Streetbites from the media perspective
The organization of mutual funds
Lessons about the Structure of Finance
Streetbites from the media perspective
 Mutual funds are collections of financial securities
 See textbook page 427 - 429 for related content on this topic.
Video for Module 10, Unit 1-of-2
What is a mutual fund - an overview (5:40)
Chapter 9.2C. Mutual funds
Mutual funds are among the largest institutional buyers of financial securities in
the U.S.A. Mutual funds collect money from many investors. The fund managers
carefully analyze possibilities and use the money to buy assets. Quite often the
managers select assets subject to guidelines that the mutual fund prospectus
describes. The prospectus is an official document describing the mutual fund to
prospective investors. The Securities Exchange Commission requires that the
prospectus contains specific information such as mutual fund objectives and
policies, risks that the fund faces, fees that investors pay, and investor services that
the fund offers. The mutual fund balance sheet in table 9.7 provides insight on
how a mutual fund operates.
Lessons about the Structure of Finance
ASSETS
2.4 million shares American Express
3.9 million shares Amgen, Inc.
0.6 million shares Anheuser-Busch
1.6 million shares Avon Products
0.1 million shares Black & Decker
15.9 million shares Cisco Systems
0.1 million shares Electronic Arts,
Inc.
3.1 million shares Fannie Mae
0.1 million shares Genentech
14.8 million shares General Electric
15.0 million shares Intel
2.4 million shares IBM
5.4 million shares Johnson &
Johnson
8.4 million shares Microsoft
4.4 million shares PepsiCo, Inc.
11.2 million shares Pfizer
0.7 million shares Starbucks Corp.
0.7 million shares United Parcel
Serv.
other equities & misc. assets
Total
assets
($millions)
84.9
187.2
31.3
84.9
5.9
208.9
3.1
LIABILITIES
223.2 Debt & misc.
7,743.2 Mutual fund shares
(176.3 million)
199.5
3.8
360.1
233.7
184.2
291.6
435.9
186.8
343.2
14.2
44.3
5,062.9
_______
$7,966.4
$7,966.4
TABLE 9.7 Balance sheet for CREF Growth Mutual fund, historical snapshot
The financial securities that mutual funds purchase almost always may be bought
directly by households. Relative to direct ownership, however, households realize
several advantages by owning mutual funds.
(a) Diversification benefits accrue from ownership of mutual funds because each fund typically own
dozens or more different security issues. Owning one share of a mutual fund represents indirect
ownership of many different securities.
(b) Investing in a mutual fund typically is easier and involves fewer transaction costs or commissions than
investing directly in stocks and bonds.
(c) Mutual funds hire talented professional investment managers. Most individual households cannot
allocate as much time as a full-time fund manager collecting information and monitoring securities.
(d) The astounding variety of mutual funds presents investors with access to a convenient mechanism for
pursuing personal investment objectives. Even though two funds may hold exactly the same set of
securities, fund characteristics may differ dramatically when each fund allocates among component
stocks differently. The analogy is that there are many different ways to combine flour, sugar, and
eggs – each combination tastes really different, too.
Lessons about the Structure of Finance
BS8 What does a mutual fund balance sheet look like?
Which one of the following statements about the balance sheet of a mutual fund that advertises
itself as a Telecommunications Fund is true?
ANSWER: B
a. the fund’s primary asset includes shares issued by the fund to investors such as you, me, or
institutional investors
b. the fund’s primary liability includes shares issued by the fund to investors such as you, me, or
institutional investors
c. the fund’s primary asset includes cash that it must pay to investors such as you, me, or
institutional investors
d. the fund’s primary liability includes equities issued by telecommunications companies such as
AT&T, Sprint, etc.
e. the fund’s primary liability includes cash that it must pay to investors such as you, me, or
institutional investors
Lessons about the Structure of Finance
Chapter 11, Unit 1 of 2
The market price for risk
Lessons about the Structure of Finance
 The behavior of individual balance sheet agents in financial markets
reveals information pertinent to the risk for return tradeoff.
 See textbook pages 522 - 537 for relevant readings.
Videos for Module 10, Unit 1-of-2
What is a mutual fund - an overview (5:40)
Efficient frontier and price of risk (11:40)
Required risk premium (1:27)
Working with price of risk (3:02) [AP11b]
Allocating between market and risk-free asset (5:14) [AP12, AP13]
Loanable funds theory of risk-free ROR (6:17)
Risk-free ROR and term premium (5:20) [AP15]
Rays of correlation (3:35)
Systematic risk premium for equity (7:02) [Example 2]
E(ROR)
A
A

