Selected Investment Indexes

1
Selected Investment Indexes

• Chapter 11

2
Background

• Chapter investigates domestic and international
  indexes for stock and bond markets
• Objectives include using indexes to
• Rapidly gain knowledge
• Confront theories with facts
• Investigate market inter-relationships
• Allocate assets
• Examine overall economic relationships

3
Long-Term Returns for Major Asset Classes

• Well examine seven U.S. price indexes
• Large company stocks (SP500)
• Long-term U.S. government bonds
• Intermediate-term U.S. government bonds
• U.S. Treasury bills
• Small company stocks
• Long-term corporate bonds
• Inflation (percentage change in CPI)

4
Long-Term Returns for Major Asset Classes

• Examine indexes because individual security
  prices reflect non-systematic events, whereas
  price indexes contain many different securitiesa
  diversified portfolio
• Allows examination of meaningful trends and
  relationship between categories of investments

5
Ibbotsons Seven Basic Indexes

• Large company stock index
• Measured by SP500 Stocks Composite Index, using
  total returns
• Annual compound growth of 11.3 from 1925-1999
• Dividends represent 4.5 and capital gains 6.6
• Annual returns fluctuated from a low of 43.3
  (in 1933) to a high of 54.0 (in 1934)

6
Ibbotsons Seven Basic Indexes

• Small company stock index
• Annual compound growth of 12.6 from 1925 to 1999
• Range from low of 58.0 (in 1937) to 142.9 (in
  1933)
• The small stocks index shows that investors were
  rewarded with a high total return as compensation
  for the unique risk involved with small stock
  investing

7
Ibbotsons Seven Basic Indexes

• Long-term corporate bond index
• Annual compound growth rate of 5.6
• Range of 8.1 (in 1969) to 42.6 (in 1982)

8
Ibbotsons Seven Basic Indexes

• Long-term government bond index
• Annual compound growth rate of 5.1
• Range from 9.2 (in 1967) to 40.4 (in 1982)
• Interestingly, the coupon income component of the
  Treasury bonds total return is gt 100, as the
  price declines exceeded the price increases

9
Ibbotsons Seven Basic Indexes

• Intermediate-term government bond index
• Annual compound growth rate of 5.2
• Range from 5.1 (in 1994) to 29.1 (in 1982)
• Return from income was 4.7 of the 5.2 total
  return

10
Ibbotsons Seven Basic Indexes

• U.S. Treasury Bill index
• Annual compound growth rate of 3.8
• Range from 0 (in 1938-1940) to 14.7 (in 1981)
• Over the 74-year sample period, T-bill returns
  exceeded inflation rate by 0.6 (or 60 basis
  points)

11
Ibbotsons Seven Basic Indexes

• Inflation in the U.S.
• Compound annual inflation rate of 3.1
• Range from 10.3 (in 1932) to 18.2 (in 1946)
• Deflation occurred during the Depression from
  1926-1933

12
Wealth Accumulation

• If you had invested 1 in the following from end
  of 1925 to end of 1999 it would have increased to

• Method of computation is (1 return)n Ending
  Wealth

13
Wealth Accumulation

• Inflation means that the purchasing power of 1
  is not the same from year-to-year (it decreases)
• 1 of purchases made in 1925 would cost 9.39 by
  1999
• 1 x (1 0.030728)74 9.39
• Therefore, the 2,845.63 after adjusting for
  inflation is only worth ? in real terms
• 2,845.63 ? 9.39 303.05 (or 1.113469 ?
  1.030728)
• While the accumulated real wealth is much lower
  than the nominal wealth, it is still an
  impressive number

14
Risk and Return
15
Risk and Return

• Risk premiums represent the additional return
  expected by investors when they select a certain
  class of asset equities compared to bonds, for
  instance

16
Risk and Return
17
Reinvestment Return

• Bonds that pay a coupon have 3 different types of
  income
• From cash flows
• From capital appreciation (or depreciation)
• From reinvestment
• When calculating returns over multiple time
  periods, it is conventionally assumed that cash
  flows are reinvested as soon as received
  (reinvestment income)
• Can represent a sizable portion of return,
  especially for bonds

18
October 19, 1987

• On October 19, 1987 the international stock
  market crashed, suffering a 22.6 loss in the
  DJIA
• However, the stock market index ended the 1980s
  with an overall gain
• Therefore, large short-run price fluctuations may
  not be that important in the long-run

