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WEBMA STER

Inflation and Interest Rates
The Federal Reserve Bank of St. Louis has several sources of information available on
interest rates and economic conditions. One publication called Monetary Trends
contains graphs and tabular information relevant to assess conditions in the capital
markets. Go to the most recent edition of Monetary Trends at http://www.stls.frb.org/
docs/publications/mt/mt.pdf and answer the following questions:
1. What is the current level of three-month and long-term Treasury yields?
2. Have nominal interest rates increased, decreased, or remained the same over
the last three months?
3. Have real interest rates increased, decreased, or remained the same over the
last two years?
4. Examine the information comparing recent U.S. inflation and long-term interest
rates with the inflation and long-term interest rate experience of Japan. Are the
results consistent with theory?




SOLUTIONS TO
1. a. The arithmetic average is (2 8 4)/3 2% per month.
b. The time-weighted (geometric) average is
< Concept
[(1 .02) (1 .08) (1 .04)]1/3 .0188 1.88% per month
CHECKS
c. We compute the dollar-weighted average (IRR) from the cash flow sequence (in $ millions):


Month

1 2 3
Assets under management at
beginning of month 10.0 13.2 19.256
Investment profits during
month (HPR Assets) 0.2 1.056 (0.77)
Net inflows during month 3.0 5.0 0.0
Assets under management
at end of month 13.2 19.256 18.486



Time
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0 1 2 3
Net cash flow* 10 3.0 5.0 18.486

*
Time 0 is today. Time 1 is the end of the first month. Time 3 is the end of the third month, when
net cash flow equals the ending value (potential liquidation value) of the portfolio.

The IRR of the sequence of net cash flows is 1.17% per month.
The dollar-weighted average is less than the time-weighted average because the negative return
was realized when the fund had the most money under management.
Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition




166 Part TWO Portfolio Theory


2. Computing the HPR for each scenario we convert the price and dividend data to rate of return data:


Business
Conditions Probability HPR

High growth 0.35 67.66% (4.40 35 23.50)/23.50
Normal growth 0.30 31.91% (4.00 27 23.50)/23.50
No growth 0.35 19.15% (4.00 15 23.50)/23.50


Using Equations 5.1 and 5.2 we obtain
E(r) 0.35 67.66 0.30 31.91 0.35 ( 19.15) 26.55%
2
26.55)2 26.55)2 26.55)2
0.35 (67.66 0.30 (31.91 0.35 ( 19.15 1331
and
1331 36.5%
3. If the average investor chooses the S&P 500 portfolio, then the implied degree of risk aversion is
given by Equation 5.7:
.10 .05
A 3.09
.182
1„2


4. The mean excess return for the period 1926“1934 is 3.56% (below the historical average), and the
standard deviation (using n 1 degrees of freedom) is 32.69% (above the historical average).
These results reflect the severe downturn of the great crash and the unusually high volatility of
stock returns in this period.
5. a. Solving
1 R (1 r)(1 i) (1.03)(1.08) 1.1124
R 11.24%
b. Solving
1 R (1.03)(1.10) 1.133
R 13.3%
6. Holding 50% of your invested capital in Ready Assets means your investment proportion in the
risky portfolio is reduced from 70% to 50%.
Your risky portfolio is constructed to invest 54% in Vanguard and 46% in Fidelity. Thus, the
proportion of Vanguard in your overall portfolio is 0.5 54% 27%, and the dollar value of your
position in Vanguard is 300,000 0.27 $81,000.
7. E(r) 7 0.75 8% 13%
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0.75 22% 16.5%
Risk premium 13 7 6%
Risk premium 13 7
.36
Standard deviation 16.5
Bodie’Kane’Marcus: II. Portfolio Theory 5. Risk and Return: Past © The McGraw’Hill
Essentials of Investments, and Prologue Companies, 2003
Fifth Edition




167
5 Risk and Return: Past and Prologue


8. The lending and borrowing rates are unchanged at rf 7% and rB 9%. The standard deviation of
the risky portfolio is still 22%, but its expected rate of return shifts from 15% to 17%. The slope of
the kinked CAL is
E(rP) rf
for the lending range
P


E(rP) rB
for the borrowing range
P

Thus, in both cases, the slope increases: from 8/22 to 10/22 for the lending range, and from 6/22 to
8/22 for the borrowing range.