B
C
 
B
D
1
2
3

FIGURE 11.1 Risk-return profiles and the Efficient frontier
The set of points along the upper surface in panel 3 made from the highest reaches of
all component feasible allocation sets is the efficient frontier.
DEFINITION 11.1 Efficient frontier
The efficient frontier is the set of portfolios that are not dominated and that are formed from all possible
risky capital investments.
Lessons about the Structure of Finance
ROR
y

r equi red
RORMarket 

x
market portfolio
risk-free
ROR
efficient frontier

capital market line
σm
σ
FIGURE 11.2 Efficient frontier and the Capital market line
DEFINITION 11.2 Capital market line
The capital market line is the set of portfolios that combine the risky portfolio at point of tangency on the
efficient frontier with the risk-free asset. Portfolios on the capital market line are not dominated by any
other capital investments.
Lessons about the Structure of Finance
Interpretation now suggests that one specific portfolio on the efficient frontier is
better than all others. That specific portfolio at the point of tangency is the market
portfolio. Market portfolio components include all possible risky capital assets where
the weight in any one equals that asset’s total market capitalization as a proportion of
total global market cap.
FORMULA 11.1 Market price for risk
The slope of the capital market line measures the equilibrium price for risk.
 slope of the


 
 capital market line 

required
RORMarket
 ROR riskfree
σm
market risk premium
.
%total market risk
FORMULA 11.2 Required rate of return ROR required and component risk premia
The “required rate of return” is the minimum discount rate that an investor willingly
accepts for computing intrinsic value. The required rate of return for any capital
required
investment A denoted RORA
equals the risk-free rate plus that asset’s risk
premium:
ROR required
 ROR riskfree  security risk premiumA
A
risk-free
where ROR
is the short-term risk-free rate and
tic risk

sources
ofidiosyncra

 
  systematic   liquidity   term   default  
 
 
 
 
 security

 

