Rates of Return

1
Chapter 2

• Rates of Return

2
Background

• Investors want to maximize their returns (or
  wealth)
• Chapter discusses
• The calculation of a return
• Historical returns offered by different types of
  investments

3
The Investors Goal

• Goal is to maximize what is earned relative to
  the amount put into an investment
• Maximize either the
• Rate of return

• Investments terminal value

Equivalent
4
The Investors Goal

• Some claim wealth-maximizing investors are
  performing harmful greedy activities
• Law abiding wealth maximization is beneficial to
  both investor and general population
• Seek out securities issued by firms producing
  high quality goods and services
• Capital is used to benefit general population
• Investors can request management actions at
  stockholder meetings
• Helps nation compete internationally
• Creates new job opportunities

5
Ethics Box The Need for Ethics in Investment

• Some level of ethics is necessary
• Ethics concerned with standards of right and
  wrong
• Concepts of trust and fairness are relevant to
  investments
• Investors trust investment firms to act in their
  best interest and to safeguard their assets
• Fairness means a level playing field and the
  absence of fraud
• Decreasing information asymmetry increases
  efficiency and fairness
• An investment professional should
• Be loyal
• Act with due care
• Keep information confidential
• Avoid conflicts of interest

6
The One-Period Rate of Return

• Rate of return measures change in an investors
  wealth over time
• Measures the success or failure of the investment
• Measures holding period return
• Defined as

7
Examples One Period Return

• You purchased one share of Coca-Cola one year ago
  for 54. You sold it today for 64, and you
  received dividends of 0.80 during the year
• Your income from dividends 80
• Your capital gain is 10 (64 - 54)
• Your return is 10.80 ? 54 20

8
Examples One Period Return

• You purchased a U.S. T-bond for 900. One year
  later you sold the bond for 910. You received
  35 in interest during the year. Your rate of
  return is

• You bought a six-month T-bill for 9,800 with a
  maturity value of 10,000. After the bond
  matures your six-month return is

• Since there are two six-month periods in one
  year, your annual return is
• 1.02042 1 1.0412 1 4.12

9
Figure 2-1Wealth Indices for Average U.S.
Investments in Different Asset Classes Compared
to Inflation, 1926-99

• If you had invested 1 on December 31, 1925 in
  each of the following, you would have

Small company stocks are the most risky, but
offer the highest return.
In some years inflation exceeds T-bill
returnsleading to a drop in purchasing power for
T-bill investors.
T-bills are the least riskysmoothest growth
path, but lowest return.
10
Table 2-1Average Annual Rate of Return and Risk
Statistics for Asset Classes and Inflation in the
U.S., 1926-99
11
Realized One-Period Rates of Return

• We can calculate one period rates of change for
  the indexes

Includes dividends, coupon interest on bonds
12
Average Rates of Return

• Arithmetic mean return (AMR) measures average
  historical one-period rates of return

• Compound average rate of return, or geometric
  mean return (GMR) is

AMR ? GMR because compound interest grows more
rapidly than simple interest
13
Example Average Rates of Return

• A three-year investment earned the following
  annual returns

• If you placed 100 in this investment at the
  beginning of year 1, at the end of the third year
  it would be worth
• 100 (1.0428)3 113.40

14
Assessing Risk

• An asset is riskier if
• Its one-period rates of return fluctuate over a
  wide range
• Such as small company stocks
• Measures of risk include
• Variancethe average of squared deviations from
  AMR

Both measure total risk

• Standard deviationsquare root of variance

15
Example Variance SD

• Calculate the variance and standard deviation of
  the previous example

16
Risk Rankings

• Both standard deviation and variance result in
  the same risk rankings
• Advantages of standard deviation
• Considers every outcome
• Unlike range which only considers high and low
  values
• Well known by statisticians
• Programmed into calculators and software
• Measures the wideness of probability
  distributions
• Measure of dispersion around arithmetic mean
• Also widely used in mathematics, econometrics,
  etc.

17
Interpreting Historical Return and Risk

• Examining the historical returns and risk leads
  to the following observations
• Large company common stocks
• Earn higher returns than bonds
• If a firm is declared bankrupt, all creditors are
  paid in full before common stockholders receive
  any proceeds
• Common stockholders usually receive nothing which
  makes it more risky than debt
• Stockholders demand a higher average rate of
  return

18
Interpreting Historical Return and Risk

• Small company stocks
• Earned highest returns of all other investments
• But, riskier than any of the other investments
• The percentage of small firms declared bankrupt
  is greater than the percentage of large firms
• Investors require a higher rate of return for
  investing in a small firm
• Long-term corporate bonds
• Bonds issued by the U.S. Treasury are unlikely to
  be defaulted
• However, bonds issued by corporations are more
  likely to be defaulted

19
Interpreting Historical Return and Risk

• Long-term U.S. Treasury bonds
• Mature about 20 years from initial offering date
• Involve no default risk
• Intermediate-term U.S. Treasury Bonds
• Mature about 5 years after issue date
• Experience smaller price fluctuations than
  long-term U.S. Treasury bonds
• U.S. Treasury bills
• Mature in less than one year
• No horizon premium necessary
• U.S. Treasury is unlikely to default
• No default premium needed
• AKA risk-free assets
• Probably no other security in world with less risk

20
Interpreting Historical Return and Risk

• Opportunity cost
• What it could earn in its highest paying
  alternative use
• Example The opportunity cost of attending
  college includes foregone wages
• Less obvious expenses than out-of-pocket expenses
• Example The opportunity cost of holding cash
  rather than investing in large company stocks was
  13.3 a year

21
Required Rate of Return

• Should only invest if you expect to earn a return
  greater than your cost of capital
• Interest expense paid for borrowed funds
• Cash dividend payment paid to stockholders
• Opportunity costs
• AKA required rate of return
• Minimum rate of return an investment must earn to
  increase investors wealth
• RRR lt r leads to a wealth increase
• RRR r leads to no change in wealth
• RRR gt r leads to a wealth decrease

22
Combining Risk Premiums To Compute Required Rate
of Return
23
Combining Risk Premiums To Compute Required Rate
of Return
24
The Largest Investors in the World

• U.S. pension funds are the largest investors in
  the world
• Hire professional money managers
• Owners/sponsors of largest pensions

25
The Largest Investors in the World

• Firms hired to manage pension assets include

26
Ethics and Pension Funds

• Managers of defined benefit plans (guarantee
  fixed income in retirement)
• Have duty to maintain sufficient funds for future
  obligations
• Some funds become overfunded
• Should these funds be allowed to divest excess
  funds?
• Managers of defined contribution plans (employee
  and employer contributions accumulate in
  individual accounts)
• Must offer at least three different funds
• Must seek to maximize risk-adjusted return
• Have a fiduciary duty to vote funds stock solely
  in beneficiaries interests

27
The Bottom Line

• Investors wish to maximize their wealth (return)
  over the long-run
• Arithmetic mean is not a compounded return like
  the geometric mean
• AMR ? GMR
• Realized returns represent historical data
• Investors desire investments with an expected
  return greater than their required rate of return
  or hurdle rate