5 probability distribution of price and one year

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5. Probability distribution of price and one-year holding period return for a 30-year U.S. Treasury bond (which will have 29 years to maturity at year’s end): Economy Probability YTM Price Capital Gain Coupon Interest HPR Boom 0.20 11.0% $ 74.05 $25.95 $8.00 17.95% Normal Growth 0.50 8.0% $100.00 $ 0.00 $8.00 8.00% Recession 0.30 7.0% $112.28 $12.28 $8.00 20.28% 6. From Table 5.3, the average risk premium for large-capitalization U.S. stocks for the period 1926-2005 was: (12.15% 3.75%) = 8.40% per year Adding 8.40% to the 6% risk-free interest rate, the expected annual HPR for the S&P 500 stock portfolio is: 6.00% + 8.40% = 14.40%
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7. The average rates of return and standard deviations are quite different in the sub periods: STOCKS Mean Standard Deviation Skewness Kurtosis 1926 – 2005 12.15% 20.26% -0.3605 -0.0673 1976 – 2005 13.85% 15.68% -0.4575 -0.6489 1926 – 1941 6.39% 30.33% -0.0022 -1.0716 BONDS Mean Standard Deviation Skewness Kurtosis 1926 – 2005 5.68% 8.09% 0.9903 1.6314 1976 – 2005 9.57% 10.32% 0.3772 -0.0329 1926 – 1941 4.42% 4.32% -0.5036 0.5034 The most relevant statistics to use for projecting into the future would seem to be the statistics estimated over the period 1976-2005, because this later period seems to have been a different economic regime. After 1955, the U.S. economy entered the Keynesian era, when the Federal government actively attempted to stabilize the economy and to prevent extremes in boom and bust cycles. Note that the standard deviation of stock returns has decreased substantially in the later period while the standard deviation of bond returns has increased. 8. a % 88 . 5 0588 . 0 70 . 1 70 . 0 80 . 0 i 1 i R 1 i 1 R 1 r = = = + = + + = b. r R i = 80% 70% = 10% Clearly, the approximation gives a real HPR that is too high. 9. From Table 5.2, the average real rate on T-bills has been: 0.72% a. T-bills: 0.72% real rate + 3% inflation = 3.72% b. Expected return on large stocks: 3.72% T-bill rate + 8.40% historical risk premium = 12.12% c. The risk premium on stocks remains unchanged. A premium, the difference between two rates, is a real value, unaffected by inflation.
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