  f   risk
 ,  risk
 ,  risk  ,  risk
 
 risk premium A
  premium   premium  premium  premium 
A 
A 
A 
A 
 


The implicit function f{.} depends upon all possible sources of systematic and
idiosyncratic risk in ways that are not fully understood. The function shows one source
of systematic risk (but there may be more) and three sources of idiosyncratic risk (these
are the main ones but there may be more of these, too). The systematic risk premium
relates directly to the market price for risk from the Capital market line. Security
investment occurs when ROR required is less that RORexpected (see rule 9.1).
Lessons about the Structure of Finance
EXERCISES 11.1
1. Analysts tell you that the risk-free rate of return equals 5.0% and the market
portfolio’s required rate of return and risk (standard deviation) equal 11.0% and 24%,
respectively. Compute according to the Capital market line the equilibrium price for risk.
For an increase in personal portfolio risk of five percentage points (and no extra
diversification benefit) how much is the increase in required risk premium. AP11b .
ANSWER: The market risk premium equals 6% (= 11% - 5%). Also, σm = 24% so
slope of the capital market line equals 1/4 (= 6% ÷ 24%). The market price for one
percentage point of risk is 25 basis points (= 1/4 × 1%) and for extra risk of 5% the
increase in required risk premium is 1.25% (= 1/4 × 5%).
Q1. What allocation between the risk-free asset and market portfolio creates a portfolio
with risk σ of 10%? Exercise 11.1 #3 AP13 Quiz25
AP13 Find allocation in OR(risk-free asset, market portfolio) providing target σ
The risk-free rate of return equals 2.5% and the market portfolio’s required rate of return and risk
(standard deviation) equal 8.0% and 17.0%, respectively. Suppose that the equilibrium price for
risk computes according to the Capital market line. Your objective is to combine the risk-free
asset with the market portfolio in order to create a portfolio with standard deviation of returns
equal to 3.4%. Find the allocation that satisfies your objective.
a. Allocate 20.0% in the risk-free asset and you achieve the objective
b. Allocate 23.0% in the risk-free asset and you achieve the objective
c. Allocate 20.0% in the market portfolio and you achieve the objective
d. Allocate 23.0% in the market portfolio and you achieve the objective
e. Allocate 26.5% in the risk-free asset and you achieve the objective
Q2. Find the return for that allocation. (Exercise 11.1 #2 AP12 modified)
risk-free
Preceding lessons establish that ROR
is a core rate important for explaining
financial equilibrium. Figure 11.3 shows supply and demand schedules driving
risk-free
determination of the short-term risk-free rate ROR
. The explanation below is
adaptation of a theory described by Irving Fisher in 1930 and coined the loanable
funds theory of interest.
Lessons about the Structure of Finance
interest
rate
price
D0
D1
S0
p0
p1
S1
p0 > p1
r0
r1
r1 > r0
q0
q1
quantity
FIGURE 11.3 Supply and demand schedules for risk-free credit market securities
Credit market competition for loanable funds: During an economic expansion companies borrow money
for purchasing plant and equipment and other factors of production from stakeholders. Households,
too, borrow money for improvements and competition for loanable funds heats up. Private sector
borrowing crowds out the government and the demand curve D0 shifts left as private credit market
securities substitute in portfolios for risk-free securities. For a given supply schedule S0 the
risk-free
equilibrium security price declines and equilibrium ROR
increases (irrespective of supply
schedule slope). Conversely, during economic contractions there are not many private credit market
securities, risk-free securities become the only game in town, demand curve shifts right toward D1
risk-free
and equilibrium ROR
declines.
Confidence or nervousness: Political and economic world events sometimes trigger a flight to quality.
Risk-free Treasury securities are the safest, highest quality possible investment. Nervousness
causes the demand curve to shift right, say to D1. For a given supply schedule S0 the equilibrium
risk-free
price rises and short-term risk-free rate ROR
declines (irrespective of supply schedule slope).
Conversely, an increase in buy-side confidence for alternative investments shifts the demand curve
risk-free
for risk-free securities left, equilibrium price falls, and equilibrium ROR
rises.
TR41 Find effects of shocks in loanable funds theory of interest
The loanable funds theory of interest is useful for explaining the level of the risk-free interest
rate. That model allows insights about effects of exogenous shocks upon movement in the riskfree rate. Find the statement that is most consistent with the loanable funds theory of interest.
a. When an economic contraction causes a reduction in the availability of private credit
market securities then, ceteris paribus, the equilibrium price for risk-free securities
increases.
b. When tax revenues are less than government expenditures and the Treasury issues new
securities then, ceteris paribus, the equilibrium risk-free rate increases.
c. When a major foreign world economy decides to sell-off their huge holdings of U.S. Treasury
securities then, ceteris paribus, the equilibrium risk-free rate declines.
d. When private companies increase their demand for loanable funds then, ceteris paribus, the
equilibrium risk-free rate declines.
e. When political and economic world events trigger a flight to high quality securities then,
ceteris paribus, the equilibrium risk-free rate increases.
Lessons about the Structure of Finance
risk-free
FORMULA 11.3 Nominal risk-free rate ROR
and the inflation premium
risk-free
The observable short-term, very liquid, default free interest rate is nominal ROR
. Relation between
risk-free
the rate for a risk-free security maturing in N periods (N ≥ 1), denoted RORN
, and term risk premium
approximates as follows:
ROR
riskfree
N
 short  term   term risk premium

 

  real risk  free    for N  period 
 interest rate  

horizon

 

For the special case when the inflation premium is the only component in the term risk premium:
ROR
riskfree
N
 short  term 