19
Maximum Minimum Returns
20
Maximum Minimum Returns

• The data on the previous slide suggest that, if
  you invest for longer time periods, the
  probability of earning a positive point increases
• Mean reversion
• If a return is at an extreme (either or -)
  during one time period, it tends to revert toward
  the mean during a later period
• Some argue that time diversification tends to
  average away some of the short-term fluctuations,
  thereby reducing risk

21
Risk-Return Relationships
The risk rankings correlate with the idea that
small company stocks have the highest average
return and Treasury bills the lowest.
22
Intertemporal Stability of Volatility

• It is desirable from a statistical viewpoint to
  have intertemporal stability (constancy through
  time) in standard deviations
• However, this constancy is not evident on the
  previous slide
• SDs exhibit heteroscedascity (instability)
• This can yield erratic statistical estimates and
  cause problems with asset pricing models
  discussed later in text

23
Cross Correlations

• Financial analysts are interested in the way
  random variables interact, or co-vary
• The correlation coefficient measures the
  inter-relationship between variables
• 1.0 ? ? ? -1.0

24
Cross Correlations
Large small company stocks tend to vary
together closely.
Bond and stock indexes tend to vary together
weakly.
25
Serial Correlation

• Serial correlation (or autocorrelation)
• Measures the extent to which the values in one
  series are related to leading or lagged values in
  the same time series of data
• Positive serial correlation occurs when data
  moves in trends
• Negative serial correlation occurs when data
  experiences reversals
• Random numbers have a zero serial correlation

26
Serial Correlation

• Observations
• Inflation moves in trends as do Treasury bills
• The absence of serial correlation in the stock
  and long-term bond indexes suggests that these
  returns tend to fluctuate in a random fashion,
  making them difficult to forecast
• Technicians disagree with this finding and claim
  they can discern useful patterns

27
Historical Risk Premia

• Risk premia are the incentives needed to
  encourage risk-averse investors to take various
  kinds of risk
• Can use risk-premia to determine the appropriate
  discount rate in valuing assets
• Real returns are inflation-adjusted returns
• The nominal rate of return can be divided into
  the real rate and the inflation premium
• Real rate nominal rate inflation
• Real rate 3.8 -3.2 0.6

28
Bond Horizon Premia

• Long-term Treasury bond prices fluctuate
  differently from Treasury bills therefore their
  returns differ
• The bond horizon premium measures the additional
  return investors desire to induce them to hold
  T-bonds rather than shorter-term T-bills
• ReturnT-bond Riskless ReturnShort-Term T-bills
  horizon premium
• ReturnT-bond 3.8 1.7
• ReturnT-bond 5.5

29
Bond Default Premia

• A long-term corporate bonds return is composed
  of
• Real riskless rate
• Inflation premium
• Horizon premium
• Default premium (difference between returns on a
  long-term corporate bond and a long-term U.S.
  T-bond)

30
Bond Default Premia

• Default risk occurs if a bond issuer omits (or
  pays late) a coupon payment(s)
• The portion of the bond default premium that
  remains after default losses are subtracted is
  called the pure default risk premium
• Investors buying callable bonds face the risk
  that interest rates will decline and the bonds
  will be called
• Empirical evidence suggest that call risk premia
  range from 5 30 basis points

31
Expected Return

• The expected return components for a non-callable
  long-horizon large corporate bond

Total Bond Default Premium 40 BPs
32
Equity Risk Premia

• Large company stock returns are composed of
  short-term riskless T-bill rate plus a risk
  premium for investing in equity
• Short-horizon premium
• Large stock total return T-bill total return
• 13.3 - 3.8 9.5 or 950 basis points
• Long-horizon premium
• Large stock total return long-term T-bond
  return
• 13.3 - 5.5 7.8 or 780 basis points
• Intermediate-horizon premium
• Large stock total return intermediate T-bond
  return
• 13.3 - 5.4 - 7.9 or 790 basis points
• Small stock risk premium
• Small stock total return large stock total
  return
• 17.6 - 13.3 - 4.3 or 430 basis points

