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RISK AND RETURNS
ACC09 FINANCIAL MANAGEMENT
PART 2
The Risk Management
Function
• Managing firms’ exposures to all
types of risk in order to maintain
optimum risk-return trade-offs and
thereby maximize shareholder
value.
• Modern risk management focuses
on adverse interest rate
movements, commodity price
changes, and currency value
fluctuations.
2
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
Web site, in whole or in part.
EFFECT OF MARKET DIVERSIFICATION
TO FIRM-SPECIFIC AND MARKET RISKS
Risk-Return Trade-off
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole
or in part.
TWO BASIC RULES IN BASIC
RISK MANAGEMENT
• REQUIRE RETURNS AT LEAST
EQUAL TO THE RISK ONE IS
WILLING TO TAKE.
• TO MEASURE RISK IS TO MEASURE
RETURN
EXPECTED VALUE OF RETURNS
• describes the numerical
average of a probability
distribution of estimated future
cash receipts from an
investment project
EXPECTED VALUE OF RETURNS
• Estimating the various amounts of cash
receipts from the project each year
under different assumptions or operating
conditions
• Assigning probabilities to the various
amounts estimated for one year, and
• Determining the mean value. The
expected present value of all, future
receipts could then be determined by
summing the expected discounted value
of all years.
EXPECTED VALUE OF RETURNS
• The GREATER the Expected
Value or Pay-off, the BETTER.
MEASUREMENTS OF RISK
•
•
•
•
•
Variance
Standard Deviation (SD)
Coefficient of Variation (CV)
Beta
Covariance
The Variability of Stock Returns
Normal distribution can be described by its
mean and its variance.
• Variance (2) – a measure of volatility in units of
percent squared
N
Variance   2 
 (k
t 1
t
 k)
2
FOR
UNGROUPED
DATA
N 1
• Standard deviation – a measure of volatility in
percentage terms
Standard deviation  Variance
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
Web site, in whole or in part.
The Variability of Stock Returns
Normal distribution can be described by its
mean and its variance.
• Variance (2) – a measure of volatility in units of
percent squared
N
Variance   2 
( (kt  k ) 2 Pt )1/ 2
t 1
FOR
GROUPED
DATA
• Standard deviation – a measure of volatility in
percentage terms
Standard deviation  Variance
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible
Web site, in whole or in part.
EXERCISE 1
• The following table summarizes the
annual returns you would have
made on two companies:
– One, a satellite and data equipment
manufacturer, and
– Two, the telecommunications giant,
from 200A to 200J.
EXERCISE 1
ONE
TWO
ONE
TWO
Year
Year
Year
200A 80.95 58.26 200E 32.02 2.94 200I
200B -47.37 -33.79 200F 25.37 -4.29 200J
200C 31.00 29.88 200G -28.57 28.86
200D 132.4 30.35 200H
0.00 -6.36
ONE
TWO
11.67 48.64
36.19 23.55
Estimate the EXPECTED RETURN,
VARIANCE, and STANDARD
DEVIATION in annual returns in each
company
Portfolio EV, Variance, and SD
• The expected return is equal to the
WEIGHTED AVERAGE returns of the
assets in the portfolio.
• The variance of a 2-asset portfolio is
equal to
• =wi2 (σi) 2 + w22 (σ2) 2 + 2 (wi)(σi) (w2)(σ2)
(r2)
• =wi2 (σi) 2 + w22 (σ2) 2 + 2 (wi) (w2)(Cov)
• The SD is equal to the square root of the
variance of the portfolio.
The Relationship Between Portfolio
Standard Deviation and the Number of
Stocks in the Portfolio
Market rewards only
systematic risk.
What really matters is systematic risk….
how a group of assets move together.
• The
risktrade-off
that diversification
is called unsystematic
The
between eliminates
S.D. and average
returns that
risk; The risk that remains, even in a diversified portfolio, is
holds for asset classes does not hold for individual
called systematic risk.
stocks!
© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly
accessible Web site, in whole or in part.