 
  real risk  free   
 interest rate  



N
t 1
(inflation rate)t 
 .
N

The inflation premium equals the arithmetic average periodic inflation rate expected throughout term N.
risk-free
risk-free
Short-term nominal risk-free interest rate ROR
is identical to ROR1
.
EXERCISES 11.2
1. The short-term real risk-free interest rate averages 3.0%. Suppose that expected
inflation is 5.6% over the next year, 5.9% during the second year, and 6.2% thereafter
perpetually. Inflation is the only component of the term premium for risk-free securities.
Find today’s interest rates for risk-free securities with terms of 2 years, 4 years and 20years. ©AP15 .
risk-free
ANSWER: The risk-free rate ROR2
equals 3% plus the inflation premium of 5.75%
[= (5.6% + 5.9%)/2] which is 8.75%. Inflation premium on a four-year bond is 5.7% [=
risk-free
(5.6% + 5.9% + 2 × 6.2%)/4] so ROR4
is 8.97%. The 20-year risk-free rate
ROR20
risk-free
is 9.15% [= 3% + (5.6% + 5.9% + 18 × 6.2%)/20].
Lessons about the Structure of Finance
Open market paper
2%
6%
U.S. government
securities
8%
Municipal securities
35%
Corporate and foreign
bonds
23%
Mortgages
20%
6%
Consumer credit
Other credit market debt
FIGURE 11.5 Components of U.S. credit market securities
Notes:
The credit market total is $57,982 billion at 9/30/2014. Data are from the Board of Governors of the Federal Reserve System, “Flow
of Funds Accounts for the United States”, table L.4.
Two procedures exist for adding risk premia to the risk-free rate and they usually lead to
risk-free
different answers. One approach adds risk premia to short-term ROR
per formula
risk-free
11.2. The other approach adds risk premia to RORN
where N is the term of the
credit market security under analysis. The difference pertains exclusively to handling
the term risk premium.
Lessons about the Structure of Finance
Lessons about the Structure of Finance
For the special limiting case when all sources of idiosyncratic risk distribute like whitenoise across all securities then diversification completely eliminates idiosyncratic risk.
Only systematic risk remains in the market portfolio. For that special limiting case
formula 11.2 simplifies as shown below.
FORMULA 11.4 Systematic risk premium and the market price for risk
The required rate of return for any capital investment A denoted RORA
required
equals
risk-free
short-term risk-free rate ROR
plus that asset’s risk premium. When idiosyncratic
risk may be eliminated completely through diversification and only one source of
systematic risk exists then:
ROR required
A
 ROR riskfree

ROR riskfree
premium for security A
systematic
risk


required
 RORmarket
 ROR riskfree 

 ρA,Market σ A 
σ
m


 market price 
.
 ρA,Market σ A 
for risk 

Rates of return for security A carry risk σA. Correlation between rates of return for A
and the market portfolio equals ρA,Market. The market price for risk equals slope of the
Capital market line and represents required return per unit of risk. The correlation
coefficient ρA,Market measures the proportion of A’s risk that requires the market price for
risk.
EXAMPLE 2 Find required rate of return given the risk-free rate and summary statistics
Suppose the risk-free rate on T-bills is 5% and the required return on the market
portfolio is 12%. Suppose also that σm = 21% and that risk for security X is σx = 27%.
Correlation ρX,Market between X and the market portfolio is 0.40. Find the risk premium
and required rate of return for security X.
SOLUTION
The market price for risk equals the market risk premium of 7% (= 12% – 5%) divided by
market risk σm and equals 1/3. Risk σx equals 27% and if each percentage point of risk
received the equilibrium market price for risk then the risk premium for X would equal
9% (= 27% × 1/3). Because correlation ρX,Market equals 0.40, however, the risk premium
only equals 3.6% (= 9% × 0.40). Thus, RORX
Lessons about the Structure of Finance
required
is 8.6% (= 5% + 3.6%).
ROR
ρ = 1.0
required
Capital market line
Market
portfolio
r e qu i red
RORMar ket
RORx
ρ = 0.83
•Y
•
required
ρ = 0.5
•
X
risk-free
•
Z
ROR
ρ = -1.0
ρ = -0.33
σX
σM
ρ = 0.0
σ
FIGURE 11.6 Capital market line and the rays of correlation
Notes: Coefficient ρ measures correlation between rates of return for the market portfolio and a
specific security. All securities with the same ρ are pushed onto the respective ray of correlation.
Correlation coefficients between the market portfolio and securities X and Y equal 0.83.
Consequently, their required rates of return align onto the same ray. Eighty-three percent of their
respective risks, σx and σy, require compensation at the market price for risk. Because σx < σy
required
required
required
then RORX
< RORY
. For security Z the risk σz is even higher but RORZ
equals
risk-free
ROR
because Z is uncorrelated with the market portfolio and merits zero risk premium.
EXAMPLE 3 Analyze two securities for by comparing ROR
required
with ROR
expected
You want to add one additional stock to your well-diversified portfolio and are
considering two alternatives. Information about stock A leads you to believe that its
expected rate of return is 10%, the standard deviation of expected returns is 38%, and
that its correlation with the market portfolio is 0.35. For stock B those figures are
expected
ROR
= 12%, σB = 32%, and ρB,Market = 0.90. The risk-free rate is 5%, the required
return for the market portfolio is 11%, and σM = 22%. Determine which one of these
securities, if either, should be added to your portfolio.
SOLUTION
Lessons about the Structure of Finance
Rule 9.1 provides the investment decision rule to invest when expected rate of return
exceeds required rate of return. For this example notice that stock A has lower
expected return than B and also σA > σB. Figure 11.7 shows this situation.
RORexpected
12%
 B
 A
10%
32%
38%
σ
FIGURE 11.7 Expected return and σ for example 3
Comparison of A directly with B suggests that B dominates A and that therefore B is a
better choice for addition to the portfolio. That analysis is incomplete and wrong!
Lessons above establish that σ does not properly measure risk relevant for
determining risk premia due to existence of diversification benefits. The illustration of
dominance in figure 11.7 is misleading. The portion of σ that represents relevant risk is
measured by the correlation coefficient with the market portfolio. Use formula 11.4 to
find required rates of return and subsequently compare them to expected rates of
return.
Compute that the market price for risk equals the market risk premium of 6% (=
required
11% – 5%) divided by market risk σm and equals 0.2727. Compute that RORA
equals 8.63% [= 5% + (0.35 × 38% × 0.2727]. Security A is a reasonable choice for
expected
required
addition to a well-diversified portfolio because RORA
> RORA
. Compute that
RORB
required
equals 12.85% [= 5% + (0.90 × 32% × 0.2727]. The 12% expected rate of
return for B does not fully compensate for its relevant risk; that is, RORB
required
expected
<
RORB
so do not buy B. Add security A to your portfolio. The impression from
figure 11.7 that B dominates A is a mirage.
Lessons about the Structure of Finance
FORMULA 11.5 Beta and the Capital asset pricing model (“CAPM”)
The required risk premium for any capital investment A equals required rate of return
required
risk-free
RORA
minus short-term risk-free rate ROR
. When idiosyncratic risk may be
eliminated completely through diversification and only one source of systematic risk
exists then the ratio of security to market risk premia is
βA 
systematic risk premium for security A
risk premium for market portfolio
covarianceA,Market