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Bodie’Kane’Marcus: II. Portfolio Theory 6. Efficient Diversification © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




6
EFFICIENT
DIVERSIFICATION


AFTER STUDYING THIS CHAPTER
YOU SHOULD BE ABLE TO:


> Show how covariance and correlation affect the power of
diversification to reduce portfolio risk.

> Construct efficient portfolios.


> Calculate the composition of the optimal risky portfolio.


> Use factor models to analyze the risk characteristics of
securities and portfolios.




168
Bodie’Kane’Marcus: II. Portfolio Theory 6. Efficient Diversification © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




Related Websites The risk measure is based on the concept of value at
risk and includes some capabilities of stress testing.
http://finance.yahoo.com
http://aida.econ.yale.edu/˜shiller/data.htm
http://moneycentral.msn.com/investor
Professor Shiller provides historical data used in his
These sites can be used to find historical price
applications in Irrational Exuberance. The site also has
information for estimating returns, standard deviation
links to other data sites.
of returns, and covariance of returns for individual
http://www.mhhe.com/edumarketinsight
securities.
The Education Version of Market Insight contains
http://www.financialengines.com
information on monthly, weekly, and daily returns. You
This site provides risk measures that can be used to
can use these data in estimating correlation coefficients
compare individual stocks to an average hypothetical
and covariance to find optimal portfolios.
portfolio.
http://www.portfolioscience.com
Here you™ll find historical information to calculate
potential losses on individual securities or portfolios.




n this chapter we describe how investors can construct the best possible risky port-

I folio. The key concept is efficient diversification.
The notion of diversification is age-old. The adage “don™t put all your eggs in
one basket” obviously predates economic theory. However, a formal model showing
how to make the most of the power of diversification was not devised until 1952, a
feat for which Harry Markowitz eventually won the Nobel Prize in economics. This
chapter is largely developed from his work, as well as from later insights that built on
his work.
We start with a bird™s-eye view of how diversification reduces the variability of
portfolio returns. We then turn to the construction of optimal risky portfolios. We fol-
low a top-down approach, starting with asset allocation across a small set of broad
asset classes, such as stocks, bonds, and money market securities. Then we show
how the principles of optimal asset allocation can easily be generalized to solve the
problem of security selection among many risky assets. We discuss the efficient set of
risky portfolios and show how it leads us to the best attainable capital allocation. Fi-
nally, we show how factor models of security returns can simplify the search for ef-
ficient portfolios and the interpretation of the risk characteristics of individual
securities.
An appendix examines the common fallacy that long-term investment horizons
mitigate the impact of asset risk. We argue that the common belief in “time diversifi-
cation” is in fact an illusion and is not real diversification.
Bodie’Kane’Marcus: II. Portfolio Theory 6. Efficient Diversification © The McGraw’Hill
Essentials of Investments, Companies, 2003
Fifth Edition




170 Part TWO Portfolio Theory


6.1 DIVERSIFICATION AND PORTFOLIO RISK
Suppose you have in your risky portfolio only one stock, say, Dell Computer Corporation.
What are the sources of risk affecting this “portfolio”?
We can identify two broad sources of uncertainty. The first is the risk that has to do with
general economic conditions, such as the business cycle, the inflation rate, interest rates, ex-
change rates, and so forth. None of these macroeconomic factors can be predicted with cer-
tainty, and all affect the rate of return Dell stock eventually will provide. Then you must add
to these macro factors firm-specific influences, such as Dell™s success in research and devel-
opment, its management style and philosophy, and so on. Firm-specific factors are those that
affect Dell without noticeably affecting other firms.
Now consider a naive diversification strategy, adding another security to the risky portfolio.
If you invest half of your risky portfolio in ExxonMobil, leaving the other half in Dell, what
happens to portfolio risk? Because the firm-specific influences on the two stocks differ (sta-
tistically speaking, the influences are independent), this strategy should reduce portfolio risk.
For example, when oil prices fall, hurting ExxonMobil, computer prices might rise, helping
Dell. The two effects are offsetting, which stabilizes portfolio return.
But why stop at only two stocks? Diversifying into many more securities continues to
reduce exposure to firm-specific factors, so portfolio volatility should continue to fall. Ulti-
mately, however, even with a large number of risky securities in a portfolio, there is no way to
avoid all risk. To the extent that virtually all securities are affected by common (risky) macro-
economic factors, we cannot eliminate our exposure to general economic risk, no matter how

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