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.

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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