2
σ market
.
(11.5a )
Rearrange the top line and obtain a formula known as the Capital asset pricing model:
systematic risk premium for security A



ROR required
A

ROR riskfree 

required
β A RORmarket
 ROR riskfree
.
(11.5b)
βA measures proportion of market risk premium applicable to security A.
EXERCISES 11.3
2. The economy wide risk free interest rate is 5.0% and the required risk premium for
the market portfolio is 7.5%. At the same time, the company’s required risk premium
according to the Capital Asset Pricing Model is 9.0%. What is the company’s ?
©AP4a .
ANSWER: Ratio of security to market risk premium equals β and is 1.20 (= 9.0% ÷
7.5%).
DEFINITION 11.3 Security market line (SML)
The Security market line is the graph showing the required rate of return as a linear function of the equity
r e qu i red
risk-free
β. Slope of the SML equals the required risk premium for the market portfolio, RORMar ket – ROR
.
Figure 11.8 illustrates the Security market line.
Lessons about the Structure of Finance
RORrequired
conservative
aggressive
 Y
RORYrequired
requi red

RORMarket
 X
RORXrequired
ROR
risk-free

βX
1.0
βY
β
FIGURE 11.8 The Security market line
AP6b Find intrinsic value and make inference from CAPM and dividend growth model
given simple setup
The company’s beta is 0.85, its dividend growth rate is 9.1%, and just yesterday it paid
a dividend of $0.90 . The economy wide risk free interest rate is 5.5%, and the
expected risk premium for the market portfolio is 10.0%. Find the stock’s intrinsic value
using the dividend constant growth model and the required rate of return implied by
Capital Asset Pricing Model. Which statement is most accurate?
a. Intrinsic value is $20.04 and if the stock price is $26.05 you should buy it
b. Intrinsic value is $15.15 and if the stock price is $26.05 you should not buy it
c. Intrinsic value is $15.15 and if the stock price is $16.03 you should buy it
d. Intrinsic value is $20.04 and if the stock price is $16.03 you should buy it
e. Intrinsic value is $17.43 and if the stock price is $16.03 you should buy it
Lessons about the Structure of Finance