The Variability of Stock Returns
• Coefficient of Variation (CV) – a better
measure of total risk than the standard
deviation, especially when comparing
investments with different expected returns
• CV = Standard Deviation = Standard Deviation
•
Mean Return
Expected Return
The Variability of Stock Returns
• Covariance (Cov) – a measure of the
general movement relationship between
two variables. It is usually measured in
terms of correlation coefficient and asset
allocation
•
•
•
•
•
Recall:
The variance of a 2-asset portfolio is equal to
=wi2 (σi) 2 + w22 (σ2) 2 + 2 (wi)(σi) (w2)(σ2) (r2)
=wi2 (σi) 2 + w22 (σ2) 2 + 2 (wi) (w2)(Cov)
How would one compute for Cov?
EXERCISE 2
• The following table summarizes the
annual returns you would have
made on two companies:
– One, a satellite and data equipment
manufacturer, and
– Two, the telecommunications giant,
from 200A to 200J.
EXERCISE 2
ONE
TWO
ONE
TWO
Year
Year
Year
200A 80.95 58.26 200E 32.02 2.94 200I
200B -47.37 -33.79 200F 25.37 -4.29 200J
200C 31.00 29.88 200G -28.57 28.86
200D 132.4 30.35 200H
0.00 -6.36
ONE
TWO
11.67 48.64
36.19 23.55
If the correlation of these two
investments is 0.54069, estimate the
variance of a portfolio composed, in
equal parts, of the two investments.
ILLUSTRATIVE PROBLEM 1
Demand for the
company's
products
Strong
Normal
Weak
Probability of this
demand occurring
0.30
0.40
0.30
1.00
Rate of Return on stock
if this demand occurs
Company 1
Company 2
100%
20%
15%
15%
-70%
10%
1. Expected or Average Stock Return
2. Variance of Stock returns of each
3. Standard Deviation of Stock returns
of each
ILLUSTRATIVE PROBLEM 2
Demand for the
company's
products
Strong
Normal
Weak
Probability of this
demand occurring
0.30
0.40
0.30
1.00
Rate of Return on stock
if this demand occurs
Company 1
Company 2
100%
20%
15%
15%
-70%
10%
4. Coefficient of Variation of each
5. Covariance
6. Assuming that you are to invest 30% of your
investment funds in Company 1 and 70% in
Company 2, and their Correlation is 0.351
compute for the: (A)Variance of 2-Asset Portfolio
(B) Standard Deviation of the 2-Asset Portfolio
The Variability of Stock Returns
• Beta Estimate (β) of an individual stock is
the correlation between the volatility (price
variation) of the stock market and the
volatility of the price of the individual
stock.
• The beta is the measure of the
undiversifiable, systematic market risk.
• SML: ki = kRF + (kM – kRF) β i
The SML commonly adopts the CAPM model
The Variability of Stock Returns
• If β = 1.0, then the Asset is an average
asset.
• If β > 1.0, then the Asset is riskier than
average.
• If β < 1.0, then the Asset is less risky than
average.
• Can beta be negative?
Most stocks have betas in the range of 0.5 to 1.5
The Variability of Stock Returns
• The Hamada equation below is used to
compute for new beta shall there be
changes in capital structure.
• β u=
Current, levered β
.
•
[1 + {(1-tax rate)(Debt/Equity)}]
•
Most stocks have betas in the range of 0.5 to 1.5
ILLUSTRATIVE PROBLEM 2
• In December 200B, AAA’s stock had a
beta of 0.95. The Treasury bill rate at that
time was 5.8%. The firm had a debt
outstanding of P1.7B and a market value
of equity of P1.5B; the corporate marginal
tax rate was 36%. The registered risk
premium at December 200B is 8.5%.
Most stocks have betas in the range of 0.5 to 1.5
ILLUSTRATIVE PROBLEM 2
•
In December 200B, AAA’s stock had a beta of 0.95. The Treasury
bill rate at that time was 5.8%. The firm had a debt outstanding of
P1.7B and a market value of equity of P1.5B; the corporate
marginal tax rate was 36%. The registered risk premium at
December 200B is 8.5%.
– Estimate the expected return on the stock.
– Assume that a decrease in risk-free rate
occurs and is attributed to an improvement in
inflation rates, but that by January of 200C,
the inflation rate deteriorates or increases by
1.25%, compute for the required rate of
return of a marginal investor.
