7 Chapter Historical Asset Returns
Road Map Part A Introduction to Finance. Part B Valuation of assets, given discount rates. Part C Determination of discount rates.
Historical asset returns.
Time value of money. Risk. Portfolio theory. Capital Asset Pricing Model (CAPM). Arbitrage Pricing Theory (APT).
Part D Introduction to corporate.
Main Issues
Asset Returns Historic Asset Returns in U.S.
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Asset Returns
Dt + Pt Dt + Pt - Pt-1 = -1 Pt-1 Pt-1
Asset returns over a given period are often uncertain:
rt =
where
Pt-1 is the price at the beginning of period Pt is the price at the end of period Dt is the dividend at the end of period.
Return on an asset is often uncertain ex ante (a random variable). It can be characterized by
all possible outcomes, and probability of each outcome (state).
We can write
Expected rate of return on an investment is the discount rate for its cash flows: E[rt] rF +
where rF is the risk-free interest rate (time value of money) is the risk premium (price of risk).
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Historical U.S. Asset Returns
Four facts from history of U.S. finanical markets:
1. Real interest rate has been slightly positive on average.
2. Return on more risky assets has been higher on average than return on less risky assets:
Average Annual Total Returns from 1926 to 2000 (Real) Asset Mean (%) StD (%) T-bills 3.9 3.2 Long term T-bonds 5.7 9.4 Long term corp. bonds 6.0 8.7 Large stocks 13.0 20.2 Small stocks 17.3 33.4 Inflation 3.2 4.4
Average Annual Total Returns from 1926 to 2000 (Real) Asset Mean (%) StD (%) T-bills 0.8 4.1 Long term T-bonds 2.7 10.6 Long term corp. bonds 3.0 9.9 Large stocks 9.7 20.3 Small stocks 13.8 32.8
c Jiang Wang
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Chapter Asset 7
Return Indices of Investments in the U.S. Capital Markets
Real returns from 1926 to 2000 Security T-Bills Long Term T-Bonds Corporate Bonds Large Stocks Small Stocks Initial Total Return $1.00 1.53 $1.00 3.81 $1.00 5.54 $1.00 154.95 $1.00 508.17
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3. Returns on risky assets can be highly correlated to each other: Cross Correlations of Annual Nominal Returns (1926 2000)
Bills T-bonds C-bonds L. stocks S. stocks Inflation T-bills 1.00 0.24 0.22 -0.03 -0.10 0.41 L.T. T-bonds 1.00 0.91 0.16 0.00 -0.14 L.t. C-bonds 1.00 0.24 0.09 -0.15 Large stocks 1.00 0.79 -0.03 Small stocks 1.00 0.08 Inflation 1.00
Cross Correlations of Annual Real Returns (1926 2000)
Bills T-bonds C-bonds L. stocks S. stocks T-bills 1.00 0.58 0.59 0.12 -0.06 L.T. T-bonds 1.00 0.95 0.24 0.04 L.t. C-bonds 1.00 0.30 0.12 Large stocks 1.00 0.79 Small stocks 1.00
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4. Returns on risky assets are serially uncorrelated.
Serial Correlations of Annual Asset Returns (1926 2000) Serial Correlation Asset Nominal return Real return T-bills ("risk-free") 0.92 0.67 Long term T-bonds -0.06 0.03 Long term corp. bonds 0.07 0.18 Large stocks 0.00 -0.00 Small stocks 0.08 0.05
(Note: The main source for the data in this subsection is Stocks, bonds, bills and inflation, 2000 Year Book, Ibbotson Associates, Chicago, 2000.)
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Homework
Readings:
BKM Chapter 5.3-5.4. BM Chapter 7.1. BKM Chapter 5. Readings package: "Risk and return in the 20th and 21st centuries" (E. Dimson, P. Marsh, and M. Staunton).
c Jiang Wang
Fall 2003
15.407 Lecture Notes