Note Returns represent arithmetic means, not
geometric means.
33
Real Returns

• Real returns represent nominal returns less the
  inflation premium

34
Inflation-Related Issues

• Money illusion occurs when investors do not
  realize that a part of ones nominal return is
  lost to inflation
• Example 200,000 to be received in 10 years if
  inflation is 3 annually will be worth less than
  200,000 in real terms

35
International Stock Markets

• Portfolio theory suggests the inclusion of
  international securities in portfolio
• Non-U.S. financial markets use different methods
  of calculating returns, taxes, transaction costs
  and reinvestment assumptions, so direct
  comparison is difficult

36
MSCI Indexes

• In 1969 Morgan Stanley Capital International
  (MSCI) started a databank that today contains
  over 50 countries, including
• All countries on previous slide plus many others,
  including
• Argentina
• Brazil
• China
• Greece
• India
• Korea
• Mexico

• Peru
• Poland
• Russia
• South Africa
• Taiwan
• Turkey

These represent emerging markets, which occur in
countries with small new markets, low trading
volume and low income.
37
Market Indexes

• Many local indexes exist for different countries
• However, the MSCI indexes are statistically
  superior, especially for foreign investors
• All the MSCI indexes are uniformly defined
  (compared to other indexes for which it is
  sometimes difficult to find detailed
  computational information)
• Website http//www.msci.com
• Makes it easier to compare different countries

38
Market Indexes

• Comparison of Five Local Indexes with MSCI Indexes

39
Emerging Market Indexes
Based on five years of monthly total returns.
40
Developed Market Indexes
Based on five years of monthly total returns.
41
Observations

• Statistics are more heterogeneous and more
  unstable for emerging markets than for developed
  markets
• Investing in emerging markets is far more risky
  than investing in developed countries
• Emerging markets have lower correlations with the
  MSCI world market index, Emerging Markets Free
  index, Europe-Australasia-Far-East index and the
  European Monetary Union index
• Developed nations trade more with each other than
  emerging markets nations, creating more
  undiversifiable risk in developed nations
• Emerging markets have large standard deviations
  and more of their risk is diversifiable
• statistically independent, uncorrelated

42
Correlations Between Developed and Emerging
Markets

• Many investors analyze possibilities for
  international diversification across a number of
  different countries
• However, if there is a great deal of correlation
  across countries, less diversification benefits
  will be achieved
• Correlations between emerging markets are lower
  and less stable across time than for developed
  markets
• Reflects the political and economic instability
  in many of these countries
• International diversification offers more risk
  reduction possibilities to multi-national
  investors than is available to domestic investors

43
Investing in Emerging Markets

• Emerging markets offer the potential for high
  gain but at the cost of extremely high risk
• Hinges on being at the right place at the right
  time
• Most of the worlds capital markets are not
  long-term survivors
• Most of the worlds capital markets have
  experienced closure due to wars, political
  upheaval, etc.

44
The Bottom Line

• Chapter summarizes statistics over 7 decades of
  investment in the U.S. as well as outside the
  U.S. (for shorter time periods)
• Data is useful for
• Providing inputs for real-life portfolio analysis
• Comparing theoretical models and realistic values
• Establishing standards of comparison

45
The Bottom Line

• Based on the data contained in the this chapter,
  weve reached the following conclusions
• A positive relationship exists between risk and
  return throughout the worlds financial markets
• This provides strong evidence that investors are
  risk averse
• Equities are riskier and provide higher returns
  than debt
• Re-investing cash flows can usually increase
  total returns
• Inflation erodes the purchasing power of
  investors wealth
• Covariances, cross correlations and serial
  correlations are useful statistics for measuring
  the behavior of random variables
• Corporate bond returns contain a default risk
  premium

46
The Bottom Line

• Equities provide higher inflation-adjusted
  returns than debt
• U.S. Treasury bills earns returns only slightly
  above inflation
• International investing is riskier than domestic
  investing
• Emerging market investing is riskier than
  developed market investing
• Emerging market investing may earn an investor
  higher risk premiums

47
Ibbotson Problem 11-3

• 1,000 invested for 10 years at 17.8
• Inflation averaged 3.2 for 10 years
• Nominal portfolio value
• 1,000(1.178)10 5,145.80
• Real portfolio value
• 5,145.80/(1.032)10 3,755.40

48
Ibbotson Problem 11-6

• 40,000 saved in eight years
• Inflation expected at 4 per year
• Inflation-adjusted value
• 40,000/(1.04)8 29,227