ILLUSTRATIVE PROBLEM 2
•
In December 200B, AAA’s stock had a beta of 0.95. The Treasury
bill rate at that time was 5.8%. The firm had a debt outstanding of
P1.7B and a market value of equity of P1.5B; the corporate
marginal tax rate was 36%. The registered risk premium at
December 200B is 8.5%.
– Assume that marginal investors become more
risk-averse and thus require a change in the risk
premium by 4%, what will be the effect on their
required rate of return?
– The current beta is 0.95. This is assumed to be
a levered beta since this has been registered
even if there is outstanding debt of P1.7B.
Compute for unlevered beta.
ILLUSTRATIVE PROBLEM 2
•
In December 200B, AAA’s stock had a beta of 0.95. The Treasury
bill rate at that time was 5.8%. The firm had a debt outstanding of
P1.7B and a market value of equity of P1.5B; the corporate
marginal tax rate was 36%. The registered risk premium at
December 200B is 8.5%.
– How much of the risk measured by beta in “g”
above can be attributed to (1) business risk,
and (2) financial leverage risk?
ILLUSTRATIVE PROBLEM 3
– Assume that the treasury bill rate is 8% and
the stock’s risk premium is equal to 7%.
Securities
A
B
C
D
E
Expected Returns
17.4%
13.8
1.7
8.0
15.0
Beta
1.29
0.68
-0.86
0.00
1.00
– 1.Use SML to calculate the required
returns
ILLUSTRATIVE PROBLEM 3
– 2. Compare the required returns and the
expected returns, determine which
securities are to be bought.
Securities
A
B
C
D
E
Expected Returns
17.4%
13.8
1.7
8.0
15.0
Beta
1.29
0.68
-0.86
0.00
1.00
– 3. Calculate beta for a portfolio with 50% A
Securities and C Securities
– 4. How much will be the required return on
the A/C portfolio in number 3 above
ILLUSTRATIVE PROBLEM 4
• PG which owns and operates grocery
stores across the Philippines, currently
has P50 million in debt and P100M in
equity outstanding. Its stock has a beta
of 1.2. It is planning a leveraged buyout
(LBO) , where it will increase its
debt/equity ratio of 8. If the tax rate is
40%, what will the beta of the equity
in the firm be after the LBO?
HOMEWORK 1
• Zuni-GAS is a regulated utility
serving Northern Luzon. The
following table lists the stock
prices and dividends on U Corp
from 200A to 200J.
HOMEWORK 1
• Compute for the expected return
Year
200A
200B
200C
200D
Price Divid
ends
36.10 3.00
33.60 3.00
37.80 3.00
30.90 2.30
Year
200E
200F
200G
200H
Price Divid Year
ends
26.80 1.60 200I
24.80 1.60 200J
31.60 1.60
28.50 1.60
Price Divid
ends
24.25 1.60
35.60 1.60
• Estimate the average annual return you
would have made on your investment
• Estimate the standard deviation and variance in annual returns.
HOMEWORK 2
• Assume you have all your wealth (P1 million)
invested in the PSE index fund, and you
expect to earn an annual return of 12
percent with a standard deviation in returns
of 25 percent. Because you have become
more risk averse, you decide to shift
P200,000 from the PSEi fund to Treasury
bills. The T bill rate is 5%. Estimate the
expected return and standard deviation of
your new portfolio
HOMEWORK 3
• Novell which had a market value of equity
of P2 billion and a beta of 1.50, announced
that it was acquiring WordPerfect, which
had a market value of equity of P 1 billion,
and a beta of 1.30. Neither firm had any
debt in its financial structure at the time of
the acquisition, and the corporate tax rate
was 40%.
• Estimate the beta for Novell after the
acquisition, assuming that the entire
acquisition was financed with equity.
HOMEWORK 2
• Novell which had a market value of equity of P2
billion and a beta of 1.50, announced that it was
acquiring WordPerfect, which had a market value
of equity of P 1 billion, and a beta of 1.30. Neither
firm had any debt in its financial structure at the
time of the acquisition, and the corporate tax rate
was 40%.
• Assume that Novell had to
borrow the P 1 billion to acquire
WordPerfect, estimate the beta
after the acquisition