainty Equivalent (CE) is the amount of cash someone
would require with certainty at a point in time to make the
individual indifferent between that certain amount and an
amount expected to be received with risk at the same
point in time.
Certainty equivalent > Expected value
Risk Preference
Certainty equivalent = Expected value
Risk Indifference
Certainty equivalent < Expected value
Risk Aversion
Most individuals are Risk Averse.

12. You have the choice between (1) a guaranteed dollar
reward or (2) a coin-flip gamble of $100,000 (50%
chance) or $0 (50% chance). The expected value
of the gamble is $50,000.
• Mary requires a guaranteed $25,000, or more, to
call off the gamble.
• Raleigh is just as happy to take $50,000 or take
the risky gamble.
• Shannon requires at least $52,000 to call off the
gamble.
Risk Attitude Example

13. Risk Attitude Example
What are the Risk Attitude tendencies of each?
Mary shows “risk aversion” because her “certainty
equivalent” < the expected value of the gamble.
Raleigh exhibits “risk indifference” because her “certainty
equivalent” equals the expected value of the gamble.
Shannon reveals a “risk preference” because her “certainty
equivalent” > the expected value of the gamble.

14. Systematic Risk is the variability of return on stocks or portfolios
associated with changes in return on the market as a whole.
Unsystematic Risk is the variability of return on stocks or portfolios not
explained by general market movements. It is avoidable through
diversification.
Total Risk = Systematic Risk +
Unsystematic Risk
Total Risk = Systematic Risk +
Unsystematic Risk

15. Total
Risk
Unsystematic risk
Systematic risk
STD
DEV
OF
PORTFOLIO
RETURN
NUMBER OF SECURITIES IN THE PORTFOLIO
Factors such as changes in the nation’s
economy, tax reform by the Congress,
or a change in the world situation.
Total Risk = Systematic Risk
+ Unsystematic Risk

16. Total
Risk
Unsystematic risk
Systematic risk
STD
DEV
OF
PORTFOLIO
RETURN
NUMBER OF SECURITIES IN THE PORTFOLIO
Factors unique to a particular company
or industry. For example, the death of a
key executive or loss of a governmental
defense contract.
Total Risk = Systematic Risk
+ Unsystematic Risk

17. An index of systematic risk.
It measures the sensitivity of a stock’s returns to changes
in returns on the market portfolio.
The beta for a portfolio is simply a weighted average of
the individual stock betas in the portfolio.
What is Beta?

18. EXCESS RETURN
ON STOCK
EXCESS RETURN
ON MARKET PORTFOLIO
Beta < 1
(defensive)
Beta = 1
Beta > 1
(aggressive)
Each characteristic
line has a
different slope.
Characteristic Lines and Different Betas

19. Comments on Beta
 If beta = 1.0, the security is just as risky as the average stock.
 If beta > 1.0, the security is riskier than average.
 If beta < 1.0, the security is less risky than average.
 Most stocks have betas in the range of 0.5 to 1.5.
7-19

20. Can the beta of a security be negative?
 Yes, if the correlation between Stock i and the market is negative
(i.e., ρi,m < 0).
 If the correlation is negative, the regression line would slope
downward, and the beta would be negative.
 However, a negative beta is highly unlikely.
7-20

21. Calculating Betas
 Well-diversified investors are primarily concerned with how a stock is
expected to move relative to the market in the future.
 Without a crystal ball to predict the future, analysts are forced to rely on
historical data. A typical approach to estimate beta is to run a regression of
the security’s past returns against the past returns of the market.
 The slope of the regression line is defined as the beta coefficient for the
security.
7-21

22. Beta Coefficients for HT, Coll, and T-Bills
7-22
rM
ri
-20 0 20 40
40
20
-20
HT: b = 1.32
T-bills: b = 0
Coll: b = -0.87

23. Comparing Expected Returns and Beta
Coefficients
Security Expected Return Beta
HT 12.4% 1.32
Market 10.5 1.00
USR 9.8 0.88
T-Bills 5.5 0.00
Coll. 1.0 -0.87
Riskier securities have higher returns, so the rank order is OK.
7-23

24. Rj is the required rate of return for stock j,
Rf is the risk-free rate of return,
bj is the beta of stock j (measures systematic
risk of stock j),
RM is the expected return for the market
portfolio.
Rj = Rf + bj(RM – Rf)
Security Market Line

25. Rj = Rf + bj(RM – Rf)
bM = 1.0
Systematic Risk (Beta)
Rf
RM
Required
Return
Risk
Premium
Risk-free
Return
Security Market Line

26. 1. The stocks of Wangi Berhad has a beta of 1.50
a. Is Wangi stock more or less risky than the market? Explain.
b. Evaluate the impact of each of the following situations on the required
rate of return.
i. The market return remains unchanged.
ii. The market return increaes by 25%
iii. The market return decreased by 15%
TUTORIAL
2. Lisa Miller at Basket Wonders is attempting to determine the rate of
return required by their stock investors. Lisa is using a 6% Rf and a long-
term market expected rate of return of 10%. A stock analyst following the
firm has calculated that the firm beta is 1.2. What is the required rate of
return on the stock of Basket Wonders?
3. Snowy has beta of 2, expected market return is 17% and risk free rate
is 9%. What is the required rate of return?

27. 1. Which of the following statements about a risk-averse individual is true?
A. He would choose an investment with a high standard deviation but a low
expected return
B. He would choose an investment with a low standard deviation and a high
expected return
C. He would choose an investment with a high expected return and a high
standard deviation
D. He would choose an investment with a low standard deviation and a low
expected return
2. If Ben holds a single aset in his portfoliom the risk exposure would be best
measured by
A. Coefficient of variation
B. Normal distributions of returns
C. Standard deviation of returns
D. None of the above

28. 3. Which of the following is systematic risk?
A. The probability that a stock’s return would drop duet o an impending major
lawsuit
B. Possibilty of an increase in the tax rate
C. Possibility of a decline in the market share due to low quality products.
D. Possibility of a decline in earnings due to a shortage of essential ingredients
required in the manufacturing of one of the products.
4. When an investor starts to add more securities to the portfolio, __________
would begin to disappear
A. Systematic risk
B. Purchasing power risk
C. Unsystematic risk
D. Default risk
5. Which of the following statement are true about standard deviation?
A. Standard deviation can be a positive or negative number
B. Standard deviation is the average of the suqared dispersion from the mean
C. Standard deviation is the square root of the variance
D. Standard deviation is a relative measure of risk

29. • Which of the following statement are true about standard deviation?
A. Standard deviation can be a positive or negative number
B. Standard deviation is the average of the suqared dispersion from the
mean
C. Standard deviation is the square root of the variance
D. Standard deviation is a relative measure of risk